The development seen within industrial automation in recent years enables the emergence of manufacturing sites that utilise technology for improved productivity, quality and safety. Increased communication demands introduced by Industry 4.0 have motivated the development of cloud-fog automation; a technique characterised by wireless communication between lower levels of the automation pyramid. Specifically, the new communication requirements gives rise to the need for efficient wireless communication between input/output devices and controllers.
This thesis presents findings from an investigation of wireless control and communication performance. A cascaded internal model control-based Proportional, Integral, Derivative controller structure is developed to control a time-critical motion system. Various communication protocols and control algorithms are considered to examine the performance behaviour. The results indicate that user datagram protocols, compared to transmission control protocols, are a promising candidate for the target purpose. However, by manipulating the control algorithm sampling interval, transmission control protocol communication yields almost equivalent control performance results.
An exploration of event-based control results in an algorithm that achieves communication reductions of over 80%. Given a consciously chosen sampling interval, control performances comparable to those of the corresponding time-based system can be maintained. The research indicates that wireless control has the potential to accomplish control performances equal to those found in wired systems.

This manuscript describes several approaches to tune the parameters of a class of passivity-based controllers for standard nonlinear mechanical systems. In particular, we are interested in controllers that preserve the mechanical system structure in closed-loop. To this end, first, we provide tuning rules for stabilization, i.e., the rate of convergence (exponential stability) and stability margin (input-to-state stability). Then, we provide guidelines to remove the overshoot while prescribing the rise time. Additionally, we propose a methodology to tune the gyroscopic-related parameters. We also provide remarks on the damping phenomena to facilitate the practical implementation of our approaches. We conclude this paper with experimental results obtained from applying our tuning rules to an underactuated and a fully-actuated mechanical configuration.

Ball and Beam system is one of the most popular and important laboratory models for teaching control systems. This paper proposes a new control strategy to the position control for the ball and beam system. Firstly, a nonlinear controller is proposed based on the backstepping approach. Secondly, in order to adapt online the dynamic control law, adaptive laws are developed to estimate the uncertain parameters. The stability of the proposed adaptive backstepping controller is proved based on the Lyapunov theorem. Simulated results are presented to illustrate the performance of the proposed approach.

We propose a solution to the problem of adaptive speed observer for a class of mechanical systems containing cross terms in the velocity (momenta). We focused our attention on mechanical systems with unknown constant input disturbances and Coulomb friction matrix, which generate products of unmeasurable velocities and unknown friction parameters. The adaptive speed observer proposed is based on the well-known Immersion and Invariance technique. We ensure global convergence of the speed observer, while the friction parameters estimation remain bounded. Our approach is validated through simulations and experimental results.

The Ball & Beam system is one of the most complete case studies in control engineering, because it is a non-linear and naturally unstable system. In this article we propose to make an optimal LQG controller for Quanser's Ball & Beam system, composed of a linear quadratic regulator (LQR) and a linear quadratic estimator (Kalman filter) with which the noise of the system's ball position signal was eliminated, managing to mitigate the problems generated by the high sensitivity to sensor noise. Starting from the state space representation of the Quanser Ball & Beam system and using the Matlab/Simulink software and its QUARC module, an optimal LQG controller was designed, simulated and implemented in the Quanser Ball & Beam system. Finally, the simulation results and implementation show that the LQG controller is effective in controlling the Ball & Beam system despite the noise presented by the feedback signal.

The purpose of this research is to construct and investigate the stability of the ball and beam control system with PID coefficients derived from the simulation and compare them. In this research, by first obtaining the mathematical model of the mechanical system and its simulation, the best PID coefficients are selected for it to minimize the settling time and the error. Then, to create this system, the types of mechanisms provided for the ball and beam control system are examined. Depending on the equipment and facilities available, the best design is chosen and built. The best design is the use of the four_bar mechanism using the servo motor and the ultrasonic sensor. The appropriate design is first developed in SolidWorks software to provide accurate measurements for the production of components. Laser cutting and 3D printers are used to produce system components. After the control system is built, the simulation coefficients in the MATLAB software are inserted into the system microcontroller program to check the system responses to the various control coefficients obtained. So doing multiple experiments indicated that the best PID coefficients for this system are PD coefficient. The difference between the experimental graph and the simulation graph is their overshoot. They also have different settling times. One of the reasons for this difference is the use of some approximations as well as disregarding friction.

Data-driven techniques are growing at an unprecedented pace due to the recent super-fast computational tools and resources and the availability of big data by sensors. In the field of dynamics and control, many researchers are investigating algorithms to learn from data to model systems, estimate physical parameters, and design controllers, especially for complex dynamical systems. However, many of these researches are still limited to simulations due to the unavoidable noise in practical cases and the limitations in data acquisition. Some techniques lack any physical meaning and it makes it hard to analyze the effect of parameters in the system's performance. Low performance to predict the system response for unseen data is another issue that researchers are dealing with. Therefore, it is of great potential to develop intelligent and robust data-driven algorithms to model and estimate parameters of the system, where the reliable model can be used for the model-based control design.

We propose a nonparametric system identification technique to discover the governing equation of nonlinear dynamic systems with a focus on practical aspects. The algorithm builds on Brunton’s work in 2016 and combines sparse regression with algebraic calculus to estimate the required derivatives of the measurements. This reduces the required derivative data for system identification. Furthermore, we make use of the concepts of K-fold cross-validation from machine learning and information criteria for model selection. This allows the system identification with fewer measurements than the typically required data for the sparse regression. The result is an optimal model for the underlining system of the data with a minimum number of terms. The proposed system identification method is applicable for multiple-input–multiple-output systems. Two examples are presented to demonstrate the proposed method. The first one makes use of the simulated data of a nonlinear oscillator to show the effectiveness and accuracy of the proposed method. The second example is a nonlinear rotary flexible beam. Experimental responses of the beam are used to identify the underlining model. The Coulomb friction in the servo motor together with other nonlinear terms of the system variables are found to be important components of the model. These are, otherwise, not available in the theoretical linear model of the system.

We also extend the sparse optimization algorithm to nonlinear systems with time delay. We further integrate the bootstrapping resampling technique with the sparse regression to obtain the statistical properties of estimation. We use Taylor expansion to parameterize time delay. The proposed algorithm in this paper is computationally efficient and robust to noise. A nonlinear Duffing oscillator is simulated to demonstrate the efficiency and accuracy of the proposed technique. An experimental example of a nonlinear rotary flexible joint is presented to further validate the proposed method.

Finally, we examine the efficiency of our identified model to design model\_based controllers. First, we propose a robust flat output-based sliding mode control for trajectory tracking and to deal with the under-actuated degree of freedom. Moreover, we investigate the optimal control design. Optimal control design needs the solution of the Hamilton-Jacobi-Bellman equation, where the nonlinearities in the model make the solution challenging or even infeasible. We propose an efficient algorithm to estimate a neural network solution to gain the feedback control law. We examine the efficiency of our algorithm through several popular examples in the optimal control community and more importantly our identified nonlinear model of rotary flexible manipulator link.

This paper develops an observer-based positioning scheme for ball-beam systems considering actuator dynamics. The practical constraints are handled systematically, including the mechanical dynamical nonlinearities, mismatched load disturbances, and parameter uncertainties. This result provides contributions as follows. First, parameter-independent observers exponentially estimate the ball velocity, motor speed, and its acceleration to remove the velocity, motor speed, and current feedback. Second, the auto-tuner automatically adjusts the desired closed-loop input-output behaviors to update its cut-off frequency in the transient operations. Third, observer-based active damping injection reduces the closed-loop ball position and actuator speed dynamics to 1 by pole-zero cancellation. Finally, disturbance observers act as a dynamic compensator by estimating the disturbances from model-plant mismatches such as dynamic nonlinearities, mismatched load disturbances, and parameter variations. The experimental study verifies the applicability of the proposed technique using the Quanser Ball-Beam hardware driven by an SRV02 servomotor.

@article{mehedi_2019,
title = {Two degrees of freedom fractional controller design: Application to the ball and beam system},
author = {Mehedi, I.M.; Al-Saggaf, U.M.; Mansouri, R.; Bettayeb, M.},
journal = {Measurement},
year = {2019},
month = {03},
volume = {135},
institution = { King Abdulaziz University, Saudi Arabia; Mouloud Mammeri University, Algeria; University of Sharjah, United Arab Emirates},
abstract = {Control engineers and researchers face challenges to design an efficient controller for Ball and beam system due to its nonlinear and unstable properties. This paper investigates two Degrees of Freedom fractional order control of the ball and beam system. It involves the model based method to design controllers’ parameters for the corresponding linear model. The fractional order controllers are specially tuned to have a constant phase margin of the open-loop. This characteristic ensures the robustness of the controllers to the variations of system gain. This paper presents a proper evaluation and comparison between integer and fractional order controllers. Performance of each controller is evaluated in terms of set-point tracking, disturbance rejection, and robustness. The comparison between two controllers is validated through both simulation and experimental results. Strengths and weaknesses in the real-time control are also indicated. },
keywords = {Fractional order controller, PD controllers, Internal model control, Unstable system, Robust control, Ball and beam system},
language = {English},
publisher = {Elsevier Ltd.},
pages = {13-22}
}

Control engineers and researchers face challenges to design an efficient controller for Ball and beam system due to its nonlinear and unstable properties. This paper investigates two Degrees of Freedom fractional order control of the ball and beam system. It involves the model based method to design controllers’ parameters for the corresponding linear model. The fractional order controllers are specially tuned to have a constant phase margin of the open-loop. This characteristic ensures the robustness of the controllers to the variations of system gain. This paper presents a proper evaluation and comparison between integer and fractional order controllers. Performance of each controller is evaluated in terms of set-point tracking, disturbance rejection, and robustness. The comparison between two controllers is validated through both simulation and experimental results. Strengths and weaknesses in the real-time control are also indicated.

@conference{oh_2018,
title = {Control of a Ball and Beam System under Intermittent Feedback},
author = {Oh, S.-Y.; Lee, K.-T.; Choi, H.-L.},
booktitle = {2018 18th Conference on Control, Automation and Systems (ICCAS)},
year = {2018},
institution = {Dong-A University, Korea; Master's Space, Korea},
abstract = {The control of a ball and beam system has been a well-known research subject and there have been a large number of related research results by far. To our best knowledge, however, all those existing results have basically assumed that their proposed controllers work under ‘good’ or ‘normal’ feedback conditions, which specifically means in this case that there is not any time period during which feedback is disrupted. In this paper, motivated by a recent open-loop time optimal result of [1], we suggest a new switching control method which can keep the states of a ball and beam system within certain bounds when there occurs a nontrivial feedback disruption during the operation of feedback controllers. Both simulation and experimental results are provided for verification. },
keywords = {Ball and beam system, Time optimal control, Switching control, Intermittent feedback},
language = {English},
pages = {56-61}
}

The control of a ball and beam system has been a well-known research subject and there have been a large number of related research results by far. To our best knowledge, however, all those existing results have basically assumed that their proposed controllers work under ‘good’ or ‘normal’ feedback conditions, which specifically means in this case that there is not any time period during which feedback is disrupted. In this paper, motivated by a recent open-loop time optimal result of [1], we suggest a new switching control method which can keep the states of a ball and beam system within certain bounds when there occurs a nontrivial feedback disruption during the operation of feedback controllers. Both simulation and experimental results are provided for verification.

@conference{shah_2018,
title = {Control of Ball and Beam with LQR Control Scheme using Flatness Based Approach},
author = {Shah, M.; Ali, R.; Malik, F.M.},
booktitle = {2018 International Conference on Computing, Electronic and Electrical Engineering (ICE Cube)},
year = {2018},
institution = {National University of Sciences and Technology, Pakistan},
abstract = {In this paper, a control design problem for a nonlinear ball and beam system is discussed. A state feedback linear quadratic regulator (LQR) based control scheme is discussed using the flatness property of the system. A state estimation is carried out with Kalman filter while utilizing differentially flat nonlinear system written in the Brunovsky canonical form. The performance of the proposed control strategy is validated through practical tracking results. },
keywords = {Nonlinear system; linear quadratic regulator; tracking; ball and beam},
language = {English},
publisher = {IEEE},
isbn = {978-1-5386-7940-1}
}

In this paper, a control design problem for a nonlinear ball and beam system is discussed. A state feedback linear quadratic regulator (LQR) based control scheme is discussed using the flatness property of the system. A state estimation is carried out with Kalman filter while utilizing differentially flat nonlinear system written in the Brunovsky canonical form. The performance of the proposed control strategy is validated through practical tracking results.

@article{ford_2018,
title = {Implementation of a Ball-and-Beam Control System Using PD Bode Design},
author = {Ford, J.K.; Emami, T.},
journal = {International Journal of Modern Engineering},
year = {2018},
volume = {18},
number = {2},
institution = {US Coast Guard Academy},
abstract = {When students are first introduced to the world of automatic control systems, they often have a lot of information to deal with at one time. It is common to see concepts such as root locus, Routh Hurwitz, Bode design, and state space modeling all introduced in a single semester. Bode design, as one of many practical methods, is the one that the authors of this paper sought to focus primarily on in order to design a controller for a ball-and-beam system. In this study, the authors looked at the open-loop frequency response of a ball-and-beam system, more specifically the magnitude and phase responses, and applied constraints such as a certain gain crossover frequency and phase margin to design a proportional-derivative (PD) compensator. },
issn = {2157-8052},
language = {English},
pages = {21-27}
}

When students are first introduced to the world of automatic control systems, they often have a lot of information to deal with at one time. It is common to see concepts such as root locus, Routh Hurwitz, Bode design, and state space modeling all introduced in a single semester. Bode design, as one of many practical methods, is the one that the authors of this paper sought to focus primarily on in order to design a controller for a ball-and-beam system. In this study, the authors looked at the open-loop frequency response of a ball-and-beam system, more specifically the magnitude and phase responses, and applied constraints such as a certain gain crossover frequency and phase margin to design a proportional-derivative (PD) compensator.

@article{rasaienia_2017,
title = {Hardware in the Loop (HIL) Analysis of Fuzzy Controller for Ball and Beam System},
author = {Rasaienia, A.},
journal = {Majlesi Journal of Mechatronic Systems},
year = {2017},
volume = {6},
number = {1},
institution = {Islamic Azad University, Iran},
abstract = {Ball and beam system is a nonlinear and unstable system which is used as an applied sample in research laboratories as a tool to represent the performance of different control algorithms. The present study utilizes hardware in the loop realization of classic (PID type) and fuzzy controllers by Sugeno fuzzy inference approach in order to evaluate their performances. All activities for design and simulation of controller were performed by MATLAB and Simulink software. Then, the simulation environment of MATLAB was linked to the operator interface as well as actuators and sensors in hardware in the loop structure by writing a real time kernel through DAQ interface cards. Simulation results show the appropriate performance of fuzzy controller in comparison to PD and PID controllers. By using fast processors for implementation of fuzzy controller, settling time, overshoot percentage and steady state error of the closed loop system were significantly improved in comparison to the common classic structure. Also, all simulation results were verified by hardware in the loop test. },
issn = {2322-1089},
keywords = {ball and beam, fuzzy control, hardware in the loop, HIL, classic control},
language = {English}
}

Ball and beam system is a nonlinear and unstable system which is used as an applied sample in research laboratories as a tool to represent the performance of different control algorithms. The present study utilizes hardware in the loop realization of classic (PID type) and fuzzy controllers by Sugeno fuzzy inference approach in order to evaluate their performances. All activities for design and simulation of controller were performed by MATLAB and Simulink software. Then, the simulation environment of MATLAB was linked to the operator interface as well as actuators and sensors in hardware in the loop structure by writing a real time kernel through DAQ interface cards. Simulation results show the appropriate performance of fuzzy controller in comparison to PD and PID controllers. By using fast processors for implementation of fuzzy controller, settling time, overshoot percentage and steady state error of the closed loop system were significantly improved in comparison to the common classic structure. Also, all simulation results were verified by hardware in the loop test.

@conference{shatri_2017,
title = {Hardware-in-the-Loop Architecture with MATLAB/Simulink and QuaRC for Rapid Prototyping of CMAC Neural Network Controller for Ball-and-Beam Plant},
author = {Shatri, V.; Kurtaj, L.; Limani, I.},
booktitle = {MIPRO 2017},
year = {2017},
institution = {University of Prishtina, Kosovo},
abstract = {Cerebellar Model Articulation Controller ( CMAC ) is type of neural network inspired from part of the brain named cerebellum. It has long history in control applications, in simulated or in real-time implementations. MATLAB/Simulink is used for rapid building of CMAC neural network controller prototypes than can run in real- time. To run the controller in the same personal computer, QuaRC is used as real-time operating system that will execute controller task along Windows operating system. Hardware-in-the-loop architecture was used to test CMAC controller in real ball-and-beam physical plant from Quanser. Library of developed Simulink functional blocks enable easy exploration of different structural aspects of CMAC neural network controller, including selection of receptive field types, receptive field widths, Albus overlays, and fully interconnected multi-dimensional receptive fields. Same CMAC controller can be used also for controlling model of the plant, which can serve as means for controller to acquire knowledge before operating with real plant. CMAC controller learned to control the plant, and progressively became main control signal generator, while control signal from primary proportional-derivative controller almost vanished. Developed library can serve as easy startup for working with CMAC networks also for other types of applications. },
language = {English},
pages = {1413-1418}
}

Cerebellar Model Articulation Controller ( CMAC ) is type of neural network inspired from part of the brain named cerebellum. It has long history in control applications, in simulated or in real-time implementations. MATLAB/Simulink is used for rapid building of CMAC neural network controller prototypes than can run in real- time. To run the controller in the same personal computer, QuaRC is used as real-time operating system that will execute controller task along Windows operating system. Hardware-in-the-loop architecture was used to test CMAC controller in real ball-and-beam physical plant from Quanser. Library of developed Simulink functional blocks enable easy exploration of different structural aspects of CMAC neural network controller, including selection of receptive field types, receptive field widths, Albus overlays, and fully interconnected multi-dimensional receptive fields. Same CMAC controller can be used also for controlling model of the plant, which can serve as means for controller to acquire knowledge before operating with real plant. CMAC controller learned to control the plant, and progressively became main control signal generator, while control signal from primary proportional-derivative controller almost vanished. Developed library can serve as easy startup for working with CMAC networks also for other types of applications.

@conference{emami_2018,
title = {Mixed Sensitivity Design of PID Controller-Applied to a Ball and Beam System},
author = {Emami, T.},
booktitle = {ASME 2017 International Mechanical Engineering Congress and Exposition},
year = {2017},
volume = {4},
institution = {United States Coast Guard Academy, USA},
abstract = {This paper presents a set of algorithm for all achievable coefficients of Proportional Integral Derivative (PID) controllers that stabilize the system and satisfy a mixed sensitivity constraint with an uncertain time delay. Additive uncertainty modeling is used to describe the uncertainty of perturbed system. Additive uncertainty modeling performs much faster response with the time running of computer programming in MATLAB. This technique is applied to a ball and beam system transfer function with the assumption of uncertain communication time delays in the system process. The goal of this application is to regulate a ball position on a beam and also satisfy the mixed sensitivity constraint. },
keywords = {control equipment, design},
language = {English},
publisher = {ASME},
isbn = {978-0-7918-5837-0}
}

This paper presents a set of algorithm for all achievable coefficients of Proportional Integral Derivative (PID) controllers that stabilize the system and satisfy a mixed sensitivity constraint with an uncertain time delay. Additive uncertainty modeling is used to describe the uncertainty of perturbed system. Additive uncertainty modeling performs much faster response with the time running of computer programming in MATLAB. This technique is applied to a ball and beam system transfer function with the assumption of uncertain communication time delays in the system process. The goal of this application is to regulate a ball position on a beam and also satisfy the mixed sensitivity constraint.

@article{sameera_2017,
title = {Position Tracking of Ball and Beam System using Fractional Order Controller},
author = {Sameera, R.; Arun, S.M.},
journal = {International Journal of Advanced Research Trends in Engineering and Technology},
year = {2017},
volume = {4},
number = {6},
institution = {Mar Baselios College of Engineering and Technology Kerala, India},
abstract = {The ball and beam system is the classical mechanical system having unstable dynamics and strong nonlinear characteristics which makes the control a challenging task. In this paper a fractional order controller is used to enhance a better position control. The fractional order PID controller is an improved form of normal PID controller with more number of controlling parameters. The ball and beam system is a cascaded system with inner loop servo motor angle control and outer loop with ball position control. The inner loop is a Proportional Derivative controller designed based on time domain specifications and the outer loop is a fractional PID controller. The controlling parameters of fractional PID are designed based on Particle Swarm Optimization (PSO) algorithm. The simulation of the proposed controller is analyzed using Matlab Simulink and the performance of the system is analyzed. },
issn = {2394-3777},
keywords = {nonlinear, position control, cascaded system, fractional order PID, Particle Swarm Optimization (PSO)},
language = {English},
pages = {174-180}
}

The ball and beam system is the classical mechanical system having unstable dynamics and strong nonlinear characteristics which makes the control a challenging task. In this paper a fractional order controller is used to enhance a better position control. The fractional order PID controller is an improved form of normal PID controller with more number of controlling parameters. The ball and beam system is a cascaded system with inner loop servo motor angle control and outer loop with ball position control. The inner loop is a Proportional Derivative controller designed based on time domain specifications and the outer loop is a fractional PID controller. The controlling parameters of fractional PID are designed based on Particle Swarm Optimization (PSO) algorithm. The simulation of the proposed controller is analyzed using Matlab Simulink and the performance of the system is analyzed.

@article{hammadih_2016,
title = {Interpolating sliding mode observer for a ball and beam system},
author = {Hammadih, M.L.; Al Hosani, K.; Boiko, I.},
journal = {International Journal of Control},
year = {2016},
institution = {Department of Electrical Engineering, The Petroleum Institute, Abu Dhabi, UAE},
abstract = {A principle of interpolating sliding mode observer is introduced in this paper. The observer incorporates multiple linear observers through interpolation of multiple estimates, which is treated as a type of adaptation. The principle is then applied to the ball and beam system for observation of the slope of the beam from the measurement of the ball position. The linearised model of the ball and beam system using multiple linearisation points is developed. The observer dynamics implemented in Matlab/Simulink Real Time Workshop environment. Experiments conducted on the ball and beam experimental setup demonstrate excellent performance of the designed novel interpolating (adaptive) observer. },
keywords = {Sliding mode, observer, nonlinear system},
language = {English},
publisher = {Taylor & Francis}
}

A principle of interpolating sliding mode observer is introduced in this paper. The observer incorporates multiple linear observers through interpolation of multiple estimates, which is treated as a type of adaptation. The principle is then applied to the ball and beam system for observation of the slope of the beam from the measurement of the ball position. The linearised model of the ball and beam system using multiple linearisation points is developed. The observer dynamics implemented in Matlab/Simulink Real Time Workshop environment. Experiments conducted on the ball and beam experimental setup demonstrate excellent performance of the designed novel interpolating (adaptive) observer.

@conference{costa_2016,
title = {Nominally Stable Predictive Control Applied to a Ball and Beam System},
author = {Costa, E.A.; Martins, M.A.F.; Schnitman, L.; de Araujo Kalid, R.},
booktitle = {XXI Brazilian Automation Congress - CBA 2016},
year = {2016},
institution = {Universidade Federal da Bahia, Brasil},
abstract = {This work proposes a nominally stabilizing model predictive control strategy for pure integrating systems composed by repeated poles. The controller proposed here is oset free through a one-step optimization formulation as the adopted state space model is incremental in the input, which is based an analytical expression of the step response of the system. The controller is applied to a ball and beam system and its performance is favorably compared to the standard nominally stable model predictive controller for the output tracking case, which is synthesized from a two-step optimization formulation. },
issn = {2525-8311},
keywords = {Model predictive control, Integrating systems, Nominal stability},
language = {Portuguese}
}

This work proposes a nominally stabilizing model predictive control strategy for pure integrating systems composed by repeated poles. The controller proposed here is oset free through a one-step optimization formulation as the adopted state space model is incremental in the input, which is based an analytical expression of the step response of the system. The controller is applied to a ball and beam system and its performance is favorably compared to the standard nominally stable model predictive controller for the output tracking case, which is synthesized from a two-step optimization formulation.

@article{bessa_2016,
title = {Verification of fixed-point digital controllers using direct and delta forms realizations},
author = {Bessa, I.V.; Ismail, H.I.; Codeiro, L.C.; Filho, J.E.C.},
journal = {Design Automation for Embedded Systems},
year = {2016},
institution = {Federal University of Amazonas, Manaus, Brazil},
abstract = {The extensive use of fixed-point digital controllers demands a growing effort to prevent design errors that appear in the discrete-time domain. The present article describes a novel verification methodology, which employs bounded model checking (BMC) based on satisfiability modulo theories (SMT) to verify the occurrence of the design errors, because of the finite word-length (FWL) format, in fixed-point digital controllers. Here, the performance realizations of the digital controllers realizations that use delta operators are compared to those that use traditional direct forms. The experimental results show that the delta-form realization substantially reduces the digital controllersÍ fragility when compared to the direct-form realization. Additionally, the proposed methodology can be very effective and efficient to verify real-world digital controllers, where conclusive results are obtained in nearly 98 % of the benchmarks. },
issn = {0929-5585},
keywords = {Fixed-point digital controllers, Direct and delta forms, Formal methods, Bounded model checking},
language = {English},
publisher = {Springer US}
}

The extensive use of fixed-point digital controllers demands a growing effort to prevent design errors that appear in the discrete-time domain. The present article describes a novel verification methodology, which employs bounded model checking (BMC) based on satisfiability modulo theories (SMT) to verify the occurrence of the design errors, because of the finite word-length (FWL) format, in fixed-point digital controllers. Here, the performance realizations of the digital controllers realizations that use delta operators are compared to those that use traditional direct forms. The experimental results show that the delta-form realization substantially reduces the digital controllersÍ fragility when compared to the direct-form realization. Additionally, the proposed methodology can be very effective and efficient to verify real-world digital controllers, where conclusive results are obtained in nearly 98 % of the benchmarks.

@article{rehan_2014,
title = {A novel anti-windup framework for cascade control systems: An application to underactuated mechanical systems},
author = {Mehdi, N.; Rehan, M.; Malik, F.M.; Bhatti, A.I.; Tufail, M.},
journal = {ISA Transactions},
year = {2014},
volume = {53},
abstract = {This paper describes the anti-windup compensator (AWC) design methodologies for stable and unstable cascade plants with cascade controllers facing actuator saturation. Two novel full-order decoupling AWC architectures, based on equivalence of the overall closed-loop system, are developed to deal with windup effects. The decoupled architectures have been developed, to formulate the AWC synthesis problem, by assuring equivalence of the coupled and the decoupled architectures, instead of using an analogy, for cascade control systems. A comparison of both AWC architectures from application point of view is provided to consolidate their utilities. Mainly, one of the architecture is better in terms of computational complexity for implementation, while the other is suitable for unstable cascade systems. On the basis of the architectures for cascade systems facing stability and performance degradation problems in the event of actuator saturation, the global AWC design methodologies utilizing linear matrix inequalities (LMIs) are developed. These LMIs are synthesized by application of the Lyapunov theory, the global sector condition and the L 2 gain reduction of the uncertain decoupled nonlinear component of the decoupled architecture. Further, an LMI-based local AWC design methodology is derived by utilizing a local sector condition by means of a quadratic Lyapunov function to resolve the windup problem for unstable cascade plants under saturation. To demonstrate effectiveness of the proposed AWC schemes, an underactuated mechanical system, the ball-and-beam system, is considered, and details of the simulation and practical implementation results are described. },
keywords = {Anti-windup compensator, Decoupled architecture, Cascade control systems, Linear matrix inequality, Underactuated mechanical system},
language = {English},
publisher = {Elsevier Ltd.},
pages = {802-815}
}

This paper describes the anti-windup compensator (AWC) design methodologies for stable and unstable cascade plants with cascade controllers facing actuator saturation. Two novel full-order decoupling AWC architectures, based on equivalence of the overall closed-loop system, are developed to deal with windup effects. The decoupled architectures have been developed, to formulate the AWC synthesis problem, by assuring equivalence of the coupled and the decoupled architectures, instead of using an analogy, for cascade control systems. A comparison of both AWC architectures from application point of view is provided to consolidate their utilities. Mainly, one of the architecture is better in terms of computational complexity for implementation, while the other is suitable for unstable cascade systems. On the basis of the architectures for cascade systems facing stability and performance degradation problems in the event of actuator saturation, the global AWC design methodologies utilizing linear matrix inequalities (LMIs) are developed. These LMIs are synthesized by application of the Lyapunov theory, the global sector condition and the L 2 gain reduction of the uncertain decoupled nonlinear component of the decoupled architecture. Further, an LMI-based local AWC design methodology is derived by utilizing a local sector condition by means of a quadratic Lyapunov function to resolve the windup problem for unstable cascade plants under saturation. To demonstrate effectiveness of the proposed AWC schemes, an underactuated mechanical system, the ball-and-beam system, is considered, and details of the simulation and practical implementation results are described.

@inproceedings{oniram_2014,
title = {Control of the Ball and Beam Using Kalman Filter – a Flatness Based Approach},
author = {Jose Oniram de Aquino Limaverde Filho, Eugenio Liborio Feitosa Fortalez},
booktitle = {Anais do XX Congresso Brasileiro de Automàtica 2014},
year = {2014},
institution = {Universidade de Brasilia, Brasil},
abstract = {The tracking control design problem for a nonlinear ball and beam system is addressed. In this paper, the flatness property of the system is here exploited for design a state feedback control scheme aiming to stabilize the systemÍs trajectory tracking error with respect to off-line planned trajectories. Differentially flat nonlinear systems can be written in the Brunovsky canonical form, which allows to perform the state estimation using the Kalman filter. In order to validate the performance of the proposed tracking control, numerical simulations and experimental results are presented and discussed. },
keywords = {Trajectory Tracking; Nonlinear Control; Differentially Flat Systems; Kalman Filter; Ball and Beam},
language = {English},
pages = {2601-2606}
}

The tracking control design problem for a nonlinear ball and beam system is addressed. In this paper, the flatness property of the system is here exploited for design a state feedback control scheme aiming to stabilize the systemÍs trajectory tracking error with respect to off-line planned trajectories. Differentially flat nonlinear systems can be written in the Brunovsky canonical form, which allows to perform the state estimation using the Kalman filter. In order to validate the performance of the proposed tracking control, numerical simulations and experimental results are presented and discussed.

@conference{medina_2014,
title = {Control Robusto del Sistema de Bola y Viga},
author = {Carlos G. Bolivar Vincenty; Keriam Z. Rosa Medina; Gerson Beauchamp Baez},
booktitle = {12thLACCEI Latin American and Caribbean Conference for Engineering and Technology (LACCEIÍ2014)},
year = {2014},
institution = {Universidad de Puerto Rico, Mayaguez},
abstract = {The objective of a control system is to regulate the dynamic behavior of a physical system through feedback. Such regulation should satisfy performance specifications even in the presence of disturbances and perturbations. When a control system performs adequately in the presence of disturbances and perturbations, it is Robust. We present a relatively simple approach to the robust control problem of the Ball-and-Beam System that can be used in basic control systems courses. The Ball and Beam System exhibits high-frequency sensor noise, unmolded highfrequency dynamics, disturbances in the process, and parameter variations of the plant. Results of controllers designed through robust control methods are presented and compared with other controllers designed by conventional methods such as the Root Locus method. It is demonstrated that a conscious design using a conventional method can depart from the performance specifications, leading to unsatisfactory performance. To demonstrate this, the real system performance for the controllers using both methods is presented and compared to the simulated performance. The performance of the system designed by the Root Locus method does not meet the performance specifications, while the performance of the system designed by robust control method does. These results were obtained from an undergraduate research project and are currently being applied in an introductory course on control systems. },
keywords = {Robust Control, Ball and Beam System, Controllers, Performance, Disturbances},
language = {Spanish}
}

The objective of a control system is to regulate the dynamic behavior of a physical system through feedback. Such regulation should satisfy performance specifications even in the presence of disturbances and perturbations. When a control system performs adequately in the presence of disturbances and perturbations, it is Robust. We present a relatively simple approach to the robust control problem of the Ball-and-Beam System that can be used in basic control systems courses. The Ball and Beam System exhibits high-frequency sensor noise, unmolded highfrequency dynamics, disturbances in the process, and parameter variations of the plant. Results of controllers designed through robust control methods are presented and compared with other controllers designed by conventional methods such as the Root Locus method. It is demonstrated that a conscious design using a conventional method can depart from the performance specifications, leading to unsatisfactory performance. To demonstrate this, the real system performance for the controllers using both methods is presented and compared to the simulated performance. The performance of the system designed by the Root Locus method does not meet the performance specifications, while the performance of the system designed by robust control method does. These results were obtained from an undergraduate research project and are currently being applied in an introductory course on control systems.

@conference{bolivar_2014,
title = {Modelling the Ball-and-Beam System From Newtonian Mechanics and from Lagrange Methods},
author = {Bolivar-Vincenty, C.G. ; Beauchamp-Baez, G.},
booktitle = {12th LACCEI Latin American and Caribbean Conference for Engineering and Technology (LACCEIÍ2014)},
year = {2014},
institution = {Universidad de Puerto Rico Recinto de Mayaguez, Puerto Rico},
abstract = {The Ball and Beam is a system commonly used to expose undergraduate students to controller design. One important step of this design process is to develop a mathematical model to describe the behavior of the sytem. There are several possible methods for deriving the equations of motion of a dynamical system. These include Langrangian methods and Newtonian mechanics. Many authors fail to adequately derive the model for the Ball-and-Beam system because they obviate several acceleration terms. Although these terms do not affect the linear model, they are important for nonlinear simulations. When the model is derived from Euler-Lagrange methods, these terms appear naturally. In this paper it is demonstrated that the equations of motion obtained from both methods are identical. From the equation of motion, nonlinear state-space equations are developed. The nonlinear equations are then linearized about the equilibrium point and a transfer function suitable for a linear controller design is obtained. },
keywords = {Ball and Beam System, Dynamical Systems, Langrangian Mechanics, Newtonian Mechanics, System Modeling},
language = {English}
}

The Ball and Beam is a system commonly used to expose undergraduate students to controller design. One important step of this design process is to develop a mathematical model to describe the behavior of the sytem. There are several possible methods for deriving the equations of motion of a dynamical system. These include Langrangian methods and Newtonian mechanics. Many authors fail to adequately derive the model for the Ball-and-Beam system because they obviate several acceleration terms. Although these terms do not affect the linear model, they are important for nonlinear simulations. When the model is derived from Euler-Lagrange methods, these terms appear naturally. In this paper it is demonstrated that the equations of motion obtained from both methods are identical. From the equation of motion, nonlinear state-space equations are developed. The nonlinear equations are then linearized about the equilibrium point and a transfer function suitable for a linear controller design is obtained.

@article{magzoub_2014,
title = {Simulation of a Ball on a Beam Model Using a Fuzzy-dynamic and a Fuzzy-static Sliding-mode Controller},
author = {Magzoub, M.A.; Saad, N.B.; Ibrahim, R.B.},
journal = {Research Journal of Applied Sciences, Engineering and Technology},
year = {2014},
volume = {8},
number = {2},
institution = {Universiti Teknologi PETRONAS, Malaysia},
abstract = {This study presents the design of a Fuzzy Static (FS) and a Fuzzy Dynamic (FD) Sliding-Mode Controllers (SMC) for both basic and complete ball on beam system. At first, the FSSMC was designed for the simplified and the complete models. Then, the FDSMC was designed on the simplified and the comprehensive models of the system in which the ball is placed on a beam as well. In addition, the lyapunov stability and linearization were used to check the stability of the system. There is an in-built issue of chattering with (FSSMC). However, (FDSMC) counter it well. Also, FDSMC is effective with respect to matched disturbance rejection. It has been found out from this research study that the designs of the models which utilize a FDSMC with a comprehensive model of the system were more efficient than the designs that utilize the basic systemÍs prototype. Lastly, a comprehensive comparative analysis is provided and MATLAB/SIMULINK outcomes confirm the dominance of FDSMC. },
issn = {2040-7459},
keywords = {Fuzzy-dynamic, fuzzy-static, Sliding Mode Control (SMC), under triggered system of a ball on a beam},
language = {English},
publisher = {Maxwell Scientific Organization},
pages = {288-295}
}

This study presents the design of a Fuzzy Static (FS) and a Fuzzy Dynamic (FD) Sliding-Mode Controllers (SMC) for both basic and complete ball on beam system. At first, the FSSMC was designed for the simplified and the complete models. Then, the FDSMC was designed on the simplified and the comprehensive models of the system in which the ball is placed on a beam as well. In addition, the lyapunov stability and linearization were used to check the stability of the system. There is an in-built issue of chattering with (FSSMC). However, (FDSMC) counter it well. Also, FDSMC is effective with respect to matched disturbance rejection. It has been found out from this research study that the designs of the models which utilize a FDSMC with a comprehensive model of the system were more efficient than the designs that utilize the basic systemÍs prototype. Lastly, a comprehensive comparative analysis is provided and MATLAB/SIMULINK outcomes confirm the dominance of FDSMC.

@conference{kumbasar_2013,
title = {A one to three input mapping IT2-FLC PID design strategy},
author = {Kumbasar, T.},
booktitle = {2013 IEEE International Conference on Fuzzy Systems (FUZZ)},
year = {2013},
institution = {Control Engineering Department Istanbul Technical University Istanbul, Turkey},
abstract = {In this study, a single input interval type-2 fuzzy PID controller with a one to three inference mapping has been developed. Since it consists of a single input variable (the feedback error), a closed form formulation of the type-2 fuzzy controller output is possible. The closed form solution is derived in terms of the tuning parameters which are chosen as the heights of lower membership functions of the antecedent interval type-2 fuzzy sets. Then, a simple strategy is proposed for a process independent type-2 fuzzy PID controller design. The developed single input type-2 fuzzy controller structure preserves the most preferred features of the PID such as simplicity, independent gain tuning and easy implementation. The one to three input mapping type-2 fuzzy controller structure has been implemented on an experimental ball and beam system. The results illustrated that the proposed type-2 fuzzy controller produces superior control performance than a one-to-one inference mapping type-2 fuzzy and conventional controllers. },
keywords = {interval type-2 fuzzy logic controllers; PID control; control curve design; independent gain tunnig; Quanser ball and beam system;},
publisher = {IEEE},
pages = {06-Jan}
}

In this study, a single input interval type-2 fuzzy PID controller with a one to three inference mapping has been developed. Since it consists of a single input variable (the feedback error), a closed form formulation of the type-2 fuzzy controller output is possible. The closed form solution is derived in terms of the tuning parameters which are chosen as the heights of lower membership functions of the antecedent interval type-2 fuzzy sets. Then, a simple strategy is proposed for a process independent type-2 fuzzy PID controller design. The developed single input type-2 fuzzy controller structure preserves the most preferred features of the PID such as simplicity, independent gain tuning and easy implementation. The one to three input mapping type-2 fuzzy controller structure has been implemented on an experimental ball and beam system. The results illustrated that the proposed type-2 fuzzy controller produces superior control performance than a one-to-one inference mapping type-2 fuzzy and conventional controllers.

@article{keshmiri_2012,
title = {Modeling and Control of Ball and Beam System Using Model Based and Non-Model Based Control Approaches},
author = {Keshmiri, M.; Jahromi, A.F.; Mohebbi, A.; Amoozgar, M.H.; Xie, W.-F.},
journal = {International Journal on Smart Sensing and Intelligent Systems},
year = {2012},
volume = {5},
number = {1},
institution = {Concordia University, Department of Mechanical and Industrial Engineering, Montreal, QC, Canada},
abstract = {The ball and beam system is a laboratory equipment with high nonlinearity in its dynamics. The aims of this research are to model the ball and beam system considering nonlinear factors and coupling effect and to design controllers to control the ball position. The LQR is designed considering two Degrees-of-Freedom and Index terms: Ball and beam, proportional derivative integral controller, linear quadratic regulator, genetic algorithm coupling dynamics. The parameters of the LQR are tuned using Genetic Algorithm (GA). Jacobian linearization method is used to linearize the system around operating-point. Due to the noise of the sensor in the experimental setup, a state observer is designed to observe the velocity of the ball. In order to compare the performance of the LQR and study the effect of simplifying assumptions, two control strategies are designed and implemented: Proportional Derivative Integral (PID) as non-model based control strategy, hybrid PID and Linear Quadratic Regulator (LQR) as combination of model based and non-model based control strategies. The experimental results of this research prove the model based control strategies outperforms the non-model based or hybrid controllers in a nonlinear and noisy ball and beam system. In addition, it is shown that the coupling dynamics cannot be eliminated as a simplifying assumption in designing the controller. },
keywords = {Ball and beam, proportional derivative integral controller, linear quadratic regulator, genetic algorithm},
language = {English}
}

The ball and beam system is a laboratory equipment with high nonlinearity in its dynamics. The aims of this research are to model the ball and beam system considering nonlinear factors and coupling effect and to design controllers to control the ball position. The LQR is designed considering two Degrees-of-Freedom and Index terms: Ball and beam, proportional derivative integral controller, linear quadratic regulator, genetic algorithm coupling dynamics. The parameters of the LQR are tuned using Genetic Algorithm (GA). Jacobian linearization method is used to linearize the system around operating-point. Due to the noise of the sensor in the experimental setup, a state observer is designed to observe the velocity of the ball. In order to compare the performance of the LQR and study the effect of simplifying assumptions, two control strategies are designed and implemented: Proportional Derivative Integral (PID) as non-model based control strategy, hybrid PID and Linear Quadratic Regulator (LQR) as combination of model based and non-model based control strategies. The experimental results of this research prove the model based control strategies outperforms the non-model based or hybrid controllers in a nonlinear and noisy ball and beam system. In addition, it is shown that the coupling dynamics cannot be eliminated as a simplifying assumption in designing the controller.

@article{barcelo-rico_2012,
title = {New possibilistic method for discovering linear local behavior using hyper-Gaussian distributed membership function},
author = {Fatima Barcelo-Rico, Jose-Luis Diez, Jorge Bondia},
journal = {Knowl Inf Syst},
year = {2012},
volume = {30},
number = {2},
institution = {Universitat Politecnica de Valencia, Spain},
abstract = {This paper presents a method to find a model of a system based on the integration of a set of local models. Mainly, properties are sought for the local models: independence of clusters and interpretability of their validity. This has been achieved through the introduction of a possibilistic clustering for the first property and a pre-fixed shape of the membership functions for the second one. A new cost index for the clustering optimization problem has been defined consisting of two terms: one for global error and another for local errors. By giving higher importance to the local errors term, local models valid regionally can be found. To avoid local optima and numerical issues, the parameters of the models are found using global optimization. This new method has been applied to several data sets, and results show how the desired characteristics can be achieved in the resulting models. },
issn = {0219-1377},
keywords = {Clustering, Global optimization, Possibilistic, Gaussian, Cost index},
language = {English},
publisher = {Springer-Verlag},
pages = {377-403}
}

This paper presents a method to find a model of a system based on the integration of a set of local models. Mainly, properties are sought for the local models: independence of clusters and interpretability of their validity. This has been achieved through the introduction of a possibilistic clustering for the first property and a pre-fixed shape of the membership functions for the second one. A new cost index for the clustering optimization problem has been defined consisting of two terms: one for global error and another for local errors. By giving higher importance to the local errors term, local models valid regionally can be found. To avoid local optima and numerical issues, the parameters of the models are found using global optimization. This new method has been applied to several data sets, and results show how the desired characteristics can be achieved in the resulting models.

@article{Rahmat2010,
title = {Application of Intelligent Controller in a Ball and Beam Control System},
author = {M. F. Rahmat and H. Wahid and N. A. Wahab},
journal = {International Journal on Smart Sensing and Intelligent Systems},
year = {2010},
volume = {3},
number = {1},
institution = {Control and Instrumentation Engineering Department (CIED). Facultyof Electrical Engineering Universiti Teknologi Malaysia},
abstract = {Ball and beam system is one of a nonlinear and unstable control system, thus providing a challenge to the control engineers and researchers. There are a number of controllers which have been studied for years that can be used to stabilize the ball and beam system. This paper investigates the performance of few different control approaches that consist of conventional controller, modern controller and intelligent controller for a ball and beam system. It will involve the derivation of the mathematical modeling that includes the linearization of the model in order to be used with the linear controllers. The works followed with designing those controllers and simulating it in MATLAB. Each controller performance will be analyzed and compared which is based on common criteriaÍs of the step response. An appropriate graphic user interface (GUI) has been developed to view the animation of the ball and beam system. },
annotation = {fuaad@fke.utm.my ;herman@fke.utm.my ;mailto:aliza@fke.utm.my ;},
keywords = {ball beam, modeling, PID controller, LQR controller, neural network controller},
pages = {45--60}
}

Ball and beam system is one of a nonlinear and unstable control system, thus providing a challenge to the control engineers and researchers. There are a number of controllers which have been studied for years that can be used to stabilize the ball and beam system. This paper investigates the performance of few different control approaches that consist of conventional controller, modern controller and intelligent controller for a ball and beam system. It will involve the derivation of the mathematical modeling that includes the linearization of the model in order to be used with the linear controllers. The works followed with designing those controllers and simulating it in MATLAB. Each controller performance will be analyzed and compared which is based on common criteriaÍs of the step response. An appropriate graphic user interface (GUI) has been developed to view the animation of the ball and beam system.

@article{muralidharan_2010,
title = {Asymptotic stabilisation of the ball and beam system: design of energy-based control law and experimental results},
author = {Muralidharan, V.; Anantharaman, S.; Mahindrakar, A.D.},
journal = {International Journal of Control},
year = {2010},
month = {06},
volume = {83},
number = {6},
institution = {Indian Institute of Technology Madras, India},
abstract = {We present a new nonlinear control law to stabilise the ball and beam system at a desired operating point. The control law is based on the interconnection and damping assignment–passivity-based control (IDA-PBC) methodology developed in Ortega, Spong, Gomez-Estern, and Blankenstien (Ortega, R., Spong, M., Gomez-Estern, F., and Blankenstien, G. (2002), ‘Stabilization of Underactuated Mechanical Systems via Interconnection and Damping Assignment’, IEEE Transactions on Automatic Control, 47, 1218–1233) that guarantees stability in the sense of Lyapunov. We present a novel proof of the asymptotic stability of the desired operating point. The validity of the proposed control law is demonstrated through the experimental results. },
keywords = {ball and beam; IDA-PBC; asymptotic stability},
language = {English},
publisher = {Taylor & Francis},
pages = {1193–1198}
}

We present a new nonlinear control law to stabilise the ball and beam system at a desired operating point. The control law is based on the interconnection and damping assignment–passivity-based control (IDA-PBC) methodology developed in Ortega, Spong, Gomez-Estern, and Blankenstien (Ortega, R., Spong, M., Gomez-Estern, F., and Blankenstien, G. (2002), ‘Stabilization of Underactuated Mechanical Systems via Interconnection and Damping Assignment’, IEEE Transactions on Automatic Control, 47, 1218–1233) that guarantees stability in the sense of Lyapunov. We present a novel proof of the asymptotic stability of the desired operating point. The validity of the proposed control law is demonstrated through the experimental results.

@article{almutairi_2010,
title = {On the sliding mode control of a Ball on a Beam system},
author = {Naif B. Almutairi, Mohamed Zribi},
journal = {Nonlinear Dynamics},
year = {2010},
volume = {59},
number = {02-Jan},
institution = {College of Engineering and Petroleum, Kuwait University},
abstract = {This paper investigates the sliding mode control of the Ball on a Beam system. A static and a dynamic sliding-mode controllers are designed using a simplified model of the system; the simplified model renders the system feedback linearizable. Then, a static and a dynamic sliding-mode controllers are designed using the complete model of the Ball on a Beam system. Simulation results indicate that the proposed controllers work well. The four proposed controllers are implemented using an experimental setup. Implementation results indicate that the proposed control schemes work well. As expected, it is found that the proposed two controllers which are designed using the complete model of the system gave better performance than the ones designed using the simplified model of the system. In addition, the experimental results indicate the two dynamic controllers greatly reduce the chattering usually associated with sliding-mode controllers. },
issn = {0924-090X},
keywords = {Sliding mode control, Underactuated system, Ball on a beam},
language = {English},
publisher = {Springer Netherlands},
pages = {221-238}
}

This paper investigates the sliding mode control of the Ball on a Beam system. A static and a dynamic sliding-mode controllers are designed using a simplified model of the system; the simplified model renders the system feedback linearizable. Then, a static and a dynamic sliding-mode controllers are designed using the complete model of the Ball on a Beam system. Simulation results indicate that the proposed controllers work well. The four proposed controllers are implemented using an experimental setup. Implementation results indicate that the proposed control schemes work well. As expected, it is found that the proposed two controllers which are designed using the complete model of the system gave better performance than the ones designed using the simplified model of the system. In addition, the experimental results indicate the two dynamic controllers greatly reduce the chattering usually associated with sliding-mode controllers.

@article{Li2010,
title = {Synchronization of ball and beam systems with neural compensation},
author = {Li, Xiaoou and Yu, Wen},
journal = {International Journal of Control, Automation and Systems},
year = {2010},
volume = {8},
number = {3},
institution = {Departamento de Computacion, CINVESTAV-IPN, Av.IPN 2508, Mexico D.F.,07360, Mexico},
abstract = {Ball and beam system is one of the most popular and important laboratory models for teaching control system. It is a big challenge to synchronize ball and beam systems. There are two problems for ball and beam synchronized control: 1) many laboratories use simple controllers such as PD control, and theory analysis is based on linear models, 2) nonlinear controllers for ball and beam system have good theory results, but they are seldom used in real applications. In this paper we first use PD control with nonlinear exact compensation for the cross-coupling synchronization. Then a RBF neural network is applied to approximate the nonlinear compensator. The synchronization control can be in parallel and serial forms. The stability of the synchronization is discussed. Real experiments are applied to test our theory results. },
annotation = {lixo@cs.cinvestav.mx ; yuw@ctrl.cinvestav.mx},
issn = {1598-6446},
keywords = {Mechanical systems; neural control; stability; synchronization},
language = {English},
publisher = {Institute of Control, Robotics and Systems and The Korean Instituteof Electrical Engineers},
pages = {491-496}
}

Ball and beam system is one of the most popular and important laboratory models for teaching control system. It is a big challenge to synchronize ball and beam systems. There are two problems for ball and beam synchronized control: 1) many laboratories use simple controllers such as PD control, and theory analysis is based on linear models, 2) nonlinear controllers for ball and beam system have good theory results, but they are seldom used in real applications. In this paper we first use PD control with nonlinear exact compensation for the cross-coupling synchronization. Then a RBF neural network is applied to approximate the nonlinear compensator. The synchronization control can be in parallel and serial forms. The stability of the synchronization is discussed. Real experiments are applied to test our theory results.

@article{Yu2009,
title = {Nonlinear PD Regulation for Ball and Beam System},
author = {Yu, W.},
journal = {International Journal of Electrical Engineering Education},
year = {2009},
volume = {46},
number = {1},
abstract = {The ball and beam system is one of the most popular laboratory experiments for control education. There are two problems for ball and beam control: (1) many laboratories use simple controllers such as PD control, but theory analysis is based on linear models, and (2) nonlinear controllers for the ball and beam system have good theory results, but they are seldom used in laboratories. Little effort has been made to analyse PD control with nonlinear models. In this paper we modify the normal PD control in two ways for the ball and beam system: parallel and serial PD regulations; then we analyse the stability of these types of PD regulations with the complete nonlinear model. Real experiments are applied to test our theory results. This paper gives a good example of how to apply nonlinear theory in the laboratory for control education. },
keywords = {ball and beam system, nonlinear compensation, PD control, stability},
pages = {59--73}
}

The ball and beam system is one of the most popular laboratory experiments for control education. There are two problems for ball and beam control: (1) many laboratories use simple controllers such as PD control, but theory analysis is based on linear models, and (2) nonlinear controllers for the ball and beam system have good theory results, but they are seldom used in laboratories. Little effort has been made to analyse PD control with nonlinear models. In this paper we modify the normal PD control in two ways for the ball and beam system: parallel and serial PD regulations; then we analyse the stability of these types of PD regulations with the complete nonlinear model. Real experiments are applied to test our theory results. This paper gives a good example of how to apply nonlinear theory in the laboratory for control education.

@article{delgado_2009,
title = {Virtual Intelligent Control Laboratory},
author = {Delgado, M.A.; López, J.A.},
journal = {Educacion en Ingenieria},
year = {2009},
number = {9},
institution = {Universidad Autónoma de Occidente, Cali, Colombia},
abstract = {This paper presents the virtual laboratory of intelligent control developed with Easy Java Simulations and designed for three plants: Level Plant Lab-Volt, SRV 02 and ball beam system. The control strate-gies implemented in the laboratory are: fuzzy control, inverse model based on artificial neural networks and PID control, in order to allow the user to make comparisons between classic control and intelligent control. This software allows students develop educational activities on intelligent control using a friendly and interactive tool. },
issn = {1900-8260},
keywords = {Virtual laboratory, intelligent control, neurocontrol, fuzzy control},
language = {Spanish},
publisher = {ACOFI},
pages = {102-110}
}

This paper presents the virtual laboratory of intelligent control developed with Easy Java Simulations and designed for three plants: Level Plant Lab-Volt, SRV 02 and ball beam system. The control strate-gies implemented in the laboratory are: fuzzy control, inverse model based on artificial neural networks and PID control, in order to allow the user to make comparisons between classic control and intelligent control. This software allows students develop educational activities on intelligent control using a friendly and interactive tool.

@article{kypuros_2008,
title = {Student-configurable, Web-accessible virtual systems for system dynamics and controls courses},
author = {Kypuros, J. A. and Connolly, T. J.},
journal = {Comput. Appl. Eng. Educ.},
year = {2008},
volume = {16},
number = {2},
abstract = {This article describes a process for disseminating, via the Internet, configurable animated simulations of physical systems„virtual systems„used to visualize System Dynamics concepts. To enable widespread use, software tools readily available under a General Public License (GPL) are used. However, the dynamic systems are simulated and animated using MATLAB¬. },
keywords = {virtual systems; system dynamics; dynamics animations; Web-facilitated curriculum},
language = {English},
publisher = {Wiley Periodicals Inc.},
pages = {92-104}
}

This article describes a process for disseminating, via the Internet, configurable animated simulations of physical systems„virtual systems„used to visualize System Dynamics concepts. To enable widespread use, software tools readily available under a General Public License (GPL) are used. However, the dynamic systems are simulated and animated using MATLAB¬.

@conference{rodrigues_2006,
title = {Controladores Neuro-Fuzzy Para Sistemas Nao-Lineares},
author = {Rodrigues, M.C.; Araujo. F.M.U.; Maitelli, A.L.},
booktitle = {CBA 2006},
year = {2006},
institution = {Universidade Federal do Rio Grande do Norte, Brazil},
abstract = {Neuro-fuzzy systems has been shown as a promising technique in industrial applications. Two models of neurofuzzy systems were developed, an ANFIS model and a NEFCON model. Both models were applied to control a ball and beam system and they had their results and neededchanges commented. The choose of inputs to controllers, the parameters and the algorithms used to learning, among other informationÍs about the hybrid systems, were commented. The results show the changes in structure after learning and the conditions to use each one controller based on their characteristics. },
keywords = {Control, Hybrid Systems, Fuzzy Systems, Artificial Neural Networks, NEFCON, ANFIS},
language = {Portuguese},
pages = {720-725}
}

Neuro-fuzzy systems has been shown as a promising technique in industrial applications. Two models of neurofuzzy systems were developed, an ANFIS model and a NEFCON model. Both models were applied to control a ball and beam system and they had their results and neededchanges commented. The choose of inputs to controllers, the parameters and the algorithms used to learning, among other informationÍs about the hybrid systems, were commented. The results show the changes in structure after learning and the conditions to use each one controller based on their characteristics.

@article{gawthrop_2005,
title = {Data compression for estimation of the physical parameters of stable and unstable linear systems},
author = {Gawthrop, P.J.; Wang, L.},
journal = {Automatica},
year = {2005},
volume = {41},
number = {8},
abstract = {A two-stage method for the identification of physical system parameters from experimental data is presented. The first stage compresses the data as an empirical model which encapsulates the data content at frequencies of interest. The second stage then uses data extracted from the empirical model of the first stage within a nonlinear estimation scheme to estimate the unknown physical parameters. Furthermore, the paper proposes use of exponential data weighting in the identification of partially unknown, unstable systems so that they can be treated in the same framework as stable systems. Experimental data are used to demonstrate the efficacy of the proposed approach. },
keywords = {Parameter estimation; Partially known systems; Basis function},
language = {English},
publisher = {Elsevier Ltd.},
pages = {1313-1321}
}

A two-stage method for the identification of physical system parameters from experimental data is presented. The first stage compresses the data as an empirical model which encapsulates the data content at frequencies of interest. The second stage then uses data extracted from the empirical model of the first stage within a nonlinear estimation scheme to estimate the unknown physical parameters. Furthermore, the paper proposes use of exponential data weighting in the identification of partially unknown, unstable systems so that they can be treated in the same framework as stable systems. Experimental data are used to demonstrate the efficacy of the proposed approach.

@inproceedings{watkins_2003,
title = {A Novel Approach to a Control Systems Laboratory},
author = {Watkins, J.M.; O'Brien Jr., R.T.},
booktitle = {Proceedings of 2003 ASME International Mechanical Engineering Congress},
year = {2003},
institution = {Systems Engineering Department, United States Naval Academy, USA},
abstract = {In controls education today, a significant gap exists between the material covered in the typical undergraduate classroom and the skills that students need to be practicing control system engineers. In order to help bridge this gap, a control systems laboratory was developed in the Systems Engineering Department at the United States Naval Academy (USNA) with the following design objectives. The first objective was to provide the students the opportunity to apply control theory to physical systems. The second objective was to develop labs where each student works through the complete control system design process. The third objective was to increase the studentsÍ exposure to sampled-data control. The paper begins with a discussion of the Quanser rapid control prototype development system and laboratory experiments. Modeling and system identification are discussed next. Key areas that areas that are emphasized include the use of a dynamic signal analyzer for frequency domain identification and the identification of Coulomb friction for simulation purposes. A unified approach for root locus and Bode design that is used through out the course is discussed next. Finally, analog and digital controller implementations are discussed. },
keywords = {Controls, education, laboratory, system identification},
language = {English},
publisher = {ASME},
isbn = {0-7918-3713-0},
pages = {1421-1428}
}

In controls education today, a significant gap exists between the material covered in the typical undergraduate classroom and the skills that students need to be practicing control system engineers. In order to help bridge this gap, a control systems laboratory was developed in the Systems Engineering Department at the United States Naval Academy (USNA) with the following design objectives. The first objective was to provide the students the opportunity to apply control theory to physical systems. The second objective was to develop labs where each student works through the complete control system design process. The third objective was to increase the studentsÍ exposure to sampled-data control. The paper begins with a discussion of the Quanser rapid control prototype development system and laboratory experiments. Modeling and system identification are discussed next. Key areas that areas that are emphasized include the use of a dynamic signal analyzer for frequency domain identification and the identification of Coulomb friction for simulation purposes. A unified approach for root locus and Bode design that is used through out the course is discussed next. Finally, analog and digital controller implementations are discussed.

@conference{bonivento_2002,
title = {A Web-Based Laboratory For Control Engineering Education},
author = {Bonivento, C.; Gentili, L.; Marconi, L.; Rappini, L.},
booktitle = {2nd International Workshop on Tele-Education in Engineering Using Virtual Laboratories},
year = {2002},
volume = {212},
institution = {University of Bologna, Italy},
abstract = {The rapid progress of internet-based networking technologies enables a remote access to engineering laboratory equipment and instruments. Since control engineering education should combine theory with practice, this feature can be especially useful to provide students with an Internet access to various experimental setups located in control laboratories. },
keywords = {Internet, Remote Laboratory, Client-Server Architecture, Automatic Control Experiment, Distance Education},
language = {English}
}

The rapid progress of internet-based networking technologies enables a remote access to engineering laboratory equipment and instruments. Since control engineering education should combine theory with practice, this feature can be especially useful to provide students with an Internet access to various experimental setups located in control laboratories.

@article{Andreev2002,
title = {Matching, Linear Systems, and the Ball and Beam},
author = {Andreev, F and D. Auckly and L. Kapitanski and S. Gosavi and W. Whiteand A. Kelkar},
journal = {Automatica},
year = {2002},
volume = {38},
number = {12},
abstract = {A recent approach to the control of underactuated systems is to look for control laws which will induce some specifed structure on the closed loop system. In this paper, we describe one matching condition and an approach for finding all control laws that fit the condition. After ananalys is of the resulting control laws for linear systems, we present the results from an experiment on a nonlinear ball and beam system. },
keywords = {Underactuated systems; Control design; Lambda-method},
language = {English},
publisher = {Elsevier Science Ltd.},
pages = {2147--2152}
}

A recent approach to the control of underactuated systems is to look for control laws which will induce some specifed structure on the closed loop system. In this paper, we describe one matching condition and an approach for finding all control laws that fit the condition. After ananalys is of the resulting control laws for linear systems, we present the results from an experiment on a nonlinear ball and beam system.

@conference{andreev_2000,
title = {Matching Control Laws for a Ball and Beam System},
author = {Andreev, F.; Auckly, D.; Kapitanski, L.; Kelkar, A.},
booktitle = {IFAC 2000},
year = {2000},
institution = {Kansas State University, KS, USA},
abstract = {This note describes a method for generating an infi nite-dimensional family of nonlinear control laws for underactuated systems. For a bal l and beam system, the entire family is found explicitly. },
keywords = {Nonlinear control, mechanical systems},
language = {English}
}

This note describes a method for generating an infi nite-dimensional family of nonlinear control laws for underactuated systems. For a bal l and beam system, the entire family is found explicitly.

@inproceedings{yari_1999,
title = {Robust compensators design for existing control systems},
author = {Yari, A.R.; Eisaka, T.},
booktitle = {Proceedings of the 1999 IEEE International Conference on Control Applications},
year = {1999},
volume = {2},
institution = {Kitami Institute of Technology, Japan},
abstract = {We propose some simple methods for designing attachable robust compensators that improve the robustness and decrease the sensitivity of attached control systems. Concerning with the practical design method of robust model matching (RMM), we propose linear-time-invariant (LTI) attachable robust compensators for LTI control systems with some structured and unstructured disturbances. First, a generalized approach to the standard RMM is proposed. Then, a new configuration for RMM that separates the robust compensator from the existing controller is proposed. We also examine the efficiency of the proposed method by a laboratory experiment. },
keywords = {compensation, control system synthesis, robust control},
language = {English},
publisher = {IEEE},
pages = {1728 - 1733}
}

We propose some simple methods for designing attachable robust compensators that improve the robustness and decrease the sensitivity of attached control systems. Concerning with the practical design method of robust model matching (RMM), we propose linear-time-invariant (LTI) attachable robust compensators for LTI control systems with some structured and unstructured disturbances. First, a generalized approach to the standard RMM is proposed. Then, a new configuration for RMM that separates the robust compensator from the existing controller is proposed. We also examine the efficiency of the proposed method by a laboratory experiment.