Magnetic Levitation System is one of practical examples which faces some nonlinearities behavior. Such systems require special types of controller parameters consideration for accurate results. In this paper, the process of tuning is to determine the system poles and getting them away from the instability region using state feedback (SF) controller methodology. The resulted controllable system parameters are estimated using LQR controller. Since the desired goal is to minimize vital parameters in the system behavior like the steady state error, settling time, raising time of the system and system overshoot, optimization techniques have been used to minimize cost function of the parameters which need to be optimized and reach for more reliable ones for better performance. Particle swarm optimization (PSO) has been used for tuning process. System operation points should be 0.61 A for electric current and 6 mm distance between coil surface and balanced metal ball, results show that using LQR controller will cause about 33% error percentage as steady state error and about 20% overshoot. Using PSO optimization technique for controller parameters will produce less steady state error of 6.5% with 4% overshoot percentage.

@article{jonnalagadda_2020,
title = {Current cycle feedback iterative learning control for tracking control of magnetic levitation system},
author = {Jonnalagadda, V.K.; Elumalai, V.K.; Agrawal, S.},
journal = {Transactions of the Institute of Measurement and Control},
year = {2020},
month = {2},
volume = {42},
number = {3},
institution = {Vellore Institute of Technology, India},
abstract = {This paper presents the current cycle feedback iterative learning control (CCF-ILC) augmented with the modified proportional integral derivative (PID) controller to improve the trajectory tracking and robustness of magnetic levitation (maglev) system. Motivated by the need to enhance the point to point control of maglev technology, which is widely used in several industrial applications ranging from photolithography to vibration control, we present a novel CCF-ILC framework using plant inversion technique. Modulating the control signal based on the current tracking error, CCF-ILC reduces the dependency on accurate plant model and significantly improves the robustness of the closed loop system by synthesizing the causal filters to counteract the effect of model uncertainty. To assess the stability, we present a maximum singular value based criterion for asymptotic stability of linear iterative system controlled using CCF-ILC. In addition, we prove the monotonic convergence of output sequence in the neighbourhood of reference trajectory. Finally, the proposed control framework is experimentally validated on a benchmark magnetic levitation system through hardware in loop (HIL) testing. Experimental results substantiate that synthesizing CCF-ILC with the feedback controller can significantly improve the trajectory tracking and robustness characteristics of maglev system. },
keywords = {ILC, PIV, intelligent control, magnetic levitation system, command following},
language = {English},
publisher = {SAGE Publications}
}

This paper presents the current cycle feedback iterative learning control (CCF-ILC) augmented with the modified proportional integral derivative (PID) controller to improve the trajectory tracking and robustness of magnetic levitation (maglev) system. Motivated by the need to enhance the point to point control of maglev technology, which is widely used in several industrial applications ranging from photolithography to vibration control, we present a novel CCF-ILC framework using plant inversion technique. Modulating the control signal based on the current tracking error, CCF-ILC reduces the dependency on accurate plant model and significantly improves the robustness of the closed loop system by synthesizing the causal filters to counteract the effect of model uncertainty. To assess the stability, we present a maximum singular value based criterion for asymptotic stability of linear iterative system controlled using CCF-ILC. In addition, we prove the monotonic convergence of output sequence in the neighbourhood of reference trajectory. Finally, the proposed control framework is experimentally validated on a benchmark magnetic levitation system through hardware in loop (HIL) testing. Experimental results substantiate that synthesizing CCF-ILC with the feedback controller can significantly improve the trajectory tracking and robustness characteristics of maglev system.

This paper presents a practical application of discrete-time L2 loop-shaping control to a Maglev system using the linear parameter-varying (LPV) framework. LMI-based conditions are obtained for the synthesis of an output-feedback LPV controller that guarantees robust stability and performance to the closed-loop system. Guidelines to design such controller are given in a simple and transparent manner. In addition, detailed modeling of the didactic plant manufactured by Quanser is carried out and the process of embedding the nonlinear equations into a discretized quasi-LPV (qLPV) model is described. Simulations and experimental results show that the proposed procedure can be an advantageous alternative to handle nonlinear systems in comparison to its linear time-invariant (LTI) version.

@conference{gandhi_2019,
title = {Fuzzy Tuner Based Modified Cascade Control for Electromagnetic Levitation System},
author = {Gandhi, R.V.; Adhyaru, D.M.},
booktitle = {2019 Australian & New Zealand Control Conference (ANZCC)},
year = {2019},
institution = {Nirma University, India},
abstract = {his research work presents the modified cascade control scheme using the Fuzzy Tuner. The proposed control structure is implemented for the Electromagnetic Levitation System (EMLS). This EMLS is a group of the highly nonlinear, unstable and electromechanically coupled system. The conventional cascade control with PID and PI controllers as primary and secondary loops is one of the widely used control approaches for the EMLS. However, the constant gains of the conventional cascade control structure may not provide the proper stabilization of the levitating object in the presence of the nonlinearities and the payload disturbances. Hence, Fuzzy Tuner is incorporated for the automatic tuning of the controller gains based on the ITAE criterion. Additionally, the nonlinear estimator is hybridized with the scheme to provide an online estimate of the vertical velocity of the EMLS. Also, the feed-forward compensator is introduced to compress the effect of the variation of the operating conditions. The experimental hardware is utilized to perform the stabilizing control and tracking control operations. The vertical payload disturbance in the range of 0-40 % is considered to check the efficacy of the proposed modified cascade controller. },
language = {English},
publisher = {IEEE},
isbn = {978-1-7281-1786-7 }
}

his research work presents the modified cascade control scheme using the Fuzzy Tuner. The proposed control structure is implemented for the Electromagnetic Levitation System (EMLS). This EMLS is a group of the highly nonlinear, unstable and electromechanically coupled system. The conventional cascade control with PID and PI controllers as primary and secondary loops is one of the widely used control approaches for the EMLS. However, the constant gains of the conventional cascade control structure may not provide the proper stabilization of the levitating object in the presence of the nonlinearities and the payload disturbances. Hence, Fuzzy Tuner is incorporated for the automatic tuning of the controller gains based on the ITAE criterion. Additionally, the nonlinear estimator is hybridized with the scheme to provide an online estimate of the vertical velocity of the EMLS. Also, the feed-forward compensator is introduced to compress the effect of the variation of the operating conditions. The experimental hardware is utilized to perform the stabilizing control and tracking control operations. The vertical payload disturbance in the range of 0-40 % is considered to check the efficacy of the proposed modified cascade controller.

@article{truong_2019,
title = {Tuning Parameters of Fuzzy Logic Controller using PSO for Maglev System},
author = {Truong, H.N.; Ngo, X.K.},
journal = {International Journal of Computer Applications},
year = {2019},
month = {09},
volume = {178},
number = {18},
institution = {Ba Ria - Vung Tau College of Technology, Vietnam},
abstract = {The paper proposes to use Particle Swarm Optimization (PSO) to tune parameters of a fuzzy logic controller for regulating a magnetic levitation (maglev) system at a desired position. PSO is a meta-heuristic search method. This method is inspired by bird flocking behavior searching for food. In this study, the rule base of the Fuzzy Logic Controller (FLC) is brought by expert experience, and the parameters of the controller including the membership function parameters and scaling gains will be optimally tuned by the PSO such that a quadratic criterion is minimized. Simulation results show that the designed fuzzy controller is able to stabilize the position of the maglev system. Besides, a state feedback controller is also used to regulate the maglev system. Although, the simulation results show that FLC gives performance better than the state feedback controller but the latter is more robust. },
keywords = {Fuzzy Logic Controller, PSO, Maglev},
language = {English}
}

The paper proposes to use Particle Swarm Optimization (PSO) to tune parameters of a fuzzy logic controller for regulating a magnetic levitation (maglev) system at a desired position. PSO is a meta-heuristic search method. This method is inspired by bird flocking behavior searching for food. In this study, the rule base of the Fuzzy Logic Controller (FLC) is brought by expert experience, and the parameters of the controller including the membership function parameters and scaling gains will be optimally tuned by the PSO such that a quadratic criterion is minimized. Simulation results show that the designed fuzzy controller is able to stabilize the position of the maglev system. Besides, a state feedback controller is also used to regulate the maglev system. Although, the simulation results show that FLC gives performance better than the state feedback controller but the latter is more robust.

@conference{sharma_2018,
title = {Modelling and state estimation for control of magnetic levitation system via a state feedback based full order observer approach},
author = {Sharma, D.; Shukla, S.B.; Ghosal, S.K.},
booktitle = {International Conference on Mechanical, Materials and Renewable Energy},
year = {2018},
volume = {377},
institution = {Indian Institute of Technology (Indian School of Mines), Dhanbad, India},
abstract = {This work proposes to develop mathematical model and event rigger control using a state observer, which precisely tracks position of the solid steel ball of magnetically actuated levitation system. The lumped uncertainties i.e. non-linarites exists in the magnetic levitation system, overwhelmed by the state observer. State space model was derived by the system equation. Based on desired specification required poles are placed using pole placement method to stabilize the closed loop system in response to a small size step input then full order observer estimate the state variables. Here ball position and coil current is directly measurable, but velocity is not directly measurable, which has been investigated in this work. },
language = {English},
series = {IOP Conf. Series: Materials Science and Engineering},
publisher = {IOP Publishing}
}

This work proposes to develop mathematical model and event rigger control using a state observer, which precisely tracks position of the solid steel ball of magnetically actuated levitation system. The lumped uncertainties i.e. non-linarites exists in the magnetic levitation system, overwhelmed by the state observer. State space model was derived by the system equation. Based on desired specification required poles are placed using pole placement method to stabilize the closed loop system in response to a small size step input then full order observer estimate the state variables. Here ball position and coil current is directly measurable,
but velocity is not directly measurable, which has been investigated in this work.

@article{oh2_2018,
title = {Robust observer‐based output feedback controller for nonlinear systems with uncertain triangular and nontriangular nonlinearities and diagonal terms},
author = {Oh, S.-Y.; Choi, H.-L.},
journal = {International Journal of Robust and Nonlinear Control},
year = {2018},
volume = {29},
number = {4},
institution = {Dong-A University, South Korea},
abstract = {In this paper, we provide a robust observer‐based output feedback control scheme for a class of nonlinear systems where there are uncertain triangular and nontriangular nonlinearities, nontrivial diagonal terms, and external disturbance. The presence of diagonal terms is the main generalized feature over the existing results. In order to handle the diagonal terms, there is a gain‐scaling factor in the proposed controller. Through the analysis, we show that all states and observer errors of the controlled system remain bounded. Moreover, the ultimate bounds of some states and observer errors can be made (arbitrarily) small by adjusting the gain‐scaling factor reflecting on the structure of nonlinearities and external disturbance. The validity of our control scheme is experimentally verified via the ball position control of an electromagnetic levitation system. },
keywords = {diagonal terms, gain-scaling factor, observer-based output feedback control, triangular and nontriangular nonlinearities, ultimate bounds},
language = {English},
publisher = {John Wiley & Sons, Ltd.}
}

In this paper, we provide a robust observer‐based output feedback control scheme for a class of nonlinear systems where there are uncertain triangular and nontriangular nonlinearities, nontrivial diagonal terms, and external disturbance. The presence of diagonal terms is the main generalized feature over the existing results. In order to handle the diagonal terms, there is a gain‐scaling factor in the proposed controller. Through the analysis, we show that all states and observer errors of the controlled system remain bounded. Moreover, the ultimate bounds of some states and observer errors can be made (arbitrarily) small by adjusting the gain‐scaling factor reflecting on the structure of nonlinearities and external disturbance. The validity of our control scheme is experimentally verified via the ball position control of an electromagnetic levitation system.

@conference{na_2017,
title = {Methods of state estimation resilient against sensor attacks and robust against exogenous disturbances},
author = {Na, G.; Seo, D.; Eun, Y.},
journal = {2017 IEEE Conference on Control Technology and Applications (CCTA)},
year = {2017},
institution = {DGIST, Republic of Korea},
abstract = {Control systems that are resilient against malicious attacks have recently become one of the important research topics. This is due to the fact that many critical infrastructures in our society such as power grid, nuclear facility, and public transportation, rely on feedback control technology, and that malfunction of said systems due to attack could be disastrous. Malicious attacks on control systems indeed occurred in recent years. The problem of resilient state estimation against sensor attacks, which is concerned of correctly estimating plant state despite of sensor attacks, have been previously addressed. Existing methods, however, lose the accuracy of the estimation if external disturbance exists. In this paper, we investigate the problem of resilient state estimation that are robust against external disturbance. Specifically, unknown input observer based state estimation has been developed to eliminate the effect of external disturbance on the state estimation that are resilient against malicious attacks on sensors. Associated design conditions have been derived. Additionally, disturbance observer based state estimation method has been developed. Validation of the proposed methods is provided through experiments. },
keywords = {Observers, Estimation error, Magnetic levitation, Robustness, Control systems, Adaptive control},
language = {English},
isbn = {978-1-5090-2183-3}
}

Control systems that are resilient against malicious attacks have recently become one of the important research topics. This is due to the fact that many critical infrastructures in our society such as power grid, nuclear facility, and public transportation, rely on feedback control technology, and that malfunction of said systems due to attack could be disastrous. Malicious attacks on control systems indeed occurred in recent years. The problem of resilient state estimation against sensor attacks, which is concerned of correctly estimating plant state despite of sensor attacks, have been previously addressed. Existing methods, however, lose the accuracy of the estimation if external disturbance exists. In this paper, we investigate the problem of resilient state estimation that are robust against external disturbance. Specifically, unknown input observer based state estimation has been developed to eliminate the effect of external disturbance on the state estimation that are resilient against malicious attacks on sensors. Associated design conditions have been derived. Additionally, disturbance observer based state estimation method has been developed. Validation of the proposed methods is provided through experiments.

@article{subramanian_2017,
title = {Multi-loop nonlinear control design for performance improvement of LTI systems},
author = {Subramanian, R.G.; Elumalai, V.K.},
journal = {ISA Transactions},
year = {2017},
institution = {Eindhoven University of Technology, The Netherlands; VIT University, India},
abstract = {This paper puts forward a multi-loop nonlinear control (MLNC) strategy to overcome the limited performance of LTI controllers due to the so-called “waterbed” effect. According to “Bode's sensitivity integral”, increasing the bandwidth or additional integral gain of LTI controller to improve the low-frequency disturbance attenuation irrefutably increases the sensitivity to high-frequency disturbances or measurement noise. Hence, it is impossible to attain the best of both worlds in the case of linear controllers. Therefore, with an aim to improve the transient and steady state performance of linear controllers, in this paper, a nonlinear control framework using circle criterion method and saturation nonlinearity, which adjusts the integral gain based on the error threshold, is discussed. The global asymptotic stability (GAS) of the MLNC strategy is theoretically proved using LaSalle's invariance principle and experimentally validated using measured frequency response function (FRF). Moreover, the performance of the MLNC strategy is compared with that of the multi-loop linear control (MLLC) strategy on a benchmark magnetic levitation system for tracking application. The cumulative power spectral density (CPSD) of tracking error, which is used as the performance index to assess the overall closed loop performance, accentuates that MLNC can yield better steady state and transient performance compared to MLLC scheme. },
keywords = {Cascade control, Magnetic levitation, Nonlinear control, Position control, Servo performance},
language = {English},
publisher = {Elsevier Ltd.}
}

This paper puts forward a multi-loop nonlinear control (MLNC) strategy to overcome the limited performance of LTI controllers due to the so-called “waterbed” effect. According to “Bode's sensitivity integral”, increasing the bandwidth or additional integral gain of LTI controller to improve the low-frequency disturbance attenuation irrefutably increases the sensitivity to high-frequency disturbances or measurement noise. Hence, it is impossible to attain the best of both worlds in the case of linear controllers. Therefore, with an aim to improve the transient and steady state performance of linear controllers, in this paper, a nonlinear control framework using circle criterion method and saturation nonlinearity, which adjusts the integral gain based on the error threshold, is discussed. The global asymptotic stability (GAS) of the MLNC strategy is theoretically proved using LaSalle's invariance principle and experimentally validated using measured frequency response function (FRF). Moreover, the performance of the MLNC strategy is compared with that of the multi-loop linear control (MLLC) strategy on a benchmark magnetic levitation system for tracking application. The cumulative power spectral density (CPSD) of tracking error, which is used as the performance index to assess the overall closed loop performance, accentuates that MLNC can yield better steady state and transient performance compared to MLLC scheme.

@article{subramanian_2017,
title = {Multi-loop nonlinear control design for performance improvement of LTI systems},
author = {Subramanian, R.G.; Elumalai, V.K.},
journal = {ISA Transactions},
year = {2017},
month = {09},
volume = {70},
institution = {Eindhoven University of Technology, The Netherlands; VIT University, India},
abstract = {This paper puts forward a multi-loop nonlinear control (MLNC) strategy to overcome the limited performance of LTI controllers due to the so-called “waterbed” effect. According to “Bode's sensitivity integral”, increasing the bandwidth or additional integral gain of LTI controller to improve the low-frequency disturbance attenuation irrefutably increases the sensitivity to high-frequency disturbances or measurement noise. Hence, it is impossible to attain the best of both worlds in the case of linear controllers. Therefore, with an aim to improve the transient and steady state performance of linear controllers, in this paper, a nonlinear control framework using circle criterion method and saturation nonlinearity, which adjusts the integral gain based on the error threshold, is discussed. The global asymptotic stability (GAS) of the MLNC strategy is theoretically proved using LaSalle's invariance principle and experimentally validated using measured frequency response function (FRF). Moreover, the performance of the MLNC strategy is compared with that of the multi-loop linear control (MLLC) strategy on a benchmark magnetic levitation system for tracking application. The cumulative power spectral density (CPSD) of tracking error, which is used as the performance index to assess the overall closed loop performance, accentuates that MLNC can yield better steady state and transient performance compared to MLLC scheme. },
keywords = {Cascade control, Magnetic levitation, Nonlinear control, Position control, Servo performance},
language = {English},
publisher = {Elsevier Ltd.},
pages = {132-138}
}

This paper puts forward a multi-loop nonlinear control (MLNC) strategy to overcome the limited performance of LTI controllers due to the so-called “waterbed” effect. According to “Bode's sensitivity integral”, increasing the bandwidth or additional integral gain of LTI controller to improve the low-frequency disturbance attenuation irrefutably increases the sensitivity to high-frequency disturbances or measurement noise. Hence, it is impossible to attain the best of both worlds in the case of linear controllers. Therefore, with an aim to improve the transient and steady state performance of linear controllers, in this paper, a nonlinear control framework using circle criterion method and saturation nonlinearity, which adjusts the integral gain based on the error threshold, is discussed. The global asymptotic stability (GAS) of the MLNC strategy is theoretically proved using LaSalle's invariance principle and experimentally validated using measured frequency response function (FRF). Moreover, the performance of the MLNC strategy is compared with that of the multi-loop linear control (MLLC) strategy on a benchmark magnetic levitation system for tracking application. The cumulative power spectral density (CPSD) of tracking error, which is used as the performance index to assess the overall closed loop performance, accentuates that MLNC can yield better steady state and transient performance compared to MLLC scheme.

@article{tran_2017,
title = {Nonlinear optimal control design considering a class of system constraints with validation on a magnetic levitation system},
author = {Tran, A.T.; Suzuki, S.; Sakamoto, N.},
journal = {IEEE Control Systems Letters},
year = {2017},
institution = {Nagoya University, Japan; Nanzan University, Japan},
abstract = {In this paper, based on the theory developed in [1], a nonlinear optimal controller is designed via stable manifold theory making use of Lagrange multipliers to take into account a class of system constraints. A feature of this method is that a discontinuous Hamiltonian system has to be solved. The existence and uniqueness of solutions of the Hamiltonian system are proven in this paper with a discussion on the stability of the designed controller. The effectiveness of the method is experimentally validated on a Quanser magnetic levitation system. The result shows that the designed nonlinear controller is able to handle the acceleration constraints with better control performance compared with the linear optimal one. },
issn = {2475-1456},
keywords = {Constrained control, Optimal control, Control applications},
language = {English},
publisher = {IEEE}
}

In this paper, based on the theory developed in [1], a nonlinear optimal controller is designed via stable manifold theory making use of Lagrange multipliers to take into account a class of system constraints. A feature of this method is that a discontinuous Hamiltonian system has to be solved. The existence and uniqueness of solutions of the Hamiltonian system are proven in this paper with a discussion on the stability of the designed controller. The effectiveness of the method is experimentally validated on a Quanser magnetic levitation system. The result shows that the designed nonlinear controller is able to handle the acceleration constraints with better control performance compared with the linear optimal one.

@article{kumar_2016,
title = {Algebraic Riccati equation based Q and R matrices selection algorithm for optimal LQR applied to tracking control of 3rd order magnetic levitation system},
author = {Kumar, V.E., Jerome, J.},
journal = {Archives of Electrical Engineering},
year = {2016},
volume = {65},
number = {1},
abstract = {This paper presents an analytical approach for solving the weighting matrices selection problem of a linear quadratic regulator (LQR) for the trajectory tracking application of a magnetic levitation system. One of the challenging problems in the design of LQR for tracking applications is the choice of Q and R matrices. Conventionally, the weights of a LQR controller are chosen based on a trial and error approach to determine the optimum state feedback controller gains. However, it is often time consuming and tedious to tune the controller gains via a trial and error method. To address this problem, by utilizing the relation between the algebraic Riccati equation (ARE) and the Lagrangian optimization principle, an analytical methodology for selecting the elements of Q and R matrices has been formulated. The novelty of the methodology is the emphasis on the synthesis of time domain design specifications for the formulation of the cost function of LQR, which directly translates the system requirement into a cost function so that the optimal performance can be obtained via a systematic approach. The efficacy of the proposed methodology is tested on the benchmark Quanser magnetic levitation system and a detailed simulation and experimental results are presented. Experimental results prove that the proposed methodology not only provides a systematic way of selecting the weighting matrices but also significantly improves the tracking performance of the system. },
keywords = {algebraic Riccatti equation, linear quadratic regulator, magnetic levitation system, weighting matrices, command following, cost function},
language = {English},
pages = {151-168}
}

This paper presents an analytical approach for solving the weighting matrices selection problem of a linear quadratic regulator (LQR) for the trajectory tracking application of a magnetic levitation system. One of the challenging problems in the design of LQR for tracking applications is the choice of Q and R matrices. Conventionally, the weights of a LQR controller are chosen based on a trial and error approach to determine the optimum state feedback controller gains. However, it is often time consuming and tedious to tune the controller gains via a trial and error method. To address this problem, by utilizing the relation between the algebraic Riccati equation (ARE) and the Lagrangian optimization principle, an analytical methodology for selecting the elements of Q and R matrices has been formulated. The novelty of the methodology is the emphasis on the synthesis of time domain design specifications for the formulation of the cost function of LQR, which directly translates the system requirement into a cost function so that the optimal performance can be obtained via a systematic approach. The efficacy of the proposed methodology is tested on the benchmark Quanser magnetic levitation system and a detailed simulation and experimental results are presented. Experimental results prove that the proposed methodology not only provides a systematic way of selecting the weighting matrices but also significantly improves the tracking performance of the system.

@article{eroglu_2016,
title = {Cascade sliding mode-based robust tracking control of a magnetic levitation system},
author = {Eroglu, Y.; Ablay, G.},
journal = {Journal of Systems and Control Engineering},
year = {2016},
volume = {230},
number = {8},
institution = {Abdullah Gül University, Kayseri, Turkey},
abstract = {Magnetic levitation systems are able to provide frictionless, reliable, fast and economical operations in wide-range applications. The effectiveness and applicability of these systems require precise feedback control designs because the magnetic levitation is an unstable process and have highly nonlinear dynamics. In this article, a robust sliding mode–based cascade control approach is proposed for effectively tracking the reference position of a magnetic levitation system. The magnetic levitation plant is described with electrical and mechanical models, and the control problems of these parts are treated with cascade controllers. An integral sliding mode and an output feedback sliding mode controllers are designed for use in the cascade loops. The performance of the sliding mode controllers is compared with a proportional–integral–velocity plus proportional–integral control structure. It is shown that the proposed control structure is able to provide a highly satisfactory tracking performance and can eliminate the effects of the inductance-related uncertainties and operating point originated disturbances. The experimental results are provided to validate the efficacy and feasibility of the approach. },
keywords = {Magnetic levitation, maglev, sliding mode control, cascade control, robust tracking},
language = {English},
publisher = {SAGE},
pages = {851-860}
}

Magnetic levitation systems are able to provide frictionless, reliable, fast and economical operations in wide-range applications. The effectiveness and applicability of these systems require precise feedback control designs because the magnetic levitation is an unstable process and have highly nonlinear dynamics. In this article, a robust sliding mode–based cascade control approach is proposed for effectively tracking the reference position of a magnetic levitation system. The magnetic levitation plant is described with electrical and mechanical models, and the control problems of these parts are treated with cascade controllers. An integral sliding mode and an output feedback sliding mode controllers are designed for use in the cascade loops. The performance of the sliding mode controllers is compared with a proportional–integral–velocity plus proportional–integral control structure. It is shown that the proposed control structure is able to provide a highly satisfactory tracking performance and can eliminate the effects of the inductance-related uncertainties and operating point originated disturbances. The experimental results are provided to validate the efficacy and feasibility of the approach.

@article{benitez_2016,
title = {Design of a Fuzzy Networked Control Systems. Priority Exchange Scheduling Algorithm},
author = {Benitez-Perez, H.; Ortega-Arjona, J.; Rojas-Vargas, J.A.; Duran-Chavesti, A.},
journal = {International Journal of Computers Communications & Control},
year = {2016},
volume = {11},
number = {2},
abstract = {This work presents a supervisory control strategy for Networked Control Systems (NCSs). This shows the identification and control of the plant using fuzzy theory. The fuzzy model incorporates the delay dynamics within the fuzzy rules based upon a real-time hierarchical scheduling strategy. A hierarchical scheduling Priority Exchange algorithm is used based upon codesign strategy following mutual correlation among control and network algorithms in order to bounded time delays. A system of magnetic levitation is presented as a case study. },
issn = {1841-9836},
keywords = {Fuzzy control, networked control system, time delay codesign},
language = {English},
publisher = {CCC Publications},
pages = {179-193}
}

This work presents a supervisory control strategy for Networked Control Systems (NCSs). This shows the identification and control of the plant using fuzzy theory. The fuzzy model incorporates the delay dynamics within the fuzzy rules based upon a real-time hierarchical scheduling strategy. A hierarchical scheduling Priority Exchange algorithm is used based upon codesign strategy following mutual correlation among control and network algorithms in order to bounded time delays. A system of magnetic levitation is presented as a case study.

@conference{jain_2016,
title = {Practical Implementation of Adaptive Gain and Variable Gain Super-Twisting Algorithms on the Magnetic Levitation System: A Comparative Study},
author = {Jain, S.; Mishra, J.P.; Talange, D.B.},
booktitle = {2016 14th International Workshop on Variable Structure Systems (VSS)},
year = {2016},
institution = {Department of Electrical Engineering, College of Engineering Pune, India},
abstract = {This paper describes the practical implementation of two well known robust control strategies over a non-linear magnetic levitation system for controlling the coil current so as to achieve the desired position. In order to make the controller robust and practically implementable, higher order sliding modes (HOSM) technique is used. Two second order sliding modes (SOSM) schemes are applied on the actual setup, based on adaptive gain super-twisting algorithm (AGSTA) and variable gain super-twisting algorithm (VGSTA). The sliding surface proposed is a linear combination of the error in coil current and its derivative. An extensive performance comparison study for both the proposed controllers on magnetic levitation system is carried out keeping the desired objective same for both the controllers. The robustness of the proposed controllers is validated in presence of disturbances and parametric uncertainties. The required control efforts to achieve the desired performance are tabulated. },
keywords = {Electromagnets, Force, Gain, Magnetic levitation, Steel, Uncertainty, Voltage control},
language = {English},
publisher = {IEEE},
pages = {28 - 33}
}

This paper describes the practical implementation of two well known robust control strategies over a non-linear magnetic levitation system for controlling the coil current so as to achieve the desired position. In order to make the controller robust and practically implementable, higher order sliding modes (HOSM) technique is used. Two second order sliding modes (SOSM) schemes are applied on the actual setup, based on adaptive gain super-twisting algorithm (AGSTA) and variable gain super-twisting algorithm (VGSTA). The sliding surface proposed is a linear combination of the error in coil current and its derivative. An extensive performance comparison study for both the proposed controllers on magnetic levitation system is carried out keeping the desired objective same for both the controllers. The robustness of the proposed controllers is validated in presence of disturbances and parametric uncertainties. The required control efforts to achieve the desired performance are tabulated.

@article{jeon_2016,
title = {Resilient State Estimation for Control Systems using Multiple Observers and Median Operation},
author = {Jeon, Heegyun; Aum, Sungmin; Shim, Hyungbo; Eun, Yongsoon},
year = {2016},
abstract = {This paper addresses the problem of state estimation for linear dynamic systems that is resilient against malicious attacks on sensors. By ïresiliencyÍ we mean the capability of correctly estimating the state despite external attacks.We propose a state estimation with a bank of observers combined through median operations and show that the proposed method is resilient in the sense that estimated states asymptotically converge to the true state despite attacks on sensors. In addition, the effect of sensor noise and process disturbance is also considered. For bounded sensor noise and process disturbance, the proposed method eliminates the effect of attack, and achieves state estimation error within a bound proportional to those of sensor noise and disturbance. While existing methods are computationally heavy because online solution of non-convex optimization is needed, the proposed approach is computationally efficient by using median operation in the place of optimization. It should be pointed out that the proposed method requires the system states being observable with every sensor, which is not a necessary condition for the existing methods. From resilient system design point of view, however, this fact may not be critical because sensors can be chosen for resiliency in the design stage. The gained computational efficiency helps implementation in practice. },
keywords = {Resilient state estimation, secure state estimation, bank of observers, linear dynamic systems, malicious attacks},
language = {English}
}

This paper addresses the problem of state estimation for linear dynamic systems that is resilient against malicious attacks on sensors. By ïresiliencyÍ we mean the capability of correctly estimating the state despite external attacks.We propose a state estimation with a bank of observers combined through median operations and show that the proposed method is resilient in the sense that estimated states asymptotically converge to the true state despite attacks on sensors. In addition, the effect of sensor noise and process disturbance is also considered. For bounded sensor noise and process disturbance, the proposed method eliminates the effect of attack, and achieves state estimation error within a bound proportional to those of sensor noise and disturbance. While existing methods are computationally heavy because online solution of non-convex optimization is needed, the proposed approach is computationally efficient by using median operation in the place of optimization. It should be pointed out that the proposed method requires the system states being observable with every sensor, which is not a necessary condition for the existing methods. From resilient system design point of view, however, this fact may not be critical because sensors can be chosen for resiliency in the design stage. The gained computational efficiency helps implementation in practice.

@article{ginoya_2016,
title = {State-and-disturbance-observer-based sliding mode control of magnetic levitation systems},
author = {Ginoya, D.; Gutte, C.M.; Shendge, P.D., Phadke, S.B.},
journal = {Transactions of the Institute of measurement and Control},
year = {2016},
institution = {Department of Instrumentation and Control, College of Engineering, Pune, Maharashtra, India},
abstract = {In this paper, a cascaded sliding mode control is designed for magnetic levitation systems usually comprised of an electrical loop and an electromechanical loop. A disturbance-observer-based sliding mode controller is designed for the electrical loop while a state-and-disturbance-observer-based sliding mode controller is designed for the electromechanical loop. The overall stability of the system is proved. The performance of the proposed scheme is compared with a conventional linear quadratic regulator combined with a proportional_integral controller by simulation as well as experimentation on a magnetic levitation setup in laboratory. },
keywords = {Disturbance observer, sliding mode control, magnetic levitation systems, state and disturbance observer, uncertain systems},
language = {English},
publisher = {SAGE}
}

In this paper, a cascaded sliding mode control is designed for magnetic levitation systems usually comprised of an electrical loop and an electromechanical loop. A disturbance-observer-based sliding mode controller is designed for the electrical loop while a state-and-disturbance-observer-based sliding mode controller is designed for the electromechanical loop. The overall stability of the system is proved. The performance of the proposed scheme is compared with a conventional linear quadratic regulator combined with a proportional_integral controller by simulation as well as experimentation on a magnetic levitation setup in laboratory.

@article{singru_2015,
title = {A state-feedback control approach via inertial delay observer for Magnetic Levitation system},
author = {Neha Singru, Divyesh Ginoya, P. D. Shendge, S.B. Phadke},
year = {2015},
institution = {College of Engineering Pune, India},
abstract = {This paper proposes the state-feedback control (SFC) with inertial delay observer (IDO) for precise position control of one inch diameter steel ball in magnetic levitation system. The state variables considered to model this system are position of ball below the electromagnet, speed of ball and current through the electromagnet. The non-linearities present in magnetic levitation system is estimated using inertial delay observer. It gives lumped uncertainty and unavailable states of the system. Simulation results are present in terms of their ability to track the reference trajectory },
keywords = {Inertial delay observer(IDO), Magnetic Levitation, Inertial delay control(IDC), State feedback control},
language = {English}
}

This paper proposes the state-feedback control (SFC) with inertial delay observer (IDO) for precise position control of one inch diameter steel ball in magnetic levitation system. The state variables considered to model this system are position of ball below the electromagnet, speed of ball and current through the electromagnet. The non-linearities present in magnetic levitation system is estimated using inertial delay observer. It gives lumped uncertainty and unavailable states of the system. Simulation results are present in terms of their ability to track the reference trajectory

@conference{sakalli_2014,
title = {Analysis of the Performances of Type-1, Self-Tuning Type-1 and Interval Type-2 Fuzzy PID Controllers on the Magnetic Levitation System},
author = {Sakalli, A.; Kumbasar, T.; Yesil, E.; and Hagras, H.},
booktitle = {2014 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)},
year = {2014},
abstract = {In this paper, we will compare the closed loop control performance of interval type-2 fuzzy PID controller with the type-1 fuzzy PID and conventional PID controllers counterparts for the Magnetic Levitation Plant. We will also compare the control performance of the interval type-2 fuzzy PID controller with the self-tuning type-1 fuzzy PID controllers. The internal structures of implemented controllers are firstly examined and then the design parameters of each controller are optimized for a given reference trajectory. The paper also show the effect of the extra degree of freedom provided by antecedent membership functions of interval type-2 fuzzy logic controller on the closed loop system performance. The real-time experiments are accomplished on an unstable nonlinear system, QUANSER Magnetic Levitation Plant, in order to show the superiority of the optimized interval type-2 fuzzy PID controller compared to optimized PID and type-1 counterparts. },
keywords = {Interval type-2 fuzzy PID controllers; self-tuning; magnetic levitation system},
language = {English},
publisher = {IEEE},
isbn = {978-1-4799-2073-0},
pages = {1859 - 1866}
}

In this paper, we will compare the closed loop control performance of interval type-2 fuzzy PID controller with the type-1 fuzzy PID and conventional PID controllers counterparts for the Magnetic Levitation Plant. We will also compare the control performance of the interval type-2 fuzzy PID controller with the self-tuning type-1 fuzzy PID controllers. The internal structures of implemented controllers are firstly examined and then the design parameters of each controller are optimized for a given reference trajectory. The paper also show the effect of the extra degree of freedom provided by antecedent membership functions of interval type-2 fuzzy logic controller on the closed loop system performance. The real-time experiments are accomplished on an unstable nonlinear system, QUANSER Magnetic Levitation Plant, in order to show the superiority of the optimized interval type-2 fuzzy PID controller compared to optimized PID and type-1 counterparts.

@conference{barbosa_2014,
title = {GA optimization of ladder-structured GOBF models},
author = {Barbosa Machado, J.},
booktitle = {2014 8th Annual IEEE Systems Conference (SysCon)},
year = {2014},
institution = {Federal University of Itajuba, Brazil},
abstract = {A new technique for systems identification using ladder-structured generalized orthonormal basis function model is presented. In this approach the model poles and the number of functions are optimized using a genetic algorithm. A fitness function based on the Akaike information criterion considering model accuracy and model parsimony provides optimal number of functions and poles of the system model. Simulated and a real examples illustrate the performance of the proposed technique. },
keywords = {Akaike information criterion; GA optimization; genetic algorithm; ladder-structured GOBF models; ladder-structured generalized orthonormal basis function model; systems identification},
publisher = {IEEE},
isbn = {978-1-4799-2087-7},
pages = {396-401}
}

A new technique for systems identification using ladder-structured generalized orthonormal basis function model is presented. In this approach the model poles and the number of functions are optimized using a genetic algorithm. A fitness function based on the Akaike information criterion considering model accuracy and model parsimony provides optimal number of functions and poles of the system model. Simulated and a real examples illustrate the performance of the proposed technique.

@inproceedings{kumada_2014,
title = {Gain scheduling control for magnetic levitation device using redundant descriptor representation},
author = {Kumada, T.; Chen, G.; Takami, I.},
booktitle = {2014 Australian Control Conference},
year = {2014},
institution = {Nanzan University, Japan},
abstract = {This paper proposes Gain Scheduling (GS) control for magnetic levitation device using redundant descriptor representation. The purpose of this study is to stably float a steel ball and let the distance between a coil and a steel ball follow the reference without error. GS control has a potential not only to deal with large variation range but also to improve the control performance. In this study, designed controllers are able to let a steel ball float stably in not a one equilibrium point but some variation range by scheduling an equilibrium point. However, designing a GS controller is difficult in the framework of state space representation. The redundancy of descriptor representation is applied to this difficulty. It is shown that a GS controller can be easily designed by introducing redundant descriptor variables. The robust stability for the system with uncertain parameters is guaranteed theoretically by using matrix polytope representation. Then, the problem is formulated as solving a finite set of Linear Matrix Inequalities (LMI) based on previous research. Finally, the effectiveness of the proposed method is verified by comparing a GS controller and a robust LQ controller in some simulations and experiments. },
language = {English},
publisher = {Engineers Australia},
isbn = {978-1-922107-39-8},
pages = {199-204}
}

This paper proposes Gain Scheduling (GS) control for magnetic levitation device using redundant descriptor representation. The purpose of this study is to stably float a steel ball and let the distance between a coil and a steel ball follow the reference without error. GS control has a potential not only to deal with large variation range but also to improve the control performance. In this study, designed controllers are able to let a steel ball float stably in not a one equilibrium point but some variation range by scheduling an equilibrium point. However, designing a GS controller is difficult in the framework of state space representation. The redundancy of descriptor representation is applied to this difficulty. It is shown that a GS controller can be easily designed by introducing redundant descriptor variables. The robust stability for the system with uncertain parameters is guaranteed theoretically by using matrix polytope representation. Then, the problem is formulated as solving a finite set of Linear Matrix Inequalities (LMI) based on previous research. Finally, the effectiveness of the proposed method is verified by comparing a GS controller and a robust LQ controller in some simulations and experiments.

@conference{guerrero_tejada_2014,
title = {Maglev Tracking Control by a State-Feedback with Integral Action and Robust Velocity Reconstruction},
author = {Guerrero Tejada, C.; Gonzalez-Olvera, M.A.; Davila, J.; Fabian-Pliego, J.C.},
booktitle = {16th Latinoamerican Congress on Automatic Control (CLCA 2014)},
year = {2014},
institution = {Universidad Autonoma de la Ciudad de Mexico, Mexico; Instituto Politecnico Nacional, Mexico},
abstract = {In this work we present a design of a LQR control for a magnetic levitator system with integral term and full-state feedback with robust exact reconstruction of the velocity for regulation and tracking, considering external perturbations and non-modeled dynamics, as well as noisy measurements. Simulation and experimental results are presented in order to show the effectiveness of the presented scheme. },
keywords = {Optimal control, Robust Exact Differentiatior, Maglev System, State-Feedback},
language = {English}
}

In this work we present a design of a LQR control for a magnetic levitator system with integral term and full-state feedback with robust exact reconstruction of the velocity for regulation and tracking, considering external perturbations and non-modeled dynamics, as well as noisy measurements. Simulation and experimental results are presented in order to show the effectiveness of the presented scheme.

@article{hossain_2013,
title = {Design of a Robust Controller for a Magnetic Levitation System},
author = {Hossain, S.},
year = {2013},
institution = {Wichita State University, USA},
abstract = {A Magnetic Levitation System (Maglev) is considered as a good test-bed for the design and analysis of control systems since it is a nonlinear unstable plant with practical uses in high-speed transportation and magnetic bearings. The objective of this project is to design a robust controller and implement it on a test-bed to help students learn the robust control design. In this project a robust controller for a maglev system is designed, using H-infinity optimization [3]. Complete mathematical models of the electrical, mechanical and magnetic systems are also developed. The design and simulations are performed under a Matlab/Simulink platform. Wincon control software of Quanser Inc. [7] is used to establish the link between the Matlab/Simulink models and the actual magnetic levitation system. },
keywords = {Robust control, stability and performance robustness},
language = {English}
}

A Magnetic Levitation System (Maglev) is considered as a good test-bed for the design and analysis of control systems since it is a nonlinear unstable plant with practical uses in high-speed transportation and magnetic bearings. The objective of this project is to design a robust controller and implement it on a test-bed to help students learn the robust control design. In this project a robust controller for a maglev system is designed, using H-infinity optimization [3]. Complete mathematical models of the electrical, mechanical and magnetic systems are also developed. The design and simulations are performed under a Matlab/Simulink platform. Wincon control software of Quanser Inc. [7] is used to establish the link between the Matlab/Simulink models and the actual magnetic levitation system.

@conference{vinodh2013,
title = {LQR based optimal tuning of PID controller for trajectory tracking of Magnetic Levitation System},
author = {Vinodh Kumar E., Jovitha Jerome},
booktitle = {International Conference on Design and Manufacturing (IConDM2013)},
journal = {Procedia Engineering},
year = {2013},
volume = {64},
abstract = {In this paper, we consider the stabilization and trajectory tracking of magnetic levitation system using PID controller whose controller gains are determined via Linear Quadratic Regulator (LQR) approach. Firstly, the nonlinear mathematical model of the system is obtained from the first principles. Then by applying Taylor's series, the non linear equation of motion is linearized around the equilibrium point to implement the stabilizing controller. Finally, the gains of the PID controller to achieve the desired response are determined using the LQR theory. Based on the natural frequency and damping ratio of the closed loop system, a new criterion for selecting the weighting matrices of LQR is proposed in this paper. Experiments are conducted on a Quanser magnetic levitation system to evaluate the performance of the proposed methodology and the experimental results prove that the proposed control strategy is effective not only in stabilizing the ball but also in rejecting the disturbance present in the system. },
keywords = {Trajectory tracking; Magnetic levitation; PID controller; Linear Quadratic Regulator; Weighting Matrices; Feed forward control},
publisher = {Elsevier B.V.},
pages = {254 - 264}
}

In this paper, we consider the stabilization and trajectory tracking of magnetic levitation system using PID controller whose controller gains are determined via Linear Quadratic Regulator (LQR) approach. Firstly, the nonlinear mathematical model of the system is obtained from the first principles. Then by applying Taylor's series, the non linear equation of motion is linearized around the equilibrium point to implement the stabilizing controller. Finally, the gains of the PID controller to achieve the desired response are determined using the LQR theory. Based on the natural frequency and damping ratio of the closed loop system, a new criterion for selecting the weighting matrices of LQR is proposed in this paper. Experiments are conducted on a Quanser magnetic levitation system to evaluate the performance of the proposed methodology and the experimental results prove that the proposed control strategy is effective not only in stabilizing the ball but also in rejecting the disturbance present in the system.

@article{ollervides_2010,
title = {Aplicacion de Control Borroso a un Sistema de Suspension Magnetica: Comparacion Experimental},
author = {Ollervides,J.; Santibanez,V.; Llama,M.; Dzul,A.},
journal = {Revista Iberoamericana de Automatica e Informatica Industrial},
year = {2010},
volume = {7},
number = {3},
institution = {Instituto Tecnologico de la Laguna, Mexico},
abstract = {Este trabajo presenta un esquema de control logico borroso de regulacion de posicion aplicado a un sistema de suspension o levitacion magnetica de una esfera metalica. El principal ingrediente de aportacion de este trabajo es la aplicacion experimental en tiempo real de dicho controlador y su comparacion con otros esquemas tanto lineales como no lineales; a saber: esquemas de control PD y PID con precompensacion, y un esquema basado en pasividad, asignacion de amortiguamiento e interconexion, introducido recientemente en la literatura. },
issn = {1697-7912},
keywords = {control borroso, sistemas no lineales, dispositivos electromagneticos, suspension magnetica, control PID},
language = {Spanish},
publisher = {Elsevier Espana},
pages = {63-71}
}

Este trabajo presenta un esquema de control logico borroso de regulacion de posicion aplicado a un sistema de suspension o levitacion magnetica de una esfera metalica. El principal ingrediente de aportacion de este trabajo es la aplicacion experimental en tiempo real de dicho controlador y su comparacion con otros esquemas tanto lineales como no lineales; a saber: esquemas de control PD y PID con precompensacion, y un esquema basado en pasividad, asignacion de amortiguamiento e interconexion, introducido recientemente en la literatura.

@article{yetendje_2010,
title = {Sensor fault-tolerant control of a magnetic levitation system},
author = {Yetendje, A., Seron, M. M., Dona, J. A. D. and Martinez, J. J.},
journal = {Int. J. Robust Nonlinear Control},
year = {2010},
volume = {20},
number = {18},
abstract = {In this paper, a fault-tolerant switching control strategy is implemented on a magnetic levitation (MAGLEV) system. Two sensors are embedded in the MAGLEV system and their measurements used by two independent estimators. Each sensors_estimator combination, together with a feedback controller can levitate and stabilize a 1-in steel ball at a desired position in the air. The paper focuses on the design and testing of a switching scheme which, at each instant of time, selects the sensors_estimator combination that provides the best closed loop performance based on a chosen criterion. Theoretical results on the system linearization around an operating point ensure local closed-loop stability and good performance under the occurrence of an abrupt fault in one of the plant sensors. Experimental results are provided which confirm the fault-tolerant capabilities of the strategy. },
keywords = {magnetic suspension; fault-tolerant control; switching control; bounded disturbances; invariant sets},
language = {English},
publisher = {John Wiley & Sons, Ltd.},
pages = {2018-2121}
}

In this paper, a fault-tolerant switching control strategy is implemented on a magnetic levitation (MAGLEV) system. Two sensors are embedded in the MAGLEV system and their measurements used by two independent estimators. Each sensors_estimator combination, together with a feedback controller can levitate and stabilize a 1-in steel ball at a desired position in the air. The paper focuses on the design and testing of a switching scheme which, at each instant of time, selects the sensors_estimator combination that provides the best closed loop performance based on a chosen criterion. Theoretical results on the system linearization around an operating point ensure local closed-loop stability and good performance under the occurrence of an abrupt fault in one of the plant sensors. Experimental results are provided which confirm the fault-tolerant capabilities of the strategy.

@inproceedings{son_2004,
title = {A New Approach to the Design of Dynamic Output Feedback Stabilizers for LTI Systems},
author = {Son, Y.I.; Shim, H.; Jo, N.H.; Kim, K.-I.},
booktitle = {Proceedings of the 2004 American Control Conference},
year = {2004},
volume = {2},
abstract = {We present a new state-space approach for designing a dynamic output feedback control law, which stabilizes a class of linear time invariant systems. All the states of the given system are not measurable and only the output is used to design the stabilizing control law. In the design scheme, however, we first assume that the given system can be stabilized by a feedback law composed of the output and its derivatives of a certain order. Beginning with this assumption, we systematically construct a dynamic system which removes the need of the derivatives. The actual order of the constructed dynamic feedback controller is the dimension of the output times the order of derivatives that are necessary. Therefore, it may be useful for order reduction of dynamic controllers. A set-point regulation problem for a magnetic levitation system is also solved without using the velocity measurement. },
issn = {0743-1619},
keywords = {control system synthesis, feedback, linear systems, magnetic levitation, stability, state-space methods},
language = {English},
publisher = {IEEE},
isbn = {0-7803-8335-4},
pages = {1451-1456}
}

We present a new state-space approach for designing a dynamic output feedback control law, which stabilizes a class of linear time invariant systems. All the states of the given system are not measurable and only the output is used to design the stabilizing control law. In the design scheme, however, we first assume that the given system can be stabilized by a feedback law composed of the output and its derivatives of a certain order. Beginning with this assumption, we systematically construct a dynamic system which removes the need of the derivatives. The actual order of the constructed dynamic feedback controller is the dimension of the output times the order of derivatives that are necessary. Therefore, it may be useful for order reduction of dynamic controllers. A set-point regulation problem for a magnetic levitation system is also solved without using the velocity measurement.

@article{Yang2004,
title = {Robust Position Control of a Magnetic Levitation System via Dynamic Surface Control Technique},
author = {Yang, Z. J. and K. Miyazaki and S. Kanae and K. Wada},
journal = {IEEE Transactions on Industrial Electronics},
year = {2004},
volume = {51},
institution = {Department of Electrical and Electronic Systems Engineering, GraduateSchool of Information Science and ElectricalEngineering, Kyushu University, Fukuoka 812-8581, Japan},
abstract = {This paper considers the position-tracking problem of a magnetic levitation system in the presence of modeling errors due to uncertainties of physical parameters. A robust nonlinear controller is designed to achieve excellent position-tracking performance. The recently developed dynamic surface control is modified and applied to the system under study, to over-come the problem of "explosion of terms" associated with the backstepping design procedure. Input-to-state stability of the control system is analyzed, and the advantages of the dynamic surface control technique over the conventional backstepping technique are verified through both theoretical and experimental studies. },
annotation = {yoh@ees.kyushu-u.ac.jp},
keywords = {backstepping design controller, design dynamic surface control technique, explosion of terms, input-to-state stability, magnetic levitation system, modeling errors, nonlinear controller, nonlinear damping, physical parameter uncertainties, position-tracking problem, robust position control, system dynamics},
pages = {26--34}
}

This paper considers the position-tracking problem of a magnetic levitation system in the presence of modeling errors due to uncertainties of physical parameters. A robust nonlinear controller is designed to achieve excellent position-tracking performance. The recently developed dynamic surface control is modified and applied to the system under study, to over-come the problem of "explosion of terms" associated with the backstepping design procedure. Input-to-state stability of the control system is analyzed, and the advantages of the dynamic surface control technique over the conventional backstepping technique are verified through both theoretical and experimental studies.

@inproceedings{kapila_2000,
title = {A multi-disciplinary undergraduate real-time experimental control laboratory},
author = {Kapila, V.; de Queiroz, M.S.; Tzes, A.},
booktitle = {Proceedings of the 2000 American Control Conference},
year = {2000},
volume = {6},
institution = {Polytechnic University , Brooklyn , NY, USA},
abstract = {This paper describes the ongoing efforts in the mechanical, aerospace, and Manufacturing Engineering Department at Polytechnic University to develop a multi-disciplinary, practice-oriented, control education program. This program exploits recent advances in PC and DSP-based real-time control hardware/software and the commercial availability of numerous educational control experimental setups. In particular, we describe the current status of the laboratory development effort and future plans },
issn = {0743-1619},
keywords = {control engineering education, laboratories, real-time systems},
language = {English},
publisher = {IEEE},
isbn = {0-7803-5519-9},
pages = {3980-3984}
}

This paper describes the ongoing efforts in the mechanical, aerospace, and Manufacturing Engineering Department at Polytechnic University to develop a multi-disciplinary, practice-oriented, control education program. This program exploits recent advances in PC and DSP-based real-time control hardware/software and the commercial availability of numerous educational control experimental setups. In particular, we describe the current status of the laboratory development effort and future plans