In this study, a new perspective for developing laser scanner rangefinder based data clustering system for a 2DOF robotic ball balancer was proposed. The study focused on detecting an object (i.e., ball) on the tilt-table robotic platform using the sensor fusion and data clustering systems proposed. Clustering system was modeled by following the principles of hierarchical clustering method. The developed system involving the clustering and sensor fusion algorithms was embedded in Matlab-Simulink environment to be able to run in real-time applications. The system was tested using an experimental platform including a 2DOF robotic ball balancer equipped with high resolution encoders and a laser scanner rangefinder. In the experiments, the goal was to detect the ball and its position not only on the flat but also on the tilted platform. A camera was also attached to the top of the experimental setup and used to monitor the location of the ball on the platform. By this way the results obtained using the proposed system could be verified for accuracy, performance and repeatability issues.

The steady-state operation and controlled position tracking in ball balancer applications are largely affected due to their nonlinear and underactuated behavior. To overcome these drawbacks, this paper develops a wavelet-based fuzzy controller which operates in closed loop with the system by measuring the ball position and the plate angle. The proposed approach adapts discrete wavelet transform for denoising the error signal and tuning the weights of the fuzzy controller. To test the effectiveness of the proposed approach, numerical simulations are performed by modeling a two degree of freedom ball balancer system. The eminence of the controller is assessed by comparing its operation on the modeled system with conventional fuzzy logic controller and by calculating the root mean square error, and time response analysis. The results showed a steady and precise response of the proposed approach to the framework of positioning ball on the plate.

@article{singh2_2020,
title = {Condition Monitoring based Control using Wavelets and Machine Learning for Unmanned Surface Vehicles},
author = {Singh, R.; Bhushan, B.},
journal = {IEEE Transactions on Industrial Electronics},
year = {2020},
institution = {Delhi Technological University, India},
abstract = {This paper proposes the idea of fault detection and diagnosis for stable operation of unmanned surface vehicles (USVs). The idea of fault classification is achieved with the help of wavelet transforms and support vector machines, and the diagnosis is performed using a fuzzy controller. Initially, a brief idea of faults that effect the stable operation of USVs are identified through two degree of freedom ball balancer setup. The laboratory setup resembles the two translational motion of USVs like surge and sway. Further, the fault data is taken from plate angle, ball position and motor input voltage for developing a fault classification algorithm. The proposed algorithm depicted improved classification accuracy when compared with conventional methods. To accommodate the operation of the system as per the operating state, a wavelet based fuzzy controller is proposed. The proposed controller solves the problem of position tracking and balancing for ball and plate system with high precision, hence achieving the stable operation. },
issn = {0278-0046},
keywords = {Ball Balancer, Unmanned Surface Vehicles, Wavelet Transform, Support Vector Machine, Fault Classification, Wavelet Fuzzy Control},
language = {English},
publisher = {IEEE}
}

This paper proposes the idea of fault detection and diagnosis for stable operation of unmanned surface vehicles (USVs). The idea of fault classification is achieved with the help of wavelet transforms and support vector machines, and the diagnosis is performed using a fuzzy controller. Initially, a brief idea of faults that effect the stable operation of USVs are identified through two degree of freedom ball balancer setup. The laboratory setup resembles the two translational motion of USVs like surge and sway. Further, the fault data is taken from plate angle, ball position and motor input voltage for developing a fault classification algorithm. The proposed algorithm depicted improved classification accuracy when compared with conventional methods. To accommodate the operation of the system as per the operating state, a wavelet based fuzzy controller is proposed. The proposed controller solves the problem of position tracking and balancing for ball and plate system with high precision, hence achieving the stable operation.

@article{singh_2020,
title = {Improved ant colony optimization for achieving self-balancing and position control for balancer systems},
author = {Singh, R.; Bhushan, B.},
journal = {Journal of Ambient Intelligence and Humanized Computing},
year = {2020},
institution = {Delhi Technological University, India},
abstract = {The balancer systems represent feedback in loop-based underactuated system which is electromechanical, multivariate, and nonlinear. This paper develops a self-balancing controller using an improved ant colony optimization (ACO) to optimize the proportional integral derivative controller (PID) controller. The proposed controller achieves self-balancing control for a ball on the plate by controlling the plate inclination angle. Initially, the modelling of the ball balancer system is achieved with the help of a two degree of freedom (2DoF) ball balancer system controlled by a PID controller. Further, ACO is employed to autonomously evaluate the condition of a process and find the optimal tuning parameters for the PID controller. The transition probability of the ACO is revised to improve the response and convergence speed of the algorithm resulting in an improved ACO. The developed control schemes were applied with the 2DoF ball balancer model both in simulation as well as for the real-time operation. The results depicted the performance of the proposed control scheme by analysing the characteristics such as transient response and steady-state error. Further, stability analysis has been done for the developed control schemes using describing function method for multiple frequencies. The results depicted the superiority of the improved ACO based PID controller over the conventional PID controller. },
keywords = {Self-balancing control, Ball balancer setup, Proportional integral derivative control, Ant colony optimization},
language = {English},
publisher = {Springer Nature Switzerland}
}

The balancer systems represent feedback in loop-based underactuated system which is electromechanical, multivariate, and nonlinear. This paper develops a self-balancing controller using an improved ant colony optimization (ACO) to optimize the proportional integral derivative controller (PID) controller. The proposed controller achieves self-balancing control for a ball on the plate by controlling the plate inclination angle. Initially, the modelling of the ball balancer system is achieved with the help of a two degree of freedom (2DoF) ball balancer system controlled by a PID controller. Further, ACO is employed to autonomously evaluate the condition of a process and find the optimal tuning parameters for the PID controller. The transition probability of the ACO is revised to improve the response and convergence speed of the algorithm resulting in an improved ACO. The developed control schemes were applied with the 2DoF ball balancer model both in simulation as well as for the real-time operation. The results depicted the performance of the proposed control scheme by analysing the characteristics such as transient response and steady-state error. Further, stability analysis has been done for the developed control schemes using describing function method for multiple frequencies. The results depicted the superiority of the improved ACO based PID controller over the conventional PID controller.

@article{jonnalagadda_2020,
title = {Nonlinear control design using Takagi-Sugeno fuzzy applied to under-actuated visual servo system},
author = {Jonnalagadda, V.K.; Elumalai, V.K.; Singh, H.; Prasad, A.},
journal = {Transactions of the Institute of Measurement and Control},
year = {2020},
institution = {Vellore Insitute of Technology, India},
abstract = {This paper presents the Takagi-Sugeno (TS) fuzzy control design for nonlinear stabilization and tracking control of a ball on plate system. To deal with the plant nonlinearity and the fuzzy convergence issue, we formulate the parallel distributed compensator (PDC) TS fuzzy model to characterize the global behaviour of the nonlinear system and synthesize a feasible control framework using a velocity compensation scheme. The nonlinear dynamics of the ball on plate system is obtained using the Euler-Lagrangian energy based approach. To identify the moving objects in the video stream, a background subtraction algorithm using thresholding technique is formulated. Moreover, the stability analysis of the TS fuzzy control is reduced to linear matrix inequality (LMI) problem and solved using the Lyapunov direct method. The potential benefits of the proposed control structure for real time test cases are experimentally assessed using hardware in loop (HIL) testing on a ball on plate system. Experimental results substantiate that the TS fuzzy scheme can significantly improve not only the tracking performance but also the robustness of the closed loop system. },
issn = {0142-3312},
keywords = {TS fuzzy, Lyapunov stability, ball on plate system, vision algorithm},
language = {English},
publisher = {SAGE Publications}
}

This paper presents the Takagi-Sugeno (TS) fuzzy control design for nonlinear stabilization and tracking control of a ball on plate system. To deal with the plant nonlinearity and the fuzzy convergence issue, we formulate the parallel distributed compensator (PDC) TS fuzzy model to characterize the global behaviour of the nonlinear system and synthesize a feasible control framework using a velocity compensation scheme. The nonlinear dynamics of the ball on plate system is obtained using the Euler-Lagrangian energy based approach. To identify the moving objects in the video stream, a background subtraction algorithm using thresholding technique is formulated. Moreover, the stability analysis of the TS fuzzy control is reduced to linear matrix inequality (LMI) problem and solved using the Lyapunov direct method. The potential benefits of the proposed control structure for real time test cases are experimentally assessed using hardware in loop (HIL) testing on a ball on plate system. Experimental results substantiate that the TS fuzzy scheme can significantly improve not only the tracking performance but also the robustness of the closed loop system.

@article{ma_2020,
title = {Observer integrated backstepping control for a ball and plate system},
author = {Ma, J.; Tao, H.; Huang, J.},
journal = {International Journal of Dynamics and Control},
year = {2020},
institution = {Beijing University of Chemical Technology, China},
abstract = {An observer integrated backstepping control is designed for a ball and plate system with the characters of cascade and model uncertainties. The model of the system is written in the cascaded strict feedback form. The uncertainties of the model and derivatives of the virtual controls are estimated by a linear extended state observer and a tracking differentiator, respectively. The convergence of the derivative estimation is studied. The actual control and virtual controls are designed based on the cascaded model with the Lyapunov theory. The stability of the closed-loop system is consequently proven. Simulations and experimental results demonstrate the excellent tracking performance of the control design. },
keywords = {Ball and plate system, backstepping, Linear extended state observer (LESO), Tracking differentiator (TD)},
language = {English},
publisher = {Springer Nature Switzerland}
}

An observer integrated backstepping control is designed for a ball and plate system with the characters of cascade and model uncertainties. The model of the system is written in the cascaded strict feedback form. The uncertainties of the model and derivatives of the virtual controls are estimated by a linear extended state observer and a tracking differentiator, respectively. The convergence of the derivative estimation is studied. The actual control and virtual controls are designed based on the cascaded model with the Lyapunov theory. The stability of the closed-loop system is consequently proven. Simulations and experimental results demonstrate the excellent tracking performance of the control design.

@article{singh3_2020,
title = {Real-time control of ball balancer using neural integrated fuzzy controller},
author = {Singh, R.; Bhushan, B.},
journal = {Artificial Intelligence Review},
year = {2020},
volume = {53},
institution = {Delhi Technological University, India},
abstract = {This paper presents the design, control, and validation of two degrees of freedom Ball Balancer system. The ball and plate system is a nonlinear, electromechanical, multivariable, closed-loop unstable system on which study is carried out to control the position of ball and plate angle. The model of the system is developed using MATLAB/Simulink, and neural integrated fuzzy and its hybridization with PID have been implemented. The performance of each controller is evaluated in terms of time response analysis and steady-state error. Comparative study of simulation and real-time control results show that by using the neural integrated fuzzy controller and neural integrated fuzzy with proportional-integral-derivative Controller, the peak overshoot is reduced as compared with the PID controller and lead the system prone to appropriate balancing. These control techniques provide a stable and controlled output to the system for ball balancing and plate angle control. },
keywords = {Ball balancer system, Neural integrated fuzzy control, Neural integrated fuzzy with PID control, Proportional-integral-derivative control},
language = {English},
publisher = {Springer Nature Switzerland},
pages = {351-368}
}

This paper presents the design, control, and validation of two degrees of freedom Ball Balancer system. The ball and plate system is a nonlinear, electromechanical, multivariable, closed-loop unstable system on which study is carried out to control the position of ball and plate angle. The model of the system is developed using MATLAB/Simulink, and neural integrated fuzzy and its hybridization with PID have been implemented. The performance of each controller is evaluated in terms of time response analysis and steady-state error. Comparative study of simulation and real-time control results show that by using the neural integrated fuzzy controller and neural integrated fuzzy with proportional-integral-derivative Controller, the peak overshoot is reduced as compared with the PID controller and lead the system prone to appropriate balancing. These control techniques provide a stable and controlled output to the system for ball balancing and plate angle control.

@article{muratore_2019,
title = {Assessing Transferability from Simulation to Reality for Reinforcement Learning},
author = {Muratore, F.; Gienger, M.; Peters, J.},
year = {2019},
institution = {Technische Universitat Darmstadt, Germany; Honda Research Institute Europe, Germany; Max Planck Institute for Intelligent Systems, Germany},
abstract = {Learning robot control policies from physics simulations is of great interest to the robotics community as it may render the learning process faster, cheaper, and safer by alleviating the need for expensive real-world experiments. However, the direct transfer of learned behavior from simulation to reality is a major challenge. Optimizing a policy on a slightly faulty simulator can easily lead to the maximization of the 'Simulation Optimization Bias' (SOB). In this case, the optimizer exploits modeling errors of the simulator such that the resulting behavior can potentially damage the robot. We tackle this challenge by applying domain randomization, i.e., randomizing the parameters of the physics simulations during learning. We propose an algorithm called Simulation-based Policy Optimization with Transferability Assessment (SPOTA) which uses an estimator of the SOB to formulate a stopping criterion for training. The introduced estimator quantifies the over-fitting to the set of domains experienced while training. Our experimental results in two different environments show that the new simulation-based policy search algorithm is able to learn a control policy exclusively from a randomized simulator, which can be applied directly to real system without any additional training on the latter. },
keywords = {Reinforcement Learning, Domain Randomization, Sim-to-Real Transfer},
language = {English}
}

Learning robot control policies from physics simulations is of great interest to the robotics community as it may render the learning process faster, cheaper, and safer by alleviating the need for expensive real-world experiments. However, the direct transfer of learned behavior from simulation to reality is a major challenge. Optimizing a policy on a slightly faulty simulator can easily lead to the maximization of the 'Simulation Optimization Bias' (SOB). In this case, the optimizer exploits modeling errors of the simulator such that the resulting behavior can potentially damage the robot. We tackle this challenge by applying domain randomization, i.e., randomizing the parameters of the physics simulations during learning. We propose an algorithm called Simulation-based Policy Optimization with Transferability Assessment (SPOTA) which uses an estimator of the SOB to formulate a stopping criterion for training. The introduced estimator quantifies the over-fitting to the set of domains experienced while training. Our experimental results in two different environments show that the new simulation-based policy search algorithm is able to learn a control policy exclusively from a randomized simulator, which can be applied directly to real system without any additional training on the latter.

@conference{muhammad_2019,
title = {CCD Camera-Based Ball Balancer System with Fuzzy PD Control in Varying Light Conditions},
author = {Muhammad, T.; Guo,Y.; Wu, Y.; Yao, W.; Zeeshan, A.},
booktitle = {2019 IEEE 16th International Conference on Networking, Sensing and Control (ICNSC)},
year = {2019},
institution = {Nanjing University of Science and Technology, China},
abstract = {The Ball Balancer System (BBS) is a 2-DOF system with visual feedback. BBS has broad applications in the field of automotive industry, defense and communication antenna’s automation. The accurate trajectory tracking in BBS has always been challenging for researchers. The proposed method focuses on designing the robust Fuzzy-tuned PD (FPD) controller having better error tracking and least oscillation of the ball in varying lighting conditions. The PD parameters, i.e., K p and K d are calculated by using the Fuzzy rules. Furthermore, the Blob analysis algorithm is proposed which can detect the ball even in changing lighting conditions. The proposed method is compared with widely used techniques, i.e., color-based segmentation and PD controller. The rectangular trajectory is achieved using Blob analysis embedded with FPD, whose results are compared with the PD controller combined with color based segmentation technique. The proposed method gave promising results. },
keywords = {Proportional derivative (PD) controller, fuzzy PD, color-based image segmentation, Blob analysis},
language = {English},
publisher = {IEEE},
isbn = {978-1-7281-0085-2 }
}

The Ball Balancer System (BBS) is a 2-DOF system with visual feedback. BBS has broad applications in the field of automotive industry, defense and communication antenna’s automation. The accurate trajectory tracking in BBS has always been challenging for researchers. The proposed method focuses on designing the robust Fuzzy-tuned PD (FPD) controller having better error tracking and least oscillation of the ball in varying lighting conditions. The PD parameters, i.e., K p and K d are calculated by using the Fuzzy rules. Furthermore, the Blob analysis algorithm is proposed which can detect the ball even in changing lighting conditions. The proposed method is compared with widely used techniques, i.e., color-based segmentation and PD controller. The rectangular trajectory is achieved using Blob analysis embedded with FPD, whose results are compared with the PD controller combined with color based segmentation technique. The proposed method gave promising results.

@article{bayar_2017,
title = {Theoretical and experimental investigation of backlash effects on a 2-DOF robotic balancing table},
author = {Bayar, G.},
journal = {Mechanika},
year = {2017},
volume = {23},
number = {1},
institution = {Mechanical Engineering Department, Bulent Ecevit University, Turkey},
abstract = {In this study, backlash effects on a 2-DOF robotic balancing table are investigated. The study focuses on de-veloping a backlash detecting system which consists of a backlash observer. Different backlash approaches are ana-lyzed and a backlash modeling strategy for a 2-DOF robot-ic balancing table is developed. Working principles of the balancer is introduced and a detailed mathematical model is provided. Equation of motion of the system and backlash observing mechanism are combined to see the effects of backlash on motion. To see the working performance of the methodology introduced in this study, motion of a ball on the robotic balancing table is modeled with including the backlash. A simulation environment is developed to test the whole system proposed. In order to verify the re-sults obtained in the simulation studies, an experimental setup of robotic ball balancing table is used. Position feed-back of the ball is obtained via a camera attached at the top of the system. Simulation and experimental results show that better control of a robotic balancing table (thus that of ball position) can be achieved when the backlash effects are observed and fed into the system. },
issn = {1392-1207},
keywords = {2-DOF robot; balancing table; backlash; observer; control},
language = {English},
pages = {100-106}
}

In this study, backlash effects on a 2-DOF robotic balancing table are investigated. The study focuses on de-veloping a backlash detecting system which consists of a backlash observer. Different backlash approaches are ana-lyzed and a backlash modeling strategy for a 2-DOF robot-ic balancing table is developed. Working principles of the balancer is introduced and a detailed mathematical model is provided. Equation of motion of the system and backlash observing mechanism are combined to see the effects of backlash on motion. To see the working performance of the methodology introduced in this study, motion of a ball on the robotic balancing table is modeled with including the backlash. A simulation environment is developed to test the whole system proposed. In order to verify the re-sults obtained in the simulation studies, an experimental setup of robotic ball balancing table is used. Position feed-back of the ball is obtained via a camera attached at the top of the system. Simulation and experimental results show that better control of a robotic balancing table (thus that of ball position) can be achieved when the backlash effects are observed and fed into the system.

@article{subramanian2_2016,
title = {Uniform Ultimate Bounded Robust Model Reference Adaptive PID Control Scheme for Visual Servoing},
author = {Subramanina, R.G.; Elumalai, V.K.; Karuppusamy, S.; Canchi, V.K.},
journal = {Journal of Franklin Institute},
year = {2016},
abstract = {This paper proposes a uniform ultimate bounded (UUB) controller framework using model reference adaptive control for visual servoing of the ball on plate system. To address the major challenges in designing a control scheme for visual servoing applications including inter-axis coupling, exogenous disturbances, and plant perturbations due to modelling errors, a robust model reference adaptive PID control scheme using e1 modification method is put forward. The key advantage of this methodology is its ability to yield asymptotic stability of the closed loop system without prior information on the plant perturbations. Moreover, exploiting the Erzberger's perfect model following condition, the algorithm obtains the pseudo inverse of the system to make the system track different test trajectories. The stability and convergence of the proposed scheme are proved using Schwarz's inequality condition and Frobenius norms. To evaluate the tracking performance, two test cases namely reference following during exogenous disturbance and tracking under plant perturbations are validated. Simulation results accentuate that the proposed scheme yields satisfactory tracking response even during plant perturbation and exogenous disturbances. },
keywords = {MRAC, Visual servoing, Robust Adaptive PID, e1-modification, Uniform ultimate boundedness 7 (UUB), Ball on plate system},
language = {English},
publisher = {Elsevier Ltd.}
}

This paper proposes a uniform ultimate bounded (UUB) controller framework using model reference adaptive control for visual servoing of the ball on plate system. To address the major challenges in designing a control scheme for visual servoing applications including inter-axis coupling, exogenous disturbances, and plant perturbations due to modelling errors, a robust model reference adaptive PID control scheme using e1 modification method is put forward. The key advantage of this methodology is its ability to yield asymptotic stability of the closed loop system without prior information on the plant perturbations. Moreover, exploiting the Erzberger's perfect model following condition, the algorithm obtains the pseudo inverse of the system to make the system track different test trajectories. The stability and convergence of the proposed scheme are proved using Schwarz's inequality condition and Frobenius norms. To evaluate the tracking performance, two test cases namely reference following during exogenous disturbance and tracking under plant perturbations are validated. Simulation results accentuate that the proposed scheme yields satisfactory tracking response even during plant perturbation and exogenous disturbances.

@inproceedings{alves_2014,
title = {Controle em Sistemas com Atraso na Rede de Comunicacao Utilizando Preditores de Estado},
author = {Uiliam Nelson Lendizion Tomaz Alves; Jose Paulo Fernandes Garcia, Marcelo Carvalho Minhoto Teixeira, Saulo Crnkowise, Fernando Barros Rodrigues},
booktitle = {Anais do XX Congresso Brasileiro de Automàtica 2014},
year = {2014},
institution = {Universidad Estadual Paulista, Brasil},
abstract = {The use of communication networks to connect elements of closed-loop control systems distant each others introduces advantages such as flexibility in control system structure and lower costs. However, this strategy also introduces new challenges, since the network used usually has a non-ideal behavior. One of the problems that arise is the appearance of delays in data transmission, both between sensors and the controller and between the controller and actuators. This paper proposes the use of state predictors cascaded to deal with constant and known data transmission delays. Simulation and bench results in a Ball Balancer system are presented and prove the efficiency of the proposed strategy. },
keywords = {State Predictors, Communication Network Delays, Ball Balancer System},
language = {Portuguese},
pages = {3313-3319}
}

The use of communication networks to connect elements of closed-loop control systems distant each others introduces advantages such as flexibility in control system structure and lower costs. However, this strategy also introduces new challenges, since the network used usually has a non-ideal behavior. One of the problems that arise is the appearance of delays in data transmission, both between sensors and the controller and between the controller and actuators. This paper proposes the use of state predictors cascaded to deal with constant and known data transmission delays. Simulation and bench results in a Ball Balancer system are presented and prove the efficiency of the proposed strategy.

@conference{shiratori_2014,
title = {Optimal quantization feedback control with variable discrete quantizer},
author = {Takumi Shiratori, Tadanao Zanma and KangZhi Liu},
booktitle = {2014 IEEE 13th International Workshop on Advanced Motion Control (AMC)},
year = {2014},
abstract = {Networked control systems (NCSs) have been receiving much attention in order to improve control performance in the field of in remote robot operation, surgery and some operations. In the NCSs, it is important to quantize necessary signals for control over a limited network channel for the sake of prevention from transmitting a large amount of data. This paper addresses a quantized feedback control system with a variable discrete quantizer. In the system, both input and a parameter of the quantizer are optimized online with the help of model predictive control (MPC). In our approach, constraints on input/output, the parameter of the quantizer and other physical and/or logical constraints can be explicitly taken into account while guaranteeing optimality. The optimization problem is reduced to a mixed integer quadratic programming. Experimental results are demonstrated to verify the effectiveness of the proposed method. },
keywords = {discrete systems, distributed parameter systems, feedback, integer programming, networked control systems, optimal control, predictive control, quadratic programming, quantisation (signal)},
language = {English},
publisher = {IEEE},
pages = {116 - 121}
}

Networked control systems (NCSs) have been receiving much attention in order to improve control performance in the field of in remote robot operation, surgery and some operations. In the NCSs, it is important to quantize necessary signals for control over a limited network channel for the sake of prevention from transmitting a large amount of data. This paper addresses a quantized feedback control system with a variable discrete quantizer. In the system, both input and a parameter of the quantizer are optimized online with the help of model predictive control (MPC). In our approach, constraints on input/output, the parameter of the quantizer and other physical and/or logical constraints can be explicitly taken into account while guaranteeing optimality. The optimization problem is reduced to a mixed integer quadratic programming. Experimental results are demonstrated to verify the effectiveness of the proposed method.

@conference{oliveira_2014,
title = {Projeto e Implementacao de um Controlador Robusto Chaveado Utilizando Modelos Fuzzy Takagi-Sugeno},
author = {Wallysonn Alves de Souza, Diogo Ramalho de Oliveira, Marcelo Carvalho Minhoto Teixeira, Luciano de Souza da Costa e Silva, Rodrigo Cardim, Edvaldo Assuncao},
booktitle = {Anais do XX Congresso Brasileiro de Automàtica 2014},
year = {2014},
abstract = {The paper presents the design and practical implementation of a recently proposed switched control design method for uncertain nonlinear plants described by Takagi-Sugeno fuzzy models. The design of the switched controllers is based on a minimum-type piecewise quadratic Lyapunov function and the minimization of the time derivative of this Lyapunov function. The conditions of the new stability criterion are represented by a kind of Bilinear Matrix Inequalities (BMIs) that can be efficiently solved by the path-following method. The methodology eliminates the need of finding the membership function expressions, that can be complicated or can be also depend on the plant uncertainties, to implement of the control law. The control design subject to failures and practical implementation of a 2D ball balancer system confirms the efficiency of the method. },
keywords = {Switched control, Control of uncertain nonlinear systems, BMIs, Failure},
language = {Portuguese},
pages = {2238-2245}
}

The paper presents the design and practical implementation of a recently proposed switched control design method for uncertain nonlinear plants described by Takagi-Sugeno fuzzy models. The design of the switched controllers is based on a minimum-type piecewise quadratic Lyapunov function and the minimization of the time derivative of this Lyapunov function. The conditions of the new stability criterion are represented by a kind of Bilinear Matrix Inequalities (BMIs) that can be efficiently solved by the path-following method. The methodology eliminates the need of finding the membership function expressions, that can be complicated or can be also depend on the plant uncertainties, to implement of the control law. The control design subject to failures and practical implementation of a 2D ball balancer system confirms the efficiency of the method.