This paper proposes an integral sliding mode control (ISMC) for a class of linear systems with ti... more This paper proposes an integral sliding mode control (ISMC) for a class of linear systems with time-varying state and input delays. An integral sliding surface is firstly constructed. Then, by using the Lyapunov-Krasovskii functional and some specified matrices, a sufficient condition is obtained in the form of linear matrix inequalities (LMIs) to ensure the sliding mode dynamics to be asymptotically stable. Furthermore, a sliding mode controller law is synthesized to guarantee that the system trajectories can be driven onto the specified sliding surface in a finite time and maintained there for all subsequent time. Finally, an inverted pendulum model is used to illustrate the advantages and effectiveness of the design method.
... matrices. is the uncertainty matrix which belongs to the following set: This kind of uncertai... more ... matrices. is the uncertainty matrix which belongs to the following set: This kind of uncertainty was extensively studied in the literature where it is referred as norm bounded uncertainty (Khargonekar, Petersen, & Zhou, 1990). ...
ABSTRACT In this paper, the problem of robust pole assignment in a disk with an H2H2 guaranteed c... more ABSTRACT In this paper, the problem of robust pole assignment in a disk with an H2H2 guaranteed cost design is addressed. The uncertain systems considered are of norm bounded type and continuous as well as discrete time. The set of gains which assigns the closed-loop poles in a disk is characterised through a Linear Matrix Inequality (LMI). A way for selecting a gain in this set, which minimises an upper H2H2 norm bound on the transfer matrix between a perturbation and a controlled output, is presented. It consists in solving a convex optimisation problem with a linear criterion and an LMILMI as a constraint.
This note proposes a systematic approach for the static output feedback control design for discre... more This note proposes a systematic approach for the static output feedback control design for discrete time linear systems. It is shown that if the open loop system satisfies some particular structural conditions, a static output feedback gain can be calculated easily, using a formula only involving the original system matrices. Among the conditions the system has to satisfy, the stronger
This paper addresses the problem of determination of stability regions, in fact regions of admiss... more This paper addresses the problem of determination of stability regions, in fact regions of admissible initial state, as large as possible, for linear systems with delayed outputs and subject to input saturation and bounded controlled outputs, through anti-windup strategies. The closed-loop system resulting from the open-loop system with delayed output, the dynamic output controller plus the anti-windup loop is modelled as a linear time-delay system with a dead-zone nonlinearity. Constructive delay-dependent stability condition is then fonnulated by using a quadratic Lyapunov-Krasovskii functional. The optimization problem for computing the anti-windup gain that maximizes the size of the associated region of stability is directly expressed as the optimization of a convex criterion under LMI constraints.
In this paper, we propose a robust hybrid control for a boost inverter. This control presents the... more In this paper, we propose a robust hybrid control for a boost inverter. This control presents the particularity of considering the real nature of the dynamics, which means, the continuous-time dynamics, voltages and currents, and the discrete-time dynamics, the switching of the transistors. Likewise, due to implementation issues a minimum dwell time is introduced in the control loop scheme. Uniform global asymptotic stability is guaranteed, ensuring that the tracking error of the system output enters into a small neighbourhood of zero. Moreover, robustness guarantee with respect to parameter variations, in terms of an error tracking output regulation, are also provided here. The effectiveness of the proposed hybrid control scheme is illustrated in simulation.
International Journal of Modelling, Identification and Control, 2018
Over the past few decades, the world demand for energy has risen steadily, forcing the world comm... more Over the past few decades, the world demand for energy has risen steadily, forcing the world communities to look for alternative sources. Photovoltaic (PV) is seen as the most appropriate solution for this demand. In this context, this paper presents a robust terminal sliding mode control (RTSMC) method for maximum power tracking of stand-alone PV systems. The design method provides good robustness properties in the face of the system uncertainties and change of environment conditions. Starting from the mathematical dependence between the open-circuit voltage (V oc) and the optimal operating voltage (V op), an MPPT design method is given. To eliminate the tracking voltage error, a RTSMC method is introduced thereafter. A pulse width modulator (PWM) is used to maintain the switching frequency constant. Compared to the P&O algorithm, the proposed methodology reduces the oscillations around the maximum power point (MPP) and provides better performance proprieties. Also, the simulations results prove the robustness qualities of the TSMC-MPPT design method.
This chapter presents the different aspects of the design methodology that has been used to cope ... more This chapter presents the different aspects of the design methodology that has been used to cope with the RCAM design problem. A quadratic approach involving robust pole placement in a disk and the solution of parameter-dependent Riccati equations is proposed. Robustness as well as performance is accounted for by robust disk pole location that ensures robust stability and provides a good transient behaviour together with a specific selection of the weighting matrices involved in the Riccati equations.
HAL (Le Centre pour la Communication Scientifique Directe), Oct 17, 2017
Using a hybrid systems approach, we address the practical stabilization of operating points for s... more Using a hybrid systems approach, we address the practical stabilization of operating points for switched affine systems, ensuring a minimum dwell time and an admissible chattering around the operating point. Two different solutions are shown to induce uniform dwell time, based on time-or space-regularization. The proposed solutions provide useful tuning knobs to separately adjust the switching frequency during transients and at the steady state. The strengths of the method are illustrated by simulating a boost converter.
Application de la commande robuste sequencee au controle de la transition operationnelle d’un sys... more Application de la commande robuste sequencee au controle de la transition operationnelle d’un systeme non lineaire Yann LABIT1, Pedro TEPPA1;2, Jacques BERNUSSOU1, Germain GARCIA1 1 Laboratoire d’Analyse et d’Architecture des Systemes du CNRS 7 Avenue du Colonel Roche, 31077 Toulouse, France 2 Universite Simon Bolivar, Valle de Sartenejas, Baruta, Caracas-Venezuelafylabit, pteppa, [email protected] Resume— Nous proposons, dans cet article, une approche systematique pour assurer la transition en stabilite d’un systeme dynamique non lineaire entre deux points operationnels. Ceci est realise dans un cadre d’un sequen- cement de lois de commande robuste issues de la satisfaction de contraintes en stabilite et en prenant compte de certaines specifications de perfor- mances locales qui restent valables dans un voisinage d’attraction d’un en- semble de points d’equilibre. L’approche proposee est implantee par l’in- termediaire de deux techniques : la premiere repose sur les fonctions cano- niques lineaires par morceaux tandis que la deuxieme se centralise sur des outils geometriques tels que les ellipsoi�
T'he steanl generator water level, (SG'VL), controJ problem in the pressurized \i\rater reactor o... more T'he steanl generator water level, (SG'VL), controJ problem in the pressurized \i\rater reactor of a nuclear power plant is considered from robust control techniques point of vie\sv. The plant is a time-varying system with a non minimum phase behavior and an unstable open-loop response. The time-varyjng nature of the pla.nt due to change jn operating po,vcr is taken into account by including slowly timevarying uncertainty in the model. A Linear Time-Invariant) (L1.'I) guaranteed cost quadratic stabilizing controller is designed in order to address some of the particular issues arising for such a control problem.
In this paper, the problem of quadratic stabilizability of uncertain singularly perturbed systems... more In this paper, the problem of quadratic stabilizability of uncertain singularly perturbed systems by dynamic output feedback is addressed. Using a time-scale decomposition. two smaller-order ε-independent quadratic stabilizability subproblems are solved and it is shown that when ε is sufficiently small the combination of the corresponding results yields a quadratic stabilizing controller for the full order uncertain system, the controller being singularly perturbed itself with the same parameter ε as that of the system.
Mimicking the medical practice, this paper deals with the control of hypnosis during a surgical i... more Mimicking the medical practice, this paper deals with the control of hypnosis during a surgical intervention thanks to a switched control strategy. The key idea consists in starting with an initial minimum time control for the induction phase followed by a dynamic output feedback for the maintenance phase. The objective during the first phase is to bring the patient from its awake state to a final state corresponding to some given depth of hypnosis, measured by the BIS, within a minimum time. Then, once the patient state is close to the desired target, the control is switched to a dynamic output feedback ensuring that the BIS stays in a given interval taking into account the saturation of the actuator and the multi-time scale dynamics in the anesthesia model. Positivity of the system is also preserved thanks to the use of input saturation and state constraints. The stability of the switched control strategy is addressed and the theoretical conditions are evaluated on different case studies.
This paper proposes an integral sliding mode control (ISMC) for a class of linear systems with ti... more This paper proposes an integral sliding mode control (ISMC) for a class of linear systems with time-varying state and input delays. An integral sliding surface is firstly constructed. Then, by using the Lyapunov-Krasovskii functional and some specified matrices, a sufficient condition is obtained in the form of linear matrix inequalities (LMIs) to ensure the sliding mode dynamics to be asymptotically stable. Furthermore, a sliding mode controller law is synthesized to guarantee that the system trajectories can be driven onto the specified sliding surface in a finite time and maintained there for all subsequent time. Finally, an inverted pendulum model is used to illustrate the advantages and effectiveness of the design method.
... matrices. is the uncertainty matrix which belongs to the following set: This kind of uncertai... more ... matrices. is the uncertainty matrix which belongs to the following set: This kind of uncertainty was extensively studied in the literature where it is referred as norm bounded uncertainty (Khargonekar, Petersen, & Zhou, 1990). ...
ABSTRACT In this paper, the problem of robust pole assignment in a disk with an H2H2 guaranteed c... more ABSTRACT In this paper, the problem of robust pole assignment in a disk with an H2H2 guaranteed cost design is addressed. The uncertain systems considered are of norm bounded type and continuous as well as discrete time. The set of gains which assigns the closed-loop poles in a disk is characterised through a Linear Matrix Inequality (LMI). A way for selecting a gain in this set, which minimises an upper H2H2 norm bound on the transfer matrix between a perturbation and a controlled output, is presented. It consists in solving a convex optimisation problem with a linear criterion and an LMILMI as a constraint.
This note proposes a systematic approach for the static output feedback control design for discre... more This note proposes a systematic approach for the static output feedback control design for discrete time linear systems. It is shown that if the open loop system satisfies some particular structural conditions, a static output feedback gain can be calculated easily, using a formula only involving the original system matrices. Among the conditions the system has to satisfy, the stronger
This paper addresses the problem of determination of stability regions, in fact regions of admiss... more This paper addresses the problem of determination of stability regions, in fact regions of admissible initial state, as large as possible, for linear systems with delayed outputs and subject to input saturation and bounded controlled outputs, through anti-windup strategies. The closed-loop system resulting from the open-loop system with delayed output, the dynamic output controller plus the anti-windup loop is modelled as a linear time-delay system with a dead-zone nonlinearity. Constructive delay-dependent stability condition is then fonnulated by using a quadratic Lyapunov-Krasovskii functional. The optimization problem for computing the anti-windup gain that maximizes the size of the associated region of stability is directly expressed as the optimization of a convex criterion under LMI constraints.
In this paper, we propose a robust hybrid control for a boost inverter. This control presents the... more In this paper, we propose a robust hybrid control for a boost inverter. This control presents the particularity of considering the real nature of the dynamics, which means, the continuous-time dynamics, voltages and currents, and the discrete-time dynamics, the switching of the transistors. Likewise, due to implementation issues a minimum dwell time is introduced in the control loop scheme. Uniform global asymptotic stability is guaranteed, ensuring that the tracking error of the system output enters into a small neighbourhood of zero. Moreover, robustness guarantee with respect to parameter variations, in terms of an error tracking output regulation, are also provided here. The effectiveness of the proposed hybrid control scheme is illustrated in simulation.
International Journal of Modelling, Identification and Control, 2018
Over the past few decades, the world demand for energy has risen steadily, forcing the world comm... more Over the past few decades, the world demand for energy has risen steadily, forcing the world communities to look for alternative sources. Photovoltaic (PV) is seen as the most appropriate solution for this demand. In this context, this paper presents a robust terminal sliding mode control (RTSMC) method for maximum power tracking of stand-alone PV systems. The design method provides good robustness properties in the face of the system uncertainties and change of environment conditions. Starting from the mathematical dependence between the open-circuit voltage (V oc) and the optimal operating voltage (V op), an MPPT design method is given. To eliminate the tracking voltage error, a RTSMC method is introduced thereafter. A pulse width modulator (PWM) is used to maintain the switching frequency constant. Compared to the P&O algorithm, the proposed methodology reduces the oscillations around the maximum power point (MPP) and provides better performance proprieties. Also, the simulations results prove the robustness qualities of the TSMC-MPPT design method.
This chapter presents the different aspects of the design methodology that has been used to cope ... more This chapter presents the different aspects of the design methodology that has been used to cope with the RCAM design problem. A quadratic approach involving robust pole placement in a disk and the solution of parameter-dependent Riccati equations is proposed. Robustness as well as performance is accounted for by robust disk pole location that ensures robust stability and provides a good transient behaviour together with a specific selection of the weighting matrices involved in the Riccati equations.
HAL (Le Centre pour la Communication Scientifique Directe), Oct 17, 2017
Using a hybrid systems approach, we address the practical stabilization of operating points for s... more Using a hybrid systems approach, we address the practical stabilization of operating points for switched affine systems, ensuring a minimum dwell time and an admissible chattering around the operating point. Two different solutions are shown to induce uniform dwell time, based on time-or space-regularization. The proposed solutions provide useful tuning knobs to separately adjust the switching frequency during transients and at the steady state. The strengths of the method are illustrated by simulating a boost converter.
Application de la commande robuste sequencee au controle de la transition operationnelle d’un sys... more Application de la commande robuste sequencee au controle de la transition operationnelle d’un systeme non lineaire Yann LABIT1, Pedro TEPPA1;2, Jacques BERNUSSOU1, Germain GARCIA1 1 Laboratoire d’Analyse et d’Architecture des Systemes du CNRS 7 Avenue du Colonel Roche, 31077 Toulouse, France 2 Universite Simon Bolivar, Valle de Sartenejas, Baruta, Caracas-Venezuelafylabit, pteppa, [email protected] Resume— Nous proposons, dans cet article, une approche systematique pour assurer la transition en stabilite d’un systeme dynamique non lineaire entre deux points operationnels. Ceci est realise dans un cadre d’un sequen- cement de lois de commande robuste issues de la satisfaction de contraintes en stabilite et en prenant compte de certaines specifications de perfor- mances locales qui restent valables dans un voisinage d’attraction d’un en- semble de points d’equilibre. L’approche proposee est implantee par l’in- termediaire de deux techniques : la premiere repose sur les fonctions cano- niques lineaires par morceaux tandis que la deuxieme se centralise sur des outils geometriques tels que les ellipsoi�
T'he steanl generator water level, (SG'VL), controJ problem in the pressurized \i\rater reactor o... more T'he steanl generator water level, (SG'VL), controJ problem in the pressurized \i\rater reactor of a nuclear power plant is considered from robust control techniques point of vie\sv. The plant is a time-varying system with a non minimum phase behavior and an unstable open-loop response. The time-varyjng nature of the pla.nt due to change jn operating po,vcr is taken into account by including slowly timevarying uncertainty in the model. A Linear Time-Invariant) (L1.'I) guaranteed cost quadratic stabilizing controller is designed in order to address some of the particular issues arising for such a control problem.
In this paper, the problem of quadratic stabilizability of uncertain singularly perturbed systems... more In this paper, the problem of quadratic stabilizability of uncertain singularly perturbed systems by dynamic output feedback is addressed. Using a time-scale decomposition. two smaller-order ε-independent quadratic stabilizability subproblems are solved and it is shown that when ε is sufficiently small the combination of the corresponding results yields a quadratic stabilizing controller for the full order uncertain system, the controller being singularly perturbed itself with the same parameter ε as that of the system.
Mimicking the medical practice, this paper deals with the control of hypnosis during a surgical i... more Mimicking the medical practice, this paper deals with the control of hypnosis during a surgical intervention thanks to a switched control strategy. The key idea consists in starting with an initial minimum time control for the induction phase followed by a dynamic output feedback for the maintenance phase. The objective during the first phase is to bring the patient from its awake state to a final state corresponding to some given depth of hypnosis, measured by the BIS, within a minimum time. Then, once the patient state is close to the desired target, the control is switched to a dynamic output feedback ensuring that the BIS stays in a given interval taking into account the saturation of the actuator and the multi-time scale dynamics in the anesthesia model. Positivity of the system is also preserved thanks to the use of input saturation and state constraints. The stability of the switched control strategy is addressed and the theoretical conditions are evaluated on different case studies.
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