Tracking Controller Design for Linear Systems in Presence of Multiple Saturation Constraints
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Tracking Controller Design for Linear Systems in Presence of Multiple Saturation Constraints E. Chater1
· F. Giri2
Received: 13 January 2016 / Revised: 28 June 2016 / Accepted: 21 August 2016 © Brazilian Society for Automatics–SBA 2016
Abstract We are considering the problem of controlling discrete-time linear systems that are subject to multiple saturation constraints. Specifically, we consider systems that are driven by an actuator whose output is subject to magnitude plus rate saturations. Moreover, the output of the considered plant is supposed to be intrinsically saturating. Then, aiming to guarantee the tracking of (compatible) reference signals, a suitable saturated linear controller is designed and the closed loop of the control system is analyzed using input– output stability approach. This allows defining the necessary conditions that ensure good tracking performances. Namely, it is shown that perfect output-reference tracking could be ensured in case of varying with l2 -vanishing rate inputs. In addition, in case of arbitrary reference inputs, it is shown that the less changing (in the mean) the inputs are, the better the average (output-reference) tracking quality is. This result entails good matching features as the system dynamics are assumed to be non-minimum phase and subject to multiple saturation constraints. A numerical example is provided to illustrate the application of the proposed control strategy. Keywords Saturation constraints · Tracking control · Non-minimum-phase systems · Global stability
B
E. Chater [email protected]
1
Ecole Normale Supérieure, Med V University, Rabat, Morocco
2
UNICAEN, GREYC Lab, UMR CNRS, Normandie University, Caen, France
1 Introduction In all control systems, the output signal of the control action cannot be applied to the plant with unlimited amplitudes and arbitrarily fast. Indeed, signal limitations arise from technological limitations introduced for system operation safety (e.g., limits of valve opening, stops in mechanical systems, voltage limits in power amplifiers…). Moreover, in some control problems, limitations are deliberately introduced, in the form of input saturations, in order to meet performance requirements (e.g., keeping a system around an operation point so that linear approximation can hold). Thus, amplitude and rate (actuator or input) saturation are unavoidable in industrial control systems. However, such limitations in magnitude and rate can lead to performance degradations and they may even cause instability of the closed loop. As a result, the problem of controlling saturated input systems has been an active research area over the last two decades (Tarbouriech et al. 2011). In fact, most results concerned linear systems subject to input (or actuator) saturation were achieved following two main approaches. The first approach consists in enforcing the control signal to stay above the allowed limits so that the closed-loop system stays in an invariance region of linear behavior. Such a positive invariant set is then a local region
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