Robust Output Feedback Control for Input-Saturated Systems Based on a Sliding Mode Observer
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Robust Output Feedback Control for Input-Saturated Systems Based on a Sliding Mode Observer Qian Wang1,2 · Zheng-Guang Wu1,3 Received: 6 August 2020 / Revised: 19 October 2020 / Accepted: 22 October 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract This paper designs a robust output feedback controller for input-saturated systems with parametric uncertainties and external disturbances based on the parametric Riccati equation and the sliding mode observer. The stability of the closed-loop system is ensured by the designed controller. The main advantages of the approach proposed in this paper are as follows: (a) the designed sliding mode observer can estimate unknown external disturbances and parametric uncertainties; (b) the designed output feedback controller can increase the state convergence speed; and (c) the control gain can be obtained from the solution of the parametric Riccati equation. The simulation results for a spacecraft rendezvous system illustrate the feasibility of the designed controller. Keywords Sliding mode observer · Output feedback · Parametric Riccati equation · Low-gain feedback
1 Introduction Input saturation nonlinearity is inevitable in practice [11]. Control system design without considering input saturation will degrade the system performance or even lead to instability of the control system. Many results have emerged for the control of input saturation systems, such as low-gain feedback control [12,13,19,20], anti-windup control [9,18,21,22] and model predictive control [10,17,23]. The low-gain feedback is parameterized by a selected low-gain parameter, and the norm of the feedback
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Zheng-Guang Wu [email protected] Qian Wang [email protected]
1
Institute of Cyber-Systems and Control, Zhejiang University, Hangzhou 310027, China
2
Institute of Information and Control, Hangzhou Dianzi University, Hangzhou 310018, China
3
Institute for Advanced Study, Chengdu University, Chengdu 610106, China
Circuits, Systems, and Signal Processing
gain approaches zero when the low-gain parameter approaches zero. In other words, an appropriate low-gain parameter can be selected to avoid input saturation. There are three main low-gain feedback design methods: eigenstructure assignment-based design [14], algebraic Riccati equation-based design [15] and Lyapunov equationbased design [24]. The aim of state feedback is to multiply each state variable of the system by the corresponding feedback coefficient and then feed it back to the input terminal and add the reference input to form a control law as the control input of the controlled system. If not all the system states can be measured, an output feedback controller must be designed. Most results related to dynamic output feedback control are based on the Luenberger full dimensional state observer [16]. However, when the control system has unknown uncertainties and external disturbance, the state estimate accuracy of the Luenberger full dimensional state observer is affected and influences the control system performan
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