Improved Function Augmented Sliding Mode Control of Uncertain Nonlinear Systems with Preassigned Settling Time
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ISSN:1598-6446 eISSN:2005-4092 http://www.springer.com/12555
Improved Function Augmented Sliding Mode Control of Uncertain Nonlinear Systems with Preassigned Settling Time Guangbin Cai, Xinyu Li, Mingzhe Hou*, Guangren Duan, and Fei Han Abstract: This paper investigates the robust tracking control of second-order uncertain nonlinear systems by adopting the function augmented sliding mode control approach. An improved version of this approach is proposed such that the exact information of the initial tracking error is not required when generating the desired trajectory of the tracking error. This evidently enlarges the application scope of the function augmented sliding mode control approach. Performance functions are introduced to form the performance envelopes for the sliding mode variables. A robust sliding mode controller is constructed such that the sliding mode variables are confined within their performance envelopes. This further guarantees that the tracking error converges to the given neighbourhood of zero within the preassigned settling time provided that proper control parameters are selected. An application example on the rendezvous control of spacecraft is also employed to illustrate the effectiveness of the proposed control approach. Keywords: Nonlinear systems, preassigned settling time, robust control, sliding mode control, uncertain systems.
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INTRODUCTION
Settling time, which characterizes the convergence rate of the system response, is recognized as an important performance specification of control system design. To achieve better performance and stronger robustness, fast convergence is usually pursued in practice. Therefore, finite time control has received considerable attention since it could guarantee that the state of a dynamic system converges to the desired point in finite time [1–5]. Although convergence can be achieved in finite time, the estimation of the settling time in the existing finite time control results explicitly depends on the initial state. This, to some extent, limits their application scope since the initial state may be unknown a priori. To overcome this problem, a strategy named fixed-time control is proposed [6,7]. It has been shown that fixed-time control could guarantee that the settling time is irrelevant to the initial condition. As a result, the research on the fixed-time control has been a hot topic and fruitful results have been obtained [8–10]. An exciting approach which can realize control with the preassigned settling time is called the function augmented sliding mode control approach, which is proposed
by Park and Tsuj [11]. Different from the traditional sliding mode control approach where the sliding mode variable is constructed directly based on the tracking error, in the function augmented sliding mode control approach, a desired trajectory of the tracking error which converges to zero in the preassigned settling time is generated, and the sliding mode variable is constructed based on the error between the tracking error and its desired trajectory,
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