Abstract
This paper addresses the problem of tracking a reference trajectory asymptotically given by a linear time-varying exosystem for a class of uncertain nonlinear MIMO systems based on the robust optimal sliding-mode control. The nonlinear MIMO system is transformed into a linear one by the input-output linearization technique, and at the same time the input-output decoupling is realized. Thus, the tracking error equation is established in a linear form, and the original nonlinear tracking problem is transformed into an optimal linear quadratic regulator (LQR) tracking problem. A LQR tracking controller (LQRTC) is designed for the corresponding nominal system, and the integral sliding-mode strategy is used to robustify the LQRTC. As a result, the original system exhibits global robustness to the uncertainties, and the tracking dynamics is the same as that of LQRTC for the nominal system. So a robust optimal sliding-mode tracking controller (ROSMTC) is realized. The proposed controller is applied to a two-link robot system, and simulation results show its effectiveness and superiority.
Highlights
Trajectory tracking control for multiple-input multipleoutput (MIMO) nonlinear systems has attached much attention during the past decades [1, 2]
This paper addresses the problem of tracking a reference trajectory asymptotically given by a linear time-varying exosystem for a class of uncertain nonlinear MIMO systems based on the robust optimal sliding-mode control
The key to solve MIMO problem is to introduce the decoupling technology, and several control schemes for decoupling have been quite mature, such as the cascade decoupling based on classical control theory [3], the linear state feedback decoupling based on modern control theory [4], the linear output feedback decoupling [5], the stable-state feedback decoupling, and the dynamic precompensate [6, 7]
Summary
Trajectory tracking control for multiple-input multipleoutput (MIMO) nonlinear systems has attached much attention during the past decades [1, 2]. The key to solve MIMO problem is to introduce the decoupling technology, and several control schemes for decoupling have been quite mature, such as the cascade decoupling based on classical control theory [3], the linear state feedback decoupling based on modern control theory [4], the linear output feedback decoupling [5], the stable-state feedback decoupling, and the dynamic precompensate [6, 7]. As a branch of exact linearization, the input-output linearization is an effective way to decouple MIMO systems [12]. It could be achieved by exact inputoutput transformation and feedback, and any higher-order nonlinear terms are not neglected. What’s more, it could avoid complicated calculations in dealing with the tracking problem for nonlinear MIMO systems, and it is easy to achieve
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