The adaptive robust control (ARC) for DC motors subjected to parametric uncertainties, disturbances and input saturation is considered in this study. To achieve high performance while keeping the control authority within saturation limit, a saturated ARC scheme is proposed. In this scheme, a variable-gain saturation function is introduced for the virtual control law, so that the amplitude of the virtual control and its derivative decrease when the control input approaches to the prescribed bound. Consequently, the virtual control and its derivative will not be excessively large, which is crucial for stabilising the system with a bounded input. We prove that the proposed controller cannot only assure global stability, but also provide desirable control performance, that is, the tracking error can be steered to the neighbourhood of the origin in finite time. Moreover, asymptotic tracking can be achieved in the presence of parametric uncertainties only. Finally, simulation results illustrate the effectiveness of the proposed controller.
The problem of robust constrained model predictive control (MPC) of systems with polytopic uncertainty is considered in this paper. New sufficient conditions for the existence of parameter-dependent Lyapunov functions are proposed in terms of linear matrix inequalities (LMIs), which will reduce the conservativeness resulting from using a single Lyapunov function. At each sampling instant, the corresponding parameter-dependent Lyapunov function is an upper bound for a worst-case objective function, which can be minimized using the LMI convex optimization approach. Based on the solution of optimization at each sampling instant, the corresponding state feedback controller is designed, which can guarantee that the resulting closed-loop system is robustly asymptotically stable. In addition, the feedback controller will meet the specifications for systems with input or output constraints, for all admissible time-varying parameter uncertainties. Numerical examples are presented to demonstrate the effectiveness of the proposed techniques.
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