Robust model predictive control : matrix inequality based approaches

魯棒模型預測控制 : 基於矩陣不等式的方法

Student thesis: Doctoral Thesis

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Author(s)

  • Weilin YANG

Detail(s)

Awarding Institution
Supervisors/Advisors
Award date2 Oct 2013

Abstract

Model predictive control (MPC) is widely used in many chemical processes. In the past two decades, a plethora of results on analysis and synthesis of MPC and robust MPC have been obtained. Many approaches have also been developed to facilitate analysis and synthesis of MPC and robust MPC, one of which is based on linear matrix inequalities (LMIs) technique. Many results on MPC using the LMI-based approach have been obtained. However, few papers investigate MPC for systems with persistent disturbances. Actually, systems are always subject to disturbances in practice. Hence, it is desirable to take into account disturbances in the analysis and synthesis of MPC. Two classes of control problems are discussed in this thesis. Firstly, predictive control methods are developed to steer the system states to the origin (equilibrium point), which guarantees input-to-state stability of the closed-loop control system. The concept of robust positively invariant set is introduced to guarantee the feasibility of the optimization problem to be solved online. The results are presented for linear parameter varying (LPV) systems, and then extended to a special class of nonlinear systems — Takagi-Sugeno (T-S) fuzzy systems. Secondly, the problem of steering the system state to a predetermined set is also investigated. Specifically, control strategies that can guarantee finite settling time are proposed. To this end, the concept of robust one-step set is introduced. The problem is discussed for both LVP systems and T-S fuzzy systems. For a special case, that is linear systems without parameter uncertainties, a varying horizon predictive control strategy is further proposed, which allows a long prediction length as well as more free variables in the optimization of system performance. To reduce the online computing work, off-line computations are considered for the varying horizon MPC strategy. This thesis also studies robust MPC of a practical energy system - a direct methanol fuel cell system. After representing the system as a T-S fuzzy model, a robust predictive controller is employed to regulate the system to a desired operating point. The simulations reveal the effectiveness of the controller in dealing with disturbances and uncertainties.

    Research areas

  • Matrix inequalities, Predictive control