Robust Explicit Solution of Multirate Predictive Control System with External Disturbances
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Robust Explicit Solution of Multirate Predictive Control System with External Disturbances Yali Jiang · Yuanyuan Zou · Yugang Niu
Received: 28 October 2012 / Revised: 12 March 2013 © Springer Science+Business Media New York 2013
Abstract This paper considers the problem of robust predictive control for a class of uncertain multirate systems, in which the output sampling period is several times larger than the one of input updating. By means of dynamic programming and multiparametric quadratic programming (mp-QP) techniques, this work proposes a novel robust explicit model predictive control (REMPC) algorithm such that the higher on-line updating speed of input can be attained. Firstly, the optimization problem is decomposed into several subproblems. For each subproblem, a constraint condition only involving current state and input is constructed. Then taking current state and future inputs as parameter variables we can obtain a robust explicit solution for the new reformulated optimization subproblem by mp-QP method. Especially, by choosing a maximal robust positive invariant set as the terminal constraint set of the optimization problem, closed-loop robust stability of the multirate control system subject to external disturbance can be guaranteed. Finally, a numerical simulation is given to show the effectiveness of the proposed method. Keywords Disturbances · Explicit predictive control · Dynamic programming · Multiparametric quadratic programming Y. Jiang · Y. Zou () · Y. Niu Key Laboratory of Advanced Control and Optimization for Chemical Process, Ministry of Education, East China University of Science and Technology, Shanghai, 200237, China e-mail: [email protected] Y. Jiang e-mail: [email protected] Y. Niu e-mail: [email protected] Y. Zou Key Laboratory of System Control and Information Processing, Ministry of Education, Shanghai, 200240, China
Circuits Syst Signal Process
1 Introduction Computer sampling control system, also known as digital control system (DCS), is widely used in practical engineering. However, in complicated industrial processes, output sampling and input updating often do not adopt the same frequency. Hence, analysis and synthesis on multirate control system have been attracting more attention in past decades, see [1, 2, 7, 14] and the references therein, and many control algorithms have been proposed in, e.g., [5, 6, 17, 19, 21]. Especially, model predictive control (MPC) has been widely applied in the design of multirate system in [9, 13, 20, 22], due to its notable advantages for constraints, multivariable and multi-target optimization, e.g., [8, 10, 12, 18, 23]. The basic idea of MPC is to obtain control action by solving a finite-horizon optimal control problem at each sampling instant. Each optimization yields a sequence of optimal control actions, in which only the first action is applied to the plant. At the next time step, the most recently available state information will be taken as the new initial condition of optimal control problem, and the computation will be repe
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