Explicit Model Predictive Control For Multirate Control System

A kind of control system with different input updating rate and output sampling rate is common in practical digital sampling control systems. For example, in many chemical processes, input updating is faster than output sampling. Usually, for this kind of control system which is called multirate control system, in the process of controller design, both the inputs online updating speed and closed-loop system stability should be satisfied. Thus, looking for more efficient controller design method becomes very important for such multirate control systems.EMPC not only has the advantages of traditional MPC, such as handling constraints, multivariable and multi-target optimization, but also can reduce the on-line computation due to the optimization problem is solved off-line by multiparametric programming method. So, for EMPC, huge computation and time-consuming of traditional MPC (Model Predictive Control) when the optimization problem is solved online repeatedly can be overcome effectively. And a new research idea for analysis and synthesis of multirate control system is provided.In this paper, we consider the explicit model predictive control problem for multirate control system (the output sampling period is several times larger than the input updating period) with constraints, uncertainty and nonlinear. The main contents conclude:(1) Aiming at the problem of EMPC for multirate control system with input and state constraints. The Explicit controller can be obtained by solving the optimization problem off-line with multiparametric linear programming. For the linear objective function, a more efficient new algorithm for searching the region in which the state lies is given out. Moreover, based on the PWA structure of explicit controller, the closed-loop stability analysis method based on LMI is given out. The constraints of the multirate control system and the fast online updating of input can be guaranteed at the same time.(2) Robust explicit model predictive control algorithm for multirate control system with norm-bounded disturbances is considered. It is based on the dynamic programming, mp-QP and robust invariant set theory. The closed-loop robust stability of the uncertain multirate control system can be guaranteed while the on-line computation time is reduced.(3) EMPC for multirate piecewise linear (PWL) control system is researched. The definition of multiple quadratic function on polytope and single value function on ordered regions are utilized, then, the optimization problem can be decomposed into multi-stage optimization problems and solved by dynamic programming and mp-QP technique to obtain the explicit controller. Both the closed-loop stability and the need of inputs on-line updating of the multirate PWL system can be ensured.