Improved Nonlinear Model Predictive Control Based on Genetic Algorithm

Abstract

Model predictive control (MPC) has made a significant impact on control engineering. It has been applied in almost all of industrial fields such as petrochemical, biotechnical, electrical and mechanical processes. MPC is one of the most applicable control algorithms which refer to a class of control algorithms in which a dynamic process model is used to predict and optimize process performance. Linear model predictive control (LMPC) has been successfully used for years in numerous advanced industrial applications. It is mainly because they can handle multivariable control problems with inequality constraints both on process inputs and outputs. Because properties of many processes are nonlinear and linear models are often inadequate to describe highly nonlinear processes and moderately nonlinear processes which have large operating regimes, different nonlinear model predictive control (NMPC) approaches have been developed and attracted increasing attention over the past decade [1-5]. On the other hand, since the incorporation of nonlinear dynamic model into the MPC formulation, a non-convex nonlinear optimal control problem (NOCP) with the initial state must be solved at each sampling instant. At the result only the first element of the control policy is usually applied to the process. Then the NOCP is solved again with a new initial value coming from the process. Due the demand of an on-line solution of the NOCP, the computation time is a bottleneck of its application to large-scale complex processes and NMPC has been applied almost only to slow systems. For fast systems where the sampling time is considerably small, the existing NMPC algorithms cannot be used. Therefore, solving such a nonlinear optimization problem efficiently and fast has attracted strong research interest in recent years [6-11]. To solve NOCP, the control sequence will be parameterized, while the state sequence can be handled with two approaches: sequential or simultaneous approach. In the sequential approach, the state vector is handled implicitly with the control vector and initial value vector. Thus the degree of freedom of the NLP problem is only composed of the control parameters. The direct single shooting method is an example of the sequential method. In the simultaneous approach, state trajectories are treated as optimization variable. Equality constraints are added to the NLP and the degree of freedom of the NLP problem is composed of both the control and state parameters. The most well-known simultaneous method is based on collocation on finite elements and multiple shooting.