Model Predictive Control for Nonlinear Systems in State Space using Fuzzy System Model

Model predictive (MPC) is a common method used in chemical process industries. Usually, the state space method is applicable for linear systems with a quadratic performance index to find the optimised control law based on a solution of the Riccatti equation. However, a nonlinear system can only be modeled by a fuzzy logic based function of the variables. The method of optimal control requires a performance index to be met, which is not necessarily a quadratic type of index but a nonlinear function of the process variables. It could be similarly modeled by another fuzzy inference system. The MPC method for such a fuzzy modeled state space system would be able to provide good predictive control for any nonlinear control system. The evaluation of the control steps by prediction for such a fuzzy model with fuzzy performance index is described in this paper. The optimal control steps are found by iterative search using the Box's Complex search method over a range of control values. Then, the prediction outputs are checked for constraint inequality satisfaction, such as pressure limit for example. Such a control step is applied at the current time step. The paper describes such a technique for a nonlinear process with a nonlinear performance index, also with constraints in the process variables.