Fuzzy model-based predictive control using Takagi–Sugeno models

Nonlinear model-based predictive control (MBPC) in multi-input multi-output (MIMO) process control is attractive for industry. However, two main problems need to be considered: (i) obtaining a good nonlinear model of the process, and (ii) applying the model for control purposes. In this paper, recent work focusing on the use of Takagi–Sugeno fuzzy models in combination with MBPC is described. First, the fuzzy model-identification of MIMO processes is given. The process model is derived from input–output data by means of product-space fuzzy clustering. The MIMO model is represented as a set of coupled multi-input, single-output (MISO) models. Next, the Takagi–Sugeno fuzzy model is used in combination with MBPC. The critical element in nonlinear MBPC is the optimization routine which is nonconvex and thus difficult to solve. Two methods to deal with this problem are developed: (i) a branch-and-bound method with iterative grid-size reduction, and (ii) control based on a local linear model. Both methods have been tested and evaluated with a simulated laboratory setup for a MIMO liquid level process with two inputs and four outputs.