An LMI and fuzzy model approach to H ∞ PI controller design

Abstract

A Linear Matrix Inequality (LMI) approach for designing the H ∞ Proportional‐Integral (PI) controller for nonlinear dynamic systems is studied. The whole operating range of a nonlinear system is partitioned into several regimes. A local linear model containing time‐varying norm‐bounded uncertain parameters is identified with parameter uncertainties for each region. These local linear models are then integrated as a norm‐bounded Tagaki‐Sugeno (TS) nonlinear fuzzy model. The robust PI control design problem based on these norm‐bounded uncertain linear models is then transformed into a series of standard H ∞ control problems, where the latter is further formulated as LMIs. By adopting the LMI expressions, a symmetric positive definite matrix with guaranteed overall system stability can be easily determined and then be further used to infer the robust multiple PI controller parameters. One chemical process, a double‐effect evaporator, is illustrated to demonstrate the effectiveness of the proposed LMI‐based H ∞ PI controller design method for nonlinear dynamic processes.