A Frequency Domain Approach for Design of Stable Fuzzy Logic Systems with Parallel Distributed Compensation

Most industrial processes are nonlinear, multivariable, with time delay, variable parameters and model uncertainty, subjected to disturbances. There exist methods that compensate the impact of these plant peculiarities but are developed for linear control systems. Most of them are based on the system frequency response since they give a compact and easy design solution. A novel frequency domain approach is suggested for the design of fuzzy logic nonlinear systems with parallel distributed compensation (PDC) from requirements for global nonlinear system stability, robustness and good performance. It uses modified transfer functions based Takagi-Sugeno-Kang (TSK) plant model and PDC and the merits of the linear control frequency design methods. The modified PDC-TSK system is represented by a number of equivalent linear systems for which equivalent frequency responses are defined and frequency domain design criteria applied to ensure stability, robustness and desired performance specifications. The approach is demonstrated for the design of a PDC for the real time control of the air temperature in a laboratory scale dryer and its effectiveness confirmed in the experiments. Key-Words: Frequency response, Fuzzy logic control system design, Nyquist plot, Parallel distributed compensation, Real time temperature control, Takagi-Sugeno-Kang plant model, Nonlinear system stability