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Design and Stability Analysis of Supervisor-based Adaptive Fuzzy Logic Control System for Temperature

The application of fuzzy logic (FL) supervisors (FLS) for on-line nonlinear auto-tuning of the basic FL controllers (FLCs) gains popularity as a simple adaptive technique for improvement of the performance of control systems for plants with nonlinearities, inertia, time-delay, model uncertainty and variable parameters. Various approaches for the FLS design are developed for different types of FLCs and performance measures considered. However, structure simplification techniques and closed loop system stability analysis are needed to promote the FLC -FLS industrial applications which constitute the aim of the present work. A parallel distributed compensation (PDC) equivalent in operation to the FLC-FLS is suggested that consists of a Sugeno model for fuzzy blending of the outputs of several linear PID controllers depending on the operation point. The PID parameters are optimized using genetic algorithms, simulations, experimental data and random inputs. The simpler in structure PDC-PID control system is validated as equivalent in operation to the supervisory control system and also its stability is proven by deriving Lyapunov conditions and solving them using linear matrix inequalities (LMI) numerical technique. All investigations are performed on the example of the control of the air temperature in a laboratory dryer using MATLAB and its real time facilities.