OPTIMAL PDC FUZZY CONTROL ALGORITHM WITH IMPROVED ROBUSTNESS

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The Parallel Distributed Compensation algorithm is advanced control scheme, which gains an increasing interest today. Different design methods were found in the last five years. The most effective methods are based on Linear Matrix Inequalities. The optimal PDC fuzzy controller for control of smooth nonlinear systems was also introduced. This paper deals with the new method, which originated from the optimal PDC fuzzy controller, and increases its robustness against disturbances in input signal and parameters. The PDC control algorithm is based on Takagi-Sugeno fuzzy modeling. The model of the nonlinear system to be controlled is a Takagi-Sugeno fuzzy model. The advantage of T-S modeling is that it combines fuzzy elements, which give a good overview of the model, with simple linear or affine local models that describe the system in a small region of its state space. The global description is obtained as a combination of these local models. Fuzzy rules for interpolation of state space regions guarantee smooth changing among different local models. Local controllers designed for each region provide control of the plant. These controllers ensure required behavior of the control system only in the small state space region and they are interpolated in the same way as local models. Design of local controllers is formulated as LMI problem. Optimal PDC controller design needs the optimality criterion that can be chosen to minimize transient response time or energy requirements for control. The controllers designed on different optimality criterion have different robustness against disturbances and plant parameters changes. The new method presented in this paper comes with the idea that two or more controllers with different robustness can be designed for the nonlinear plant. Besides the optimal controller that performs required transient response there is also robust one that is designed to guarantee stability if the system changes or the noise is on a high level. The T-S fuzzy control system examines signal disturbances and validity of the model. Then the fuzzy interpolation of optimal and robust controllers gives the regulator that is robust enough and also provides a good transient response.

PDC controller, Takagi-Sugeno modeling, robust control, linear matrix inequalities, optimal control

POLANSKÝ, M.

2003

1. 1. 2003

Štrbské pleso

80-227-1902-1

Proceedings from 14th International Conference on Process Control '03

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