51. Membership Function Dependent Observer-Based Controller Design for A T-S Fuzzy System
- Author
-
Ling Huang, Wen-Bo Xie, Yu-Long Wang, and Jian Zhang
- Subjects
0209 industrial biotechnology ,Observer (quantum physics) ,02 engineering and technology ,Fuzzy control system ,Separation principle ,Inverted pendulum ,020901 industrial engineering & automation ,Mathematics (miscellaneous) ,Control and Systems Engineering ,Control theory ,0202 electrical engineering, electronic engineering, information engineering ,Piecewise ,020201 artificial intelligence & image processing ,State observer ,Electrical and Electronic Engineering ,Membership function ,Mathematics - Abstract
The problems of observer-based feedback control and stability analysis for a T-S fuzzy system are investigated in this paper. Based on system output variable, a membership function dependent observer and a controller subject to observer errors are constructed to estimate the unknown system state and establish the closed-loop feedback control system. The derived stability criteria, which is not numerically solvable, is converted to a solvable optimization problem. An improved membership function dependent approach is proposed to reduce the conservativeness. The approximated values of membership functions and their derivatives are calculated based on the proposed piecewise-function method. Then, a piecewise decaying rate setting technique is presented to adjust the error convergent speed. A three-rule fuzzy system stability analysis example is given to show the conservativeness reduction effects, while an inverted pendulum cart control process is used to show the effectiveness of the proposed observer-based control scheme.
- Published
- 2017