An Algebraic Fuzzy Pole Placement Approach to Stabilize Nonlinear Mechanical Systems

Based on the general structure of mechanical systems described by their state-space representation, the Takagi-Sugeno fuzzy modeling, and the controllability property of fuzzy systems, an algebraic and practical approach to computing the fuzzy gain capable of ensuring the stability property of the Takagi-Sugeno fuzzy model is proposed in this article. The main idea consists of finding a continuous fuzzy gain such that any linear behavior, defined by the adequate selection of eigenvalues, is induced in the closed-loop fuzzy system. Therefore, by continuity, if the fuzzy model is an approximation sufficiently close to the mechanical system, then such a nonlinear system is also stabilized by the fuzzy controller. A notable advantage of the proposed method, when compared with similar approaches, is the simplicity of the resulting gain. The validity of the approach is illustrated through the numerical simulation of a sufficiently complex nonlinear system.

Automated summary

Based on the state-space representation, Takagi-Sugeno fuzzy modeling, and controllability of fuzzy systems, this article proposes an algebraic and practical approach to compute the fuzzy gain for ensuring the stability of the Takagi-Sugeno fuzzy model. The approach involves finding a continuous fuzzy gain that induces a desired linear behavior in the closed-loop system, thereby stabilizing the nonlinear system.