Takagi-Sugeno Fuzzy Modeling and Control for Effective Robotic Manipulator Motion

Abstract: Robotic manipulators are widely used in applications that require fast and precise motion. Such devices, however, are prompt to nonlinear control issues due to the flexibility in joints and the friction in the motors within the dynamics of their rigid part. To address these issues, the Linear Matrix Inequalities (LMIs) and Parallel Distributed Compensation (PDC) approaches are implemented in the Takagy-Sugeno Fuzzy Model (T-SFM). We propose the following methodology; initially, the state space equations of the nonlinear manipulator model are derived. Next, a Takagy-Sugeno Fuzzy Model (T-SFM) technique is used for linearizing the state space equations of the nonlinear manipulator. The T-SFM controller is developed using the Parallel Distributed Compensation (PDC) method. The prime concept of the designed controller is to compensate for all the fuzzy rules. Furthermore, the Linear Matrix Inequalities (LMIs) are applied to generate adequate cases to ensure stability and control. Convex programming methods are applied to solve the developed LMIs problems. Simulations developed for the proposed model show that the proposed controller stabilized the system with zero tracking error in less than 1.5 s.