Fuzzy optimal control using generalized Takagi–Sugeno model for multivariable nonlinear systems

• Several algorithms of FLC-LQR are developed to obtain enhanced performance of nonlinear unstable multivariable systems.
• The multivariable nonlinear system is represented by a generalized (T–S) model.
• Good response and zero steady state error in front of disturbances and modeling errors.
• A comparison is carried out with other algorithms to show the superiority of the proposed ones.
• A two-link robot is chosen to evaluate the validity of the proposed algorithms.

In this work, the main objective is to obtain enhanced performance of nonlinear multivariable systems. Several algorithms of Fuzzy Logic Controller based Linear Quadratic Regulator (FLC-LQR) are presented. The multivariable nonlinear system is represented by a generalized Takagi–Sugeno (T–S) model developed by the authors in previous works. This model has been improved using the well known weighting parameters approach to optimize local and global approximation. In comparison with existent works, the proposed controller is based on the calculation of the control action in each point of the state space according to the dynamic properties of the nonlinear system at that point. This control methodology offers a robust, well damped dynamic response and zero steady state error when the system is subjected to disturbances and modeling errors. A two-link robot system is chosen to evaluate the robustness of the proposed controller algorithms.

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