18. LQR-Based TS-Fuzzy Logic Controller Design for Inverted Pendulum-Coupled Cart System

In this paper, an effective design technique for heuristic Takagi-Sugeno fuzzy logic controller (TS-FLC) for nonlinear inverted pendulum (IP) and cart system has been proposed. IP is linearized around distinct combinations of localized points and their respective linear quadratic regulator (LQR) gains are obtained. Set of these localized points are used to decide the range of input fuzzy membership function, and the LQR controller gains are used to obtain basic TS rule base for nonlinear model. Angle and angular velocity are used to design the controller for upright stabilization of pendulum. Cart position and cart velocity are the inputs for cart control. The main aim is to control pendulum in upright unstable equilibrium point and cart position at desired value simultaneously. Physical constraints of the system such as cart track length and controller output are considered in the designing of FLC. The results obtained by FLC are compared with LQR. The results show that FLC is better than LQR because it can be further tuned to satisfy the constraints. Simulation results show the effectiveness and robustness of proposed TS-FLC over LQR controller.