Fuzzy LMI servo controller for uncertain ball and beam system

This paper describes the design of a fuzzy logic controller for ball and beam system based on linear matrix inequality (LMI) techniques. The uncertain ball and beam system is represented by a simplified Takagi-Sugeno (TS) fuzzy model. Parallel distributed compensation (PDC) technique is then used to design control gains for fuzzy regions. The convex fuzzy summation of these gains is found to stabilize the system for various initial conditions. The stabilizing loop is restructured as servo loop afterwards to track the reference commands. MATLAB simulations are performed to validate the proposed controller for ball and beam system with parametric uncertainty where it is also compared with pole placement controller.