Fuzzy control of a quintuple inverted pendulum with the LQR method and 2-ary fuzzy piecewise interpolation function

This paper focuses on controlling a quintuple inverted pendulum (IP) using linear quadratic regulator (LQR) and fuzzy control method. First, the mathematical model of the quintuple IP is presented, and its controllability is verified. Based on the discussion of multiple factors related to the stability of the IP and the LQR theory, a non-diagonal weight matrix is constructed and a method to set the value of the matrix elements is suggested. Finally, an efficient fuzzy controller based on 2-ary piecewise interpolation function is designed, and the simulation of the quintuple IP is described in detail. The results of the simulation show the validation of the proposed method