Stabilising the triple inverted pendulum by variable gain linear quadratic regulator

Abstract

A variable gain linear quadratic regulator (VGLQR) for multivariable non-linear control systems is designed. This control scheme, which can be viewed as a novel gain scheduling controller, consists of linearising the non-linear system to a family of time-invariant systems about sampling points and using LQR method to obtain optimal feedback gain in every sampling interval. In addition, a fast algorithm based on Schur method for online solving the algebraic Riccati equation is discussed in detail, and a software package, which is used to solve algebraic Riccati equation at each sampling point, is developed during the present research. A triple inverted pendulum is stabilised by using the VGLQR method and the results of simulation and physical experiments are displayed. The results of experiments demonstrate that the present control scheme is of good stability and robustness.