A Triple Inverted Pendulum Control System Design

Abstract

Robust design of a triple inverted pendulum control system is discussed in this chapter.

The triple inverted pendulum is an interesting control system that resembles many features found in, for instance, walking robots and flexible space structures, and other industrial applications. This kind of pendulum system is difficult to control due to the inherent instability and nonlinear behavior.

In the pendulum control-system design we first model the uncertainties as a mixed type that consists of complex uncertainties in the actuators, and real uncertainties in the moments of inertia and in the viscous friction coefficients. A 2-degree-of-freedom (2DOF) design framework is adopted. Both $\mathcal{H}_{\infty}$ suboptimal and μ-controllers are designed. The $\mathcal{H}_{\infty}$ controller shows better transient and disturbance responses but does not ensure robust stability nor robust performance. The μ-controller achieves both robust stability and robust performance, however, at the price of poorer time responses. The μ-controller designed is initially of quite high order, which makes it unsuitable for implementation in practice. A model reduction is then conducted that leads to a reduced-order controller maintaining the required robust stability and robust performance of the closed-loop system.