Robust controller design for rotary inverted pendulum using H∞ and 𝝁-synthesis techniques

Abstract

An 𝐻⁢∞ controller is designed to control a rotary inverted pendulum in its upright equilibrium position. The key contribution of this work is a robust controller architecture design to accommodate for uncertainty in actuator model. Robust stability and performance for a given degree of actuator and measurement uncertainty is achieved using the well established techniques of 𝜇‐synthesis and 𝐻⁢∞ robust control methods. The design focuses on stabilizing an Inverted Pendulum in an upright position within a tolerable desired angle margin (𝛼). A dynamic plant is designed based on already established theories and published papers. It is observed that the plant is completely observable for the pendulum angle and the motor arm link angle. These two signals are also measurable via encoders and is used as an input for the controller. The output of the controller is voltage actuation which drives the motor to stabilize the pendulum in an upright position (= 0 with +/− 10 deg tolerance). A Robust Stability analysis is done along with Robust Performance, to study the stability and performance margins under modelled uncertainties. As a comparative study, a rudimentary pole placement method is also analyzed.