Mixed H2/H-infinity Controller Design for Triple Inverted Pendulum System

Abstract

The steady increase in reliance on robotic systems in industrial applications arises the need to ensure their reliability despite the presence of external disturbances in the environment they work in and their parameters variations due to several factors like: change of temperature, wear and tear effect, and payload variation. Traditional controllers usually fail to maintain the system's stability and performance in the presence of uncertainty, while robust controllers aim to guarantee stability and desired performance across a range of possible uncertainties in the system through incorporating these uncertainties into their design process. This paper investigates the robustness of three controllers namely, H2 controller, H-infinity controller, and mixed H2/H-infinity controller, applied to the triple inverted pendulum system which translates to robustly control legged robots and robotic arms. The results show that among the three controllers, only the mixed H2/H-infinity control system is robustly stable and maintains its performance with stability margin 1.1864 and performance margin 1.1662. Index Terms— H2, H-infinity, Mixed H2/H-infinity, Robust Control, triple inverted pendulum.