Abstract—Double inverted pendulum system is highly nonlinear and unstable system, thus its stability is a matter of concern, particularly when the system components have parametric uncertainty. The aim is to balance the two pendulums vertically on a movable cart. This paper presents first the dynamic modeling of the system based on Euler –Lagrangian method and then uncertain model is obtained by considering the parametric uncertainty in moment of inertia of pendulums and friction coefficient of hinges and cart. In this paper, reference trajectory control, disturbance rejection and robust performance using H∞ and μ synthesis controllers are made. Both controller shows good transient response, disturbance rejection and robust stability, but μ synthesis controller provides the superior robust performance as compared to H∞ controller.

Index Terms—Double inverted pendulum system(DIPS), H∞ Controller, Interconnected system, Linear Fractional Transformation (LFT), μ- Synthesis Controller

Cite: Narinder Singh and Karansher Bhangal, "Robust Control of Double Inverted Pendulum System," Jounal of Automation and Control Engineering, Vol. 5, No. 1, pp. 14-20, June, 2017. doi: 10.18178/joace.5.1.14-20