State Feedback via Judicious Pole Placement and Linear Quadratic Regulator – Application to Rotary Inverted Pendulum

Abstract

In control system regulatory concept, placing a closed loop poles too far from the origin in the stability region produces fast regulation time but require huge forcing energy as tradeoff. As such, stabilizing unstable system with minimum energy is needed though give challenge to designer. At the design phase, designer may ponder the optimized energy while compromising the possible catastrophic stabilization phenomena due to minimal forcing thrust towards the poles. In this manuscript, a simple Linear Quadratic Regulator (LQR) is proposed as an alternative to full state feedback (FSF) with judicious pole placement. The efficacy of both approaches was observed by exploiting a Rotary Inverted Pendulum (RIP) as testbed. Beforehand, the RIP system dynamics are developed in time domain. RIP is an under-actuated mechanical system that inherently nonlinear and unstable. The main control objectives of RIP are; swing-up control, stabilization control, switching control and trajectory control. The methodology involved the appearance of weighted matrices that necessity to the minimum cost function. The Riccati and Lyapunov criterion are also exploited to facilitate design. The result shows the comparative transient performances of the two.