Feedback Linearization for Robust Deadzone Compensation: Application to LQR-Controlled Cart-Pole System

Abstract

This paper proposes a feedback linearization approach for robust compensation of deadzones in nonlinear mechatronic systems, demonstrating its effectiveness through a case study of a cart-pole system controlled by the Linear Quadratic Regulator (LQR). While the LQR controller offers optimal performance for linear systems, the inherent nonlinearities, deadzone effects, and limit cycles present in non-ideal underactuated systems can significantly compromise its robustness. The proposed deadzone compensation technique aims to augment the LQR controller robustness and resilience to uncertainties while maintaining its inherent optimality and stability. The present solution enforces the linearity of the driving motion unit of the cart-pole system, therefore boosting its asymptotic stability. The deadzone compensator can experimentally eliminate limit cycles arising from different sources of deadzone, restoring the desired converging behaviour of the control system. Over 90% attenuation of the limit cycles could be consistently achieved in the closed loop stabilized response of the physical system.