Novel Observer-Based Input-Constrained Control of Nonlinear Second-Order Systems with Stability Analysis: Experiment on Lever Arm

Abstract

In this survey, the stability of input-constrained control for a widely used class of second-order systems is investigated. A continuous prediction-based approach is utilized to calculate the limited current control input by minimizing the next tracking error of nonlinear second-order system. The Karush–Kuhn–Tucker theorem is used to analytically solve the resulting constrained optimization problem. The constrained stability is analyzed by equating the constrained solution with the solution obtained from an optimal controller with time-varying weight on the control input. The proposed constrained controller adapts itself to real conditions by using information about the perturbations obtained from an extended state observer (ESO). Simulation studies for a lever arm indicates that the constrained controller presented in the closed form is much faster than the common nonlinear model predictive control method which requires an online dynamic optimization at each sampling time. Accordingly, experimental implementation of the proposed controller is conducted on a fabricated platform consisting of a lever arm. The results show that the proposed constrained controller can successfully track different time-varying positions for the arm by admissible torques generated by a DC motor. The comparative results with an adaptive backstepping controller indicate higher performance for the proposed ESO-based controller in compensating for the perturbations and external disturbance.