Adaptive approximate input–output linearizing control with applications to ball and beam mechanism

Abstract

This paper presents the design and implementation of adaptive control with approximate input–output linearization for underactuated open-loop unstable non-linear mechanical systems. Control of a ball and beam (BB) mechanism is selected as a benchmark problem for testing the designed control. The method of input–output linearization is reviewed and an adaptive input–output linearizing control design procedure is given. An approximate BB model is developed using Euler–Lagrange equations, and input–output linearization-based adaptive tracking control is designed for the system. The model is parameterized with respect to ball mass for adaptive tracking, and the proposed control structure is tested via computer simulations and experiments. The results present the tracking performance of designed control for various ball masses, and reveal the proposed method’s capability to cover ball mass variations over non-adaptive control. The proposed control exhibits improved error performance in the presence of parametric variations in the plant. Results of the BB control case reveal successful control of underactuated non-linear mechanisms when a system parameter is unknown or time varying.