Analysis of the Gains Tuning Problem in a Backstepping Controller Applied to an Electrohydraulic Drive

Abstract

This paper highlights the problem of tuning the gains of a non-adaptive backstepping controller in an electrohydraulic servo system. While the other non-adaptive controllers in the literature have precise gains tuning methods, the non-self-tuning backstepping controller has no rigorous gain tuning method. The proposed study aims to analyze the contribution of each backstepping controller gain in the closed-loop performance. Our final goal is to establish a rigorous gains-tuning method for the non-adaptive backstepping controller. The study starts with the development of three-stage gains backstepping controller using a non-conventional time derivative Lyapunov function. This particular Lyapunov function makes it possible to analyze the response of the system when all the controller gains are cancelled. Then, we analyze the effect of each gain by cancelling out the values of the others. The first simulation results show that the convergence of the tracking error to zero is not maintained when all gains are set to 0 despite the presence of a negative definite of the Lyapunov function time derivative. In this case, the equilibrium point is not the expected one as time goes to infinity. The second set of results indicates that adjusting the gain related to the feedback of the actual output only ensures the asymptotic convergence of the tracking error to zero as time goes to infinity. However, developing a heuristic tuning of the three controller gains like Ziegler Nichols tuning remains a challenge.