Self-Tuning of Adaptive Backstepping Control for Reference Tracking

Abstract This paper presents a nonlinear control approach based on backstepping techniques for a high-speed linear axis driven by pneumatic artificial muscles (PAMs). Its guided carriage is actuated by a nonlinear drive system consisting of two pulley tackles with PAMs mounted at both sides. This allows for an increased workspace as well as higher carriage velocities as compared to a direct actuation. The proposed control scheme has a cascaded structure, where backstepping control concepts are used for a fast inner pressure control loop as well as an outer position control. Hysteresis of the PAMs is not modelled directly but counteracted by an additional adaptive parameter in the outer control loop. The main contribution of this paper is the investigation of a self-tuning algorithm that optimises the controlled system behaviour. Based on several criteria, the gradient of an evaluation cost function (ECF) w.r.t. the control design parameters is approximated and used for an optimisation. Two different variants of the self-tuning adaptive backstepping control are compared with each other using realistic simulations of a given test rig. The obtained results show an excellent closed-loop performance after tuning – compared with the initial design.