Adaptive Neural Zeta-Backstepping With Predefined Damping Ratio. Application to DC Motors

This brief presents an adaptive neural zeta-backstepping control strategy for a class of uncertain nonlinear systems, which allows these systems to be practically stabilized with predefined damping ratios. By introducing the zeta-backstepping technique, system damping ratios can be predetermined based on specific parameter selection rules. To reduce the impact of unknown nonlinearities, neural networks (NNs) with gradient descent training are applied to compensate such nonlinearities online. A new filter, called dynamic command filter, is used to construct the gradient of the NNs. By resorting to second-order Lyapunov stability criteria, it is proved that the closed-loop system is practically stable and has predefined damping ratio. Finally, experiments on a perturbed direct current (DC) motor system demonstrate the advantages of the proposed method.

I. Introduction

Backstepping is a popular nonlinear design technique applied in many practical systems. For instance, automatic parking control of an autonomous vehicle was addressed in [1] by using switching control and backstepping. A saturated adaptive-law-based backstepping control method for attitude tracking control of a quadrotor hover system was presented in [2]. In [3], a backstepping control scheme was designed for control systems with multisource disturbances, actuator saturation, and nonlinearities in the discrete time domain, and its effectiveness was verified with a spacecraft attitude control system. The formation control problem of underwater vehicles was investigated in [4], where a novel robust backstepping-based coordination protocol was developed. A surface electromyography-driven variable stiffness control framework was proposed in [5] for an upper limb bilateral rehabilitation system, whose low-level controller was designed by a cascaded backstepping position control scheme. In [6], a backstepping-based boundary state-feedback controller was presented that allows gantry crane systems to transport a payload to a target position with less shaking.