On construction of the control that provides the desired trajectory of the movement of the single-link manipulator with elastic joint

Abstract

The law of rotation of the electric motor, which ensures a global asymptotic direction of the trajectory of the model of a single-link manipulator with an elastic joint to a given program trajectory is obtained The elasticity of the joint is modeled by a torsion spring, the elastic force of which is considered to be nonlinearly dependent on the displacement. This fact makes it impossible to apply the usual approach and greatly complicates the task of control construction. The fact that some parameters of the model can be uncertain and, in some way, depend on some numerical parameter, the area of change of which is unknown in advance, also adds complexity. However, the use of DSC (Dynamic Surface Control) technique allows us to get the desired control. The development of the DSC technique, which consists in a specific choice of parameters and constants of filters, is proposed. It avoids the growth of the order of the auxiliary system, as well as a significant complication of the form of both the auxiliary system of differential equations and the control law, the so-called “explosion of terms”. It allows us to obtain explicitly the corresponding auxiliary function and to prove that the proposed control law solves the control problem. The robustness of such control is also proved, and the region of robustness in the system parameters space is defined. The obtained results are illustrated by the example of a mechanical model.