An Exact Impedance Control of DC Motors Using Casimir Functions

Abstract

This chapter gives a new and exact impedance control of DC motor. From Hogan’s original work, the control input for impedance control is torque input since the impedance control is designed for Lagrangian systems. However, in actual situation, there exist dynamics between the torque and control input and this dynamics can be dominant in certain scale. In such situation, if we neglect the dynamics or try to cancel the dynamcis, the standard impedance control can lose the stability or the control performance at least. To overcome this problem, we need an new impedance control which takes the dynamics into account wihtout canceling any dynamics. In this chapter we give a solution for this problem by focusing on Casimir function which is rarely used in the conventional robotics. The rest of this chapter is organized as follwows. In Section 2, we give a new model of DC motor with dynamics between the torque and control input. In Section 3, we propose a new impedance control which is based on Casimir function. Casimir function is one of the properties of port-Hamiltonian systems. In Section 4, we confirm the proposed method in numerical simulation and we conclude this chapter in Section 5.