Cascaded control of feedback interconnected nonlinear systems: Application to robots with AC drives

Abstract

In this paper we are interested in the design of global tracking controllers for feedback interconnected nonlinear systems with partial state measurements. We assume the forward subsystem is an underactuated Euler-Lagrange system and that, in the absence of the latter, a stabilizing controller is known for the feedback subsystem. This scenario, which appears in many practical applications with the forward subsystem representing the actuator dynamics, leads naturally to a classical cascaded (nested-loop) control scheme. Our main contribution is the establishment of conditions under which we can design an inner-loop controller for the Euler-Lagrange system such that global tracking is achieved. These are expressed in terms of actuator-sensor couplings, the “strength” of the subsystems interconnection, and the requirement of linear dependence on the unmeasurable variables. Interestingly enough, this analysis does not invoke the standard time-scale separation assumptions prevalent in cascaded schemes, but uses instead some “growth” conditions on the interconnections. The design is carried out using passivity arguments, and relies on energy shaping plus damping injection ideas. To insure asymptotic tracking of the inner loop the derivative of its reference, which is the output of the outer loop controller, is typically needed. To overcome this problem we add a nonlinear observer. The procedure is used to design an output feedback global tracking position controller for robot manipulators actuated by AC drives. To illustrate the generality of the method we consider a fairly large class of AC drives, which includes as particular cases induction, synchronous and stepper motors. Instrumental for the observer design is the utilisation of a new robot controller which is linear in the link velocities.