Showing papers by "Petar V. Kokotovic published in 1987"

An integral manifold approach to the feedback control of flexible joint robots

Abstract: The control problem for robot manipulators with flexible joints is considered. The results are based on a recently developed singular perturbation formulation of the manipulator equations of motion where the singular perturbation parameter µ is the inverse of the joint stiffness. For this class of systems it is known that the reduced-order model corresponding to the mechanical system under the assumption of perfect rigidity is globally linearizable via nonlinear static-state feedback, but that the full-order flexible system is not, in general, linearizable in this manner. The concept of integral manifold is utilized to represent the dynamics of the slow subsystem. The slow subsystem reduces to the rigid model as the perturbation parameter µ tends to zero. It is shown that linearizability of the rigid model implies linearizability of the flexible system restricted to the integral manifold. Based on a power series expansion of the integral manifold around µ = 0, it is shown how to approximate the feedback linearizing control to any order in µ. The result is then an approximate feedback linearization which, assuming stability of the fast variables, linearizes the system for all practical purposes.

Singular perturbation techniques in control theory

Abstract: This paper discusses typical applications of singular perturbation techniques to control problems in the last fifteen years. The first three sections are devoted to the standard model and its convergence, stability and controllability properties. The next two sections deal with linear-quadratic optimal control and one with cheap (near-singular) control. Then the composite control and trajectory optimization are considered in two sections, and stochastic control in one section. The last section returns to the problem of modeling, this time in the context of large scale systems. The bibliography contains more than 250 titles.

Integral manifold as a tool for reduced-order modeling in nonlinear systems: A synchronous machine case study

Abstract: Nonlinear systems in which invariant or, more generally, integral manifolds exist, appear in many important applications: networks with weakly coupled areas, electromechanical systems, electric machines, adaptive control, etc. In a class of such systems two-time scale properties assure the existence of "slow manifolds." When a "speed-ratio parameter" ? is zero, some states in these systems remain constant and form a "frozen" manifold M0. The slow manifold M? is an ?-perturbation of M0. Using a synchronous machine example, this paper presents the slow manifold as a tool for decomposition and reduced order modeling of nonlinear systems.

Stability of slow adaptation for non-SPR systems with disturbances

Abstract: Sufficient conditions are given for the existence of a bounded uniformly asymptotically stable (u.a.s.) solution of the model reference adaptive control system. These conditions, which do not require any matching assumptions or knowledge of the order of the plant, provide an estimate of the region of attraction and a bound on the average squared tracking error for which the u.a.s. property of the solution is preserved.

Self-tuning of conflicting oscillatory modes: A case study

Abstract: An analysis of a single parameter self-tuning scheme for a high order system is presented and applied to a typical power system stabilizer, as a representative of systems in which stabilization of some modes decreases the damping of other modes. Integral manifolds and averaging are used to find conditions for convergence to a compromise setting of the conflicting modes.