Abstract
Based on recent results from analytical dynamics, this paper develops a class of tracking controllers for controlling general, nonlinear, structural and mechanical systems. Unlike most control methods that perform some kind of linearization and/or nonlinear cancellation, the methodology developed herein views the nonlinear control problem from a different perspective. This leads to a simple and new control methodology that is capable of ‘exactly’ maintaining the nonlinear system along a certain trajectory, which, in general, may be described by a set of differential equations in the observations/measurements. The approach requires very little computation compared with standard approaches. It is therefore useful for online real–time control of nonlinear systems. The methodology is illustrated with two examples.
Highlights
There are several methodologies that have been developed to date for the control of nonlinear systems that have tracking requirements
The methodology that we propose in this paper is inspired by a central result related to the analytical dynamics of constrained motion (Udwadia 2000; Udwadia & Kalaba 1992, 1993, 1995, 2000, 2002)
In this paper we have provided a powerful new methodology for controlling nonlinear structural and mechanical systems
Summary
There are several methodologies that have been developed to date for the control of nonlinear systems that have tracking requirements (see, for example, Sastry 1999; Slotine & Li 1991; Vidyasagar 1993). The methodology that we propose in this paper is inspired by a central result related to the analytical dynamics of constrained motion (Udwadia 2000; Udwadia & Kalaba 1992, 1993, 1995, 2000, 2002) This leads us to view the nonlinear control problem from a new and different perspective. (iv) the force of constraint is such that, in the presence of the impressed force F , the constrained system exactly satisfies the set (1.2); and (v) we assume that the constrained system satisfies the initial conditions given in (1.1). With this background, we are ready to ‘reframe’ the problem of constrained motion in analytical dynamics as a tracking-control problem.
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