The maximally achievable degree of robustness of stability, in the sense of coprime factor perturbations, is determined for linear servo systems.Abstract-The design of a controller such that the closed-loop system will track reference signals or reject disturbance signals from a specified class is known as the 'servomechanism problem' or the 'regulator problem'. For the regulator problem to be solvable with robust closed-loop stability, the plant obviously needs to be such that the regulation problem and the robust stabilization problem are solvable separately. In this paper we determine the extra conditions that are necessary and sufficient for the two problems to be solved simultaneously. It turns out that these conditions can be given a simple geometric interpretation in terms of a multivariable version of the Nyquist curve of the plant.
The design of a controller such that the closed-loop system will track reference signals or reject disturbance signals from a specified class is known as the "servomechanism problem" or the "regulator problem." We show here that the regulator problem can be looked at as an interpolation problem for a subspace-valued function that can be viewed as a multivariable version of the Nyquist curve. The result is applied to obtain a simple parametrization of all solutions.
Linear complementarity systems are used to model discontinuous dynamical systems such as networks with ideal diodes and mechanical systems with unilateral constraints. In these systems mode changes are modeled by a relation between nonnegative, complementarity variables. We consider approximating systems obtained by replacing this non-Lipschitzian relation with a Lipschitzian function and investigate the convergence of the solutions of the approximating system to those of the ideal system as the Lipschitzian characteristic approaches to the (non-Lipschitzian) complementarity relation. It is shown that this kind of convergence holds for linear passive complementarity systems for which solutions are known to exist and to be unique. Moreover, this result is extended to systems that can be made passive by pole shifting.
Among the most common purposes are the tracking of reference signals and the rejection of disturbance signals in the face of uncertainties. The related design problem is called the "robust regulation problem." Here we investigate the tradeoff between the robust regulation constraint and the requirement of robust stability with respect to perturbations in the normalized coprime factors of the plant. We use an approach in terms of subspace-valued functions associated to plant and controller. In this way, necessary and sufficient conditions for robust regulation with robust stability can be related to a simple geometric property.
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