Showing papers by "Edward J. Davison published in 1990"

Decentralized stabilization and pole assignment for general proper systems

Abstract: Considered is the problem of finding existence conditions and a controller synthesis procedure, using decentralized control, for assigning the poles of a linear time-invariant proper system described by a state-space model (C, A, B, D), where no assumption is made regarding the structure of D. This problem has direct application to the decentralized stabilization problem, decentralized robust servomechanism problem, etc., and is a nontrivial extension to the standard decentralized problem where it is assumed that the direct feedthrough terms either are absent or have a block-diagonal structure. >

Decentralized Robust Control for Dynamic Routing of Large Scale Networks

Abstract: A variable structure decentralized controller for dynamic routing in multi-destination large-scale data communication networks is presented. A dynamic model, which can incorporate different processing delays at different nodes, is developed to describe the network dynamics. It is shown that the proposed controller guarantees stability and clears the queues of the system in the absence of external input flows. The controller also keeps the queue lengths bounded in the presence of external flow rates, which do not exceed a certain maximum flow rate (obtained by solving a LP optimization problem - there is no solution to the routing problem if these rates are exceeded). Furthermore, the controller is also robust with respect to variations in the processing delay constants. Some simulation results are presented to illustrate the controller's performance in a number of practical cases.

Adaptive Control of a Family of Plants

Abstract: Consider a linear time-invariant (LTI) plant which is not completely specified, but instead belongs to a finite set of known plants, say {P i : i ∈ p}. Our objective is to design a controller which provides “good” tracking and disturbance rejection, in a sufficiently well-defined sense, for this partially known plant. We first design a high-performance LTI controller K i for each possible P i if the pair (P i , K j ) is stable iff i = j and has no eigenvalues on the imaginary axis for any i, j ∈ p and if an upper bound on the magnitude of the unmeasurable disturbance signal is available, then it is shown that a switching mechanism can be used to find the correct LTI controller; furthermore, each LTI controller need only be tried once. This kind of problem often arises in an industrial setting, and is often approached using heuristic “gain-scheduling” techniques.

A decentralized discrete-time controller for dynamic routing

Abstract: A decentralized controller for dynamic routing in multi-destination large-scale data communication networks is presented. A dynamic model, which can incorporate different processing delays at different nodes, is developed to describe the network dynamics. It is assumed that the rate of messages being sent out from one node to another (the control signals) is updated at discrete time instants, which is the usual case in practice. It is shown that the proposed controller guarantees stability and clears the queues of the system in the absence of external input flows. The controller also keeps the queue lengths bounded in the presence of external flow rates which do not exceed a certain maximum flow rate (obtained by solving an LP optimization problem; there is no solution to the routing problem if these rates are exceeded). >

Pointwise gap metrics on transfer matrices

Abstract: A new family of metrics, called pointwise gap metrics, in the space of real rational matrices of fixed size is developed. These metrics are then used to study open-loop and closed-loop stability robustness of lumped linear time-invariant finite-dimensional continuous-time systems. It is shown that pointwise gap metrics have the desired qualitative properties for the study of stability robustness. Necessary and sufficient conditions on the open- and closed-loop stability robustness are obtained in terms of the radii of the pointwise gap metric balls centered at the nominal plant and/or the nominal controller. The new metric is compared with the available metrics, e.g. the gap metric and the graph metric. All these metrics induce the same topology. It is shown that many of the quantitative properties of pointwise gap metrics are the same as those of the gap metric, although they differ in value. In the scalar case they have a very simple expression which is potentially useful for accessing the relationship between the uncertainty of physical parameters and the uncertainty measured by pointwise gap metrics. >

Controller design for MSAT-a third generation spacecraft

Abstract: The control of a large flexible space structure (LFSS) as modeled by the mobile communications satellite (MSAT) configuration is considered. In this problem, the MSAT vehicle is highly unsymmetric and highly flexible, with noncollocated sensors/actuators. It is desired to find a controller, based on a design model of MSAT, which, when applied to an unspecified evaluation model of MSAT, solves the following problems: regulating the orientation of MSAT (three outputs), regulating the horn/reflector relative position (six outputs) in the presence of unknown disturbances, stabilizing rigid body and elastic body modes of the system, and avoiding undesirable spillover effects caused by the controller (robustness). A summary of results obtained in designing a controller to solve the problem, together with some representative output simulations, is given. >

Tensor Product Methods in Stability Robustness Analysis

Abstract: One of the methods recently utilized in the stability robustness analysis uses various matrix compositions. This paper gives an overview of this method using a tensor product theoretic perspective. The applications of this method to the stability robustness of matrices with unstructured uncertainties, one-parameter uncertainties or double-parameter uncertainties are then discussed.