Showing papers by "Edward J. Davison published in 1975"

Multivariable tuning regulators: The feedforward and robust control of a general servomechanism problem

Abstract: A new notion of compensator identification, as opposed to the conventional plant identification problem, is introduced in this paper. It is assumed that it is desired to synthesize a robust feedforward-feedback controller for an unknown plant so that asymptotic tracking, in the presence of disturbances, occurs. The only assumptions made regarding the description of the plant model are that 1) the plant is linear and time-invariant and 2) the uncontrolled plant is stable. Note that it is assumed that the order of the plant model is unknown. It is assumed that the control inputs to the plant can be excited, that the outputs of the plant which are desired to be regulated can be measured, and that the class of disturbance inputs and reference inputs is known. In addition, it is also assumed in the feedforward controller case, that the disturbance inputs can be measured and be excited; this assumption is not required in the robust feedback controller case. Necessary and sufficient conditions which allow the robust feedforward-feedback compensator to be synthesized so that the controlled system is stable and so that asymptotic tracking, in the presence of both measurable and unmeasurable disturbances, occurs are obtained. An algorithm which allows the controllers to be synthesized is given. Some numerical examples are included to illustrate the results.

The robust decentralized control of a general servomechanism problem

Abstract: The decentralized robust control of a completely general servomechanism problem is considered in this paper. Necessary and sufficient conditions, together with a characterization of all decentralized robust controllers which enables asymptotic tracking to occur, independent of disturbances in the plant and perturbations in the plant parameters and gains of the system, is obtained. A new type of compensator called a decentralized servo-compensator which is quite distinct from an observer is introduced. It is shown that this compensator, which corresponds to an integral controller in classical control theory, must be used in any decentralized servomechanism problem to assure that the controlled system is stablizable and achieves robust control; in particular, it is shown that a decentralized robust controller of a general servomechanism problem consists of two devices (i) a decentralized servo-compensator and (ii) a decentralized stabilizing compensator. It is then shown that, under certain mild conditions, there almost always is a solution to the robust decentralized servomechanism problem for any composite system consisting of a number of subsystems interconnected in any arbitrary manner. This last observation has important implications for process control.

On pole assignment in linear multivariable systems using output feedback

Abstract: The general problem of pole assignment in a linear, time-invariant multivariable system via output feedback is considered. It is shown that given a controllable-observable system ( C,A,B ) in which A \in R^{n \times n} , rank B = m , rank C = r , then for almost all ( B,C ) pairs, \min (n,m + r-1) poles can be assigned arbitrarily close to \min (n, m + r-1 ) specified symmetric values by using output feedback.

New results on the controllability and observability of general composite systems

Abstract: Using Rosenbrock's frequency domain approach [1], necessary and sufficient conditions are obtained for a general series-parallel or feedback composite system to be controllable or/and observable. The conditions are given in terms of the state equations of the composite system and are very simple to compute. Using these results, it is shown that a general series-parallel feedback cascade system is controllable or/and observable for "almost all" interconnection matrices, provided some mild conditions on the subsystems are imposed.

A generalization of the output control of linear multivariable systems with unmeasurable arbitrary disturbances

Abstract: The results of a previous paper [1] on the regulation and tracking of a servomechanism problem are extended to include control inputs on the outputs of the system and for the case that the state is not available for measurement.

Design of decoupled control systems A frequency domain approach

Abstract: In this paper a frequency domain approach is used for the design of decoupled control systems. Necessary and sufficient conditions for the existence of proportional output feedback laws as well as a constructive procedure for finding these feedback laws are given. A simple relationship between the overall system transfer functions and the output feedback laws is derived.

The numerical solution of X = A_{1}X + XA_{2} + D, X(0) = C

Abstract: The numerical solution of the general matrix differential equation \dot{X} = A_{1}X + XA_{2} + D, X(0) = C for X is considered where A 1 and A 2 are stable matrices. The algorithm proposed requires only 8n^{2} words of memory (for large n ) and converges in approximately 50n^{3} \mu s where μ is the multiplication time of the digital computer, and n = \max(n_{1},n_{2}) where A_{1} \in R^{n_{1} \times n_{1}} , A_{2} \in R^{n_{2} \times n_{2}} . The algorithm is particularly suitable for systems where n is large (e.g, n \gg 10 ).

On the computation of minimal indices for linear multivariable systems

Abstract: This paper presents an algorithm for the computation of the minimal indices for linear multivariable systems. The same algorithm can be used to determine the rank of a transfer function. As an application, this algorithm is shown to be useful in the design of non-interacting control systems.

Correction to "The output control of linear time-invariant multivariable systems with unmeasurable arbitrary disturbances"

Abstract: The controller characterization result obtained in the above-named article [ibid., VOI. AC-17. pp. 621-630, Oct. 1972] via equations (64) and (66) is not complete; on applying the same argument as used there, a more general expression is obtained for (66) and presented here.

Decentralized control in large multivariable systems

Abstract: A general description of the decentralized control problem, with particular emphasis on large scale systems, is made. In this problem, constraints on the structure of the information flow between the manipulated inputs of the system and measured outputs of the system are imposed. Typically, it is desired to find a controller for this system (subject to the above constraints), so that stability of the resultant closed loop system is obtained, and so that regulation/tracking of the outputs of the system occurs, independent of any input disturbances occurring in the system. A motivation for dealing with the decentralized problem is made, classical ways of solving the problem are described, and recent results obtained on the problem are surveyed. Some numerical examples are included, in particular, a power system consisting of three interconnected synchronous machines; it is shown in this power system that there is no real advantage is using a (more complex) centralized control system over the conventional (and more simple) decentralized control system which is normally applied.