Showing papers by "Edward J. Davison published in 1976"

The robust control of a servomechanism problem for linear time-invariant multivariable systems

Abstract: Necessary and sufficient conditions are found for there to exist a robust controller for a linear, time-invariant, multivariable system (plant) so that asymptotic tracking/regulation occurs independent of input disturbances and arbitrary perturbations in the plant parameters of the system. In this problem, the class of plant parameter perturbations allowed is quite large; in particular, any perturbations in the plant data are allowed as long as the resultant closed-loop system remains stable. A complete characterization of all such robust controllers is made. It is shown that any robust controller must consist of two devices 1) a servocompensator and 2) a stabilizing compensator. The servocompensator is a feedback compensator with error input consisting of a number of unstable subsystems (equal to the number of outputs to be regulated) with identical dynamics which depend on the disturbances and reference inputs to the system. The sorvocompensator is a compensator in its own right, quite distinct from an observer and corresponds to a generalization of the integral controller of classical control theory. The sole purpose of the stabilizing compensator is to stabilize the resultant system obtained by applying the servocompensator to the plant. It is shown that there exists a robust controller for "almost all" systems provided that the number of independent plant inputs is not less than the number of independent plant outputs to be regulated, and that the outputs to be regulated are contained in the measurable outputs of the system; if either of these two conditions is not satisfied, there exists no robust controller for the system.

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

Abstract: A new notion of computer identification, as opposed to the conventional plant identification problem, is introduced in this paper. It is assumed that it is desired to aynthesize 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: (i) the plant is linear and plant-invariant, (ii) the uncontrolled plant is stable. Note that it is assumed that the order of the plant modal is unknown. Necessary and sufficient conditions which allow the robust feed-forward-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 optimal decentralized control of a large power system: Load and frequency control

Abstract: The load and frequency control of a multi-area interconnected power system is studied. In this problem, the system is assumed to be subject to unknown constant disturbances, and it is desired to obtain, if possible, robust decentralized controllers so that the frequency and tieline/net-area power flow of the power system are regulated. The problem is solved by using some structural results recently obtained in decentralized control, in conjunction with a parameter optimization method which minimizes the dominant eigenvalue of the closed-loop system. A class of minimum order robust decentralized controllers which solves this general multi-area load and frequency control problem is obtained. Application of these results is then made to solve the load and frequency control problem for a power system consisting of nine synchronous machines (described by a 119th-order system). It is shown that the load and frequency controller obtained in this case is not likely to be significantly improved by using more complex controllers; in particular, it is shown that the conventional controller, used in regulating the net-area power flow of a system, is not likely to be significantly improved upon by using more complex controllers.

The steady-state invertibility and feedforward control of linear time-invariant systems

Abstract: The notion of steady-state invertibility of a system is introduced, which is concerned about the problem of being able to find an input so that the output of a stable system is asymptotically equal to a specified output of a certain class of functions. Necessary and sufficient conditions are found for a linear time-invariant system to be steady-state invertible. Application of these results is then made to find necessary and sufficient conditions for a feedforward controller to exist for a general linear time-invariant system, so that asymptotic tracking, in the presence of a general class of measurable disturbances occurs. Explicit feedforward controllers which will accomplish this are obtained. Properties of the steady-state invertibility condition are then obtained; in particular, it is shown that a system is "almost always" steady-state invertible if the number of plant inputs is not less than the number of outputs; if the number of plant inputs is less than the number of outputs, then a system is "almost never" steady-state invertible. It is then shown that a system which is minimum phase and which has at least the same number of inputs as outputs is always steady-state invertible.

Correction to "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.

Decentralized Stabilization and Regulation 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 coventional (and more simple) decentralized control system which is normally applied.

Canonical Forms of Linear Multivariable Systems

Abstract: This paper considers the problem of finding a complete set of invariants and canonical forms for a linear, time-invariant, multivariable system $(A,B,C)$ under a group of transformations. The group consists of input coordinate transformations, state coordinate transformations and state feedback transformations. A set of canonical forms is derived. A set of invariants called the transmission zeros is given, which has application to the servomechanism problem.

Output detectability, steady-state invertibility and the general servomechanism problem

Abstract: The notion of output detectability of a system is introduced which is concerned about the problem of being able to detect the effect of disturbances on the output of a system using different measurable outputs. Necessary and sufficient conditions are found for a linear time-invariant system to be output-detectable. Properties of the output-detectability condition are then obtained; in particular, it is shown that a system is "almost always" output-detectable, if the number of measurable outputs is not less than the number of disturbances; if the number of measurable outputs is less than the number of disturbances, then a system is "almost never" output detectable. Application of these results is then made to find necessary and sufficient conditions for a solution to exist to a general servomechanism problem, in which the measured outputs of the system are, in general, different from the outputs to be regulated. Explicit controllers which solve this general servomechanism problem are obtained. It is then shown that there is "almost always" a solution to this general servomechanism problem if and only if the number of control inputs is not less than the number of outputs to be regulated and the number of measured outputs is not less than the number of disturbances. A frequency-domain interpretation of output-detectability and the solvability of the general servomechanism problem is then made and it is shown, in particular, that for stable, minimum phase systems which have sufficient inputs and measurable outputs, there always exists a solution to the servomechanism problem.