Linear Regulator Design Research Articles

Design algorithms for a sensitivity constrained suboptimal regulator

The problem of finding the linear feedback control comprised of state and trajectory sensitivity terms which minimizes an infinite-time quadratic cost functional containing sensitivity variables is discussed. Since trajectory sensitivity cannot be accurately modelled in a closed-loop formulation the control feeds back approximate sensitivity terms. As the minimizing control is dependent on initial conditions, necessary conditions for a minimum are derived which satisfy various alternative sets of initial condition criteria. An efficient computer algorithm, based on a gradient search technique, is proposed for finding the feedback gains. By means of a numerical example it is shown that it is possible to reduce trajectory sensitivity while retaining certain desirable features of the linear optimal regulator design. Finally an algorithm is suggested for finding the linear feedback control comprised of state terms alone which minimizes the augmented cost functional.

Incomplete state feedback design of linear regulators

A time-domain approach for the design of an incomplete state feedback control law for linear regulators is presented by comparing the impulse response matrix of the suboptimal system with that of the optimal system. A computational procedure is given for the design of the suboptimal control law.

Design of Linear Regulators for Nonlinear Stochastic Systems

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Suboptimal Control Study of a Nuclear Power Plant

Concepts of modern control theory and, in particular, of optimal control have been used to develop a general and systematic method of regulator design starting from the non-linear mathematical model of the plant. This method was applied to the study of the control of a nuclear reactor plant of the SGHWR type (steam generating heavy water reactor), of 105 MW electric power, working at the Atomic Energy Authority Establishment, Winfrith, Dorset, England. The optimal linear regulator, computed for the free system, is incorporated into the system with saturation limits on its control inputs. This is one reason for suboptimality. Then only measurable state variables carrying large amounts of feedback control (compared with the rest of the variables) were used on the regulator, hence the second reason for suboptimality. In the course of this work a new method of optimal linear regulator design for external disturbances was applied. It is computationally very simple and also permits a simple calculation of transients by using the same eigenvector matrix regardless of the disturbance. * Soreq Nuclear Research Centre, Yavne, Israel. ** CDC 6600 with a store of 131K of 60 bit-long

Sensitivity Analysis in the Optimal Design of Synchronous Machine Regulators

The usual procedure for the optimal design of linear regulators for synchronous machines is to minimize a chosen quadratic cost function subject to the system dynamics constraints. However, the optimal control synthesized in such a straightforward fashion is unsatisfactory, since it is dependent on the particular choice of system control parameters made by the investigators. Furthermore, in practice, there may be a departure of these parameters from their nominal values. In an attempt to resolve these difficulties, the paper presents a method of synthesizing optimal control in such a way as to minimize a certain cost function, while choosing the system controllable parameters in the region of near-zero sensitivity. Considering a three-machine system as an illustrative example, this method is used as a basis for the selection of voltage regulator gains. It is shown that choosing the gains in the region of low sensitivity of the optimal cost function enhances the system transient response. The method is simple and is capable of handling multi-parameter sensitivity analysis in the framework of optimal control.

Design of low sensitivity optimal regulators for synchronous machines

The usual procedure for the optimal design of linear regulators for synchronous machines is to minimize a chosen quadratic performance index subject to the system dynamics constraint. However, the optimal control synthesized in such a straightforward fashion is unsatisfactory due to the departure of the system parameters from their nominal values or due to the divergence between the mathematical model and the physical system. In an attempt to resolve this difficulty, the paper presents a method of synthesizing optimal control in such a way as to minimize not only a certain cost function, but also the sensitivity of the cost function and trajectory sensitivity. It is shown that the optimal control so obtained will result in a system whose cost function and transient response are little sensitive to first-order variations in plant parameter values. A numerical example involving a synchronous machine swinging against an infinite bus is used to demonstrate the feasibility of incorporating sensitivity consider...

Design of regulators using time-multiplied quadratic performance indices

The design of linear regulators, optimal with respect to a time-multiplied quadratic performance index, is considered. Since it is not possible to minimize the normal form of the index with constant feedback gains, a suitably modified index is used and a design which is optimal in an average sense is obtained.

Extension of stable operating regions of synchronous machines using low-sensitivity excitation control

In the usual design of optimal linear regulators for synchronous machines, the controller is designed for a particular set of system operating conditions. However, in actual system operation, these conditions are subject to load demands. Consequently, the optimal controller designed for a certain operating condition will no longer yield a satisfactory performance at others. The paper endeavours to overcome this problem by proposing a method for designing optimal controllers with low sensitivity to systemloading conditions, while avoiding the complexity of the resulting controller structure. A numerical example involving a synchronous machine swinging against an infinite busbar is used to demonstrat the usefulness of low-sensitivity controllers in extending the stable operating region.

Linear Regulator Design for a Load and Frequency Control

The results of a dynamic optimization procedure in the design of load and frequency control (LFC) of power systems are presented. This design is based on the optimal linear regulator theory, accommodated to satisfy the performance objectives of the LFC in large multiarea interconnections. A proportional-plus-integral control law is considered. The paper also analyzes the influence of system and design parameters on power system performance considering two-and three-area interconnections. Finally, the problems of implementation are discussed.

Optimal Stabilization of a Multi-Machine System

The optimal linear regulator design technique of determining the weighting matrix Q with dominant eigenvalue shift, developed in a companion paper[6], is applied to the optimal stabilization of a multi- machine system. Two cases are studied, the first is with one optimal controller uE1 on one machine of the m-machine system and the other with m optimal controllers uEM for the m-machine system. For comparison arison a one optimal controller uE on one machine with the rest approximated as an infinite system and m optimal controllers of individual idual design are also investigated. Nonlinear tests are given. It is found that uEI control is better than uE control, uEM control is better still than UEI control, and individual uE controllers are not good for the overall system.

Optimal Power System Stabilization Through Excitation and/or Governor Control

For an optimal linear regulator design a performance function of the quadratic form must be chosen. The question arises of how to decide the weighting matrix Q of the performance function. A new method is developed in this paper to determine Q in conjunction with a left shift of the dominant eigenvalues as far as the practical controllers permit. The method is then applied to the optimal control design of a typical power system. Three cases are investigated, the first with an optimal excitation control uE, the second with optimal governor controls uG and uG, with and without the dash-pot, and the third with uE plus uG control. The stabilizing signals thus obtained are given nonlinear tests on the same power system. It is found from the results that the optimal controls are more effective than conventional excitation control, that the optimal governor control without dash-pot is just as good as the optimal excitation control, and that the optimal uE plus uG control is the best way to stabilize a power system.

Design of linear regulators optimal for time-multiplied performance indices

Design of linear regulators optimal for time-multiplied performance indices

A note on optimal linear regulators with incomplete state feedback

The design of optimal linear regulators with incomplete state feedback has been reported in a recent paper [1]. This correspondence deals with the practical utility of such controllers and the difficulties encountered in designing higher order systems.