Near-optimal control of high-order systems using low-order models †

Sinha, Ν.Κ.; Bruin, Hubert de

doi:10.1080/00207177308932373

Cited by 13 publications

(4 citation statements)

References 8 publications

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“…Particularly, Sinha and de Bruin (1973) made a comparison of the nearness of the optimal control obtained from the various low-order models with the actual optimum for a given high-order system. In turn, Genesio and Pomk (1973) considered the minimization of the maximum error between the optimal values of the performance indices for the reduced model and the system for the least-squares problem, and Leondes and Pezet (1975) discussed the integrated square error between outputs of the system and model with model based control in the least-squares problem.…”

Section: Hasiewicz and A Stankiewiczmentioning

confidence: 99%

Optimal reduction of linear systems for the least-squares control problem

Hasiewicz

Stankiewicz

1985

International Journal of Control

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Section: Hasiewicz and A Stankiewiczmentioning

confidence: 99%

Optimal reduction of linear systems for the least-squares control problem

Hasiewicz

Stankiewicz

1985

International Journal of Control

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“…Existing techniques for reducing the order of a multiinput, multi-output, state-space model can be divided into two categories: modal approaches and least squares approaches (Sinha and De Bruin, 1973;Wilson, 1974). Various modal approaches are briefly described below; least squares methods have been considered elsewhere (Wilson, 1974).…”

Section: Model Reductionmentioning

confidence: 99%

Model reduction and the design of reduced‐order control laws

1974

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This paper is concerned with the problem of designing satisfactory loworder (incomplete state feedback) controllers starting with a high-order, state-space model. Two design approaches are considered: the control law reduction technique, recently developed by the authors (Wilson et al., 19731, and the well-known model reduction approach. These two design techniques are used to develop a variety of low-order controllers for a double-effect evaporator starting with a 10th-order model. Experimental and simulated response data from the computer-controlled evaporator demonstrate the superiority of the control law reduction approach in this application. It is also shown that several of the previously published modal approaches to model reduction are basically equivalent since they yield identical reduced-order models. ROBERT SCOPEIn many practical applications of modern control theory the most difficult problem is to obtain a suitable process model. An analytical approach using basic chemical engineering principles often results in a dynamic model which consists of a large number of nonlinear differential equations. The model is usually too complicated for use in controller design or for implementation as part of the actual control system. Consequently, for purposes of control system design it is common practice to linearize the model and assume time-invariant behavior. Fortunately, the resulting linear "state-space model" (that is, a set of firstorder differential equations) will usually adequately describe the process transients in the region of normal operation and provide a suitable basis for control system design. However, many of the multivariable control design techniques (Gould, 1969) result in a control law that requires the availability of all elements of the state vector. Such control laws are frequently impractical because of their complexity and because in many applications it is not practical to measure or estimate all of the state variables. Hence there has been widespread interest in developing control laws that require only a subset of the state vector to be available. The resulting controllers are usually referred to as incomplete state feedback or low-order controllers.This investigation is concerned with the problem of designing a satisfactory low-order, multivariable controller starting with a high-order, state-space model of a process. To be judged satisfactory, the low-order controller should perform almost as well as more complicated high-order (state-feedback) controllers. Emphasis is placed on discrete process models and discrete controllers since they are more convenient than their continuous counterparts for on-line implementation via digital process computers. Two basic approaches were used to design loworder controllers:1. Model Reduction Approach. The original high-order model is simplified using a modal analysis to eliminate selected state variables, that is, to reduce the order of the model. The resulting low-order model then serves as a basis for designing a low-order controller usin...

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“…To illustrate the type of responses to be e~pected using the above scheme, consider the seventh-order system and the second-order Ie 2 model given in The responses "t>1ill be evaluated for the follovling cost functions: The plot of the above optimal and suboptimal responses is shown in It is interesting to note, that the true optimal cost for the seventh-order system has been computed in reference [45] in the case of J 1 , and is given as 6.175. The error in suboptimal cost, as a percentage of the correct value, is 1.17%.…”

Section: Problem Formulationmentioning

confidence: 99%

Adaptive Nuclear Reactor Control Based on Optimal Low-Order Linear Models

Bereznai

1973

IEEE Trans. Nucl. Sci.

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Near-optimal control of high-order systems using low-order models †

Cited by 13 publications

References 8 publications

Optimal reduction of linear systems for the least-squares control problem

Optimal reduction of linear systems for the least-squares control problem

Model reduction and the design of reduced‐order control laws

Adaptive Nuclear Reactor Control Based on Optimal Low-Order Linear Models

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