The principle of matching: a necessary and sufficient condition for inputs restricted in magnitude and rate of change

Lane, Phil

doi:10.1080/00207179508921574

Cited by 18 publications

(10 citation statements)

References 13 publications

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“…A standard form of a convex optimization problem can be found in, for example, [7]. It is noted that in the proposed method for computing the peak output, other finite difference schemes for approximating derivatives and integrals can also be used as long as the resultant optimization problem in (35) is convex.…”

Section: ) ḟ ∞ D∞ Is Replaced Bymentioning

confidence: 99%

“…Example 1. In this example, the peak outputsv(P1) of output ports 1-5 are computed by the proposed method and are compared with the results obtained from Lane s method [7] , which was derived from an analytical optimization technique.…”

Section: Numerical Examplesmentioning

confidence: 99%

“…Both P1 and P2 are useful in certain practical applications in which all the possible inputs are transient (see, for example, [7,10,11]). However, since P2 has more restrictions than P1, it can be seen that P2 contains less fictitious inputs (that is, inputs that cannot happen or are not likely to happen in practice).…”

Section: Introductionmentioning

confidence: 99%

“…In Section 3, the details of the numerical procedure developed in this paper are provided in the form of a convex optimization problem. In Section 4, numerical examples are given by reconsidering the computation of the peak outputs of the wind turbine system given in [7,10]. Specifically, the peak outputsv(P1) are obtained using the proposed method and are compared with those obtained by using Lane s method [7] ; the peak outputs forv(P2) are also computed and discussed.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Computation of peak output for inputs restricted in L 2 and L ∞ norms using finite difference schemes and convex optimization

Silpsrikul

Arunsawatwong

2009

Int. J. Autom. Comput.

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Control systems designed by the principle of matching gives rise to problems of evaluating the peak output. This paper proposes a practical method for computing the peak output of linear time-invariant and non-anticipative systems for a class of possible sets that are characterized with many bounding conditions on the two-and/or the infinity-norms of the inputs and their derivatives. The original infinite-dimensional convex optimization problem is approximated as a large-scale convex programme defined in a Euclidean space, which are associated with sparse matrices and thus can be solved efficiently in practice. The numerical results show that the method performs satisfactorily, and that using a possible set with many bounding conditions can help to reduce the design conservatism and thereby yield a better match.

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Section: ) ḟ ∞ D∞ Is Replaced Bymentioning

confidence: 99%

Section: Numerical Examplesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Computation of peak output for inputs restricted in L 2 and L ∞ norms using finite difference schemes and convex optimization

Silpsrikul

Arunsawatwong

2009

Int. J. Autom. Comput.

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“…It should be noted that criterion (1) is frequently used in practice to monitor the performances of the control systems and has long been investigated by many authors (see, for example, [1], [2], [3], [4], [5], [6] and also the references therein). Moreover, the condition becomes remarkably useful in the design of critical systems [7], [4] (see also [8]), where any violation of the bound ε may give rise to unacceptable consequences.…”

Section: Introductionmentioning

confidence: 99%

Design of nonlinear feedback systems with inputs and outputs satisfying bounding conditions

Arunsawatwong

Abed

2010

2010 IEEE International Symposium on Computer-Aided Control System Design

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This paper develops a method for designing a feedback system comprising a static memoryless nonlinearity and linear time-invariant convolution subsystems so as to ensure that the error and the controller output stay within prescribed bounds for all time and for all inputs having bounded magnitude and bounded slope. Since the original design criteria are computationally intractable, we derive practical sufficient conditions for ensuring them. The conditions provide surrogate design criteria that are in keeping with the method of inequalities. Essentially, the nonlinearity is replaced with a fixed gain and an equivalent disturbance; thus, the nominal system used during the design process becomes linear and the associated performance measures are readily obtainable by known methods. To illustrate the usefulness of the method, a design example of a hydraulic force control system is given.Index Terms-nonlinear systems; peak output; worst case performance; control systems design; principle of matching; method of inequalities.

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Foundation of Control Systems Design

Zakian¹

Control Systems Design

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The principle of matching: a necessary and sufficient condition for inputs restricted in magnitude and rate of change

Cited by 18 publications

References 13 publications

Computation of peak output for inputs restricted in L 2 and L ∞ norms using finite difference schemes and convex optimization

Computation of peak output for inputs restricted in L 2 and L ∞ norms using finite difference schemes and convex optimization

Design of nonlinear feedback systems with inputs and outputs satisfying bounding conditions

Foundation of Control Systems Design

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