Synthesis of optimal control systems with near sensitivity feedback

Rao, S.; Soudack, A. C.

doi:10.1109/tac.1971.1099677

Cited by 22 publications

(8 citation statements)

References 14 publications

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“…[l]- [5], that is, assuming u, to be zero. Following the same procedures, we can obtain the optimal controller gain K(s).…”

Section: K(s)=f(sxl-w(s)f(s)tmentioning

confidence: 99%

“…However, the sensitivity reduction is not significant. Several authors (2)(3)(4)(5)(6)(7)(8) attempted to reduce the sensitivity by augmenting the trajectory sensitivity equation with the state equation and/or output equation and by modifying the performance index to include a weighting on the quadratic trajectory sensitivity term, and/or defined the control law by output feedback. All back owing to the fact that the variation of control due to the changes system paramters, (dti/das), is not known a priori.…”

Section: Introductionmentioning

confidence: 99%

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Design of low sensitivity controllers: Preregulator approach

Liou¹,

1985

Journal of the Chinese Institute of Engineers

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Since the trajectory sensitivity can not be modeled accurately in a closed-loop formulation, the linear preregulator design techniques are investigated to approximate the sensitivity information, and two methods leading to transfer-function matrix form are developed. The obtained control systems have shown much improvement in reducing the sensitivity, specially for Method B. The advantages of Method B over Method A are that the difficulty of obtaining the steady state control law in terms of the reference input can be prevented and that the controller containing an integral action can be obtained to ensure that there is no steady-state error.

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“…[l]- [5], that is, assuming u, to be zero. Following the same procedures, we can obtain the optimal controller gain K(s).…”

Section: K(s)=f(sxl-w(s)f(s)tmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Design of low sensitivity controllers: Preregulator approach

Liou¹,

1985

Journal of the Chinese Institute of Engineers

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“…Now, from Eqs. [4], [5], [9], [12] and the discrete Parseval's theorem, Eq. [3] can be written as kt C14] At the optimum, the U{z) will minimize the performance index J, and the necessary and sufficient condition for optimality is that…”

Section: -Zmentioning

confidence: 99%

“…In the popular methods of parameter sensitivity reduction by the inclusion of a quadratic trajectory sensitivity term in the linear regulator (3)(4)(5)(6)(7), the form of the feedback controller contains both state variable and trajectory sensitivity terms.…”

Section: Introductionmentioning

confidence: 99%

Low‐sensitivity controllers for discrete‐time systems

Liou¹,

Tu²

1985

Journal of the Chinese Institute of Engineers

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The problem of trajectory sensitivity considered in the literature was restricted to the continuous-time systems. Some of the criteria provided in previous work (9, 10) are extended to the discrete-time control systems. Two methods based on the Z-domain design technique are developed to overcome the difficulty of obtaining the variations of control due to the changes of system parameters. The obtained Z-domain controllers are particularly suitable for implementation on a microprocessor or digital computer. mm m (9 .10)

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“…This is done by adding a quadratic trajectory sensitivity term into the cost functional and using the augmented dynamical system (Fleming and Newmann [7], Kreindler [14], and Rao and Soudack [19]). At present, most optimization methods for decision-making problems under uncertainty treat important characteristics such as sensitivity and uncertainty either by means of system constraints or by embedding them into the overall performance index.…”

Section: Introductionmentioning

confidence: 99%

The uncertainty sensitivity index method (USIM) and its extension

Haimes

1988

Naval Research Logistics

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This article deals with optimization problems that have some uncertain parameters with unknown probabilities. The article proposes a strategy of transferring the system's uncertainty associated with these optimization problems into a norm or a set of norms that is added to the original objective function(s) within a multiobjective framework. The uncertainty sensitivity index method (USIM) proposed by Haimes and Hall [1977] is extended to several general cases. A robust algorithm is developed to guarantee an ideal solution for cases where the nominal value of the uncertain parameter is itself an uncertain variable. A design problem is also addressed to identify the best‐compromise values of the system's parameters by integrating the USIM with the envelope approach.

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Synthesis of optimal control systems with near sensitivity feedback

Cited by 22 publications

References 14 publications

Design of low sensitivity controllers: Preregulator approach

Design of low sensitivity controllers: Preregulator approach

Low‐sensitivity controllers for discrete‐time systems

The uncertainty sensitivity index method (USIM) and its extension

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