Control system design via infinite linear programming

Deodhare, Girish; Vidyasagar, M.

doi:10.1080/00207179208934289

Cited by 21 publications

(5 citation statements)

References 11 publications

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“…Less conventionalbut many times more importantobjective functions can be used as additional constraints or shaping constraints. These functions are typically defined to measure certain attributes of the temporal response such as the rise ( t r ) and settling time ( t s ) and the overshoot ( y os ) or undershoot ( y us ) and to account for a physical control constraint (| u | max ); in particular, for the positive-gain case they can be written as follows: Similar functions have been suggested in connection with a multiobjective design, l 1 optimal design, and pole placement. , In this article we show that they can be used as shaping constraints for reaching the desired performance in the tuning problem formulation.…”

Section: Design-and-tuning Problem Formulationmentioning

confidence: 93%

Shaping Time-Domain Responses with Discrete Controllers

Giovanini

Marchetti

1999

Ind. Eng. Chem. Res.

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A model-based design and tuning method for discrete controllers for single-input−single-output systems is presented in this article. It stresses the possibility of specifying the desired closed-loop behavior by using a set of time-domain conditions defining the performance that is desirable in the controlled output. The problem formulation is developed in the time domain since this is the domain where many important and different design conditions can be visualized and written in an easy mathematical form, particularly for most continuous chemical processes. This approach allows shaping the time-domain closed-loop response by one or more constraints representing the limits of minimum performance desired when specific changes on either the setpoint or the load disturbance are expected. Model uncertainties caused by slow time-variant or nonlinear systems can also be accounted for, guaranteeing robust performance and stability of the closed-loop system.

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Section: Design-and-tuning Problem Formulationmentioning

confidence: 93%

Shaping Time-Domain Responses with Discrete Controllers

Giovanini

Marchetti

1999

Ind. Eng. Chem. Res.

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“…A related, but distinct, problem to those considered here has been treated in [2], where the -norm of the error response was minimized subject to bounds being placed on the overshoot and/or undershoot. We follow [2] in using the modern Fenchel duality framework for their re-formulation as infinite-dimensional convex optimization problems.…”

Section: Introductionmentioning

confidence: 99%

“…We follow [2] in using the modern Fenchel duality framework for their re-formulation as infinite-dimensional convex optimization problems. This necessitates the use of conjugate functionals and the concept of quasi relative interior.…”

Section: Introductionmentioning

confidence: 99%

Fundamental limitations on the time-domain shaping of response to a fixed input

Hill¹,

Eberhard²,

Wenczel³

et al. 2002

IEEE Trans. Automat. Contr.

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In this paper, we examine time-domain limitation-of-performance problems in feedback control system design. The main result is a theorem which gives a dual formulation to the problem of determining absolute limits on the time-domain shaping of the response to a fixed input. The duals that arise are particularly illuminating. They have a simple interpretation as optimizing the impulse response of a transfer function whose poles are readily constructed from the data. Much insight is obtainable from the dual, for example, in helping to classify classes of plants with the same quantitative behavior. New results on classical performance measures, such as overshoot and undershoot, are presented. We also examine minimization of the difference between the maximum and minimum values of the error response, a quantity we term fluctuation.

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“…This approach can be used in the tradeoff between overshoot and settling-time requirements. Deohare and Vidyasagar [5] studied and solved the problem of designing a non-overshooting controller that minimizes the integral absolute error (IAE) performance using infinite linear programming approach. A LQG-like parameterization scheme was suggested by Harn and Kosut [6], where descent-based design methods are developed for minimizing the cost function with respect to the controller parameters.…”

Section: Introductionmentioning

confidence: 99%

Controller design for optimal tracking response in discrete‐time systems

Sebakhy

Yousef

2007

Optim Control Appl Methods

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The problem of designing a controller, which results in a closed-loop system response with optimal time-domain characteristics, is considered. In the approach presented in this paper, the controller order is fixed (higher than pole-placement order) and we seek a controller that results in closed-loop poles at certain desired and pre-specified locations; while at the same time the output tracks the reference input in an optimal way. The optimality is measured by requiring certain norms on the error sequence-between the reference and output signals-to be minimum. Several norms are used. First, l 2 -norm is used and the optimal solution is computed in one step of calculations. Second, l ∞ -norm (i.e. minimal overshot) is considered and the solution is obtained by solving a constrained affine minimax optimization problem. Third, the l 1 -norm (which corresponds to the integral absolute error-(IAE)-criterion) is used and linear programming techniques are utilized to solve the problem. The important case of finite settling time (i.e. deadbeat response) is studied as a special case. Examples that illustrate the different design algorithms and demonstrate their feasibility are presented.

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Control system design via infinite linear programming

Cited by 21 publications

References 11 publications

Shaping Time-Domain Responses with Discrete Controllers

Shaping Time-Domain Responses with Discrete Controllers

Fundamental limitations on the time-domain shaping of response to a fixed input

Controller design for optimal tracking response in discrete‐time systems

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