Computer-aided analysis and design of control systems using model approximation techniques

Aguirre, Luís A.

doi:10.1016/0045-7825(94)90175-9

Cited by 7 publications

(6 citation statements)

References 37 publications

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“…This implies that advance knowledge of the controller is needed prior to model reduction. A similar sentiment has been expressed by Aguirre, who has investigated model order reduction techniques for controller design. In this work, a distinction is made between open-loop model reduction.…”

Section: Controller Approximation Methodsmentioning

confidence: 55%

“…Open-loop model reduction attempts to match the process transfer functions, while closed-loop model reduction attempts to match the closed-loop system response for a prespecified controller. Aguirre 5 states that an excellent open-loop approximation will not necessarily guarantee a reducedorder model which produces an accurate simplified closed-loop system.…”

Section: Controller Approximation Methodsmentioning

confidence: 99%

“…Because by definition then Equation A.2 can be simplified to yield or Then, the derivative at the point of linearization, x j , is given by On the right-hand side of eq A. 5, there is only one nonconstant quantity, and as shown in eq 3.7, it can be expressed as follows:…”

Section: Appendixmentioning

confidence: 99%

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Controller Approximation Using Semidefinite Programming

Thake

McLellan

Forbes

1999

Ind. Eng. Chem. Res.

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Controller design, and the resulting control system performance, is frequently limited by the capabilities of the available control system hardware. When the control system hardware provides only a small set of fixed controller structures (e.g., proportional−integral−derivative, PID) or limited programming capabilities, it may be desirable to use the available functional elements in a manner such that the implemented fixed structure controller matches the performance of some reference advanced controller as closely as possible. This paper presents a systematic method for approximating the performance of an advanced controller with simpler fixed structure controllers using semidefinite programming. Tuning of the simple, fixed structure controller is obtained by matching a specific desired behavior of the advanced controller. The proposed method is illustrated using two case studies: the approximation of a linear quadratic regulator for a distillation column by a multiloop PID controller and cross-direction profile control for a paper machine.

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Section: Controller Approximation Methodsmentioning

confidence: 55%

Section: Controller Approximation Methodsmentioning

confidence: 99%

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Controller Approximation Using Semidefinite Programming

Thake

McLellan

Forbes

1999

Ind. Eng. Chem. Res.

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“…13 Aguirre reviewed some model approximation techniques that are also applicable to reduced-order controller design and compared their performance. 14 Since the early 1980s, several computational tools have been developed that integrate process identification and PI/PID tuning. A °stro ¨m and Ha ¨gglund 15 proposed relay autotuning for closed-loop determination of the critical parameters and subsequently applied the Z-N rules to tune PID controllers.…”

Section: Introductionmentioning

confidence: 99%

“…Low-order controllers via the IMC methodology have also been obtained as a result of prior model reduction . Aguirre reviewed some model approximation techniques that are also applicable to reduced-order controller design and compared their performance …”

Section: Introductionmentioning

confidence: 99%

Low-Order Controller Design Using Global Optimization

Schmidt¹,

Sourlas²

2001

Ind. Eng. Chem. Res.

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The paper presents an optimization-based fixed-order controller design method. A minimization problem is formulated where the objective function is an l 1 -l ∞ performance measure that quantifies time-domain performance. To achieve an optimization search over all stabilizing fixedorder controllers, a controller parametrization is used that is based on the Youla parametrization and also includes a quadratic equality constraint. The resulting infinite-dimensional optimization problem is nonconvex and is solved by identifying converging sequences of upper and lower bounds. The algorithm is demonstrated through an example. Finally, the paper introduces a global optimization method for the solution of the aforementioned optimization problem. The method is based on the branch-and-bound technique and employs interval analysis to achieve range and dimension reduction in the branching space. Two implementations of interval computations are presented, and the most efficient one consists of a modified interval Newton method that capitalizes on the structure of the problem's equations. The performance of this hybrid method as well as its scaling characteristics are demonstrated through a PI controller optimization example.

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