Synthetic generation of the gradient for an iterative controller optimization method

Bruyne, F. De; Carrette, P.

doi:10.23919/ecc.1997.7082085

Cited by 19 publications

(9 citation statements)

References 3 publications

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“…This result shows that even if the operators C À1 C 0 and T 0 do not commute, the descent method (14) might still be locally convergent using this approximation method.…”

Section: Theoremmentioning

confidence: 87%

“…[14] for linear systems and [7] for non-linear systems. In [15] it is remarked that in practice IFT seems to be robust w.r.t.…”

Section: Gradient Approximationsmentioning

confidence: 99%

“…d @yðqÞ @yðqÞ=@q i ¼ # T T 0 ðqÞA i ðqÞeðqÞ Here # T T 0 ðqÞ is an identified model of the closed-loop system. This idea is used in [14], where IFT is applied to a resonant system where the gradient experiment was not physically realizable due to high excitation of resonant nodes. The identification is assumed to be simplified by the assumption that the closed-loop system is typically of low order and that possible non-linear effects in G 0 are reduced by the feedback.…”

Section: Gradient Approximationsmentioning

confidence: 99%

“…We have given sufficient conditions for local convergence around the point T 0 ðq c Þ ¼ T d for a method using the steepest descent method (14) in which the step-size tends to zero and where the gradient of the output w.r.t. the controller is approximated using approximation method M1.…”

Section: Corollarymentioning

confidence: 99%

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Gradient approximations in iterative feedback tuning for multivariable processes

Jansson

Hjalmarsson

2004

Adaptive Control & Signal

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Iterative feedback tuning (IFT) is a model free control tuning method using closed-loop experiments. For single-input single-output (SISO) systems only 2 or 3, depending on the controller structure, closed-loop experiments are required. However for multivariable systems the number of experiments increases to be proportional to the dimension of the controller. In this contribution several methods are proposed to reduce the experimental time by approximating the gradient of the cost function. One of these methods uses the same technique of shifting operators as is used in IFT for SISO systems. This method is further analysed and sufficient conditions for local convergence are derived. It is shown that even if there are commutation errors due to the approximation method, the numerical optimization may still converge to the true optimum.

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“…This result shows that even if the operators C À1 C 0 and T 0 do not commute, the descent method (14) might still be locally convergent using this approximation method.…”

Section: Theoremmentioning

confidence: 87%

“…[14] for linear systems and [7] for non-linear systems. In [15] it is remarked that in practice IFT seems to be robust w.r.t.…”

Section: Gradient Approximationsmentioning

confidence: 99%

Section: Gradient Approximationsmentioning

confidence: 99%

Section: Corollarymentioning

confidence: 99%

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Gradient approximations in iterative feedback tuning for multivariable processes

Jansson

Hjalmarsson

2004

Adaptive Control & Signal

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“…In [4] this problem is solved by filtering the output signal back through the actual closed-loop system, demanding three experiments for the computation of each tuning direction. Another approach consists of performing an open-loop, identification of a high order parametric model for T ( p ) , reducing the number of experiments to just one [2]. Given that T ( p ) is required only for filtering a virtual signal, a non-parametric representation of this filter suffices to reach the final result.…”

Section: Derivatives Of the Cost Functionmentioning

confidence: 99%

Iterative feedback tuning via minimization of the absolute error

Kammer

Bruyne

Bitmead

Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304)

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This paper introduces a mechanism for controller tuning based on the optimization of a cost function suited to batch production. The cost function penalizes the absolute value of the difference between the desired and the actual signals, i.e. the absolute value of the error. The main innovation in this work is the computation and estimation of the partial derivatives of such a cost function with respect to the parameters of the controller.Besides the computation of those derivatives, we provide auxiliary mechanisms that allow the estimation of efficient tuning directions and a stable implementation of the controller updating scheme. Simulation results indicate the viability of this approach.

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Iterative feedback tuning—an overview

Hjalmarsson

2002

Adaptive Control & Signal

381

228

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Adaptive and iterative control algorithms based on explicit criterion minimization are briefly reviewed and an overview of one such algorithm, iterative feedback tuning (IFT) , is presented. The basic IFT algorithm is reviewed for both single-input/single-output and multi-input/multi-output systems. Subsequently the application to non-linear systems is discussed. Stability and robustness aspects are covered. A survey of existing extensions, applications and related methods is also provided. ; 16:373-395 H. HJALMARSSON Sensitivity modelsLater it was recognized that for linear time-invariant, processes, the sensitivity of any signal, sðtÞ say, in the system w.r.t. any scalar parameter r in the system, i.e. the partial derivative @sðtÞ=@r;

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Synthetic generation of the gradient for an iterative controller optimization method

Cited by 19 publications

References 3 publications

Gradient approximations in iterative feedback tuning for multivariable processes

Gradient approximations in iterative feedback tuning for multivariable processes

Iterative feedback tuning via minimization of the absolute error

Iterative feedback tuning—an overview

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