Robust controller design by convex optimization based on finite frequency samples of spectral models

Galdos, Gorka; Karimi, Alireza; Longchamp, R.

doi:10.1109/cdc.2010.5718094

Cited by 8 publications

(11 citation statements)

References 14 publications

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“…that is equivalent to (6). Moreover, it can be shown that the number of encirclements of the critical point by L and L d is equal.…”

Section: Design Specificationsmentioning

confidence: 92%

“…In this case a scenario approach can be used that guarantees the satisfaction of all constraints with a probability level when they are only satisfied for a finite number of randomly chosen scheduling parameters [3]. Some of the effects of gridding in frequency and additional constraints that can be imposed for ensuring good behavior between the grid points are described in [6].…”

Section: Optimization Problemmentioning

confidence: 99%

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H∞ gain-scheduled controller design for rejection of time-varying narrow-band disturbances applied to a benchmark problem

Karimi

Emedi

2013

European Journal of Control

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A new method for H-infinity gain-scheduled controller design by convex optimization is proposed that uses only frequencydomain data. The method is based on loop shaping in the Nyquist diagram with constraints on the weighted infinity-norm of closed-loop transfer functions. This method is applied to a benchmark for adaptive rejection of multiple narrow-band disturbances. First, it is shown that a robust controller can be designed for the rejection of a sinusoidal disturbance with known frequency. The disturbance model is fixed in the controller, based on the internal model principle, and the other controller parameters are computed by convex optimization to meet the constraints on the infinity-norm of sensitivity functions. It is shown next that a gain scheduled-controller can be computed for a finite set of disturbance frequencies by convex optimization. An adaptation algorithm is used to estimate the disturbance frequency which adjusts the parameters of the internal model in the controller. The simulation and experimental results show the good performance of the proposed control system.

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“…that is equivalent to (6). Moreover, it can be shown that the number of encirclements of the critical point by L and L d is equal.…”

Section: Design Specificationsmentioning

confidence: 92%

Section: Optimization Problemmentioning

confidence: 99%

H∞ gain-scheduled controller design for rejection of time-varying narrow-band disturbances applied to a benchmark problem

Karimi

Emedi

2013

European Journal of Control

Self Cite

View full text Add to dashboard Cite

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“…This can be done because a second order system can be considered as the sum of two first order systems with a pair of complex conjugated poles (10). The final analysis was done on one of these first order systemsG (s) = b s−p in (13), the other one was neglected because it did not significantly contribute to the error.…”

Section: Normalised First Order Systemmentioning

confidence: 99%

“…Although this paper focusses on the LPM, the reader should be aware that the results can also be applied to other problems where a polynomial approximation of the frequency response function is needed, like for example control design [10], [11], [12]. In some design techniques, a controller is designed directly from a discrete set of frequency response function measurements that need to be interpolated.…”

Section: Introductionmentioning

confidence: 99%

Bounding the Polynomial Approximation Errors of Frequency Response Functions

Schoukens

Vandersteen

Pintelon

et al. 2013

IEEE Trans. Instrum. Meas.

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Abstract-Frequency response function (FRF) measurements take a central place in the instrumentation and measurement field because many measurement problems boil down to the characterisation of a linear dynamic behaviour. The major problems to be faced are leakage-and noise errors. The local polynomial method (LPM) was recently presented as a superior method to reduce the leakage errors with several orders of magnitude while the noise sensitivity remained the same as that of the classical windowing methods. The kernel idea of the LPM is a local polynomial approximation of the FRF and the leakage errors in a small frequency band around the frequency where the FRF is estimated. Polynomial approximation of FRF's is also present in other measurement and design problems. For that reason it is important to have a good understanding of the factors that influence the polynomial approximation errors. This article presents a full analysis of this problem, and delivers a rule of thumb that can be easily applied in practice to deliver an upper bound on the approximation error of FRF's. It is shown that the approximation error for lowly damped systems is bounded by (BLP M /B 3dB ) R+2 with BLP M the local bandwidth of the LPM, R the degree of the local polynomial that is selected to be even (user choices), and B 3dB the 3 dB bandwidth of the resonance, which is a system property.

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“…All the values in Table 3 are in per-unit system. ω is the desired closed-loop bandwidth [17] [22]. Typically, the bandwidth is the range of frequencies for which the gain is significant.…”

Section: Choice Of Operating Pointsmentioning

confidence: 99%

A Multi-Model Approach to Design a Robust SVC Damping Controller Using Convex Optimization Technique to Enhance the Damping of Inter-Area Oscillations Considering Time Delay

Abdlrahem¹,

Albalawi²

2017

EPE

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This paper introduces a multi-model approach to design a robust supplementary damping controller. The designed fixed-order supplementary damping controller adjusts the voltage reference set point of SVC. There are two main objectives of the controller design, damping low frequencies oscillations and enhancing power system stability. This method relies on shaping the closed-loop sensitivity functions in the Nyquist plot under the constraints of these functions. These constraints can be linearized by choosing a desired open-loop transfer function. The robust controller is designed to minimize the error between the open-loop of the original plant model and the desired transfer functions. These outcomes can be achieved by using convex optimization methods. Convexity of the problem formulation ensures global optimality. One of the advantages of the proposed approach is that the approach accounts for multi-model uncertainty. In contrast to the methods available in the literature, the proposed approach deals with full-order model (i.e., model reduction is not required) with lower controller order. The issue of time delay of feedback signals has been addressed in this paper for different values of time delay by applying a multi-model optimization technique. The proposed approach is compared to other existing techniques to design a robust controller which is based on H 2 under pole placement. Both techniques are applied to the 68-bus system to evaluate and validate the robust controller performance under different load scenarios and different wind generations.

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Robust controller design by convex optimization based on finite frequency samples of spectral models

Cited by 8 publications

References 14 publications

H∞ gain-scheduled controller design for rejection of time-varying narrow-band disturbances applied to a benchmark problem

H∞ gain-scheduled controller design for rejection of time-varying narrow-band disturbances applied to a benchmark problem

Bounding the Polynomial Approximation Errors of Frequency Response Functions

A Multi-Model Approach to Design a Robust SVC Damping Controller Using Convex Optimization Technique to Enhance the Damping of Inter-Area Oscillations Considering Time Delay

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