Multi-time-scale systems control via use of combined controllers

Kodra, Kliti; Zhong, Ningfan; Gajić, Zoran

doi:10.1109/ecc.2016.7810688

Cited by 7 publications

(3 citation statements)

References 15 publications

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“…where R > 0 and Q ≥ 0 are the weighting matrices. The optimizing performance criterion (21) of the closed-loop optimal control problem, subject to the singularly perturbed system differential Equation 20, has the solution…”

Section: Exact Decomposition Of the Algebraic Riccati Equationmentioning

confidence: 99%

“…Therefore, a rearrangement for the rows of matrix A is necessary to ensure the nonsingularity of sub-matrix A 4 and that the system conforms to the explicit standard singular perturbation form (19). As described in [21], such can be established through the use of the Schur transformation. Algebraically [22], for any given square matrix there exists a unitary similarity transformation known as the Schur's form, where…”

Section: Slow-fast Decomposition Of the Wt With Dfig Systemmentioning

confidence: 99%

“…Notice that, the eigenvalues in Table 2 are equal to those in Table 1, which indicates that the method proposed in Section 3 successfully decomposed the original system into pure-slow and pure-fast subsystems. In order to obtain the optimal gain that minimizes the performance criteria in (21), Equation (23) should be solved. The weighting matrices R and Q were chosen as identity matrices with the appropriate dimensions as follows:…”

Section: Original System Eigenvaluesmentioning

confidence: 99%

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Optimal Control of Wind Turbine Systems via Time-Scale Decomposition

Al-Iedani

Gajić

2020

Energies

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In this paper, we design an optimal controller for a wind turbine (WT) with doubly-fed induction generator (DFIG) by decomposing the algebraic Riccati equation (ARE) of the singularly perturbed wind turbine system into two reduced-order AREs that correspond to the slow and fast time scales. In addition, we derive a mathematical expression to obtain the optimal regulator gains with respect to the optimal pure-slow and pure-fast, reduced-order Kalman filters and linear quadratic Gaussian (LQG) controllers. Using this method allows the design of the linear controllers for slow and fast subsystems independently, thus, achieving complete separation and parallelism in the design process. This solves the corresponding ill-conditioned problem and reduces the complexity that arises when the number of wind turbines integrated to the power system increases. The reduced-order systems are compared to the original full-order system to validate the performance of the proposed method when a wind turbulence and a large-signal disturbance are applied to the system. In addition, we show that the similarity transformation does not preserve the performance index value in case of Kalman filter and the corresponding LQG controller.

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Section: Exact Decomposition Of the Algebraic Riccati Equationmentioning

confidence: 99%

Section: Slow-fast Decomposition Of the Wt With Dfig Systemmentioning

confidence: 99%

Section: Original System Eigenvaluesmentioning

confidence: 99%

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