Optimal Controller Design for Interconnected Power Networks With Predetermined Degree of Stability

Azimi, Seyed Mohammad; Naghizadeh, Ramezan Ali; Kian, A.R.

doi:10.1109/jsyst.2018.2877922

Cited by 6 publications

(4 citation statements)

References 37 publications

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“…The baseline LQR is transformed into a self-tuning-regulator by retrofitting it with a self-adjusting degree-of-stability (DoS) [ 21 ]. The QPI is equipped with a reconfiguration block that relocates the system’s closed-loop poles on the left-hand side of the vertical line, s = − β ( t ), on the complex s -plane; where, β (.)…”

Section: Hierarchical Self-tuning-regulator Designmentioning

confidence: 99%

“…Despite its optimality and guaranteed stability, the LQR lacks robustness against exogenous disturbances, model variations, and identification errors [ 19 , 20 ]. The robustness of the generic LQR can be improved by prescribing a “Degree-of-Stability” (DoS) in its structure [ 21 ]. The DoS design relocates the system’s eigenvalues on the left-hand of the line s = − β in the complex plane, where, " s " is the Laplace operator and β >0 is a preset parameter that defines the LQR’s DoS [ 22 ].…”

Section: Introductionmentioning

confidence: 99%

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An experimental comparison of different hierarchical self-tuning regulatory control procedures for under-actuated mechatronic systems

2021

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This paper presents an experimental comparison of four different hierarchical self-tuning regulatory control procedures in enhancing the robustness of the under-actuated systems against bounded exogenous disturbances. The proposed hierarchical control procedure augments the ubiquitous Linear-Quadratic-Regulator (LQR) with an online reconfiguration block that acts as a superior regulator to dynamically adjust the critical weighting-factors of LQR’s quadratic-performance-index (QPI). The Algebraic-Riccati-Equation (ARE) uses these updated weighting-factors to re-compute the optimal control problem, after every sampling interval, to deliver time-varying state-feedback gains. This article experimentally compares four state-of-the-art rule-based online adaptation mechanisms that dynamically restructure the constituent blocks of the ARE. The proposed hierarchical control procedures are synthesized by self-adjusting the (i) controller’s degree-of-stability, (ii) the control-weighting-factor of QPI, (iii) the state-weighting-factors of QPI as a function of “state-error-phases”, and (iv) the state-weighting-factors of QPI as a function of “state-error-magnitudes”. Each adaptation mechanism is formulated via pre-calibrated hyperbolic scaling functions that are driven by state-error-variations. The implications of each mechanism on the controller’s behaviour are analyzed in real-time by conducting credible hardware-in-the-loop experiments on the QNET Rotary-Pendulum setup. The rotary pendulum is chosen as the benchmark platform owing to its under-actuated configuration and kinematic instability. The experimental outcomes indicate that the latter self-adaptive controller demonstrates superior adaptability and disturbances-rejection capability throughout the operating regime.

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Section: Hierarchical Self-tuning-regulator Designmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An experimental comparison of different hierarchical self-tuning regulatory control procedures for under-actuated mechatronic systems

2021

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“…The prescribed Degree-of-Stability (DoS) LQR design robustifies the system's performance by reorganizing its closed-loop poles on the left side of the user-specified line 𝑠 = −𝛽 in the complex s-plane; where, "𝑠" is the Laplace operator and 𝛽 ≥ 0 is a preset parameter that dictates the controller's DoS [17]. As compared to the conventional LQR, this augmentation reasonably improves the regulator's phase margin and aids in directing the applied control yield to improve the controller's robustness [18]. Unfortunately, this augmentation also makes the procedure sub-optimal by making a compromise between the disturbance-rejection capability and control input economy [19].…”

Section: Introductionmentioning

confidence: 99%

Fuzzy-Immune-Regulated Adaptive Degree-of-Stability LQR for a Self-Balancing Robotic Mechanism: Design and HIL Realization

Saleem

Iqbal

2023

IEEE Robot. Autom. Lett.

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This letter formulates a fuzzy-immune adaptive system for the online adjustment of the Degree-of-Stability (DoS) of Linear-Quadratic-Regulator (LQR) procedure to strengthen the disturbance attenuation capacity of a self-balancing mechatronic system. The fuzzy-immune adaptive system uses pre-configured control input-based rules to alter the DoS parameter of LQR for dynamically relocating the closed-loop system's eigenvalues in the complex plane's left half. The corresponding changes in the eigenvalues are conveyed to the Riccati equation, which eventually yields the self-adjusting LQR gains. This arrangement allows for the flexible manipulation of the applied control effort and the response speed as the error conditions change. The efficacies of the self-tuning LQR scheme are verified by performing custom-designed hardware-in-theloop experiments on the Quanser rotary inverted pendulum system. As compared to the DoS-LQR, the proposed controller improves the pendulum's transient recovery time, overshoots, input demands, and offsets by 32.3%, 50.5%, 33.9%, and 33.3%, respectively, under disturbances. These experimental outcomes verify that the proposed self-tuning LQR law considerably improves the system's disturbance attenuation capability.

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“…Moreover, the selection of state and control weighting-factors for the LQR's cost-function is an ill-posed problem [10]. The numerical ill-conditioning problem associated with the LQR is generally solved by specifying a predetermined "Degree-of-Stability" (DoS) in its design [11]. Where in, the closed-loop poles of the system are allocated on the left-hand of the line s = −β in the complex s-plane, where, s is the Laplace operator and β > 0 is a preset hyper-parameter that defines the DoS [12].…”

Section: Introductionmentioning

confidence: 99%

Self-tuning state-feedback control of a rotary pendulum system using adjustable degree-of-stability design

2020

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Optimal Controller Design for Interconnected Power Networks With Predetermined Degree of Stability

Cited by 6 publications

References 37 publications

An experimental comparison of different hierarchical self-tuning regulatory control procedures for under-actuated mechatronic systems

An experimental comparison of different hierarchical self-tuning regulatory control procedures for under-actuated mechatronic systems

Fuzzy-Immune-Regulated Adaptive Degree-of-Stability LQR for a Self-Balancing Robotic Mechanism: Design and HIL Realization

Self-tuning state-feedback control of a rotary pendulum system using adjustable degree-of-stability design

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