Design approach of weighting matrices for LQR based on multi-objective evolution algorithm

Li, Yong; Liu, Jianchang; Wang, Yu

doi:10.1109/icinfa.2008.4608180

Cited by 13 publications

(4 citation statements)

References 9 publications

(6 reference statements)

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“…Population‐based heuristic techniques such as GAs has been used for optimization and selection of optimum weighting matrices for a class of LQR formulations for the design of fractional order PID controller 30,31 . In Reference 32, the authors proposed, a multi‐objective approach to optimize the weighting matrices Q and R for a touchstone problem application. The optimization of parameters of the matrices have been done based on GAs, the approach can have broad pragmatic applications including clustering of data in case of earthquake and control design for buck converter, 33,34 respectively.…”

Section: Fractional‐order‐based Lqrmentioning

confidence: 99%

Fractional‐order filter‐based enhanced full state feedback control design with multi‐objective formulation using grey wolf optimization algorithm

Kumar

Dhillon

Kumar³

2022

Optim Control Appl Methods

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A perturbed fractional-order filter (FOF)-based LQR control design with multiple performance indices is proposed in this paper. Three variants of the FOF-based linear quadratic regulator (LQR) system have been proposed along with choices on the commensurate order of state feedback law. The multi-objective problem formulation has been done with three performance objectives to address the different issues of design. The first performance index constitutes a weighted sum of ITAE (Integral Time of Absolute Error) and the difference between the eigenvalues of the plant and the LQR controlled plant, chosen to minimize the large oscillations as well as relative stability with respect to eigenvalues. A new lower bound of the singular values have been addressed to ensure the robust stability of the system through the formulation of a second performance objective. It is the minimization of singular values of the return ratio matrix at the plant's input. The third and the last performance index aims minimization of maximum singular values of the perturbation transfer function at the plant's output, so as to guarantee no closed-loop right half plane zeros. The multi-objective optimization problem is solved and the optimal solutions are obtained via Grey Wolf Optimization Algorithm. The simulation results validate the performance and effectiveness of the proposed control design.

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Section: Fractional‐order‐based Lqrmentioning

confidence: 99%

Fractional‐order filter‐based enhanced full state feedback control design with multi‐objective formulation using grey wolf optimization algorithm

Kumar

Dhillon

Kumar³

2022

Optim Control Appl Methods

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“…݂ ଷ ሺܳ, ܴሻ can be calculated by using the simulation results according to (9). Smaller value of ݂ ଷ ሺܳ, ܴሻ means better control effect for the controller.…”

Section: System Descriptionmentioning

confidence: 99%

“…In recent years, both native and abroad scholars applied MOEA based multi-objective optimization to control field, and achieved many valuable research results [8]. Yong Li and Jianchang Liu and Yu Wang applied NSGAІІ based multi-objective optimization to designed Controller of double inverted pendulum system [9]. The control effort looks better than the [8] method.…”

Section: Introductionmentioning

confidence: 99%

Weighting Matrix Selection Method for LQR Design Based on a Multi-Objective Evolutionary Algorithm

Nekoui

Bozorgi

2011

AMR

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This paper introduces an application of Multi-Objective Evolution Algorithm (MOEA) to design Q and R weighting matrices in Linear Quadratic regulators (LQR). Considering the difficulty of designing weighting matrices for a linear quadratic regulator, a multi-objective evolutionary algorithm based approach is proposed. The LQR weighting matrices, state feedback control rate and consequently the optimal controller are obtained by means of establishing the multi-objective optimization model of LQR weighting matrices and applying MOEA to it, which makes control system meet multiple performance indexes simultaneously. Controller of double inverted pendulum system is designed using the proposed approach. Simulation results show that it has shorter adjusting time and smaller amplitude value deviating from steady-state than a Non-dominated Sorting Genetic Algorithm LQR ( NSGA- LQR )weighting matrices design approach.

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“…An LQR is designed by minimizing a cost function which is quadratic and dependent on state weight matrix, Q, and input weight matrix, R. Convenient selection of these tuning parameters creates satisfactory results while maintaining the control cost minimum. Different selection procedures for the weight matrices have been proposed in the past [19,20]. Bryson and Ho [21] proposed an inverse square method where the weights of the states are represented by diagonal weight matrix.…”

Section: Introductionmentioning

confidence: 99%

A Numerical and Experimental Study of Optimal Velocity Feedback Control for Vibration Suppression of a Plate-Like Structure

Boz

Aridogan

Basdogan

2015

Journal of Low Frequency Noise, Vibration and Active Control

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This study presents a numerical and an experimental study on an active vibration control system. The system includes a fully-clamped plate and two surface bonded piezoelectric actuators and a collocated velocity sensor at one of the actuator locations. One of the piezoelectric actuators is used for disturbance actuation and the other one is used for control actuation. A model based optimal velocity feedback controller is used as control algorithm. The disturbance and actuator models are obtained through experimental characterization of the plate under the effect of the disturbance source. A representative SIMULINK model is built in parallel to the development of the experimental setup in order to investigate performance of the controller for various control parameters. After the model based optimal controller is designed, performance of the optimal velocity feedback controller is validated with the experimental study by comparing the vibration suppression values at multiple modes of the structure. Results show that the developed control methodology effectively suppresses the vibration amplitudes at multiple modes of the structure and also vibration attenuation levels can be predicted accurately with the simulations for various controller design parameters. It is also demonstrated that using an optimal controller enhances the performance of the system as opposed to just using velocity feedback algorithm for the active vibration control of the smart plate.

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Design approach of weighting matrices for LQR based on multi-objective evolution algorithm

Cited by 13 publications

References 9 publications

Fractional‐order filter‐based enhanced full state feedback control design with multi‐objective formulation using grey wolf optimization algorithm

Fractional‐order filter‐based enhanced full state feedback control design with multi‐objective formulation using grey wolf optimization algorithm

Weighting Matrix Selection Method for LQR Design Based on a Multi-Objective Evolutionary Algorithm

A Numerical and Experimental Study of Optimal Velocity Feedback Control for Vibration Suppression of a Plate-Like Structure

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