• Earthquakes and Structures
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• v.27 no.5
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• pp.401-417
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• 2024

This study presents a method for optimization of weighting matrices of the linear quadratic regulator (LQR) control algorithm in order to design an optimal active control system using metaheuristic algorithms. The LQR is a widely used control technique in engineering for designing optimal controllers for linear systems by minimizing a quadratic cost function. However, the performance of the LQR strongly depends on the appropriate selection of weighting matrices, which are usually determined by some thumb rule or exhaustive search method. In the present study, for the optimization of weighting matrices, four metaheuristic algorithms including, Particle Swarm Optimization (PSO), Genetic Algorithm (GA), Grey Wolf Optimizer (GWO) and, Whale Optimization Algorithm (WOA) are considered. To generate optimal weighting matrices, the objective function used consists of displacement and absolute acceleration. During the optimization process, a response effectiveness factor is also checked for displacement and acceleration as a constraint for the proper selection of weighting matrices. To study the effectiveness of optimized active control system to those for the exhaustive search method, the various controlled responses of the system are compared with the corresponding uncontrolled system. The optimized weighting matrices effectively reduce the displacement, velocity, and acceleration responses of the structure. Based on the simulation study, it can be observed that GWO performs well compared to the PSO, GA, and WO algorithms. By employing metaheuristic algorithms, this study showcases a more efficient and effective approach to finding optimal weighting matrices, thereby enhancing the performance of active control systems.

• Proceedings of the Earthquake Engineering Society of Korea Conference
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• 2002.03a
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• pp.475-482
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• 2002

This paper provides the systematic procedure to determine the weighting matrices of optimal controllers considering structural energy. Optimal controllers consist of LQR and ILQR. The weighting matrices are needed first in the conventional optimal control design strategy. However, they are in general dependent on the experienced knowledge of controll designers. Applying the Lyapunov function to the total structural energy and using the contrition that its derivative is negative, we can determine the weighting matrices without difficulty. It is proven that the control efficiency is achieved well for LQR and ILQR.

• Journal of the Earthquake Engineering Society of Korea
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• v.6 no.6
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• pp.49-53
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• 2002

This paper provides the systematic procedure to determine the weighting matrices of optimal controllers considering structural energy. Optimal controllers consist of LQR and ILQR. The weighting matrices are needed first in the conventional optimal control design strategy. However, they are in general dependent on the experienced knowledge of control designers. Applying the Lyapunov function to total structural energy and using the condition that its derivative is negative, we can determine the weighting matrices without difficulty. It is proven that the control efficiency with using determined weighting matrices is achieved well for LQR and ILQR controllers.

• 제어로봇시스템학회:학술대회논문집
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• 1989.10a
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• pp.473-476
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• 1989

Quadratic weighting matrices have an effect on the transition and steady state responses in a LQ tracking problem. They are usually decided on trial and error in order to get a good response. In this paper a method is presented which calculates a steady - state deviation without solving Riccati equation. By using this method, a new procedure for selecting the weighting matrices is proposed when a tolerance on the steady - state deviation is given.

• Proceedings of the KIEE Conference
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• 1997.07c
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• pp.841-843
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• 1997

In this paper we present a Genetic approach to select weighting matrices of LQ(Linear Quadratic) controller for optimal TCSC(Thyristor Controlled Series Capacitor) control. A design of LQ controller depends on choosing weighting matrices. The selection of weighting matrices is usually carried out by trial and error, which is not a trivial problem. We proposed a efficient method using GA of finding weighting matrices for optimal control law. The proposed GA method was applied to design LQ controller of TCSC in one machine infinite bus system and showed good results.

• Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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• v.16 no.6
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• pp.40-50
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• 2002

In this paper, we present a GA(Genetic Algorithm) approach to select weighting matrices of an optimal LQ(Linear Quadratic) controller for SVC(Static VAR Compensator). A SVC, one of the FACTS(Flexible AC Transmission System), constructed by a FC(Fixed Capacitor) and a TCR(Thyristor Controlled Reactor), was designed and implemented to improve the damping of a synchronous generator, as well as to control the system voltage Also, a design of LQ controller depends on choosing weighting matrices. The selection of weighting matrices which is not a trivial solution is usually carried out by trial and error. We proposed an efficient method using GA of finding weighting matrices for optimal control law. Thus, we proved the usefulness of proposed method to improve the stability of single machine-infinite bus with SVC system by eigenvalues analysis and simulation.

• Journal of Communications and Networks
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• v.18 no.6
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• pp.892-901
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• 2016

In the multi-user multiple-input multiple-output (MIMO) system, orthogonal random beamforming (ORBF) scheme is proposed to serve multiple users simultaneously in order to achieve the multi-user diversity gain. The opportunistic space-division multiple access system (OSDMA-S) scheme performs multiple weighting matrices during the training phase and chooses the best weighting matrix to be used to broadcast data during the transmitting phase. The OSDMA-S scheme works better than the original ORBF by decreasing the inter-user interference during the transmitting phase. To save more time in the training phase, a partly random multiple weighting matrices selection scheme is proposed in this paper. In our proposed scheme, the Base Station does not need to use several unitary matrices to broadcast pilot symbol. Actually, only one broadcasting operation is needed. Each subscriber generates several virtual equivalent channels with a set of pre-saved unitary matrices and the channel status information gained from the broadcasting operation. The signal-to-interference and noise ratio (SINR) of each beam in each virtual equivalent channel is calculated and fed back to the base station for the weighting matrix selection and multi-user scheduling. According to the theoretical analysis, the proposed scheme relatively expands the transmitting phase and reduces the interactive complexity between the Base Station and subscribers. The asymptotic analysis and the simulation results show that the proposed scheme improves the throughput performance of the multi-user MIMO system.

• 제어로봇시스템학회:학술대회논문집
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• 1988.10b
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• pp.729-733
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• 1988

In this paper, a new procedure for selecting weighting matrices in linear discrete time quadratic optimal control problems (LQ-problem) is proposed. In LQ problems, the quadratic weighting matrices are usually decided on trial and error in order to get a good response. But using the proposed method, the quadratic weights are decided in such a way that all poles of the closed loop system are located in a desired area for good responses as well as for stability and values of the quadratic cost functional are kept less then a specified value. The closed loop systems constructed by this method have merits of LQ problems as well as those of pole assignment problems. Taking into consideration that little is known about the relationship among the quadratic weights, the poles and the values of cost functional, this procedure is also interesting from the theoretical point of view.

• Proceedings of the KIEE Conference
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• 1998.07c
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• pp.1024-1026
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• 1998

In this paper we present a Neural network approach to select weighting matrices of Linear-Quadratic-Gaussian (LQG) controller for TCSC control. The selection of weighting matrices is usually carried out by trial and error. A weighting matrices of LQG control selected effectively using Neural network. It is shown that simulation results in application of this method to one machine infinite bus system are satisfactory.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.48 no.3
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• pp.212-219
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• 1999

In this paper we present a neural network approach to select weighting matrices of Linear-Quadratic-Gaussian(LQG) controller for TCSC control. The selection of weighting matrices is usually carried out by trial and error. A weighting matrices of LQG control are selected effectively using Kohonen network. It is shown that simulation results in application of this method to three machine nine bus system are satisfactory.