• 제어로봇시스템학회:학술대회논문집
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• 1989.10a
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• pp.884-889
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• 1989

In this paper, a new procedure for selecting weighting matrices in linear discrete time quadratic optimal control problem (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 region for good responses as well as for stability and values of the quadratic cost function are kept less then a specified value.

• 제어로봇시스템학회:학술대회논문집
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• 1986.10a
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• pp.209-211
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• 1986

The continuous time linear quadratic problem (LQP) has been applied to the control of a 8-tray distillation column using the code VASP. The weighting matrices for the state variables and control variables were adjusted iteratively. The simulation results of the optimal control with 2 inputs and 2 outputs showed that the LQP method is very satisfactory for a rapid response and feedback control, and any desired response could be obtained by adjusting the weighting matrices Q under = and R under =. The feedback gain matrix K under = was also determined.

• Smart Structures and Systems
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• v.23 no.3
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• pp.243-261
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• 2019

This paper introduces an appropriate technique to estimate the weighting matrices used in the linear quadratic regulator (LQR) method for active structural control. For this purpose, a parameter is defined to regulate the relationship between the structural energy and control force. The optimum value of the regulating parameter, is determined for single degree of freedom (SDOF) systems under seismic excitations. In addition, the suggested technique is generalized for multiple degrees of freedom (MDOF) active control systems. Numerical examples demonstrate the robustness of the proposed method for controlled buildings under a wide range of seismic excitations.

• Proceedings of the KIEE Conference
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• 2002.07a
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• pp.226-228
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• 2002

This paper presents a new control approach for designing a coordinated controller for static VAR compensator system. A SVC constructed by a Fixed Capacitor and a Thyristor Controlled Reactor is designed and implemented to improve the damping of a synchronous generator, as well as controlling the system voltage. A design of linear quadratic controller based on optimal controller depends on choosing weighting matrices. A coordinated optimal controller is achieved by minimizing a quadratic performance index using dynamic programming techniques. 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. Thus, we prove the usefulness of proposed method to improve the stability of single machine-infinite bus with SVC system.

• The Proceedings of the Korean Institute of Illuminating and Electrical Installation Engineers
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• v.13 no.2
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• pp.234-234
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• 1999

The aim of this paper is to suggest a design method of the optimal model following control system using genetic algorithm (GA). This control system is designed by applying GA with reference model to the optimal determination of weighting matrices Q, R that are given by LQ regulator problem. The method to do this is that all the diagonal elements of weighting matrices are optimized simultaneously by GA, in the search domain selected adequately. And we design the model following control system to boi1er-turbine equipment by the proposed method. The model following control system designed by this method has the better command tracking performance than that of the control system designed by the trial-and-error method. The effectiveness of this control system is verified by computer simulation.

• Journal of Institute of Control, Robotics and Systems
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• v.11 no.10
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• pp.864-869
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• 2005

This paper proposes a new method for LQR controller design. It is unsystematic and difficult to design an LQR controller by trial and error. The proposed method is capable of systematically calculating weighting matrices for desired pole(s) by the pole's moving-range in S-plane and the relational equation between closed-loop pole(s) and weighting matrices. This will provide much-needed functionality to apply LQR controller. The example shows the feasibility of the proposed method.

• Journal of Institute of Control, Robotics and Systems
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• v.13 no.6
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• pp.574-580
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• 2007

This paper deals with LQR controller design method tor system having complex poles. The proposed method is capable of systematically calculating weighting matrices based on the pole's moving-range and the relational equation between closed-loop pole(s) and weighting matrices. The method moves complex poles to complex poles or two distinct real poles. This will provide much-needed functionality to apply LQR controller. The example shows the feasibility of the proposed method.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.21 no.6
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• pp.634-639
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• 2020

In general, the stability and response characteristics of the system can be improved by changing the pole position because a nonlinear system can be linearized by the product of a 1st and 2nd order system. Therefore, a controller that moves the pole can be designed in various ways. Among the other methods, LQ control ensures the stability of the system. On the other hand, it is difficult to specify the location of the pole arbitrarily because the desired response characteristic is obtained by selecting the weighting matrix by trial and error. This paper evaluated a method of selecting a weighting matrix of LQ control that moves multiple double poles with Jordan blocks to real poles. The relational equation between the double poles and weighting matrices were derived from the characteristic equation of the Hamiltonian system with a diagonal control weighting matrix and a state weighting matrix represented by two variables (ρ_d, ϕ_d). The Moving-Range was obtained under the condition that the state-weighting matrix becomes a positive semi-definite matrix. This paper proposes a method of selecting poles in this range and calculating the weighting matrices by the relational equation. Numerical examples are presented to show the usefulness of the proposed method.

• Journal of Institute of Control, Robotics and Systems
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• v.15 no.3
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• pp.249-254
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• 2009

This paper studies the problem of pole placement by an LQ controller for system having two distinct real poles. Using the so-called Pole's Moving Range (PMR) drawn in the s-plane and relational equations between closed-loop system poles and weighting matrices, we calculate the state weighting matrix to move two distinct real poles to a pair of complex poles. By numerical examples, we show that the proposed method is applied to improve system performance.

• Proceedings of the KIEE Conference
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• 1989.11a
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• pp.407-410
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• 1989

Optimizing transient response for both tracking reference signals and disturbance rejection is determined by the poles and zeros of the transfer function. Thus, optimal pole assignment and how should weighting matrix for the performance index be chosen is very important to achieve optimum transient response. This paper focus its attention on the choosing and analysis of weighting matrix for optimum pole assignment. Optimum pole assignment is defined for linear time-invariant continuous systems.