• Journal of the Korean Institute of Telematics and Electronics
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• v.22 no.3
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• pp.91-94
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• 1985

A method optimizing selection of a state weighting matrix is presented. The state weight-ing matrix is chosen so that the closed-loop system responses closely match to the ideal model responses. An algorithm is presented which determines a positive semidefinite state weighting matrix in the linear quadratic optimal control design problem and an numerical example is given to show the effect of the present algorithm.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.19 no.2
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• pp.608-616
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• 2018

If a general nonlinear system is linearized by the successive multiplication of the 1st and 2nd order systems, then there are four types of poles in this linearized system: the pole of the 1st order system and the equal poles, two distinct real poles, and complex conjugate pair of poles of the 2nd order system. Linear Quadratic (LQ) control is a method of designing a control law that minimizes the quadratic performance index. It has the advantage of ensuring the stability of the system and the pole placement of the root of the system by weighted matrix adjustment. LQ control by the weighted matrix can move the position of the pole of the system arbitrarily, but it is difficult to set the weighting matrix by the trial and error method. This problem can be solved using the characteristic equations of the Hamiltonian system, and if the control weighting matrix is a symmetric matrix of constants, it is possible to move several poles of the system to the desired closed loop poles by applying the control law repeatedly. The paper presents a method of calculating the state weighting matrix and the control law for moving the equal poles with Jordan blocks to two real poles using the characteristic equation of the Hamiltonian system. We express this characteristic equation with a state weighting matrix by means of a trigonometric function, and we derive the relation function (${\rho},\;{\theta}$) between the equal poles and the state weighting matrix under the condition that the two real poles are the roots of the characteristic equation. Then, we obtain the moving-range of the two real poles under the condition that the state weighting matrix becomes a positive semi-finite matrix. We calculate the state weighting matrix and the control law by substituting the two real roots selected in the moving-range into the relational function. As an example, we apply the proposed method to a simple example 3rd order system.

• Journal of Mechanical Science and Technology
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• v.17 no.3
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• pp.329-335
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• 2003

EALQR (Linear Quadratic Regulate. design with Eigenstructure Assignment capability) has the capability of exact assignment of eigenstructure with the guaranteed margins of the LQR for MIMO (Multi-Input Multi-Output) systems. However, EALQR undergoes a restriction on the state-weighting matrix Q in LQR to be indefinite with respect to the region of allowable closedloop eigenvalues. The definiteness of the weighting matrix is closely related to the robustness property of a given system. In this paper, we derive a relation between the indefinite weighting matrix Q and the robustness property for EALQR. The modified frequency domain inequality, that could be guaranteed by EQLQR with an indefinite weighting matrix, is presented.

• 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 Electrical Engineering and Technology
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• v.10 no.1
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• pp.227-242
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• 2015

This paper proposes a weighting factor optimization method in predictive control algorithm for torque ripple reduction in an induction motor fed by an indirect matrix converter (IMC). In this paper, the torque ripple behavior is analyzed to validate the proposed weighting factor optimization method in the predictive control platform and shows the effectiveness of the system. Therefore, an optimization method is adopted here to calculate the optimum weighting factor corresponds to minimum torque ripple and is compared with the results of conventional weighting factor based predictive control algorithm. The predictive control algorithm selects the optimum switching state that minimizes a cost function based on optimized weighting factor to actuate the indirect matrix converter. The conventional and introduced weighting factor optimization method in predictive control algorithm are validated through simulations and experimental validation in DS1104 R&D controller platform and show the potential control, tracking of variables with their respective references and consequently reduces the torque ripple.

• 제어로봇시스템학회:학술대회논문집
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• 2005.06a
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• pp.2081-2086
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• 2005

This paper proposes the receding horizon $H_{\infty}$ predictive control (RHHPC) for systems with a state-delay. We first proposes a new cost function for a finite horizon dynamic game problem. The proposed cost function includes two terminal weighting terns, each of which is parameterized by a positive definite matrix, called a terminal weighting matrix. Secondly, we derive the RHHPC from the solution to the finite dynamic game problem. Thirdly, we propose an LMI condition under which the saddle point value satisfies the well-known nonincreasing monotonicity. Finally, we shows the asymptotic stability and $H_{\infty}$-norm boundedness of the closed-loop system controlled by the proposed RHHPC. Through a numerical example, we show that the proposed RHHC is stabilizing and satisfies the infinite horizon $H_{\infty}$-norm bound.

• 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.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.33B no.3
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• pp.9-16
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• 1996

LQ-servo is a robustness guaranteed multivariable controller design method based on the LQR structure to improve command following with output feedback. in this paper we introduce a weighting factor on the low frequency part of the state weighting matrix in the performance index in order to increase the low frequency gain of loop transfer function matrix T(s) in the loop shaping design method.

• 제어로봇시스템학회:학술대회논문집
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• 2002.10a
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• pp.83.4-83
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• 2002

$\bullet$ We present a state-feedback RHC for discrete-time TS fuzzy systems with input constriants. $\bullet$ The controller employ the current and one-step past information on the fuzzy weighting functions. $\bullet$ It is obtained from the finite horizon optimization problem with the invariant ellipsoid constraint $\bullet$ Under parameterized LMI conditions on the terminal weighting matrix $\bullet$ The closed-loop system stability is guaranteed. $\bullet$ The parameterized linear matrix inequalities are relaxed to a finite number of solvable LMIs.

• Nuclear Engineering and Technology
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• v.29 no.1
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• pp.68-77
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• 1997

The reactor power control system is described in the fashion of the order increased LQR system. To obtain the optimal state feedback gain vectors, the weighting matrix of the performance function should be determined. Since the contentional method has some limitations, stochastic searching methods are investigated to optimize the LQR weighting matrix using the modified genetic algorithm combined with the simulated annealing, a new optimizing tool named the hybrid MGA-SA is developed to determine the weighting parameters of the LQR system. This optimizing tool provides a more systematic approach in designing the LQR system. Since it can be easily incorporated with any forms of the cost function, it also provides the great flexibility in the optimization problems.