• Journal of the Korea Academia-Industrial cooperation Society
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• v.21 no.1
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• pp.20-27
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• 2020

In general, a nonlinear system is linearized in the form of a multiplication of the 1st and 2nd order system. This paper reports a design method of a weighting matrix and control law of LQ control to move the double poles that have a Jordan block to a pair of complex conjugate poles. This method has the advantages of pole placement and the guarantee of stability, but this method cannot position the poles correctly, and the matrix is chosen using a trial and error method. Therefore, a relation function (𝜌, 𝜃) between the poles and the matrix was derived under the condition that the poles are the roots of the characteristic equation of the Hamiltonian system. In addition, the Pole's Moving-range was obtained under the condition that the state weighting matrix becomes a positive semi-definite matrix. This paper presents examples of how the matrix and control law is calculated.

• Journal of the Korea Institute of Military Science and Technology
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• v.21 no.4
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• pp.437-446
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• 2018

This paper describes the real-time logic implementation of orthogonal matching pursuit(OMP) algorithm for compressive sensing digital receiver. OMP contains various complex-valued linear algebra operations, such as matrix multiplication and matrix inversion, in an iterative manner. Xilinx Vivado high-level synthesis(HLS) is introduced to design the digital logic more efficiently. The real-time signal processing is realized by applying dataflow architecture allowing functions and loops to execute concurrently. Compared with the prior works, the proposed design requires 2.5 times more DSP resources, but 10 times less signal reconstruction time of $1.024{\mu}s$ with a vector of length 48 with 2 non-zero elements.

• 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 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 the Korea Society of Computer and Information
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• v.16 no.5
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• pp.101-107
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• 2011

The optimum weight vector is studied to remove interference and jamming signals in adaptive array antenna system. The optimum weight vector is calculated to apply a minimum variance algorithm and cost function in linearly constrained conditions, and accurately estimates target's signal. Adaptive array antenna system is the system which improves signal to noise ratio(SNR) and decreases interference and jammer power. Adaptive array antenna system delays at tap output of antenna array element. Each tap finally makes the complex signal of one in multiplier complex weight. In order to obtain optimum's weight calculation, optimum weight vector is used in this paper. After simulation, resolution is increased below $3^{\circ}$, and sidelobe is decreased about 10 dB.