• Journal of Institute of Control, Robotics and Systems
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• v.15 no.8
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• pp.804-811
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• 2009

This paper deals with the relationship between zeros and step response of the second and third order LTI(Linear Time Invariant) SISO(Single-Input and Single-Output) systems. As well known, if a system has a single unstable zero, it shows the step response with undershoot and, on the other hand, a stable zero slower than the dominant pole causes the system to have the step response with overshoot. Generally, in the case of a system with two unstable real zeros, it is known to have B type undershoot[7]. But there are many complex cases of the step response extrema corresponding to zeros location in third order systems. This paper investigates the whole cases depending on DC gains of the additive equivalence systems and they are to be classified by the region of zeros which are related to the shape of the step response. Moreover, monotone nondecreasing conditions are proposed in the case of complex conjugate zeros as well as the case of two stable zeros.

• International journal of advanced smart convergence
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• v.6 no.4
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• pp.33-40
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• 2017

In this paper, complex quadruplet zeros of microwave filter systems are investigated. For the cascaded systems the chain matrices are most conveniently used to derive the voltage transfer function of Laplace transform with cascaded two-port subsystems. The convenient relations of transfer function and chain matrix are used in order to find the transmission zeros. Starting from a ladder network, we introduced a crossed-coupled lumped element, in order to show the improved response of bandpass filter. By solving the transmission zero characteristic equation derived from the cascaded subsystems, we found the zeros of filter system with externally cross-coupled lumped elements. With the cross-coupled elements of capacitors, the numerator polynomial of system transfer function is used to locate the quadruplet zeros in complex plane. When the two pairs of double are on the zeros -axis, with the perturbed values of element, we learned that the transition band of lowpass filter is improved. By solving the characteristic equation of cascaded transfer function, we can obtain the zeros of the cross-coupled filter system, as a result of perturbed values on lumped element.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.47.2-47
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• 2001

This paper is concerned with the limiting zeros, as the sampling period tends to zero, of a multivariable discrete-time system composed of an approximate fractional-order hold (AFROH), a continuous-time plant and a sampler in cascade. An approximate fractional-order hold is proposed to implement fractional-order hold (FROH) and is applied to instead of the zero-order hold (ZOH). The implementing problem of the fractional-order hold is overcome. The properties of the limiting zeros are studied and the location problem of them is solved. In addition, a stability condition of the zeros for sufficiently small sampling period is derived ...

• International journal of advanced smart convergence
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• v.7 no.1
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• pp.7-14
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• 2018

In this paper, we derive a transfer function of cross-coupled microwave filter systems by using a characteristics of chain matrices. Depending on the lumped element of capacitor or inductor, the cross-coupled system is negatively- or positively system. We used a ladder network as a starting system composed of several subsystems connected in chain. Each subsystem is descrived by Laplace impedance. By solving the transmission zero characteristic equation derived from the cascaded subsystems, we can find the zeros of filter system with externally cross-coupled lumped elements. With the cross-coupled elements of capacitors, the numerator polynomial of system transfer function is used to locate the quadruplet zeros in complex plane. We show the polynomoials of numerator and denominator of cascaded transfer function, obtaining the zeros of the cross-coupled system.

• 제어로봇시스템학회:학술대회논문집
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• 2002.10a
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• pp.44.4-44
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• 2002

This paper investigates some conditions such that zeros are added to the system with a monotone nondecreasing step response in order to hold the monotonicity as before. Two conditions are presented for the cases that a real zero and complex conjugate zeros are added to the system satisfying the monotonicity condition, respectively. To exemplify the proposed results, some simple examples via computer simulation are shown in this paper. Proposed conditions can be easily used in the control system design since they are only formulated in terms of pole-zero configurations.

• Journal of Institute of Control, Robotics and Systems
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• v.16 no.4
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• pp.313-318
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• 2010

This paper deals with the relationship between zeros and step response of the second and third order LTI (Linear Time Invariant) SISO (Single-Input and Single-Output) systems with complex poles. Although it has been known that the maximum number of local extrema is less than the number of zeros in the system with only real poles[8], some cases with complex poles are shown in this paper to have many local extrema. This paper proposes monotone nondecreasing conditions and describes the relationship between the transient response and the number of local extrema in step response with each region of zeros.

• 제어로봇시스템학회:학술대회논문집
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• 2003.10a
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• pp.30-35
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• 2003

In the control system analysis and synthesis, the nonminimum phase system has some difficulties due to the undershoot behaviour and the constrained sensitivity function. SISO problems has been widely investigated in the literatures, and it is well known that the undershoot cannot be eliminated by any linear feedback control. However, the undershoot compensation in MIMO system is less studied, and this paper is to deal with the zero property and the nonminimum phase behaviour of the MIMO system. Firstly, some definitions of the zeros will be introduced. Second, some systems including nonminimum phase transmission zeros are exemplified to show that the undershoot behaviour could be eliminated by a linear feedback in MIMO systems.

• Proceedings of the KIEE Conference
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• 2005.10b
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• pp.158-160
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• 2005

This paper presents a new approach to the problem of designing a cascaded three-parameters controller for a given linear time invariant (LTD plant in unity feedback system. We consider a proportional-integral-derivative (PID) and a first-order controller with specified overshoot and settling time. This problem is difficult to solve because there may be no analytical solution due to the use of low-order controller and furthermore. the zeros of controller just appear in the zeros of feedback system. The key idea of our method is to impose a constraint on the controller parameters so that the zeros of resulting controller are distant from the dominant pole of closed-loop system to the left as far as the given interval. Two methods realizing the idea are suggested. We have employed the characteristic ratio assignment (CRA) in order to deal with the time response specifications. It is noted that the proposed methods are accomplished only in parameter space. Several illustrative examples are given.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.55 no.1
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• pp.20-23
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• 2006

This paper presents a new approach to the problem of designing a cascaded three-parameters controller for a given linear time invariant (LTI) plant in unity feedback system. We consider a proportional-integral-derivative (PID) and a first-order controller with the specified overshoot and settling time. This problem is difficult to solve because there may be no analytical solution due to the use of low-order controller. Furthermore, the zeros of controller just appear in the zeros of feedback system. The key idea of our method is to impose a constraint on the controller parameters so that the zeros of resulting controller are distant from the dominant pole of closed-loop system to the left as far as the given interval. Two methods realizing the idea are suggested. We have employed the characteristic ratio assignment (CRA) in order to deal with the time response specifications. It is noted that the proposed methods are accomplished only in parameter space. Several illustrative examples are given.

• International Journal of Internet, Broadcasting and Communication
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• v.6 no.1
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• pp.9-12
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• 2014

We present a mathematical method for calculation of transmission zero locations, determining a filtering characteristics of two-port systems. By adjusting element values based on the zero locations, the frequency-selectivity is characterized. The characteristic polynomial of ladder networks in externally-loaded feed-forward systems is considered by adopting chain matrices for subsystems. This method can be extended to other types of lumped systems with cross-coupled sections. We find out the zeros by solving characteristics polynomials of closed-form expressions in terms of Laplace impedances of elements. The pairs of complex zeros are shown to be solely from the cross-coupled portion of the system.