• The Transactions of the Korean Institute of Electrical Engineers D
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• v.51 no.11
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• pp.483-493
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• 2002

The damping ratio ${\xi}$ of the unit-step response of a second-order discrete system is a function of only the location of the closed-loop poles and is not directly related to the location of the system zero. However, the peak overshoot of the response is the function of both the damping ratio ${\xi}$ and an angle ${\alpha}$, which is the phasor angle of the damped sinusoidal response and is determined by the relative location of the zero with respect to the closed-loop poles. Therefore, if the zero and the open-loop poles are relatively adjusted, through pole-zero cancellation, to maintain the desired (or designed) closed-loop poles, the damping ratio ${\xi}$ will also be maintained, while the angle ${\alpha}$ changes. Accordingly, when the closed-loop system poles are fixed, the peak overshoot is considered as a function of the angle ${\alpha}$ or the system zero location. In this paper the effects of the relative location of the zero on the system performance of a second-order discrete system is studied, and a design method of digital compensator which achieves a minimum peak overshoot while maintaining the desired system mode and the damping ratio of the unit step response is presented.

• Proceedings of the KIEE Conference
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• 1999.11c
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• pp.512-514
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• 1999

The damping ratio $\zeta$ of a continuous 2nd order response which passes all the points of the discrete response of a 2nd order discrete system(envelope curve) is a function of only the location of the closed-loop pole and ie not at all related to the location of the zero. And the peak overshoot of the envelope curve is uniquely specified by the damping ratio $\zeta$, which is a function of solely the closed-loop pole location, and the angle $\alpha$ which is determined by the relative location of the zero with respect to the closed-loop complex pole. Therefore, if the zero slides on the real axis with the closed-loop complex poles being fixed, then the angle $\alpha$ changes however the damping ratio $\zeta$ does not. Accordingly, when the closed-loop system poles are fixed, the peak overshoot is function of $\alpha$ or the system zero. In this thesis the effects of the relative location of the zero on the system performance of a second order discrete system is studied.

• Transactions on Control, Automation and Systems Engineering
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• v.2 no.4
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• pp.262-267
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• 2000

In this paper, the magnitude of undershoot and overshoot in a prototype second order system with one positive real zero is computed by the analytic methods. Also, it will be shown that the peak times of the undershoot and overshoot can be calculated using the impulse and step response of the second order system. Three different cases are investigated: underdamped(p<ζ<1), critically damped(ζ=1) and overdamped(ζ>1) cases. We deal with the undamped(ζ=0) case as a special case of the underdamped. And a compensation method is proposed to reduce undershoots of the nonmininmun phase system using feedforward compensator.

• Proceedings of the KIEE Conference
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• 2002.11c
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• pp.382-386
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• 2002

The damping ratio $\zeta$ of the unit-step response of a second-order discrete system is a function of only the location of the closed-loop poles and is not directly related to the location of the system zero. However, the peak overshoot of the response is the function of both the damping ratio $\zeta$ and an angle $\alpha$, which is the phasor angle of the damped sinusoidal response and is determined by the relative location of the zero with respect to the closed-loop poles. Accordingly, when the closed-loop system poles are fixed, the peak overshoot is considered as a function of the angle $\alpha$ or the system zero location. In this paper the effects of the relative location of the zero on the system performance of a second-order discrete system is studied, and a design method of digital compensator which achieves arbitrary steady-state response with minimum peak overshoot while maintaining the desired system mode and the damping ratio of the unit step response is presented.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.65 no.11
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• pp.1854-1859
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• 2016

Consider a linear fourth-order system with no zero that is represented in terms of four specific parameters: two damping ratios and two natural frequencies. We investigate several interesting questions about the maximum overshoot of the system with respect to the four-tuple parameters. Some remarkable results are presented.

• 제어로봇시스템학회:학술대회논문집
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• 2003.10a
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• pp.301-306
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• 2003

PID controller is applied mostly to two-order system. In third-order or higher- system, it's impossible to get high response quality because of having more zero point than the number of zero point being in the PID controller. To solve those, Jung & Dorf suggested a new type of PIDA controller and solved problen of a third-order system. But, as the result of getting step response using PIDA controller, rising time is very quickly but wide overshoot is happened. Beside designing PIDA controller with using CDM(Coefficient Diagram Method) suggested by shunji manabe. But, In Performance standard, CDM decreases overshoot to desired but rising time is very slow. Therefore this paper suggest a PD-PIDA controller for low overshoot with PD type Pre-compensator. This paper applied designed PD-PIDA controller to position control of 3-Phase induction motor.

• 제어로봇시스템학회:학술대회논문집
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• 2005.06a
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• pp.1521-1523
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• 2005

PID controller is applied mostly to two-order system. In third-order or higher- system, it's impossible to get high response quality because of having more zero point than the number of zero point being in the PID controller. To solve those, Jung & Dorf suggested a new type of PIDA controller and solved problen of a third-order system.. But, as the result of getting step response using PIDA controller, rising time is very quickly but wide overshoot is happened. Beside designing PIDA controller with using CDM(Coefficient Diagram Method) of Shunji Manabe decreases overshoot to desired but rising time is very slow. Therefore this paper suggest a I-PDA controller for low overshoot and fast responsibility. This paper applied designed PD-PIDA controller to position control of 3-Phase induction motor.

• Structural Engineering and Mechanics
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• v.65 no.1
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• pp.91-98
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• 2018

Three structure-dependent integration methods with no numerical dissipation have been successfully developed for time integration. Although these three integration methods generally have the same numerical properties, such as unconditional stability, second-order accuracy, explicit formulation, no overshoot and no numerical damping, there still exist some different numerical properties. It is found that TLM can only have unconditional stability for linear elastic and stiffness softening systems for zero viscous damping while for nonzero viscous damping it only has unconditional stability for linear elastic systems. Whereas, both CEM and CRM can have unconditional stability for linear elastic and stiffness softening systems for both zero and nonzero viscous damping. However, the most significantly different property among the three integration methods is a weak instability. In fact, both CRM and TLM have a weak instability, which will lead to an adverse overshoot or even a numerical instability in the high frequency responses to nonzero initial conditions. Whereas, CEM possesses no such an adverse weak instability. As a result, the performance of CEM is much better than for CRM and TLM. Notice that a weak instability property of CRM and TLM might severely limit its practical applications.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.41 no.3
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• pp.1-8
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• 2004

This paper proposes an LQ-PID controller to reduce errors occurring between input and output speeds in braking or emergency braking and to solve delay of speed or the excessive overshoot problems occurring at the speed control of induction motor. The conventional LQ controller is a method that move the poles in locations that satisfy design specifications such as overshoot and settling time etc. by state-feedback. So it may not be able to satisfy the overshoot requirement in case of the existence of zero in the closed loop transfer function. To attack this zero-problem it is presented a new design methodology of LQ-PID controller by introducing an analytic technique to eliminate the effect of zeros on the closed loop transfer function.

• Structural Engineering and Mechanics
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• v.65 no.1
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• pp.121-128
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• 2018

Three structure-dependent integration methods with no numerical dissipation have been successfully developed for time integration. Although these three integration methods generally have the same numerical properties, such as unconditional stability, second-order accuracy, explicit formulation, no overshoot and no numerical damping, there still exist some different numerical properties. It is found that TLM can only have unconditional stability for linear elastic and stiffness softening systems for zero viscous damping while for nonzero viscous damping it only has unconditional stability for linear elastic systems. Whereas, both CEM and CRM can have unconditional stability for linear elastic and stiffness softening systems for both zero and nonzero viscous damping. However, the most significantly different property among the three integration methods is a weak instability. In fact, both CRM and TLM have a weak instability, which will lead to an adverse overshoot or even a numerical instability in the high frequency responses to nonzero initial conditions. Whereas, CEM possesses no such an adverse weak instability. As a result, the performance of CEM is much better than for CRM and TLM. Notice that a weak instability property of CRM and TLM might severely limit its practical applications.