• Title/Summary/Keyword: Robust root-locus

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Intelligent PID Controller Design Using Root-Locus Analysis for Systems with Parameter Uncertainties (불확실한 파라미터를 갖는 시스템을 위한 근궤적법을 이용한 지능형 PID 제어기 설계)

  • Shin, Young-Joo
    • Journal of the Korean Society for Precision Engineering
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    • v.25 no.10
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    • pp.67-76
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    • 2008
  • In this research, a simple technique for designing PID controller, which guarantees robust stability for two-mass systems with parameter uncertainties as well as rigid-body behavior and zero steady-state error,is described. As well, such a PID controller is designed to mate two important frequencies, at which the given system is excited, very close so that an appropriate reference profile generated by using command shaping techniques can cover those two frequencies. Root-locus analysis. which shows traces of closed-loop poles for the given system, is used to design this PID controller. Finally, feedforward controller is added to improve tracking performance of the closed-loop system. Simulation for a system with a flexible mode and parameter uncertainties is executed to prove the feasibility of this technique.

The Combined Classical/Modern Technique for Optimal Fesign of Robust Motion Controller (강인한 운동제어기의 최적 설계를 위한 고전적 기법과 현대적 기법의 결합)

  • 김삼수
    • 제어로봇시스템학회:학술대회논문집
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    • 1990.10a
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    • pp.485-492
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    • 1990
  • This paper propose a optimal design method for robust notion controllers of under-water vehicles using the combined technique between classical and modern theories. The proposed method is presented which utilizes classical control methods to obtain a good robustness and modern control methods to set optimal gains. LQ, SVD, multivariable frequency analysis and Bode-Root Locus (BRL) plot are used.

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Time-Varying Sliding Mode Following Root Locus for Higher-Order Systems (고차 시스템을 위한 근궤적을 따르는 시변 슬라이딩 모드)

  • Kim, Ga-Gue;Choi, Bong-Yeol
    • Journal of Institute of Control, Robotics and Systems
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    • v.5 no.4
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    • pp.379-384
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    • 1999
  • In this paper, we present a new time-varying sliding surface to achieve fast and robust tracking of higher-order uncertain systems. The surface passes through an initial error, and afterwards, it moves towards a predetermined target surface by means of a variable named by sliding surface gain and its intercept. Specifically, the sliding surface gain is determined so that its initial value can minimize a shifting distance of the surface and that the system roots in sliding mode can follow certain stable trajectories. The designed sliding mode control forces the system errors to stay always on the proposed surface from the beginning. By this means, the system remains insensitive to system uncertainties and disturbances for the whole time. To illustrate the effectiveness of the proposed method, the comparative study with conventional time-invariant sliding mode control is performed.

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Regulation control of a dc motor by ϵ-PID controller based on the frequency response analysis

  • Alhassan Dodo Adamou Soudeize;Ji-Sun Park;Ho-Lim Choi
    • Journal of IKEEE
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    • v.27 no.4
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    • pp.391-398
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    • 2023
  • In this paper, we propose an alternative analysis to regulate DC motors using a PID controller with a gain scaling factor. We start by providing a systematic design method for selecting the PID gains of our proposed controller by seeing the effect of ϵ on damping ratio, overshoot and settling time from the frequency response analysis. With the help of matlab (simulink), We proceed to show that the proposed controller provides robust stability against system parameter uncertainty and the effect of the gain scaling factor on steady-state error. The validity of our control method along with the analysis is verified with the simulation results.

Robust PID $\times$ (n-1) Stage PD Controller

  • Numsomran, Arjin;Julsereewong, Prasit;Ukakimaparn, Prapart;Trisuwannawat, Thanit;Tirasesth, Kitti
    • 제어로봇시스템학회:학술대회논문집
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    • 1999.10a
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    • pp.298-301
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    • 1999
  • This paper presents a design technique based on the root locus method fur a class of $n^{th}$ order plants using PID (Proportional-Integral-Derivative) x (n-1) stage PD controller. It is intended to satisfy both transient and steady state response specifications. This controller can be used instead of a conventional PID controller for the higher order plants to obtain better performances. The controlled system is approximated as a stable and robust second order controlled system. Only adjusting the controller gain, the desired performances of the controlled system are satisfied. For the stable plant including the plant with small dead time, the controlled system is made robustly stable. In case of the unstable plant, when the controller gain is adjusted higher than the critical value, the unstable plant can also be made stable. Robustness properties given by this controller proposed in this paper have also been demonstrated by numerical examples.

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PID $\times$ (n-1) Stage PD Controller for SISO Systems

  • Prasit, Julseeewong;Prapart, Ukakimaparn;Thanit, Trisuwannawat;Anuchit, Jaruvanawat;Kitti, Tirasesth
    • 제어로봇시스템학회:학술대회논문집
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    • 1998.10a
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    • pp.407-412
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    • 1998
  • A design technique based on the root locus approach for the SISO (Single-Input Single-Output) systems using PID (Proportional-Integral-Derivative) ${\times}$ (n-1) stage PD as a controller for the n$\^$th/ order plant is presented. The controller is designed based on transient and steady state response specifications. This controller can be used instead of a conventional PID controller. The overall system is approximated as a stable and robust second order system. The desired performances are achieved by increase the gain of the controller. In addition, the controller gain can be adjusted to obtain faster response with a little overshoot. The simulation results show the merits of this approach.

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Trajectory Tracking Controller for Semiconductor Equipment Motors based on PI Observer (PI 관측기 기반 반도체 장비 모터의 궤적 추종 제어기 설계)

  • Yun Seong Cho;Hyeon Jun Choi;Sang Min Jeon;Ji Hoon Shin;Jae Young Lee;Bum Joo Lee;Young Ik Son
    • Journal of the Semiconductor & Display Technology
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    • v.22 no.2
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    • pp.96-103
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    • 2023
  • This paper presents a robust position tracking controller for a motor used in semiconductor equipment, utilizing the motor angle measurement. Precise position control is challenging due to the presence of uncertainties in various motor applications. The proposed controller consists of a PD (Proportional-Derivative) controller and a PIO (Proportional-Integral Observer) to estimate the system's state and equivalent disturbance compensating for the uncertainties. Since the stability alternates as the observer gain increases, we have investigated it through the closedloop root locus under the system parameters change. The analysis has showed that the inertia of the motor is the main parameter that affects it, and by adjusting the control gain appropriately, the system can be rendered to be stable even when the inertia of the motor changes. The effectiveness of the proposed control algorithm is validated through computer simulations, followed by a comparison of its performance with the results of a previous study.

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Structural vibration control using $H_{\infty}$ control theory : unceratinty model ($H_{\infty}$제어이론을 이용한 구조진동제어 - 불확실성 모델)

  • 송병석
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 1995.04a
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    • pp.240-245
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    • 1995
  • 제어이론의 역사적 발전사를 고찰해보면 1930년대부터 1960년대까지를 고전 제어(classical control) 시대로 분류되고 이때 주로 사용되었던 용어들은 주파수역(frequency domain)에서 사용된 개념인 극점(pole), 영점(zero), Nyquist, 근궤적(root-Locus) 선도(plot)등으로 대표된다. 그 다음단계인 현대 제어(modern control) 시대 (1960년대-1980년대)때는 새로운 개념들이 도입 되었는데 시간역(time domain)에서 사용되는 상태공간(state-space) 모델, 가제어성(controllability), 가관측성(observability), Kalman 필터, LQG 제어 등이다. 1980년대부터 현재까지를 강인제어(robust control) 시대로 분류하는데 이것의 특징들은 극점이나 영점 대신 상태공간 모델을 사용하여 주파수역에서 정의되는 개념들인 H$_{\infty}$ 합성법, .$\mu$ 해석법, LQG/LTR 및 QFT, Lyapunov 등으로 대표된다. 현대제어시대때는 제어기 K는 공칭 플랜트 모델 G$_{0}$를 기준으로 설계되었으나 실제로 공칭 플랜트 모델은 실제 플랜트와 항상 같을 수가 없었다. 따라서 실제 플랜트 G는 G=G$_{0}$ + .DELTA.G로 표현되며 여기서 .DELTA.G는 플랜트 불 확실성(plant uncertainty), 즉 실제 플랜트와 공칭 플랜트의 차이를 나타낸 다. 이 플랜트 불확실성은 제어기가 실제 응용되어 사용되었을 때 제대로 작동하지 않는 주요 이유중에 하나이다. 이와 같은 상황에서 안정도 강인성 (stability robustness) 및 성능 강인성(performance rosubtness)의 보장은 상 당히 중요한 문제로 대두되었으며 주어진 플랜트 불확실성하에서 이러한 강이성들이 보장되는 제어이론들 중 H$_{\infty}$ 제어이론이 많이 연구/응용 되고 있다. 특히 공칭 플랜트 모델과 함께 사용되는 플랜트 모델과 함께 사용되는 플랜트 불확실성 모델은 직접적으로 성능 및 안정도에 영향을 미치므로 주의 깊게 선정해야 한다.

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