Cited time in webofscience Cited time in scopus

Study of Noise-Induced Tracking Error Phenomenon in Systems with Anti-windups

Study of Noise-Induced Tracking Error Phenomenon in Systems with Anti-windups
Alternative Title
일반적인 구조의 Anti-windup 기법이 적용된 PI 제어시스템에서의 노이즈에 의한 추종 오차 현상 분석
Lee, Ju Seung
DGIST Authors
Lee, Ju SeungEun, Yong SoonKim, Jong Hyun
Eun, Yong Soon
Kim, Jong Hyun
Issued Date
Awarded Date
2015. 8
Measurement noiseAnti-windupPI controlNoise induced tracking errorSaturating actuatorNoise induced tracking error포화 동작기측정 노이즈PI 제어
PI controller has been widely used in various industrial fields and played important role of eliminating the tracking error. In PI controlled system with saturation actuator, method called “Anti-windup” has been used for avoiding undesirable phenomenon such as performance degradation, instability, and windup [2-3]. In PI controlled systems with anti-windup, tracking loss due to measurement noise has been recently discovered, where measurement noise persistently triggers anti-windup mechanism in a certain operation range that result in non-zero steady state tracking error, which was called “Noise Induced Tracking Error (NITE)” [10]. Such a system was analyzed under both zero-mean Gaussian noise and quantification of the tracking loss is given in terms of system parameters and noise standard deviation.
In this work, we show that NITE could occur in all PI controlled systems if both anti-windup and measurement noise exist, regardless of anti-windups. We also extend the existing results to a case with uniformly distributed noise. Using stochastic averaging approach, we quantify the noise induced tracking error with respect to system parameters and noise characteristics, and shows that the phenomenon of tracking loss occurs with uniformly distributed noise as well. Conditions under which the tracking loss occurs are derived. The result is compared with that under zero mean Gaussian noise with the same level of standard deviation.
We suggest two solutions to prevent NITE. One method is using a virtual saturation. We explain how effective the virtual saturation to mitigate NITE. An analysis of internal stability based on linear matrix inequalities is conducted on the system with a virtual saturation. The other method is changing static P gain to dynamic P gain. Dynamic P gain plays the role of eliminating an effect of noise in the systems. The result shows that NITE does not occur due to the two solutions. We also show the differences between two solutions. ⓒ 2015 DGIST
Table Of Contents
1.1 Motivation 1 --
1.2 Purpose 1 --
1.3 Outline 2 --
II. Problem statement 3 --
2.1 Anti-windups 3 --
2.2 Gaussian noise and uniformly distributed noise 5 --
III. Analysis 8 --
3.1 Transforming the system using stochastic averaging theory 8 --
3.1.1 Case I : Gaussian noise 9 --
3.1.2 Case II : uniform noise 10 --
3.2 Quantifying NITE 12 --
3.3 Examples 13 --
IV. Solutions 18 --
4.1 Virtual saturation 18 --
4.1.1 Virtual saturation limit 22 --
4.1.2 Stability base on LMI 24 --
4.2 Dynamic P gain 27 --
4.3 Result 31 --
V. Application 35 --
5.1 Electro-active polymer 35 --
5.2 Applying the solutions in the system 37 --
VI. Conclusion 41 --
VII. Appendix I 42 --
VIII. Appendix II 46 --
IX. Appendix III 49 --
X. Appendix IV 53 --
XI. Appendix V 56
Information and Communication Engineering
Related Researcher
  • 은용순 Eun, Yongsoon 전기전자컴퓨터공학과
  • Research Interests Resilient control systems; Control systems with nonlinear sensors and actuators; Quasi-linear control systems; Intelligent transportation systems; Networked control systems
Files in This Item:


기타 데이터 / 2.24 MB / Adobe PDF download
Appears in Collections:
Department of Electrical Engineering and Computer Science Theses Master


  • twitter
  • facebook
  • mendeley

Items in Repository are protected by copyright, with all rights reserved, unless otherwise indicated.