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Analyzing noise-induced tracking errors in control systems with saturation: A stochastic linearization approach

Analyzing noise-induced tracking errors in control systems with saturation: A stochastic linearization approach
Lee, JuseungOssareh, Hamid. R.Eun, Yongsoon
DGIST Authors
Lee, JuseungOssareh, Hamid. R.Eun, Yongsoon
Issued Date
Adaptive control systemsBandwidthErrorsFeedback controlLinearizationSpurious signal noiseAsymptoticsFeedback control systemIn-controlMeasurement NoiseNoise bandwidthNonlinear instrumentationStochastic averagingStochastic linearizationTracking error analysisTracking errorsStochastic systems
Noise Induced Tracking Error (NITE) refers to the tracking error of the mean of the output in feedback control systems with nonlinear instrumentation subject to zero-mean measurement noise. Most of the previous work rely on the stochastic averaging for NITE analysis, the validity of which requires that the bandwidth of the zero mean measurement noise is much higher than that of the system. This is because the results obtained by stochastic averaging are asymptotic with respect to the noise bandwidth. Due to the asymptotic nature of the analysis tool, it is not straightforward to provide a quantitative argument for high bandwidth. An alternative method in the literature that can analyze NITE is stochastic linearization for random input, which is analogous to the well known describing function approach for sinusoidal input. Unlike stochastic averaging, stochastic linearization is not an asymptotic approximation. Therefore, analysis can be carried out for any given noise bandwidth. We carry out NITE analysis using stochastic linearization for a class of LPNI systems that are prone to NITE; identify the system conditions under which the averaging analysis of NITE may yield inaccurate results for a finite noise bandwidth; and prove that the results from the two methods agree as the noise bandwidth approaches infinity. In addition, an existing NITE mitigation strategy is extended based on the proposed method. Numerical examples are given to illustrate the results. © 2021 The Franklin Institute
Pergamon Press Ltd.
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
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Department of Electrical Engineering and Computer Science DSC Lab(Dynamic Systems and Control Laboratory) 1. Journal Articles


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