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Technical Briefs

Compensating Random Time Delays in a Feedback Networked Control System With a Kalman Filter

[+] Author and Article Information
Alexander C. Probst

Department of EECS, Oregon State University, Corvallis, OR 97331; Institute for System Dynamics, Universität Stuttgart, Stuttgart 70569, Germany

Mario E. Magaña

Department of EECS, Oregon State University, Corvallis, OR 97331

Oliver Sawodny

Institute for System Dynamics, Universität Stuttgart, Stuttgart 70569, Germany

J. Dyn. Sys., Meas., Control 133(2), 024505 (Mar 09, 2011) (6 pages) doi:10.1115/1.4003094 History: Received June 19, 2009; Revised June 15, 2010; Published March 09, 2011; Online March 09, 2011

This paper presents procedures to handle time delays in a feedback control loop in which both measurement and control signals are sent through a network, where random time delays occur. Even when time stamps are utilized, for example, the control signal time delay still must be estimated. Using a Padé approximation and a Kalman filter, we can estimate the mean time delay. Furthermore, methods are described to estimate the time delay of every packet instead of the mean for the measurement channel, which greatly enhances the performance of the Padé approximation approach. This is done by matching the measurements to the expected measurements provided by the filter with maximum likelihood. The methods are applied to an inverted pendulum to assess performance.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

Structure of closed loop with networks causing random time delays and packet loss

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Figure 2

Illustration of time delay uncertainty versus measurement uncertainty

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Figure 3

An unstable inverted pendulum on a horizontally movable cart, which has its mass above its pivot point, must be actively balanced in order to remain upright

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Figure 4

Influence of different sampling times on the basis of a setpoint change in x with random exponential time delay with mean τ¯sc=0.25 s and with T=0.02 s

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Figure 5

Inverted pendulum in x and θ without time delay

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Figure 6

Simulation with T=0.02 s and a random exponential time delay with mean τ¯sc=τ¯ca=0.04 s=2T without the network link showing benefits of time stamps

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Figure 7

Padé approximation compensating for input time delay τca while using time stamps for the output time delay

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Figure 8

Using only maximum likelihood allocation to estimate measurement time delay with τ¯ca=τ¯sc=0.04 s and without time stamps

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Figure 9

Histogram of actual and estimated time delays with τ¯ca=τ¯sc=0.04 s

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Figure 10

Time delays both in input and output channels and a Padé approximation for the estimation and compensation of the total time delay

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Figure 11

Estimation of the total time delay τ¯sc+τ¯ca

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Figure 12

Inverted pendulum with time delays both in input and output channels and a Padé approximation for estimation and compensation of the total time delay

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