Experimental stability analysis of networked control systems with constant time-delays
T. Kniknie · TU/e Research Portal · 2006
To control a remote (dynamical) system, data networks can be used. This has some advantages, but also introduces a time-delay between the controller and the plant. Systems, that use a network to close the control loop, are called Networked Control Systems (NCSs). This research treats the experimental validation of the influence of constant time-delays on the stability of an NCS. Under certain assumptions concerning the properties of a network, a model is formulated, representing an NCS with constant time-delays. A second-order dynamical system (an inertia controlled by a PD controller) is used to analyze the stability properties for different controller gains and different constant time-delays. The stability analysis for this system shows that the maximum allowable velocity feedback gain for a stable system varies with the amount of delay in a remarkable manner. It increases until a delay δt = 0.25h, with h the sample time, and then decreases for increasing delay. This peak in the stability region can be explained with the aid of a Bode and Nyquist diagrams. The Bode and Nyquist diagrams show that a time-delay lowers the phase of the system response, but also the magnitude. At higher time-delays the decrease of the magnitude can not compensate for the phase lag anymore. To validate the stability analysis, experiments are performed. First, a suitable setup is chosen, based on the extent to which it represents a real NCS, the ease of use, reliability and accuracy. After comparing, the PATO experimental setup is chosen to conduct the experiments. The system parameters of the setup are estimated, based on Frequency Response Function (FRF) measurements. From the FRF measurements it can be concluded that besides a time-delay, due to discretization, more time-delay is present in the system, which will influence the stability properties. The measurements are conducted, using a step function in the position as reference profile for the motor. The stability of the system is evaluated experimentally by determining whether the error is constant. The final measurements do not show resemblance to the analysis of the model. The reason for this mismatch most probably is the presence of static friction in the setup. Consequently a step function is not a suitable reference profile, since the friction effects dominate. Another reason is that a velocity estimator and a lowpass filter are used in the experiments, but these are not included in the model. Therefore, the model may not be a good representation of the real setup. It is recommended to decrease the step in the time-delay, to obtain more measurement points. The method to determine the stability of the system has to be altered, because a step in the ii Abstract reference position results in static friction problems. A constant reference velocity may lead to better results. The model has to be reconsidered, because the velocity estimation and lowpass filter are not included in the model. It is interesting to also investigate the control performance properties, like bandwidth and settling time.