Robust Time-Delay Filter
Introduction
A variety of lightweight structures are characterized by significant residual vibration when they undergo slewing maneuvers. Development of techniques to result in quiescent states at the end of a maneuver is of great interest. Feedback and feedforward approaches have been studied to address this problem. This work details a simple technique to filter reference inputs to vibratory systems via a time-delay filter. The issue of robustness to modeling uncertainties is also addressed.
In this article, design of time-delay filter which cancel the underdamped poles of the system is
described.
A Java Applet is provided to illustrate the
time-delay and robust time-delay filter.
The parameters of the time-delay filter for the system
which is designed to cancel the underdamped poles of the system, are
The transfer function of the time-delay filter is
.
Uncertainties in estimated values of the damping and natural frequency of the system can result in significant residual vibrations. The filter can be desensitized to modeling errors by cascading two time-delay filter such as the ones designed above. The transfer function of the resulting time-delay filter is
.
Details of the development and analysis of results can be found in the materials cited in the section on references shown at the bottom of this page.
The sensitivity of the time-delay filter is illustrated by plotting the residual energy of the system as a function of the normalized uncertain stiffness.
Below is an Applet which illustrates the different control profiles. The spring stiffness can be chosen by using the rightmost drop-down list. The other drop-down list allows the selection of the control profile. The Start button starts the simulation. The Stop button can be used to stop the simulation at any point in time. Before selecting a new control profile or spring stiffness, the simulation must have stopped.
The work presented in this article has been described in more detail in the following publication:
- Singh, T. & Vadali, S. R. 1993. Robust Time-Delay Control. ASME Journal of Dynamic Systems, Measurement and Control, 115(2(A)), 303-306.
- Singh, T. & Vadali, S. R. 1995. Robust Time-Delay Control of Multimode Systems. International Journal of Control, 62(6), 1319-1339.