Minimax Time-Delay Filter
Introduction
The robust time-delay filters desensitizes the filter around the nomial values of the uncertain parameters. If knowledge about the range of uncertainty and the distribution of uncertaintly is know, it can be incorporated into the design process. The minimax filter is a technique to design time-delay filters which minimize the worst performance of the system over the entire range of uncertaintly.
In this article, design of time-delay filter which minimize the maximum maginitude of the
residual energy over the specified range of uncertainty is described.
A Java Applet is provided to illustrate the
Minimax time-delay filter.
The time-delay filtered system
includes uncertain parameters whose uncertainty is described by the equation
The optimization problem to be solved is to determine the parameters of the transfer function of the time-delay filter to minimize the maximum magnitude of the residual energy over the uncertain range as is shown schematically below.
.
Minimax Time-Delay filters are designed for a spring-mass system
where the spring stiffness is uncertain and lies in the range 0.7 to 1.3
with a nominal value of 1. The graph below illustrates that the minimax filter
significantly reduces the maximum magnitude of the residual energy
over the range of uncertainty for two and three time-delay filters.
.
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.
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., 2002. Minimax Design of Robust Controllers for Flexible Systems . Journal of Guidance, Control and Dynamics, 25(5), 868-875.
- Singh T., 2002. Minimax Design of Robust Controllers for Flexible Systems American Control Conference, May 8-10, Anchorage, Alaska.