Time Delay Compensation in the Frequency Domain

It is well-known that the design of the control for a given plant becomes more difficult if there are time delays in the control loop. The classical approach in this situation is to try to extract the delay from the control loop and design the control for the delay-free plant. In this paper, the effects of the time delay in the controlled plant are analyzed in the frequency domain and filters are designed to counteract these effects. The perfect filter is not realizable and some approximations are suggested. From this viewpoint, the dynamics of the plant are not so relevant in such a way that the approach can be applied for any stable/unstable minimum phase/non-minimum phase plant. Another option is the use of a notch filter to reshape the frequency response and increase the phase margin of the controlled plant. Several examples illustrate the results.