Tutorial 17: Control theory, Part 3

Control systems use feedback to help achieve the two goals of stabilizing a system and causing the system to perform well. Often it takes some time for the information about the system (or the state of the system) that is being "fed back" to reach the feeding information back to the controller, the problem of delays in feedback systems has, once again, come to the fore. In this paper, the author presents five complementary ways to analyze delays in the feedback loop when output feedback is used. These are (1) the standard Nyquist plot; (2) an extended Nyquist plot; (3) a discretized model; (4) a matrix version of the discretized model; and (5) an approximation using Pade approximants.