The industrial process is known to have a time delay in the loop. In practice, it is often the case that the magnitude of system time delays cannot be precisely determined. The magnitude of the time delay may change in an unpredictable manner depending on the process environment. A robust control system should be able to operate satisfactorily in the presence of the system time delays.
(a) Develop an m-file script to compute and plot the phase margin for the industrial process when the time delay, T, varies between 0 and 5 seconds. Use the pade function with a second-order approximation to approximate the time delay. Plot the phase margin as a function of the time delay.
(b) Determine the maximum time delay allowable for system stability. Use the plot generated in part (a) to compute the maximum time delay approximately.