ABSTRACT
Po= Pis[ I+ c + ~t/ Rf2-1 )e-1/r] (7-191) We see again (Fig. 7-59a) that Po experiences a sudden jump at t = 0, but now it only jumps "part way," proceeding the remaining amount on an exponential curve. The frequency response
Other systems, called phase-lead compensators, can have r 1 > r, and in fact we have already used two of these (the electrical version) in the system of Fig. 7-13. Many items of hardware that we need to use in dynamic systems have lagging behavior which may make them too slow for a certain application. We can often speed up the overall system by cascading the unavoidable lagging component with a suitably chosen lead compensator. Analysis (left for the problems) of these devices
gives the step and frequency reponses of Fig. 7-60. The step response again jumps up instantly, but now it overshoots and returns to steady-state on an exponential curve. The frequency response shows an amplitude ratio that increases with frequency before leveling off. This increase can counteract the decrease which is typical of "slow" hardware which we may want to speed up.
