A Technical Note on a Semigraphical Synthesis Procedure

The problem of synthesizing a controller to yield a specified overall system phase margin requires specification of both the time constant (or constants) and the gain of the controller, but the choice of the two is not independent. A graphical technique is developed for plotting the relationship between the gain and the time constant in a straightforward manner. A logical criterion results upon which to base the controller design. The method is presented for a first order controller, but the approach may be extended to multiple time constant controllers. The method is applied in the frequency domain to linear elements. Phase shifting nonlinearities can be accommodated by judicious use of describing function results.