On some restrictions in parametric synthesis of PID controllers

The article highlights solving the problem of parametric synthesis of PID Controllers of integer and fractional orders. The methods of synthesis for the given margins and indices of the relative stability of PID Controllers of integral and fractional orders have been developed. There have been developed algorithms for calculating the limiting values of the controller differential gain, at which the boundary of the region of a given stability margin has a cusp. Applying the criterion for low-frequency disturbance compensation helps to define the limiting values of the relative stability margin and indices. To implement the proposed algorithms there have been developed the software in the environment of the Maple package of symbolic calculations. Application of the developed algorithms allows to narrow the search area for the PID Controllers optimal parameters.