Lead/Lag compensator design for unstable delay processes based on new gain and phase margin specifications

This paper considers a lead/lag compensator design problem for a class of unstable delay processes based on a new set of gain and phase margin specifications. Due to the nature of the unstable system, both upper and lower gain margins are required to measure the true stability robustness with regard to gain change. In addition to a phase margin, such a combined margin problem leads to a set of nonlinear and coupled equations which have no analytical solution. Thus, an effective graphical method is developed such that the solution is determined from the intersections of the curves constructed by a transformed set of nonlinear equations. The tuning procedure is presented and examples are given for its illustration and comparison.