10.1. Role of Correctors: Precision-Stability Dilemma

The correction methods covered in this chapter refer to considerations of scalar behavior. It is fundamental to understand that the specifications stipulating the closed loop performances will be translated by the constraints on the frequency response of the open loop corrected system.

The search for a compromise between stability and rapidity generally leads to imposing, on the closed loop, a behavior similar to that of a second order system having conjugated complex number poles. The choice of the damping value ? is imposed by the required degree of stability. That is why it is indispensable to have a good knowledge of the relations between the parameters and the behavior of the second order systems in order to be able to use specifications defining the performances required from the closed loop final system. The general principle of a specification list is based on two points:

• interpretation of specifications in order to obtain the characteristics of a second order model of the closed loop needed;

• search for the constraints on the open loop introducing the behavior sought in closed loop.

For reasons of clarity, let us recall the main results of the previous chapter concerning the analysis of the behavior of systems.