Specifications for a control system design often involve certain requirements associated with the time response of the closed-loop system. The requirements are specified by the behaviour of the controlled variable or by the control error on well defined test signals. The most important test signal is a unit step on the input of the control system and requirements are placed on the behaviour of the controlled variable , as shown in Figure 7.8. The requirements for a unit step response are expressed in terms of the following standard quantities:
These standard quantities are measures of some properties of the control system. and essentially characterise the damping and and the speed, i.e. the dynamics of the control behaviour. The steady-state error as described in section 7.2 is a typical characteristic of the static behaviour.
These quantities describe the deviation of the step response from the ideal case described in section 7.1 and the goal of the design of a control system is to hold them as small as possible. In most cases one can restrict the values of the three quantities , and .