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:
is the magnitude of the overshoot after the first
crossing of the steady-state value (100%). This value is normally
expressed as a percentage of the steady-state value of the
controlled variable.
is the time required to reach the maximum
overshoot.
is the time for the controlled variable first to
reach and thereafter remain within a prescribed percentage
of the steady-state value. Common values of
are 2%, 3% or 5%.
is the time required to reach first the steady-state value
(100%). It may also be defined as the time to reach the vicinity
of the steady-state value particularly for a response with no
overshoot, e.g. the time between 10% and 90%. The 
rise
time
is defined as the time to first reach 50% of
the final value.
Similarly, the behaviour on step disturbances can be characterised as shown in Figure 7.9. Here likewise the terms 'maximum overshoot' and 'settling time' are defined.
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
.
