Section 8–7 / Zero-Placement Approach to Improve Response Characteristics 595Hence,
Clearly, ifGydis given, thenGynis fixed, butGyris not fixed, because Gc2is independ-
ent ofGyd.
It will be seen in Section 8–7 that, in such a two-degrees-of-freedom control system,
both the closed-loop characteristics and the feedback characteristics can be adjusted
independently to improve the system response performance.
Characteristics 8–7 Zero-Placement Approach to Improve Response
RESPONSE CHARACTERISTICS
We shall show here that by use of the zero-placement approach presented later in this
section, we can achieve the following:
The responses to the ramp reference input and acceleration reference input exhibit
no steady-state errors.
In high-performance control systems it is always desired that the system output follow
the changing input with minimum error. For step, ramp, and acceleration inputs, it is
desired that the system output exhibit no steady-state error.
In what follows, we shall demonstrate how to design control systems that will exhibit
no steady-state errors in following ramp and acceleration inputs and at the same time
force the response to the step disturbance input to approach zero quickly.
Consider the two-degrees-of-freedom control system shown in Figure 8–31. Assume
that the plant transfer function is a minimum-phase transfer function and is
given by
Gp(s)=K
A(s)
B(s)
Gp(s)
Gyn=
Gyd-Gp
Gp
Gyr=Gc2 Gyd+
Gp-Gyd
Gp
Gc 1 (s) Gp(s)R(s) Y(s)D(s)Gc 2 (s)++
++Figure 8–31
Two-degrees-of-
freedom control
system.