Page 424 - Mechanical Engineers' Handbook (Volume 2)

8 Compensation and Alternative Control Structures 415

nized are series compensation, parallel (or feedback) compensation, and feedforward com-
pensation. The three structures are loosely illustrated in Fig. 34, where we assume the final
control elements have a unity transfer function. The transfer function of the controller is
G (s). The feedback elements are represented by H(s), and the compensator by G (s). We
1
c
assume that the plant is unalterable, as is usually the case in control system design. The
choice of compensation structure depends on what type of specifications must be satisfied.
The physical devices used as compensators are similar to the pneumatic, hydraulic, and
electrical devices treated previously. Compensators can be implemented in software for dig-
ital control applications.

8.1 Series Compensation
The most commonly used series compensators are the lead, the lag, and the lead–lag com-
pensators. Electrical implementations of these are shown in Fig. 35. Other physical imple-
mentations are available. Generally, the lead compensator improves the speed of response;
the lag compensator decreases the steady-state error; and the lead–lag affects both. Graphical
aids, such as the root-locus and frequency response plots, are usually needed to design these
compensators (Ref. 1, Chapter 8; Ref. 2, Chapter 9; and Ref. 4, Chapter 11).

8.2 Feedback Compensation and Cascade Control
The use of a tachometer to obtain velocity feedback, as in Fig. 24, is a case of feedback
compensation. The feedback compensation principle of Fig. 3 is another. Another form is
cascade control, in which another controller is inserted within the loop of the original control
system (Fig. 36). The new controller can be used to achieve better control of variables within
the forward path of the system. Its set point is manipulated by the first controller.
Cascade control is frequently used when the plant cannot be satisfactorily approximated
with a model of second order or lower. This is because the difficulty of analysis and control
increases rapidly with system order. The characteristic roots of a second-order system can
easily be expressed in analytical form. This is not so for third order or higher, and few
general design rules are available. When faced with the problem of controlling a high-order
system, the designer should first see if the performance requirements can be relaxed so that
the system can be approximated with a low-order model. If this is not possible, the designer
should attempt to divide the plant into subsystems, each of which is second order or lower.
A controller is then designed for each subsystem. An application using cascade control is
given in Section 11.

8.3 Feedforward Compensation
The control algorithms considered thus far have counteracted disturbances by using mea-
surements of the output. One difficulty with this approach is that the effects of the disturbance
must show up in the output of the plant before the controller can begin to take action. On
the other hand, if we can measure the disturbance, the response of the controller can be
improved by using the measurement to augment the control signal sent from the controller
to the final control elements. This is the essence of feedforward compensation of the distur-
bance, as shown in Fig. 34c.
Feedforward compensation modified the output of the main controller. Instead of doing
this by measuring the disturbance, another form of feedforward compensation utilizes the