Page 419 - Mechanical Engineers' Handbook (Volume 2)

410 Basic Control Systems Design

set of specifications for control system performance generally should include the following
considerations for given forms of the command and disturbance inputs:

1. Equilibrium specifications
(a) Stability
(b) Steady-state error
2. Transient specifications
(a) Speed of response
(b) Form of response
3. Sensitivity specifications
(a) Sensitivity to parameter variations
(b) Sensitivity to model inaccuracies
(c) Noise rejection (bandwidth, etc.)
In addition to these performance stipulations, the usual engineering considerations of
initial cost, weight, maintainability, and so on must be taken into account. The considerations
are highly specific to the chosen hardware, and it is difficult to deal with such issues in a
general way.
Two approaches exist for designing the controller. The proper one depends on the quality
of the analytical description of the plant to be controlled. If an accurate model of the plant
is easily developed, we can design a specialized controller for the particular application. The
range of adjustment of controller gains in this case can usually be made small because the
accurate plant model allows the gains to be precomputed with confidence. This technique
reduces the cost of the controller and can often be applied to electromechanical systems.
The second approach is used when the plant is relatively difficult to model, which is
often the case in process control. A standard controller with several control modes and wide
ranges of gains is used, and the proper mode and gain settings are obtained by testing the
controller on the process in the field. This approach should be considered when the cost of
developing an accurate plant model might exceed the cost of controller tuning in the field.
Of course, the plant must be available for testing for this approach to be feasible.

7.1 Performance Indices

The performance criteria encountered thus far require a set of conditions to be specified—
for example, one for steady-state error, one for damping ratio, and one for the dominant
time constant. If there are many such conditions, and if the system is of high order with
several gains to be selected, the design process can get quite complicated because transient
and steady-state criteria tend to drive the design in different directions. An alternative ap-
proach is to specify the system’s desired performance by means of one analytical expression
called a performance index. Powerful analytical and numerical methods are available that
allow the gains to be systematically computed by minimizing (or maximizing) this index.
To be useful, a performance index must be selective. The index must have a sharply
defined extremum in the vicinity of the gain values that give the desired performance. If the
numerical value of the index does not change very much for large changes in the gains from
their optimal values, the index will not be selective.
Any practical choice of a performance index must be easily computed, either analyti-
cally, numerically, or experimentally. Four common choices for an index are the following: