1. Aims of Control Systems Analysis and Design¶
1.1 Analysis¶
Objectives: Determination of the following system characteristics:
degree and extent of system stability
steady-state (d-c) performance (accuracy)
transient performance
Methods of analysis
determine differential equations or transfer functions for each component
choose suitable representation, e.g. block diagram
formulate system model by connecting components together
determine system response.
For the latter there are several methods used:
Direct solution to find steady-state and transient solutions. (Difficult with high order systems – relative stability difficult to study in time domain)
Four graphical methods (described in Section 2)
Root locus
Bode diagram
Nyquist diagram
Nichols chart
(The last three are all frequency response methods)
1.2 Design Objectives¶
To meet performance specifications. Performance specifications are constraints on the system characteristics which are a number of ways of specifying these constraints. These fall into two broad classes
Time domain criteria
Frequency domain criteria
The required response is prescribed in either or both forms. In general, the constraints define:
speed of response
relative stability
system accuracy or allowable error.
These are described in Section 4.