Page 152 - MATLAB an introduction with applications

Control Systems ——— 137

The MATLAB command

nyquist (A, B, C, D, iu, w) ...(3.43)
considers the user-supplied frequency vector w. The vector w specifies the frequency at which the frequency
response should be determined.

3.20 TRANSIENT-RESPONSE ANALYSIS IN STATE SPACE
In this section, we present the transient-response analysis of systems in state space using MATLAB.
Specifically, we present the step response, impulse, ramp response and responses to other forms of simple
inputs.
3.20.1 Unit Step Response
For a control system defined in a state space form as in Eq. (3.39), the MATLAB command
step (A, B, C, D) ...(3.44)
will generate plots of unit step responses, with the time vector automatically determined provided t is not
explicitly provided in the step commands.
The MATLAB command step (sys) may also be used to obtain the unit-step response of a system.
The command
step (sys) ...(3.45)
can be used where the system is defined by
sys = tf (num, den) ...(3.46)
or
sys = ss (A, B, C, D) ...(3.47)
The following MATLAB step commands with left hand arguments are used then no plot is shown on the
screen:
[y, x, t] = step [num, den, t]
[y, x, t] = step (A, B, C, D, iu) ...(3.48)
[y, x, t] = step (A, B, C, D, iu, t )
Hence, in order to obtain the response curves, plot commands should be used. The matrices x and y contain
the state response of the system and the output respectively, computed at the time points t. In Eq. (3.48),
iu is a scalar index of the inputs of the system, which specifies the input to be used for the response, and
t is the user specified time. The step command in Eq. (3.48) can be used to obtain a series of step response
plots, one for each input and output combination of
x = Ax + Bu
y = Cx + Du ...(3.49)
when the system involves multiple inputs and multiple outputs.

3.20.2 Impulse Response
The following MATLAB commands may be used to obtain the unit impulse response of a control system:

impulse (num, den) ...(3.50)
impulse(A, B, C, D) ...(3.51)

F:\Final Book\Sanjay\IIIrd Printout\Dt. 10-03-09