Page 151 - MATLAB an introduction with applications

136 ——— MATLAB: An Introduction with Applications

3.18 BODE DIAGRAMS OF SYSTEMS DEFINED IN STATE SPACE

Let the control system defined in state space be
x = Ax + Bu
y = Cx + Du ...(3.39)
where
A = state matrix (nxn matrix)
B = control matrix (nxr matrix)
C = output matrix (mxn matrix)
D = output matrix (mxn matrix)
u = control vector (r – vector)
x = state vector (n – vector)
y = output vector (m – vector)
The MATLAB command bode[A, B, C, D] may be used to obtain the Bode diagram of this system. In fact,
the command bode[A, B, C, D] gives a series of Bode plots, one for each input of the system, with the
frequency range automatically determined.
If we use the scalar iu as an index into the inputs of the control system that specifies which input is to be
used for the Bode plot, then the MATLAB command Bode[A, B, C, D iu] produces the Bode plots from the
input iu to all the outputs (y , y , ....., y ) of the system with the frequency range automatically determined.
1
2
m
u 
1

If the system has three inputs, then u = u 2

u 

3
For a system with only one input u, then the MATLAB command
Bode[A, B, C, D] ...(3.40)
or
Bode [A, B, C, D, 1] can be used. ...(3.41)

3.19 NYQUIST PLOTS OF A SYSTEM DEFINED IN STATE SPACE

Consider the system defined in state space given by Equation (3.39). Nyquist plots of the system defined
in Eq. (3.39) may be obtained by using the MATLAB command
nyquist (A, B, C, D) ...(3.42)
The MATLAB command given by Eq. (3.42) produces a series of Nyquist plots one corresponding to each
input and output combination of the system, with the frequency range automatically determined.
If we used the scalar iu as an index to the inputs of the control system that specifies which input is to be
used for the Nyquist plot, then the MATLAB command nyquist (A,B,C,D,iu,w) produces Nyquist plots
from the input to all the outputs (y , y , ....., y ) of the system with the frequency range automatically
m
1
2
determined.

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