Modern Control Engineering

(Chris Devlin) #1
440 Chapter 7 / Control Systems Analysis and Design by the Frequency-Response Method

Drawing Nyquist Plots of a System Defined in State Space. Consider the


system defined by


where state vector (n-vector)


output vector (m-vector)


control vector (r-vector)


state matrix (n*nmatrix)


control matrix (n*rmatrix)


output matrix (m*nmatrix)


D= direct transmission matrix (m*rmatrix)


C=


B=


A=


u=


y=


x=


y=Cx+Du


x# =Ax+Bu


MATLAB Program 7–8


% ---------- Nyquist plot----------


num = [1];


den = [1 1 0];


w = 0.1:0.1:100;


[re,im,w] = nyquist(num,den,w);


plot(re,im)


v = [-2 2 -5 5]; axis(v)


grid


title('Nyquist Plot of G(s) = 1/[s(s + 1)]')


xlabel('Real Axis')


ylabel('Imag Axis')


Real Axis


  • 21 – 1.5 – 1 – 0.5 0 0.5 1.5 2


Imag Axis


  • 2


1


  • 5


5


  • 1


2


  • 3

  • 4


0

3

4

Nyquist Plot of G(s)=1/[s(s+1)]

Figure 7–40
Nyquist plot of

forv 7 0.

G(s)=

1

s(s+ 1 )

A MATLAB program using this nyquistcommand is shown in MATLAB Program 7–8. The
resulting Nyquist plot is presented in Figure 7–40.

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