Modern Control Engineering

The open-loop transfer function of the compensated system is

Using MATLAB Program 7–32 the magnitude and phase-angle curves of the designed open-loop

transfer function Gc(s)G(s)can be obtained as shown in Figure 7–153. Note that the denominator

polynomialden1was obtained using the convcommand, as follows:

=

40s^2 +24s+3.2

s^5 +9.02s^4 +24.18s^3 +16.48s^2 +0.32s

Gc(s)G(s)=

(s+0.4)(s+0.2)

(s+4)(s+0.02)

40

s(s+1)(s+4)

558 Chapter 7 / Control Systems Analysis and Design by the Frequency-Response Method

MATLAB Program 7–31

numc = [1 0.6 0.08];

denc = [1 4.02 0.08];

bode(numc,denc)

title('Bode Diagram of Lag–Lead Compensator')

Frequency (rad/sec)

Bode Diagram of Lag-Lead Compensator

− 50

0

50

− 20

− 15

Phase (deg); Magnitude (dB)

− 10

0

− 5

10 −^310 −^210 −^1100101102

Figure 7–152

Bode diagram of the

designed lag–lead

compensator.

a = [1 4.02 0.08];

b = [1 5 4 0];

conv(a,b)

ans =

1.0000 9.0200 24.1800 16.4800 0.320000 0

The Bode diagram of the lag–lead compensator Gc(s)can be obtained by entering MATLAB

Program 7–31 into the computer. The resulting plot is shown in Figure 7–152.

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