Consider the system of Example 8.1.
(a) Design a PI filter to achieve a phase margin of \(60^{\circ}\).
(b) Obtain the system step response using MATLAB. Compare this response to that of the system of Example 8.1, which is plotted in Fig. 8-14.

Example 8.1

We will consider the design of a servomotor system as described in Section 1.5. Suppose that
the servo is to control the horizontal (azimuth) angle for pointing a radar antenna. Then, in the
closed-loop system of Fig. 8-6, c(t) is the azimuth angle of the antenna, and r(t) is the commanded,
or desired, azimuth angle. The plant transfer function derived in Section 1.5 is second
order; however, we will assume that the armature inductance cannot be neglected, resulting in a
third-order transfer function. Then suppose that the parameters of the plant are such that

Fig. 8-6

Fig. 8-14

Transcribed Image Text:

G(z) = = Since the fastest time constant is 0.5 s, we will choose T to be one-tenth that value (a rule of thumb often used), or T = 0.05 s. Then || Z - Z Z - Z Gp(s) 1 = 1 s(s+ 1)(0.5s + 1) 1 s(s + 1)(0.5s + 1). 1 -1.5 S 1 0.05z Z (z - 1) + 2 s + 1 1.5z + Z-1 Z -0.5 s+2 2z 0.9512 0.5z z - 0.9048] The frequency response of this system was calculated by computer and is given in Table 8-1 and plotted in Fig. 8-8. Suppose that it is desired to design a unity de gain phase-lag compensator