Advanced Modern Control System Theory and Design

ANSWERS TO SELECTED PROBLEMS

CHAPTER 1

1. 1.4.
2. 1.6.
   1. Crossover frequency = 4.483 rad/sec, phase margin = 32.44°, gain margin = 8.657dB.
   2. K = 9.9
   3. Crossover frequency = 13.61 rad/sec, phase margin = −30.62°, gain margin = −11.26 dB.

CHAPTER 2

1. 2.1.
   1. The electrical network illustrated in Table 2.4^‡, items 3, with

      

      and cascaded with an amplifier whose gain is 4.6 will satisfy the specifications

   2. The electrical network illustrated in Table 2.4^‡, item 4, with

      

      and cascaded with an amplifier whose gain is 4.6 will satisfy the specifications.

   3. The electrical network illustrated in Table 2.4^‡, item 5, with

      

      will satisfy the specifications.

2. 2.2.
   1. ζ = 0.5; ω_n = 4 rad/sec; maximum percent overshoot = 16.4%; steady-state error = 0.25.
   2. b = 0.15.
   3. Maximum percent overshoot = 1.5%; steady-state error = 0.4.
   4. Add a high-pass filter in cascade with the tachometer as illustrated in Figure 2.15.
3. 2.5.
   1. G_c(s) = 1 + 0.382s.
   2. b = 0.382.
4. 2.7.
5. 2.8.

   1. the attenuation of 1/178.6 due to the two lead networks is assumed ...