Answer Happy

6-5. Consider the block diagram of an antenna control system shown in Fig. P8.6-5. This system is described in Section 1.5. Let T = 0.05 and the sensor gain be unity (H = 1). It was shown in Problem 7.5-5 that 20 0.02268z + 0.02052 G(z) L s-(s + 6) (z - 1)(z - 0.7408) = The frequency response for G(z) is given in Table P7-24. Chapter 8 • Digital Controller Design (a) Find the system phase margin with K = 1 and D(z) = 1. (b) To reduce steady-state errors, K is increased to 5. Design a unity-dc-gain phase-lag controller that yields a system phase margin of 45°. (c) Design a unity-dc-gain phase-lead controller, with K = 5, that yields a system phase margin of 45°. (d) Using MATLAB, find the unit step response for the systems of parts (b) and (c). Compare the rise times and the percent overshoot for the two systems. Computer Digital controller Amplifier Motor, gears, and pedestal 20 3² +65 R(z) + M(s) D(z) DIA K (s) e(t) r(k) Sensor V.(z) 0.4 T Binary data -
Ww 3 |G(jww) |G(jww)[dB ZG(ww) 0.1 0.100 33.32874 30.4564 -91.09 0.2 0.200 16.65748 24.4321 -92.19 0.3 0.300 11.09735 20.9042 -93.29 0.4 0.400 8.31502 18.3970 -94.38 0.5 0.500 6.64381 16.4479 -95.47 0.6 0.600 5.52819 14.8510 -96.56 0.7 0.699 4.73007 13.4965 -97.65 0.8 0.799 4.13040 12.3187 -98.73 0.9 0.899 3.66305 11.2754 -99.81 1.0 0.999 3.28834 10.3377 -100.89 2.0 1.998 1.58193 3.9759 -111.28 3.0 2.994 0.99511 -0.0619 -120.81 4.0 3.986 0.69524 -3.1949 -129.31 5.0 4.974 0.51456 -5.8345 -136.78 6.0 5.955 0.39576 -8.1482 -143.31 7.0 6.929 0.31327 -10.2199 -149.03 8.0 7.895 0.25375 -12.0995 -154.07 9.0 8.852 0.20951 -13.8203 -158.54 10.0 9.799 0.17582 -15.4069 -162.54 20.0 18.546 0.05320 -26.7969 -188.55 30.0 25.740 0.02706 -34.2817 -203.49 40.0 31.416 0.01738 -40.4880 -213.67