Need a feedback controller expert to help solve this problem, please help.
Posted: Fri Apr 29, 2022 8:25 am
Need a feedback controller expert to help solve this
problem, please help.
3. For the antenna control problem in the figure below Computer Digital controller Amplifier Motor, gears, and pedestal 20 R(z) M(s) D(z) DIA K e(s) (1) r(k) s? +65 Sensor Voz) 0.4 Binary data assume T = 0.05, and the digital controller D(z) and amplifier gain K = 1. The frequency response for G(s) (-0.7408) practically identical to the previous problem, except that instead of a Bode plot, we now have the frequency response specified in tabular form) Gl=)=(1-")z[69]- 00268 +0.92083 is tabulated on the next page (Note: That this problem is
00 TABLE P7.7-2 Frequency Response for Problem 7.7-2 6 |G(jw) |G(jo) dB ZG(0) 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
a. Find the system gain margin with K = 1 and D(z) = 1. b. To design the steady-state error due to step inputs, K is increased to 5. Design a unity gain phase-lag controller that yields a phase margin of 75º. c. Repeat b) using a unity gain phase-lead controller! d. Use simulink to simulate the step response with the lead and lag controllers. Which of the 2 controllers do you think will have a "faster” response (measured either by the rise time or the settling time) and why? Is this what you observe in the plots of the step responses ? Note that the overshoots should be comparable (are they ?) because the phase margins are the same. However, they might not be the same because the resulting closed-loop systems are third order, and besides, also have a zero!
problem, please help.
- Need A Feedback Controller Expert To Help Solve This Problem Please Help 1 (35.68 KiB) Viewed 18 times
- Need A Feedback Controller Expert To Help Solve This Problem Please Help 2 (74.28 KiB) Viewed 18 times
00 TABLE P7.7-2 Frequency Response for Problem 7.7-2 6 |G(jw) |G(jo) dB ZG(0) 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
a. Find the system gain margin with K = 1 and D(z) = 1. b. To design the steady-state error due to step inputs, K is increased to 5. Design a unity gain phase-lag controller that yields a phase margin of 75º. c. Repeat b) using a unity gain phase-lead controller! d. Use simulink to simulate the step response with the lead and lag controllers. Which of the 2 controllers do you think will have a "faster” response (measured either by the rise time or the settling time) and why? Is this what you observe in the plots of the step responses ? Note that the overshoots should be comparable (are they ?) because the phase margins are the same. However, they might not be the same because the resulting closed-loop systems are third order, and besides, also have a zero!