[Control System Engineering]

2. (50%) A plant to be controlled is Gr(s) = 1/{s(s+2)}. The magnitude and phase ange of the plant is given in the following table. o radio dB = 20 log(Gojol 0.1 13.9 -93 0.3 4.3 -98 0.4 1.8 -101 0.5 -0.3 -104 F | 0.6 0.8 -1.9 -4.7 -6.9 -15.0 -20.7 -28.6 -34.1 -40.2 -59.1 -80.0 -107 -112 -117 -135 -146 -158 -164 -169 -176 -179 5 7 10 30 100 a. Draw the Bode plot of this system. Use the available semilog paper. Determine gain margin and phase margin of the system. If the system is controlled using feedback with unity gain, is the dosed-loop system stable? (20%) b. If we use proportional controller K, whatis the gaink to make the static velocity errar constant 10. Note that Go(s) = G (s Gz(s). If we use this gain, calculate phase margin of the system. (10%) c. Design a lead compensator G1(s) = (p/z) (s+z)/(s+p) where Ipl > Iz| so that the static gain GO) = 1 and a phase margin 45. You can use either Bode, Nichols, or Nyquist (pdar) plot. (20%) 2. (50%) A plant to be controlled is Gr(s) = 1/{s(s+2)}. The magnitude and phase ange of the plant is given in the following table. o radio dB = 20 log(Gojol 0.1 13.9 -93 0.3 4.3 -98 0.4 1.8 -101 0.5 -0.3 -104 F | 0.6 0.8 -1.9 -4.7 -6.9 -15.0 -20.7 -28.6 -34.1 -40.2 -59.1 -80.0 -107 -112 -117 -135 -146 -158 -164 -169 -176 -179 5 7 10 30 100 a. Draw the Bode plot of this system. Use the available semilog paper. Determine gain margin and phase margin of the system. If the system is controlled using feedback with unity gain, is the dosed-loop system stable? (20%) b. If we use proportional controller K, whatis the gaink to make the static velocity errar constant 10. Note that Go(s) = G (s Gz(s). If we use this gain, calculate phase margin of the system. (10%) c. Design a lead compensator G1(s) = (p/z) (s+z)/(s+p) where Ipl > Iz| so that the static gain GO) = 1 and a phase margin 45. You can use either Bode, Nichols, or Nyquist (pdar) plot. (20%)