Homework Answers
From the Bode magnitude plot of the open-loop system, it is observed that the low-frequency gain is constant and it is approximately equal to 52.5 dB. As the gain at low frequency is constant, the system is a type-0 system (i.e it has no pole at s =0).
Now, steady-state error in response to the unit step reference signal, ess = 1/ ( 1 + Kp )
where Kp = position error constant = 
ess= 1/ ( 1 + Kp ) = 1/ ( 1 + 421.697 ) = 0.00237 unit (ans)
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2. (10 points) Adapted from [DB P8.23: The frequency response for the forward path of a unity feedback control system i...
4. (20 points) Adapted from [DB AP5.7]: Consider the unity feedback system with variable gain K...
4. (20 points) Adapted from [DB AP5.7]: Consider the unity feedback system with variable gain K shown (a) Assume that the complex poles dominate and estimate the 2% settling time and percent overshoot (b) Using MATLAB, determine the actual settling times and percent overshoots of the full third- in Figure 2. We are constrained to keep 1000 s K 5000. in response to a unit step for K 1000, 2000, 3000, 4000, and 5000 order system for the values of...
Problem 2: (20 points) Consider a unity feedback system with the following forward path transfer function...
Problem 2: (20 points) Consider a unity feedback system with the following forward path transfer function G(s) = - cla_K(s + a)(8+3) s(s2 +1) (1) Construct the root locus for K >0 and a = 5; (2) Construct the root locus for a > 0 and K = 10.
The Bode diagram of the forward-nath transfer function of a unity-feedback control system is obtained experimentally when the forward gain Kis set at its nominal valuc. (a) Find the gain and phase ma...
The Bode diagram of the forward-nath transfer function of a unity-feedback control system is obtained experimentally when the forward gain Kis set at its nominal valuc. (a) Find the gain and phase margins of the system from the diagram as best you can read them. Find the gain- and phase-crossover frequencies. (b) Repeat part (a) if the gain is doubled from its nominal value. (c) Repeat part (a) if the gain is 10 times its nominal value. (d) Find out...
QUESTION 2 Given that a control system has a forward path of G(s) and negative unity...
QUESTION 2 Given that a control system has a forward path of G(s) and negative unity feedback and unit- step input is applied to the system. If G(s) is given as: K G(s)= s(s4) Draw the block diagram of the system. a) Derive the closed-loop transfer function of the system. b) If the gain K 6, determine the settling time of the resulting second-order system at 2% c) tolerance band Its corresponding steady state error. d) Sketch the controlled output...
VHQ-2, Problem 2: A negative unity feedback system with a forward path transfer function Ka K...
VHQ-2, Problem 2: A negative unity feedback system with a forward path transfer function Ka K (Tm8+1) for some scalar gains Ka, K and time constantTm of Write down the system's transfer function. Assuming that K-2, find the values of Ka and Tm so that the system has the fastest response to a step input with no overshoot and a settling time of 0.2 seconds
Problem #5: You did such a great job in Problem #4, your boss trust you to evaluate another controls team work to determine best path forward with determining this control response that uses a PI con...
Problem #5: You did such a great job in Problem #4, your boss trust you to evaluate another controls team work to determine best path forward with determining this control response that uses a PI controller. 180 160 140 120 100- 80 60 40 20 0 200 400 1,000 600 800 Time (ms)
Problem #5: You did such a great job in Problem #4, your boss trust you to evaluate another controls team work to determine best path forward with...
The Bode plots for a plant, G(s), used in a unity feedback system are shown in Figure P10.7. Do the following: Find the gain margin, phase margin, zero dB frequency, 180° frequency, and the closed-l...
The Bode plots for a plant, G(s), used in a unity feedback
system are shown in Figure P10.7. Do the following:
Find the gain margin, phase margin, zero dB frequency, 180°
frequency, and the closed-loop bandwidth.
Use your results in Part a to estimate the damping ratio,
percent overshoot, settling time, and peak time.
ANSWERS GIVEN BY PROFESSOR
1. Gain margin = 20dB, Phase margin = 55 deg, Zero dB frequency
= 1rad/s, 180deg frequency = 4.5rad/s, bandwidth (-7dB) closed-loop...
The center frequency is not given. I believe that it must be find based on the body plot. Problem 6:The Bode plot for a passive series RLC bandpass filter is shown in Fig. 2. This filter was built...
The center frequency is not given. I believe that it must be
find based on the body plot.
Problem 6:The Bode plot for a passive series RLC bandpass filter is shown in Fig. 2. This filter was built from a 10 μ F capacitor. What is the filter's center frequency, wo, and its quality factor,昱? If you wanted to double the filter's center frequency without changing its quality factor, using the same 10 pu F capacitor, then how would you...
The forward-path transfer functions of unity-feedback control systems are given in the following equations. Plot the Bode diagram of G(ja)/K, and do the following: (1) Find the value of K so that the...
The forward-path transfer functions of unity-feedback control systems are given in the following equations. Plot the Bode diagram of G(ja)/K, and do the following: (1) Find the value of K so that the gain margin of the system is 20 dB. (2) Find the value of K so that the phase margin of the system is 45°. (a) G(s) G+0.55) (b) Gs)- s(1 +0.1s) (1 0.2s)(10.5s) (d) Go +3 (c) G(s)-3 (s +3) (s+3)4 Ke-s G1+55) (e) G (1+0.1s+0.012 G)2...
1. Consider a unity feedback control system with the transfer function G(s) = 1/[s(s+ 2)] in...
1. Consider a unity feedback control system with the transfer function G(s) = 1/[s(s+ 2)] in the forward path. (a) Design a proportional controller that yields a stable system with percent overshoot less that 5% for the step input (b) Find settling time and peak time of the closed-loop system designed in part (a); (c) Design a PD compensator that reduces the settling time computed in (b) by a factor of 4 while keeping the percent overshoot less that 5%...
4. (20 points) Adapted from [DB AP5.7]: Consider the unity feedback system with variable gain K shown (a) Assume that the complex poles dominate and estimate the 2% settling time and percent overshoot (b) Using MATLAB, determine the actual settling times and percent overshoots of the full third- in Figure 2. We are constrained to keep 1000 s K 5000. in response to a unit step for K 1000, 2000, 3000, 4000, and 5000 order system for the values of...
Problem 2: (20 points) Consider a unity feedback system with the following forward path transfer function G(s) = - cla_K(s + a)(8+3) s(s2 +1) (1) Construct the root locus for K >0 and a = 5; (2) Construct the root locus for a > 0 and K = 10.
The Bode diagram of the forward-nath transfer function of a unity-feedback control system is obtained experimentally when the forward gain Kis set at its nominal valuc. (a) Find the gain and phase margins of the system from the diagram as best you can read them. Find the gain- and phase-crossover frequencies. (b) Repeat part (a) if the gain is doubled from its nominal value. (c) Repeat part (a) if the gain is 10 times its nominal value. (d) Find out...
QUESTION 2 Given that a control system has a forward path of G(s) and negative unity feedback and unit- step input is applied to the system. If G(s) is given as: K G(s)= s(s4) Draw the block diagram of the system. a) Derive the closed-loop transfer function of the system. b) If the gain K 6, determine the settling time of the resulting second-order system at 2% c) tolerance band Its corresponding steady state error. d) Sketch the controlled output...
VHQ-2, Problem 2: A negative unity feedback system with a forward path transfer function Ka K (Tm8+1) for some scalar gains Ka, K and time constantTm of Write down the system's transfer function. Assuming that K-2, find the values of Ka and Tm so that the system has the fastest response to a step input with no overshoot and a settling time of 0.2 seconds
Problem #5: You did such a great job in Problem #4, your boss trust you to evaluate another controls team work to determine best path forward with determining this control response that uses a PI controller. 180 160 140 120 100- 80 60 40 20 0 200 400 1,000 600 800 Time (ms)
Problem #5: You did such a great job in Problem #4, your boss trust you to evaluate another controls team work to determine best path forward with...
The Bode plots for a plant, G(s), used in a unity feedback
system are shown in Figure P10.7. Do the following:
Find the gain margin, phase margin, zero dB frequency, 180°
frequency, and the closed-loop bandwidth.
Use your results in Part a to estimate the damping ratio,
percent overshoot, settling time, and peak time.
ANSWERS GIVEN BY PROFESSOR
1. Gain margin = 20dB, Phase margin = 55 deg, Zero dB frequency
= 1rad/s, 180deg frequency = 4.5rad/s, bandwidth (-7dB) closed-loop...
The center frequency is not given. I believe that it must be
find based on the body plot.
Problem 6:The Bode plot for a passive series RLC bandpass filter is shown in Fig. 2. This filter was built from a 10 μ F capacitor. What is the filter's center frequency, wo, and its quality factor,昱? If you wanted to double the filter's center frequency without changing its quality factor, using the same 10 pu F capacitor, then how would you...
The forward-path transfer functions of unity-feedback control systems are given in the following equations. Plot the Bode diagram of G(ja)/K, and do the following: (1) Find the value of K so that the gain margin of the system is 20 dB. (2) Find the value of K so that the phase margin of the system is 45°. (a) G(s) G+0.55) (b) Gs)- s(1 +0.1s) (1 0.2s)(10.5s) (d) Go +3 (c) G(s)-3 (s +3) (s+3)4 Ke-s G1+55) (e) G (1+0.1s+0.012 G)2...
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