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Automatic control Course.. Please answer all the
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Q2. Fig Q2 shows the block diagram of an unstable system with transfer function G(s) -...
Q2. Fig Q2 shows the block diagram of an unstable system with transfer function G(s) - under the control of a lead compensator (a) Using the Routh's stability criterion, determine the conditions on k and a so that the closed-loop system is stable, and sketch the region on the (k, a)- plane where the conditions are satisfied. Hence, determine the minimum value of k for the lead compensator to be a feasible stabilizing controller. (10 marks) (b) Suppose α-2. Given...
Question 6 The open-loop transfer function G(s) of a control system is given as G(8)- s(s+2)(s +5...
Question 6 The open-loop transfer function G(s) of a control system is given as G(8)- s(s+2)(s +5) A proportional controller is used to control the system as shown in Figure 6 below: Y(s) R(s) + G(s) Figure 6: A control system with a proportional controller a) Assume Hp(s) is a proportional controller with the transfer function H,(s) kp. Determine, using the Routh-Hurwitz Stability Criterion, the value of kp for which the closed-loop system in Figure 6 is marginally stable. (6...
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%...
Consider the electro-mechanical feedback control system shown in Figure 3. The voltage Ea(s) - Liea(t)) is...
Consider the electro-mechanical feedback control system shown in Figure 3. The voltage Ea(s) - Liea(t)) is generated by an amplifier whose transfer function is Ga(s) -5 The position sensor has a transfer function H(s) 1 and the pre-compensator transfer function is pot X (s) Ea(s) The "Electro-Mechanical System" block, is X(s) Ea(s) 5.05s3 101s2 +505.2s 100 R(s) Amplifier, |Ea(S)Electro-MechanicalX(S) Controller, Gc(s) K, pot Ga(s) System, G(s) Encoder H(s) Figure 3: Electro-mechanical control system for Question 3 Consider a proportional controller...
please use MATLAB, screenshot the code and the plots. Answer all parts. Laboratory description: The speed...
please use MATLAB, screenshot the code and the plots. Answer all
parts.
Laboratory description: The speed control of a high-speed train is represented by the system shown in Figure 1. The transfer function of the train dynamics is as follows. G(s) = 2 + 10s + 20 Laboratory assignment: Part A. For the open-loop system described by the following block diagram, assume that the input r(t) is a unit step. (1) Compute the steady-state system output Yss. (2) Find the...
The parameters are as follows k=10 a=0.50 b=0.3 c=0.6 d=9 w_1=12 w_2=15 Kv=30 A feedback control system (illustrated in Figure 1) needs to be designed such that the closed-loop system is asymptotical...
The parameters are as follows
k=10 a=0.50 b=0.3 c=0.6 d=9 w_1=12 w_2=15
Kv=30
A feedback control system (illustrated in Figure 1) needs to be
designed such that the closed-loop system is asymptotically stable
and such that the following design criteria are met:
the gain crossover frequency wc should be between
w1 and w2.
the steady-state error should be zero in response to a unit
step reference.
the velocity constant should be greater than Kv (in
other words, the steady-state unit...
Q.4 A position control system is shown in Figure Q4. Assume that K(s) = K, the plant 50 s(0.2s +1) transfer function is given by G(s) s02s y(t) r(t) Figure Q4: Feedback control system. (a) Design a l...
Q.4 A position control system is shown in Figure Q4. Assume that K(s) = K, the plant 50 s(0.2s +1) transfer function is given by G(s) s02s y(t) r(t) Figure Q4: Feedback control system. (a) Design a lead compensator so that the closed-loop system satisfies the following specifications (i) The steady-state error to a unit-ramp input is less than 1/200 (ii) The unit-step response has an overshoot of less than 16% Ts +1 Hint: Compensator, Dc(s)=aTs+ 1, wm-T (18 marks)...
Problem 3: (30 Consider a block diagram which represents the satellite control system with a cont...
Problem 3: (30 Consider a block diagram which represents the satellite control system with a controller Ge(s) (a) Assuming no initial conditions, find the output response y(t) when the impulse input is applied to the system, where Gc(s) is a proportional gain K. (10) (b) Design a lead-compensator Ge(s) for which the complex pole of the closed-loop system has 0.5 of damping ratio () and 2 rad/s of undamped natural frequency (on) (The zero of a lead-compensator is given as...
PROBLEMA: (25%) A closed-loop control system is shown below Ds) T(O) U(A) C(s) (a) Show that a proportional controller (C(s)-kp) will never make the closed-loop system stable. (8%) (Hint: you nee...
PROBLEMA: (25%) A closed-loop control system is shown below Ds) T(O) U(A) C(s) (a) Show that a proportional controller (C(s)-kp) will never make the closed-loop system stable. (8%) (Hint: you need to calculate the closed-loop pole locations and make discussion for the two possible cases.) (Medim) (b) When a PD controller is used (C(s)kp+ kps), calculate the steady state tracking error when both R(s) and D(s) are unit steps. (8%) (Easy) (e) Suppose R(s) is a unit step and D(s)...
Q. 1 (5 marks) For the system in Fig. (a). Assume proportion control, Gc(s)-K, sketch the root lo...
pls answer dont just copy other solution or ur catching a
dislike
Q. 1 (5 marks) For the system in Fig. (a). Assume proportion control, Gc(s)-K, sketch the root locus for the closed-loop system (b). Using the angle condition, prove that s12 +j2 is not on the root locus. (c). Design a lead compensator Ge(s) - K such that the dominant closed-loop poles are located at s1--2 2. (d), What are the zero and pole of lead compensator G() (e)....
Q2. Fig Q2 shows the block diagram of an unstable system with transfer function G(s) - under the control of a lead compensator (a) Using the Routh's stability criterion, determine the conditions on k and a so that the closed-loop system is stable, and sketch the region on the (k, a)- plane where the conditions are satisfied. Hence, determine the minimum value of k for the lead compensator to be a feasible stabilizing controller. (10 marks) (b) Suppose α-2. Given...
Question 6 The open-loop transfer function G(s) of a control system is given as G(8)- s(s+2)(s +5) A proportional controller is used to control the system as shown in Figure 6 below: Y(s) R(s) + G(s) Figure 6: A control system with a proportional controller a) Assume Hp(s) is a proportional controller with the transfer function H,(s) kp. Determine, using the Routh-Hurwitz Stability Criterion, the value of kp for which the closed-loop system in Figure 6 is marginally stable. (6...
Consider the electro-mechanical feedback control system shown in Figure 3. The voltage Ea(s) - Liea(t)) is generated by an amplifier whose transfer function is Ga(s) -5 The position sensor has a transfer function H(s) 1 and the pre-compensator transfer function is pot X (s) Ea(s) The "Electro-Mechanical System" block, is X(s) Ea(s) 5.05s3 101s2 +505.2s 100 R(s) Amplifier, |Ea(S)Electro-MechanicalX(S) Controller, Gc(s) K, pot Ga(s) System, G(s) Encoder H(s) Figure 3: Electro-mechanical control system for Question 3 Consider a proportional controller...
please use MATLAB, screenshot the code and the plots. Answer all
parts.
Laboratory description: The speed control of a high-speed train is represented by the system shown in Figure 1. The transfer function of the train dynamics is as follows. G(s) = 2 + 10s + 20 Laboratory assignment: Part A. For the open-loop system described by the following block diagram, assume that the input r(t) is a unit step. (1) Compute the steady-state system output Yss. (2) Find the...
The parameters are as follows
k=10 a=0.50 b=0.3 c=0.6 d=9 w_1=12 w_2=15
Kv=30
A feedback control system (illustrated in Figure 1) needs to be
designed such that the closed-loop system is asymptotically stable
and such that the following design criteria are met:
the gain crossover frequency wc should be between
w1 and w2.
the steady-state error should be zero in response to a unit
step reference.
the velocity constant should be greater than Kv (in
other words, the steady-state unit...
Q.4 A position control system is shown in Figure Q4. Assume that K(s) = K, the plant 50 s(0.2s +1) transfer function is given by G(s) s02s y(t) r(t) Figure Q4: Feedback control system. (a) Design a lead compensator so that the closed-loop system satisfies the following specifications (i) The steady-state error to a unit-ramp input is less than 1/200 (ii) The unit-step response has an overshoot of less than 16% Ts +1 Hint: Compensator, Dc(s)=aTs+ 1, wm-T (18 marks)...
Problem 3: (30 Consider a block diagram which represents the satellite control system with a controller Ge(s) (a) Assuming no initial conditions, find the output response y(t) when the impulse input is applied to the system, where Gc(s) is a proportional gain K. (10) (b) Design a lead-compensator Ge(s) for which the complex pole of the closed-loop system has 0.5 of damping ratio () and 2 rad/s of undamped natural frequency (on) (The zero of a lead-compensator is given as...
PROBLEMA: (25%) A closed-loop control system is shown below Ds) T(O) U(A) C(s) (a) Show that a proportional controller (C(s)-kp) will never make the closed-loop system stable. (8%) (Hint: you need to calculate the closed-loop pole locations and make discussion for the two possible cases.) (Medim) (b) When a PD controller is used (C(s)kp+ kps), calculate the steady state tracking error when both R(s) and D(s) are unit steps. (8%) (Easy) (e) Suppose R(s) is a unit step and D(s)...
pls answer dont just copy other solution or ur catching a
dislike
Q. 1 (5 marks) For the system in Fig. (a). Assume proportion control, Gc(s)-K, sketch the root locus for the closed-loop system (b). Using the angle condition, prove that s12 +j2 is not on the root locus. (c). Design a lead compensator Ge(s) - K such that the dominant closed-loop poles are located at s1--2 2. (d), What are the zero and pole of lead compensator G() (e)....
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