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Q. 1 (5 marks)...
Q. 1 (5 marks) For the system in Fig. (a). Assume proportion control, Gc(s)-K, sketch the root lo...
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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)....
Q. 1 (10 marks) For the system in Fig. 1 (a) Assume proportion control. Ge(s) =...
Q. 1 (10 marks) For the system in Fig. 1 (a) Assume proportion control. Ge(s) = K. sketch the root locus for the closed-loop system (b). Using the angle condition, prove that s1 =-2 +j2 is not on the root locus. (c). Design a lead compensator such that the dominant closed-loop poles are located at s-2tj2. (d). What are the zero and pole of lead compensator Ge(s)? (e). With Ge (s) has the zero and pole found in (c), sketch...
Question 1 (60 points) Consider the following block diagram where G(s)- Controller R(s) G(s) (a) Sketch the root locus assuming a proportional controller is used. [25 points] (b) Design specifica...
Question 1 (60 points) Consider the following block diagram where G(s)- Controller R(s) G(s) (a) Sketch the root locus assuming a proportional controller is used. [25 points] (b) Design specifications require a closed-loop pole at (-3+j1). Design a lead compensator to make sure the root locus goes through this point. For the design, pick the pole of the compensator at-23 and analytically find its zero. (Hint: Lead compensator transfer function will be Ge (s)$+23 First plot the poles and zeros...
Question 1 (60 points) Consider the following block diagram where G (s) Froarss RMs) GIs) Gls) (a) Sketch the root locus assuming a proportional controller is used. (b) Assume design spocifications r...
Question 1 (60 points) Consider the following block diagram where G (s) Froarss RMs) GIs) Gls) (a) Sketch the root locus assuming a proportional controller is used. (b) Assume design spocifications require a closed-loop pole at (-3+ j1). Design a lead compensator sure the root locus goes through this point. For the design, pick the pole of the compensator at -23 and analytically find its zero location. (c) Sketch the root locus with the lead compensator in place.
Question 1...
4. A lead compensator with a transfer function Ge(s)=K(+0.5/(s+3) has been designed for a Space vehicle...
4. A lead compensator with a transfer function Ge(s)=K(+0.5/(s+3) has been designed for a Space vehicle with the transfer function 1/s' such that at the dominant closed loop poles are located at -1 +/-j1. (0) What is the angle deficiency of the uncompensated system at the designed point provided by the location of the dominant poles? Show that the compensator provides the necessary lead angle at the designed point to satisfy the root locus angle criterion. What value of K...
4. A lead compensator with a transfer function Ge(s) = K(s+0.5)/(s+3) has been designed for a...
4. A lead compensator with a transfer function Ge(s) = K(s+0.5)/(s+3) has been designed for a Space vehicle with the transfer function 1/s? such that at the dominant closed loop poles are located at -1 +/-jl. (1) What is the angle deficiency of the uncompensated system at the designed point provided by the location of the dominant poles? Show that the compensator provides the necessary lead angle at the designed point to satisfy the root locus angle criterion. (iii) What...
Consider a unity feedback control architecture where P(s) = 1/s^2 and C(s) = K * ((s + z)/(s + p)...
Consider a unity feedback control architecture where P(s) =
1/s^2 and C(s) = K * ((s + z)/(s + p)) . It is desired to design
the controller to place the dominant closed-loop poles at sd = −2 ±
2j. Fix the pole of the compensator at −20 rad/sec and use root
locus techniques to find values of z and K to place the closed–loop
poles at sd .
Problem 4 (placing a zero) Consider a unity feedback control architecture...
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...
Consider the automobile cruise-control system shown below: Engine ActuatorCarburetor 0.833 and load 40 3s +1 Compensator R(s)E(s) Ge(s) s +1 -t e(t) Sensor 0.03 1) Derive the closed-loop transfer fun...
Consider the automobile cruise-control system shown below: Engine ActuatorCarburetor 0.833 and load 40 3s +1 Compensator R(s)E(s) Ge(s) s +1 -t e(t) Sensor 0.03 1) Derive the closed-loop transfer function of V(s)/R(s) when Gc(s)-1 2) Derive the closed-loop transfer function of E(s)/R(s) when Ge(s)-1 3) Plot the time history of the error e(t) of the closed-loop system when r(t) is a unit step input. 4) Plot the root-loci of the uncompensated system (when Gc(s)-1). Mark the closed-loop complex poles on...
Problem 3: Consider a unity feedback system with a plant model given by 10(s- 5) and a controller...
Problem 3: Consider a unity feedback system with a plant model given by 10(s- 5) and a controller given by s + p for K 0 and some real z and p. a) Use the root-locus technique to determine the sign of z and p so that the closed-loop system is stable for all K E (0, K) for some Ku> 0. b) Sketch the possible forms of the root-locus in terms of the pole and zero locations of Ge(s)....
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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)....
Q. 1 (10 marks) For the system in Fig. 1 (a) Assume proportion control. Ge(s) = K. sketch the root locus for the closed-loop system (b). Using the angle condition, prove that s1 =-2 +j2 is not on the root locus. (c). Design a lead compensator such that the dominant closed-loop poles are located at s-2tj2. (d). What are the zero and pole of lead compensator Ge(s)? (e). With Ge (s) has the zero and pole found in (c), sketch...
Question 1 (60 points) Consider the following block diagram where G(s)- Controller R(s) G(s) (a) Sketch the root locus assuming a proportional controller is used. [25 points] (b) Design specifications require a closed-loop pole at (-3+j1). Design a lead compensator to make sure the root locus goes through this point. For the design, pick the pole of the compensator at-23 and analytically find its zero. (Hint: Lead compensator transfer function will be Ge (s)$+23 First plot the poles and zeros...
Question 1 (60 points) Consider the following block diagram where G (s) Froarss RMs) GIs) Gls) (a) Sketch the root locus assuming a proportional controller is used. (b) Assume design spocifications require a closed-loop pole at (-3+ j1). Design a lead compensator sure the root locus goes through this point. For the design, pick the pole of the compensator at -23 and analytically find its zero location. (c) Sketch the root locus with the lead compensator in place.
Question 1...
4. A lead compensator with a transfer function Ge(s)=K(+0.5/(s+3) has been designed for a Space vehicle with the transfer function 1/s' such that at the dominant closed loop poles are located at -1 +/-j1. (0) What is the angle deficiency of the uncompensated system at the designed point provided by the location of the dominant poles? Show that the compensator provides the necessary lead angle at the designed point to satisfy the root locus angle criterion. What value of K...
4. A lead compensator with a transfer function Ge(s) = K(s+0.5)/(s+3) has been designed for a Space vehicle with the transfer function 1/s? such that at the dominant closed loop poles are located at -1 +/-jl. (1) What is the angle deficiency of the uncompensated system at the designed point provided by the location of the dominant poles? Show that the compensator provides the necessary lead angle at the designed point to satisfy the root locus angle criterion. (iii) What...
Consider a unity feedback control architecture where P(s) =
1/s^2 and C(s) = K * ((s + z)/(s + p)) . It is desired to design
the controller to place the dominant closed-loop poles at sd = −2 ±
2j. Fix the pole of the compensator at −20 rad/sec and use root
locus techniques to find values of z and K to place the closed–loop
poles at sd .
Problem 4 (placing a zero) Consider a unity feedback control architecture...
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...
Consider the automobile cruise-control system shown below: Engine ActuatorCarburetor 0.833 and load 40 3s +1 Compensator R(s)E(s) Ge(s) s +1 -t e(t) Sensor 0.03 1) Derive the closed-loop transfer function of V(s)/R(s) when Gc(s)-1 2) Derive the closed-loop transfer function of E(s)/R(s) when Ge(s)-1 3) Plot the time history of the error e(t) of the closed-loop system when r(t) is a unit step input. 4) Plot the root-loci of the uncompensated system (when Gc(s)-1). Mark the closed-loop complex poles on...
Problem 3: Consider a unity feedback system with a plant model given by 10(s- 5) and a controller given by s + p for K 0 and some real z and p. a) Use the root-locus technique to determine the sign of z and p so that the closed-loop system is stable for all K E (0, K) for some Ku> 0. b) Sketch the possible forms of the root-locus in terms of the pole and zero locations of Ge(s)....
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