What are the steps in solving this with applying Z transforms the given information.
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What are the steps in solving this with applying Z transforms
the given information.
Problem 1....
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...
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...
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)....
Please solve parts (a) and (b) neatly and show problem solving. Ignore reference to part 1, but please still plot the root loci. For the system given in Figure 1 a) Design a PD compensator with the t...
Please solve parts (a) and (b) neatly and show problem solving.
Ignore reference to part 1, but please still plot the root
loci.
For the system given in Figure 1 a) Design a PD compensator with the transfer function: to give a dominant root of the closed-loop characteristic equation of the compen- sated system at s -1+j1 (i.e., a settling time Ts of less than 6 seconds and a maximum overshoot Mo of less than 10%). Required Pre-Practical work] (b)...
PROBLEM 4 Suppose that a system is shown in Figure 4. There are three controllers that might be incorporated into this system. 1. Ge (s)-K (proportional (P) controller) 2. GS)K/s (integral (I) contro...
PROBLEM 4 Suppose that a system is shown in Figure 4. There are three controllers that might be incorporated into this system. 1. Ge (s)-K (proportional (P) controller) 2. GS)K/s (integral (I) controller) 3. G (s)K(1+1/s) (proportional, integral (PI) controller) The system requirements are T, < 10 seconds and P0 10% for a unit step response. (a) For the (P) controller, write a piece of MATLAB code to plot root locus for 0<K<,and find the K value so that the...
Problem 2 Wis) R(s) U(s) Gol (s) D a (s) E(s) H(s) Given a system as in the diagram above, use MATLAB to solve the problems: Assume we want the closed-loop system rise time to be t, 0.18 sec S + Z H(...
Problem 2 Wis) R(s) U(s) Gol (s) D a (s) E(s) H(s) Given a system as in the diagram above, use MATLAB to solve the problems: Assume we want the closed-loop system rise time to be t, 0.18 sec S + Z H(s) 1 Gpl)s(s+)et s(s 1) s + p a) Assume W(s)-0. Draw the root locus of the system assuming compensator consists only of the adjustable gain parameter K, i.e. Dct (s) Determine the approximate range of values of...
solve quastion 3,4 and 5 B. Tasks and Guide 1. System description and Mathematical modeling The...
solve quastion 3,4 and 5
B. Tasks and Guide 1. System description and Mathematical modeling The antenna positioning system is shown in Fig. 1. In this problem we consider the yaw angle control system, where 0(t) is the yaw angle. Suppose that the gain of the power amplifier is 5 , and that the gear ratio and the angle sensor (the shaft encoder and the data hold) are such that (t)= 0.40(t) where the units of v,(t) are volts and...
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...
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...
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)....
Please solve parts (a) and (b) neatly and show problem solving.
Ignore reference to part 1, but please still plot the root
loci.
For the system given in Figure 1 a) Design a PD compensator with the transfer function: to give a dominant root of the closed-loop characteristic equation of the compen- sated system at s -1+j1 (i.e., a settling time Ts of less than 6 seconds and a maximum overshoot Mo of less than 10%). Required Pre-Practical work] (b)...
PROBLEM 4 Suppose that a system is shown in Figure 4. There are three controllers that might be incorporated into this system. 1. Ge (s)-K (proportional (P) controller) 2. GS)K/s (integral (I) controller) 3. G (s)K(1+1/s) (proportional, integral (PI) controller) The system requirements are T, < 10 seconds and P0 10% for a unit step response. (a) For the (P) controller, write a piece of MATLAB code to plot root locus for 0<K<,and find the K value so that the...
Problem 2 Wis) R(s) U(s) Gol (s) D a (s) E(s) H(s) Given a system as in the diagram above, use MATLAB to solve the problems: Assume we want the closed-loop system rise time to be t, 0.18 sec S + Z H(s) 1 Gpl)s(s+)et s(s 1) s + p a) Assume W(s)-0. Draw the root locus of the system assuming compensator consists only of the adjustable gain parameter K, i.e. Dct (s) Determine the approximate range of values of...
solve quastion 3,4 and 5
B. Tasks and Guide 1. System description and Mathematical modeling The antenna positioning system is shown in Fig. 1. In this problem we consider the yaw angle control system, where 0(t) is the yaw angle. Suppose that the gain of the power amplifier is 5 , and that the gear ratio and the angle sensor (the shaft encoder and the data hold) are such that (t)= 0.40(t) where the units of v,(t) are volts and...
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