Homework Answers
Add Answer to:
A closed-loop system is represented by the block element schematic shown below, where 3B S+2 and...
2. Consider the closed-loop system shown below: R(S) MS to Gs)_ G(S) H(s) A. Obtain the...
2. Consider the closed-loop system shown below: R(S) MS to Gs)_ G(S) H(s) A. Obtain the transfer function of the closed-loop system. B. Obtain the sensitivity of the closed-loop system to the variations of G(s) (SC). How can one tune G(s) such that the sensitivity of the system to G(S) is minimized? C. Obtain the sensitivity of the closed-loop system to the variations of H(s) (S). What is the lowest possible value of this sensitivity?
Consider the following closed-loop system, where Y(s) R(s)+ KcP Ks Assume the following nominal values: Ko-2....
Consider the following closed-loop system, where Y(s) R(s)+ KcP Ks Assume the following nominal values: Ko-2. 〈 = 0.8; ω,-4; Ks-2. Use transfer function sensitivity calculations in answering the questions below. a) With proportional controller gain K 10 and r(t) a step input, determine the percentage change in steady-state output y(t) if Ko increases 5% from its nominal value. (12 pts.) b) Repeat part (a) with Kc - 50. (6 pts.) c) With proportional controller gain Kc 10 and r(t)...
(a) (i) Show that the sensitivity of the closed-loop transfer function T(s) to variations in the...
(a) (i) Show that the sensitivity of the closed-loop transfer function T(s) to variations in the plant transfer function G(s), in figure 4, is given by 1 SI - SG = 1+G(s)H(s) (ii) If G(s) = and H(s) = 10 (figure 4) and the dc gain of the plant transfer function G(s) changes by 1%, what is the corresponding change in the dc gain of the closed-loop system? [40%] (b) A feedback system is to control output angular position 0....
(9 pts) If a system whose Unilateral Laplace Transform is: H(s)--is put into a closed loop...
(9 pts) If a system whose Unilateral Laplace Transform is: H(s)--is put into a closed loop with a proportional gain feedback K. S-0.3 (3 pts) Write the transfer function of the closed loop system a. b. (3 pts) What would the gain of the system need to be for the system to be marginally stable (i.e. at s = 0)? (3 pts) What would the gain of the system need to be for the system to have a time constant...
PROBLEM 2 Suppose that a system is shown in Figure 2. Based on for loop, write a piece of MATLAB code to calculate the closed loop poles for 0sKs5 and plot the outputs where the poles are represented...
PROBLEM 2 Suppose that a system is shown in Figure 2. Based on for loop, write a piece of MATLAB code to calculate the closed loop poles for 0sKs5 and plot the outputs where the poles are represented by "W" letter. Find the interval of K parameter for stability using Routh-Hurwitz method. Calculate the poles of the closed loop transfer function where K attains the minimum value such that the system is stable. R(s) 52(K - 3)s + K Figure...
Consider the following closed-loop system: ID(S) Cis) P(s) R(s) — 0 40 52 + 20s +...
Consider the following closed-loop system: ID(S) Cis) P(s) R(s) — 0 40 52 + 20s + Recall that E(s) = R(s) - Y(s). a) What is steady-state error, ess, in response to a unit step at disturbance input D(s) when a = 12? b) What is steady-state error, ess, in response to a unit step at disturbance input D(s) when a = 12.3? c) What is the fractional change in a between parts (a) and (b)? In other words, what...
d(t) Figure 1: Figure for Question 3 (b) (5 pts) Suppose H is an integrator (ie, ,nd C is a first order system with transfer function 2 Is the closed-loop system stable? Obtain the asymptotic val...
d(t) Figure 1: Figure for Question 3 (b) (5 pts) Suppose H is an integrator (ie, ,nd C is a first order system with transfer function 2 Is the closed-loop system stable? Obtain the asymptotic value of the error e when z and d are steps, respectively z au and d-Au, with α and β positive constants. Justify your steps.
d(t) Figure 1: Figure for Question 3 (b) (5 pts) Suppose H is an integrator (ie, ,nd C is a...
Problem 3 (25%): The closed-loop system has the block diagram shown below. Controlle Process Sensor s + l (a) (5%) Sketch the root locus of the closed-loop system. (b) (5%) Determine the range of...
Problem 3 (25%): The closed-loop system has the block diagram shown below. Controlle Process Sensor s + l (a) (5%) Sketch the root locus of the closed-loop system. (b) (5%) Determine the range of K that the closed-loop system is stable. (c) (5%) Find the percentage of overshoot and the steady state error due to a unit step input of the open loop system process. (d) (5%) Find the steady-state error due to a unit step input of the closed-loop...
Y(s) C(s) G(s) R(S) Figure 1: Closed-loop system Q2 Consider the setup in Figure 1 with S s1 (i) ...
Y(s) C(s) G(s) R(S) Figure 1: Closed-loop system Q2 Consider the setup in Figure 1 with S s1 (i) Design a K,τ, α in the lead compensator 1TOS so that the closed-loop system shown in Figure 1 has a steady state error of.0 for a unit ramp reference input at R and a phase margin of about 45 degrees K, α, τ without Bode plots. When you add phase with the lead compensator add an additional 10 degrees of phase....
Question# 1 (25 points) For a unity feedback system with open loop transfer function K(s+10)(s+20) (s+30)(s2-20s+2...
Question# 1 (25 points) For a unity feedback system with open loop transfer function K(s+10)(s+20) (s+30)(s2-20s+200) G(s) = Do the following using Matlab: a) Sketch the root locus. b) Find the range of gain, K that makes the system stable c) Find the value of K that yields a damping ratio of 0.707 for the system's closed-loop dominant poles. d) Obtain Ts, Tp, %OS for the closed loop system in part c). e) Find the value of K that yields...
2. Consider the closed-loop system shown below: R(S) MS to Gs)_ G(S) H(s) A. Obtain the transfer function of the closed-loop system. B. Obtain the sensitivity of the closed-loop system to the variations of G(s) (SC). How can one tune G(s) such that the sensitivity of the system to G(S) is minimized? C. Obtain the sensitivity of the closed-loop system to the variations of H(s) (S). What is the lowest possible value of this sensitivity?
Consider the following closed-loop system, where Y(s) R(s)+ KcP Ks Assume the following nominal values: Ko-2. 〈 = 0.8; ω,-4; Ks-2. Use transfer function sensitivity calculations in answering the questions below. a) With proportional controller gain K 10 and r(t) a step input, determine the percentage change in steady-state output y(t) if Ko increases 5% from its nominal value. (12 pts.) b) Repeat part (a) with Kc - 50. (6 pts.) c) With proportional controller gain Kc 10 and r(t)...
(a) (i) Show that the sensitivity of the closed-loop transfer function T(s) to variations in the plant transfer function G(s), in figure 4, is given by 1 SI - SG = 1+G(s)H(s) (ii) If G(s) = and H(s) = 10 (figure 4) and the dc gain of the plant transfer function G(s) changes by 1%, what is the corresponding change in the dc gain of the closed-loop system? [40%] (b) A feedback system is to control output angular position 0....
(9 pts) If a system whose Unilateral Laplace Transform is: H(s)--is put into a closed loop with a proportional gain feedback K. S-0.3 (3 pts) Write the transfer function of the closed loop system a. b. (3 pts) What would the gain of the system need to be for the system to be marginally stable (i.e. at s = 0)? (3 pts) What would the gain of the system need to be for the system to have a time constant...
PROBLEM 2 Suppose that a system is shown in Figure 2. Based on for loop, write a piece of MATLAB code to calculate the closed loop poles for 0sKs5 and plot the outputs where the poles are represented by "W" letter. Find the interval of K parameter for stability using Routh-Hurwitz method. Calculate the poles of the closed loop transfer function where K attains the minimum value such that the system is stable. R(s) 52(K - 3)s + K Figure...
Consider the following closed-loop system: ID(S) Cis) P(s) R(s) — 0 40 52 + 20s + Recall that E(s) = R(s) - Y(s). a) What is steady-state error, ess, in response to a unit step at disturbance input D(s) when a = 12? b) What is steady-state error, ess, in response to a unit step at disturbance input D(s) when a = 12.3? c) What is the fractional change in a between parts (a) and (b)? In other words, what...
d(t) Figure 1: Figure for Question 3 (b) (5 pts) Suppose H is an integrator (ie, ,nd C is a first order system with transfer function 2 Is the closed-loop system stable? Obtain the asymptotic value of the error e when z and d are steps, respectively z au and d-Au, with α and β positive constants. Justify your steps.
d(t) Figure 1: Figure for Question 3 (b) (5 pts) Suppose H is an integrator (ie, ,nd C is a...
Problem 3 (25%): The closed-loop system has the block diagram shown below. Controlle Process Sensor s + l (a) (5%) Sketch the root locus of the closed-loop system. (b) (5%) Determine the range of K that the closed-loop system is stable. (c) (5%) Find the percentage of overshoot and the steady state error due to a unit step input of the open loop system process. (d) (5%) Find the steady-state error due to a unit step input of the closed-loop...
Y(s) C(s) G(s) R(S) Figure 1: Closed-loop system Q2 Consider the setup in Figure 1 with S s1 (i) Design a K,τ, α in the lead compensator 1TOS so that the closed-loop system shown in Figure 1 has a steady state error of.0 for a unit ramp reference input at R and a phase margin of about 45 degrees K, α, τ without Bode plots. When you add phase with the lead compensator add an additional 10 degrees of phase....
Question# 1 (25 points) For a unity feedback system with open loop transfer function K(s+10)(s+20) (s+30)(s2-20s+200) G(s) = Do the following using Matlab: a) Sketch the root locus. b) Find the range of gain, K that makes the system stable c) Find the value of K that yields a damping ratio of 0.707 for the system's closed-loop dominant poles. d) Obtain Ts, Tp, %OS for the closed loop system in part c). e) Find the value of K that yields...
Most questions answered within 3 hours.
-
Where is the error in this code sequence?
String s1 = "Hello";
String s2 = "ello";...
asked 10 months ago -
Financial data for Joel de Paris, Inc., for last year
follow:
Joel de Paris, Inc.
Balance...
asked 10 months ago -
Consider this reaction:
Al2(SO4)3 (aq)+ BaCl3
(aq) Al2Cl6 (aq)- +
3BaSO4(s) . What is the...
asked 10 months ago -
Suppose that Savneet is considering increasing her
recent random sample from 20 car rentals to 40...
asked 10 months ago -
Trucks arrive at an unloading terminal at an average rate of 120
per hour.
Trucks arrive...
asked 10 months ago -
Why are methanol and ethanol completely soluble in water while
octanol is not very little soluble....
asked 10 months ago -
A facilities manager at a university reads in a research report
that the mean amount of...
asked 10 months ago -
When the CuSO4 is rehydrated by adding water to the anhydrous
compound, is this an endothermic...
asked 10 months ago -
A ray of sunlight is passing from diamond into crown glass; the
angle of incidence is...
asked 10 months ago -
A block of mass 0.249 kg is placed on top of a light, vertical
spring of...
asked 10 months ago -
how do the kidneys compensate in the presences of acidosis
a) trigger hyperventilate
b) reserve acid...
asked 10 months ago -
Question 501 pts
The rental rate of capital to the firm increases. Which of the
following...
asked 10 months ago