Homework Answers
Code:
syms s h;
G = ((s+20)*(s+30))/((s+25)*(s+35));
K = 15;
Kp = limit(K*G,s,0)
Kv = limit(K*s*G,s,0)
Ka = limit(K*s^2*G,s,0)
step_error = 1/(1+Kp)
ramp_error = 1/Kv
para_error = 1/Ka
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Question #3 (25 points): A unity feedback system has the following forward transfer function: K(s+20)(s +30) G(S) =...
1. A unity feedback system with its forward transfer function G(s) - K(s+a)/s(s+B) is to be...
1. A unity feedback system with its forward transfer function G(s) - K(s+a)/s(s+B) is to be designed to meet the following requirements: (1) the steady-state error for a unit ramp input equals to 0.1 and (2) the closed-loop poles will be located at -1 + j1. Find K, a, and B in order to meet the specifications. (12 points) 2. Given a unity feedback system with its forward transfer function G(s) shown below: s" (s +a) Find the values of...
A unity feedback system with the forward transfer function G(s)=K/(s+1)(s+3)(s+6) is operating wi...
A unity feedback system with the forward transfer function
G(s)=K/(s+1)(s+3)(s+6) is operating with a closed-loop step
response that has 15% overshoot. Do the following:
a) Evaluate the steady-state error for a unit step input
b) Design a PI control to reduce the steady-state error to zero
without affecting its transient response
c) Evaluate the steady-state error and overshoot for a unit step
input to your compensated system
A unity feedback system with the forward transfer function G(s) is operating with...
17. Consider unity feedback system with uncompensated forward transfer function a given by: K G(s) s+3)(s 6) The system...
17. Consider unity feedback system with uncompensated forward transfer function a given by: K G(s) s+3)(s 6) The system requires a damping ratio of 0.5. If the design point is at -1.54 j2.66, design a PI controller to drive the steady-state error of the response to zero
17. Consider unity feedback system with uncompensated forward transfer function a given by: K G(s) s+3)(s 6) The system requires a damping ratio of 0.5. If the design point is at -1.54 j2.66,...
PROBLEM: A unity feedback system with the forward transfer function K G(s) s(s+7) is operating with...
PROBLEM: A unity feedback system with the forward transfer function K G(s) s(s+7) is operating with a closed-loop step response that has 15% overshoot. Do the following: a. Evaluate the steady-state error for a unit ramp input. b. Design a lag compensator to improve the steady-state error by a factor of 20. c. Evaluate the steady-state error for a unit ramp input to your compensated system. d. Evaluate how much improvement in steady-state error was realized.
A unity feedback system with the forward transfer function G (s) = s(s+2)(s15) is operating with ...
A unity feedback system with the forward transfer function G (s) = s(s+2)(s15) is operating with a closed-loop step response that has 15% overshoot. Do the following: a) Evaluate the settling time for a unit step input b) Design a PD control to yield a 15% overshoot but with a threefold reduction in settling time; c) Evaluate the settling time, overshoot, and steady-state error with the PD control.
A unity feedback system with the forward transfer function G (s) =...
A unity feedback system with the forward transfer function G)2)(s +5) is operating with a closed-...
A unity feedback system with the forward transfer function G)2)(s +5) is operating with a closed-loop step response that has 15% overshoot. Do the following: a) Evaluate the settling time for a unit step input; b) Design a PD control to yield a 15% overshoot but with a threefold reduction in settling time; c) Evaluate the settling time, overshoot, and steady-state error with the PD control.
A unity feedback system with the forward transfer function G)2)(s +5) is operating with...
Problem 3 (25) Consider the unity-feedback system with the open-loop transfer function: 10 G(s) = 1...
Problem 3 (25) Consider the unity-feedback system with the open-loop transfer function: 10 G(s) = 1 Obtain the steady-state output of the system when it is subjected to each of the following inputs: a)r(t) sin(t30*) b) r(t) 2cos(2t - 45) c) r(t) sin(t+30") + 2cos(2t -45)
Problem 3 (25) Consider the unity-feedback system with the open-loop transfer function: 10 G(s) = 1 Obtain the steady-state output of the system when it is subjected to each of the following inputs: a)r(t)...
Problem 3 A unity feedback system has the loop transfer function G(s) = Kata) s(s +...
Problem 3 A unity feedback system has the loop transfer function G(s) = Kata) s(s + (a) Find the breakway and entry points on the real axis. (b) Find the gain and the roots when the real part of the complex roots is located at -2 (c) Sketch the root locus. Problem 4 The forward path G(s) of a unity feedback system with input R(s) and output Y (s) is given by G(o) 106I) (a) What is the type of...
4. A unity feedback system has the following forward transfer function G(s) = s(s+a) (a) Determin...
4. A unity feedback system has the following forward transfer function G(s) = s(s+a) (a) Determine K and ath Answer: K 831,000 and a 832 (b) Determine K and a that gives ess-001 and a 10% overshoot Answer: K14000 and a 140
4. A unity feedback system has the following forward transfer function G(s) = s(s+a) (a) Determine K and ath Answer: K 831,000 and a 832 (b) Determine K and a that gives ess-001 and a 10% overshoot Answer:...
1. A system with a unity feedback has a forward transfer function of G(s) 60 G(s)...
1. A system with a unity feedback has a forward transfer function of G(s) 60 G(s) s(0.4s+1)(s1)(s +6) a. Show that the system has a non-zero error only when the ramp input is applied. What is the magnitude of the corresponding error constant? b. What are the errors of the system due to step input and parabola input? c. A PD controller with proportional gain of Kp and derivative gain of Kp added to the design. Draw the block diagram...
1. A unity feedback system with its forward transfer function G(s) - K(s+a)/s(s+B) is to be designed to meet the following requirements: (1) the steady-state error for a unit ramp input equals to 0.1 and (2) the closed-loop poles will be located at -1 + j1. Find K, a, and B in order to meet the specifications. (12 points) 2. Given a unity feedback system with its forward transfer function G(s) shown below: s" (s +a) Find the values of...
A unity feedback system with the forward transfer function
G(s)=K/(s+1)(s+3)(s+6) is operating with a closed-loop step
response that has 15% overshoot. Do the following:
a) Evaluate the steady-state error for a unit step input
b) Design a PI control to reduce the steady-state error to zero
without affecting its transient response
c) Evaluate the steady-state error and overshoot for a unit step
input to your compensated system
A unity feedback system with the forward transfer function G(s) is operating with...
17. Consider unity feedback system with uncompensated forward transfer function a given by: K G(s) s+3)(s 6) The system requires a damping ratio of 0.5. If the design point is at -1.54 j2.66, design a PI controller to drive the steady-state error of the response to zero
17. Consider unity feedback system with uncompensated forward transfer function a given by: K G(s) s+3)(s 6) The system requires a damping ratio of 0.5. If the design point is at -1.54 j2.66,...
PROBLEM: A unity feedback system with the forward transfer function K G(s) s(s+7) is operating with a closed-loop step response that has 15% overshoot. Do the following: a. Evaluate the steady-state error for a unit ramp input. b. Design a lag compensator to improve the steady-state error by a factor of 20. c. Evaluate the steady-state error for a unit ramp input to your compensated system. d. Evaluate how much improvement in steady-state error was realized.
A unity feedback system with the forward transfer function G (s) = s(s+2)(s15) is operating with a closed-loop step response that has 15% overshoot. Do the following: a) Evaluate the settling time for a unit step input b) Design a PD control to yield a 15% overshoot but with a threefold reduction in settling time; c) Evaluate the settling time, overshoot, and steady-state error with the PD control.
A unity feedback system with the forward transfer function G (s) =...
A unity feedback system with the forward transfer function G)2)(s +5) is operating with a closed-loop step response that has 15% overshoot. Do the following: a) Evaluate the settling time for a unit step input; b) Design a PD control to yield a 15% overshoot but with a threefold reduction in settling time; c) Evaluate the settling time, overshoot, and steady-state error with the PD control.
A unity feedback system with the forward transfer function G)2)(s +5) is operating with...
Problem 3 (25) Consider the unity-feedback system with the open-loop transfer function: 10 G(s) = 1 Obtain the steady-state output of the system when it is subjected to each of the following inputs: a)r(t) sin(t30*) b) r(t) 2cos(2t - 45) c) r(t) sin(t+30") + 2cos(2t -45)
Problem 3 (25) Consider the unity-feedback system with the open-loop transfer function: 10 G(s) = 1 Obtain the steady-state output of the system when it is subjected to each of the following inputs: a)r(t)...
Problem 3 A unity feedback system has the loop transfer function G(s) = Kata) s(s + (a) Find the breakway and entry points on the real axis. (b) Find the gain and the roots when the real part of the complex roots is located at -2 (c) Sketch the root locus. Problem 4 The forward path G(s) of a unity feedback system with input R(s) and output Y (s) is given by G(o) 106I) (a) What is the type of...
4. A unity feedback system has the following forward transfer function G(s) = s(s+a) (a) Determine K and ath Answer: K 831,000 and a 832 (b) Determine K and a that gives ess-001 and a 10% overshoot Answer: K14000 and a 140
4. A unity feedback system has the following forward transfer function G(s) = s(s+a) (a) Determine K and ath Answer: K 831,000 and a 832 (b) Determine K and a that gives ess-001 and a 10% overshoot Answer:...
1. A system with a unity feedback has a forward transfer function of G(s) 60 G(s) s(0.4s+1)(s1)(s +6) a. Show that the system has a non-zero error only when the ramp input is applied. What is the magnitude of the corresponding error constant? b. What are the errors of the system due to step input and parabola input? c. A PD controller with proportional gain of Kp and derivative gain of Kp added to the design. Draw the block diagram...
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