Find the output response as a function of time.
The system shown in Figure P4.6 has a unit step input. Find the output response as a function of time. Assume the system is underdamped.
Homework Answers
Answer the following questions: К R(s) C(s) к, ST1 Find the closed loop transfer function from...
Answer the following questions: К R(s) C(s) к, ST1 Find the closed loop transfer function from R(s) to C(s) for the system of the diagram above. Draw the root locus for the system in the diagram above as a function of K Draw the unit step response for the system in the diagram above marking the settling time, peak time and maximum output. Find all the possibilities: overdamped, critically damped, underdamped. Find an expression to the steady state error to...
66. The system shown in Figure P6.16 has G (s) = 1/s(s+2) (s + 4). Find...
66. The system shown in Figure P6.16 has G (s) = 1/s(s+2) (s + 4). Find the following: R(s) + E() K G,G) KES FIGURE P6.16 a. The value of K, for which the inner loop will have two equal negative real poles and the associated range of K, for system stability. b. The value of K, at which the system oscillates and the associated frequency of oscillation. c. The gain Ki at which a real closed-loop pole is at...
Homework 04 Due: Final Exam System: G1 Time (seconds): 2 25 Ampltude: 2.4 Problem 1) Considering the four different res...
Homework 04 Due: Final Exam System: G1 Time (seconds): 2 25 Ampltude: 2.4 Problem 1) Considering the four different responses recorded at different occasions to a step input of (t)-2u(t) shown in Figure P1; (a) Propose a transfer function that produced the Step Respons e System: G2 Time (sec.): 323 Amplitude: 1.96 underdamped response System: G4 Time (se conds): 9.11 Amplitude: 1.9 (b) Write a general expression for the response of G1 (c) What would be the order of the...
Problem 1: (Time Response) Derive the transfer function (s) of the electrical circuit shown below. Then...
Problem 1: (Time Response) Derive the transfer function (s) of the electrical circuit shown below. Then obtain the response e (0) when the input (1) is a unit step of magnitude E, (i.e., e(t) = E, (t)). Assume that the initial charge in the capacitor is zero. e/o)
thx!!!! Question 3 (5.5 marks) a) Find the transfer function of the electrical circuit shown in...
thx!!!!
Question 3 (5.5 marks) a) Find the transfer function of the electrical circuit shown in Figure 1. What is the value of the steady state gain(s), if any? b) If R1 1, R2 = 2n, C\ = 2- 10-3F, C 1-10-3F, calculate the time constants of the system (if any). c) Find the initial and final values of the unit impulse response of the circuit d) Derive the time-domain expression of the output if the input is the function...
(25 points) Find the discrete time unit step response of the system with transfer function G(2)...
(25 points) Find the discrete time unit step response of the system with transfer function G(2) = 2(2+1)
3. The a-transform of the unit-step response (the output when the input is ure) of a...
3. The a-transform of the unit-step response (the output when the input is ure) of a causal LTI discrete-time system is S(a)-3 1.5 Determine the impulse response of the system.
Question three The figure below shows a unit step response of a second order system. From...
Question three The figure below shows a unit step response of a second order system. From the graph of response find: 1- The rise timet, 2- The peak timet, 3- The maximum overshoot Mp 4- The damped natural frequency w 5. The transfer function. Hence find the damping ratio ζ and the natural frequency ah-Find also the transfer function of the system. r 4 02 15 25 35 45 Question Four For the control system shown in the figure below,...
3. (15 points) Find the equations of motion for mi and m2 as shown in Figure 1.jo) is the input force of the system and xi is the output function of the system. Assume gravity is not a factor. of...
3. (15 points) Find the equations of motion for mi and m2 as shown in Figure 1.jo) is the input force of the system and xi is the output function of the system. Assume gravity is not a factor. of the system, find the transfer f (t) C3 m2 mi Figure 1
3. (15 points) Find the equations of motion for mi and m2 as shown in Figure 1.jo) is the input force of the system and xi is the...
A linear time invariant system has an impulse response given by h[n] = 2(-0.5)" u[n] –...
A linear time invariant system has an impulse response given by h[n] = 2(-0.5)" u[n] – 3(0.5)2º u[n] where u[n] is the unit step function. a) Find the z-domain transfer function H(2). b) Draw pole-zero plot of the system and indicate the region of convergence. c) is the system stable? Explain. d) is the system causal? Explain. e) Find the unit step response s[n] of the system, that is, the response to the unit step input. f) Provide a linear...
Answer the following questions: К R(s) C(s) к, ST1 Find the closed loop transfer function from R(s) to C(s) for the system of the diagram above. Draw the root locus for the system in the diagram above as a function of K Draw the unit step response for the system in the diagram above marking the settling time, peak time and maximum output. Find all the possibilities: overdamped, critically damped, underdamped. Find an expression to the steady state error to...
66. The system shown in Figure P6.16 has G (s) = 1/s(s+2) (s + 4). Find the following: R(s) + E() K G,G) KES FIGURE P6.16 a. The value of K, for which the inner loop will have two equal negative real poles and the associated range of K, for system stability. b. The value of K, at which the system oscillates and the associated frequency of oscillation. c. The gain Ki at which a real closed-loop pole is at...
Homework 04 Due: Final Exam System: G1 Time (seconds): 2 25 Ampltude: 2.4 Problem 1) Considering the four different responses recorded at different occasions to a step input of (t)-2u(t) shown in Figure P1; (a) Propose a transfer function that produced the Step Respons e System: G2 Time (sec.): 323 Amplitude: 1.96 underdamped response System: G4 Time (se conds): 9.11 Amplitude: 1.9 (b) Write a general expression for the response of G1 (c) What would be the order of the...
Problem 1: (Time Response) Derive the transfer function (s) of the electrical circuit shown below. Then obtain the response e (0) when the input (1) is a unit step of magnitude E, (i.e., e(t) = E, (t)). Assume that the initial charge in the capacitor is zero. e/o)
thx!!!!
Question 3 (5.5 marks) a) Find the transfer function of the electrical circuit shown in Figure 1. What is the value of the steady state gain(s), if any? b) If R1 1, R2 = 2n, C\ = 2- 10-3F, C 1-10-3F, calculate the time constants of the system (if any). c) Find the initial and final values of the unit impulse response of the circuit d) Derive the time-domain expression of the output if the input is the function...
(25 points) Find the discrete time unit step response of the system with transfer function G(2) = 2(2+1)
3. The a-transform of the unit-step response (the output when the input is ure) of a causal LTI discrete-time system is S(a)-3 1.5 Determine the impulse response of the system.
Question three The figure below shows a unit step response of a second order system. From the graph of response find: 1- The rise timet, 2- The peak timet, 3- The maximum overshoot Mp 4- The damped natural frequency w 5. The transfer function. Hence find the damping ratio ζ and the natural frequency ah-Find also the transfer function of the system. r 4 02 15 25 35 45 Question Four For the control system shown in the figure below,...
3. (15 points) Find the equations of motion for mi and m2 as shown in Figure 1.jo) is the input force of the system and xi is the output function of the system. Assume gravity is not a factor. of the system, find the transfer f (t) C3 m2 mi Figure 1
3. (15 points) Find the equations of motion for mi and m2 as shown in Figure 1.jo) is the input force of the system and xi is the...
A linear time invariant system has an impulse response given by h[n] = 2(-0.5)" u[n] – 3(0.5)2º u[n] where u[n] is the unit step function. a) Find the z-domain transfer function H(2). b) Draw pole-zero plot of the system and indicate the region of convergence. c) is the system stable? Explain. d) is the system causal? Explain. e) Find the unit step response s[n] of the system, that is, the response to the unit step input. f) Provide a linear...
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