A 2nd order dynamic system has a damping ratio, ζ = 0.5 and natural frequency, ωn = 8 rad/s. The transfer gain is K = 2. There are no zeros of the system. If the general response to an impulse input has the form:h(t) =e(–ωnζt)[Asin(ωdt) + Bcos(ωdt)]; whereωd is the damped frequency. Find damped natural frequency (ωd), value of constants A and B. Hint: To find A and B, find h(t) using “Transfer Function Property” and compare it with the given expression for h(t) in the problem statement.
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A 2nd order dynamic system has a damping ratio, ζ = 0.5 andnatural frequency, ωn...
8. A second order lag process has a resonant frequency, (o, of 10 rad/sec, a damping ratio of 0.1, and a steady state gain, G, of 1. Use the Bode diagram in figure given to determine the gain, m,...
8. A second order lag process has a resonant frequency, (o, of 10 rad/sec, a damping ratio of 0.1, and a steady state gain, G, of 1. Use the Bode diagram in figure given to determine the gain, m, in decibel, and the phase angle B, in degrees for the following values of the radiant frequency. Convert your decibel gain values, m, to ordinary gain values, g. (a) 0.1 rad/s, (b) 10 rad/s. 20 10 ζ-0.5 2.0 10 () ζ-20.0...
Ex: Determine the frequency response of a pressure transducer that has a damping ratio of 0.5 and a ringing frequency of 1200 Hz. The frequency response of a measurement system is determined by...
Ex: Determine the frequency response of a pressure transducer that has a damping ratio of 0.5 and a ringing frequency of 1200 Hz. The frequency response of a measurement system is determined by M(o) and φ(a) as defined in Equations(30) and (31). Since ω.-conv 1-7 , the natural frequency of the pressure transducer is found to be on-8706 rad/s. The frequency response at selected frequencies is computed from Equations 30 and 31 as follows [1-(w/m)212+/240/m)2 M(o) 1.00 1.04 1.07 1.15...
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...
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,...
1. Figure 1 plots a two-order system frequency response at five different damping ratios. The damping...
1. Figure 1 plots a two-order system frequency response at five different damping ratios. The damping ratios are 0.0.25, 0.5, 1.0, and 2.0, respectively. [5 marks] Output signal y(t) yo) - > (a) Identify the corresponding damping ratio of each curve (A1, A2, A3, A4, AS) tttt (b) If the natural frequency of this two-order system is 100 Hz and its damping ratio is A3, roughly estimate the response time for the system to reach the final stable state. tttttttt
5. For each of the following, determine if the system is underdamped, undamped, critically damped or overdamped ad sket...
5. For each of the following, determine if the system is underdamped, undamped, critically damped or overdamped ad sketch the it step response (a) G (s) = (c) G(s)-t 2+68+ (d) G (s) = 36 6. The equation of motion of a rotational mechanical system is given by where θ° and θί are respectively, output and input angular displace- ments. Assuming that all initial conditions are zero, determine (a) the transfer function model. (b) the natural frequency, w natural frequency,...
can help to solve this ? Thank you Consider the second order system when damping ratio...
can help to solve this ? Thank
you
Consider the second order system when damping ratio = 8.6. and natural angles frequency = 5 rad/sec, find the rise time, Peak time, max. overshoot, and setting time (20/5) when the system is sub-pected to a unit-step input.
b) Given a second order system with the following open loop transfer function where damping ratio,...
b) Given a second order system with the following open loop transfer function where damping ratio, } = 0.707 and natural frequency, Wn= 2.5. wn? G(S) = S2 + 23wns +wn? i. Determine the steady state error to an appropriate input via a calculation method using the transfer function. Compare your answer with the steady state error from the exact frequency response for this system given in Figure Q4(b). (5 marks) ii. Evaluate the difference of the exact frequency response...
A second order mechanical system of a mass connected to a spring and a damper is subjected to a s...
A second order mechanical system of a mass connected to a spring and a damper is subjected to a sinusoidal input force mx+cx + kx = A sin(at) The mass is m-5 kg, the damping constant is c = 1 N-sec/m, the spring stiffness is 2 N/m, and the amplitude of the input force is A- 3 N. For this system give explicit numerical values for the damping factor 5 and the un-damped natural frequency Using the given formulas for...
5. For each of the following, determine if the system is underdamped, undamped, critically damped or...
5. For each of the following, determine if the system is underdamped, undamped, critically damped or overdamped ad sketch the it step response (a) G (s) = (c) G(s)-t 2+68+ (d) G (s) = 36 6. The equation of motion of a rotational mechanical system is given by where θ° and θί are respectively, output and input angular displace- ments. Assuming that all initial conditions are zero, determine (a) the transfer function model. (b) the natural frequency, w natural frequency,...
8. A second order lag process has a resonant frequency, (o, of 10 rad/sec, a damping ratio of 0.1, and a steady state gain, G, of 1. Use the Bode diagram in figure given to determine the gain, m, in decibel, and the phase angle B, in degrees for the following values of the radiant frequency. Convert your decibel gain values, m, to ordinary gain values, g. (a) 0.1 rad/s, (b) 10 rad/s. 20 10 ζ-0.5 2.0 10 () ζ-20.0...
Ex: Determine the frequency response of a pressure transducer that has a damping ratio of 0.5 and a ringing frequency of 1200 Hz. The frequency response of a measurement system is determined by M(o) and φ(a) as defined in Equations(30) and (31). Since ω.-conv 1-7 , the natural frequency of the pressure transducer is found to be on-8706 rad/s. The frequency response at selected frequencies is computed from Equations 30 and 31 as follows [1-(w/m)212+/240/m)2 M(o) 1.00 1.04 1.07 1.15...
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...
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,...
1. Figure 1 plots a two-order system frequency response at five different damping ratios. The damping ratios are 0.0.25, 0.5, 1.0, and 2.0, respectively. [5 marks] Output signal y(t) yo) - > (a) Identify the corresponding damping ratio of each curve (A1, A2, A3, A4, AS) tttt (b) If the natural frequency of this two-order system is 100 Hz and its damping ratio is A3, roughly estimate the response time for the system to reach the final stable state. tttttttt
5. For each of the following, determine if the system is underdamped, undamped, critically damped or overdamped ad sketch the it step response (a) G (s) = (c) G(s)-t 2+68+ (d) G (s) = 36 6. The equation of motion of a rotational mechanical system is given by where θ° and θί are respectively, output and input angular displace- ments. Assuming that all initial conditions are zero, determine (a) the transfer function model. (b) the natural frequency, w natural frequency,...
can help to solve this ? Thank
you
Consider the second order system when damping ratio = 8.6. and natural angles frequency = 5 rad/sec, find the rise time, Peak time, max. overshoot, and setting time (20/5) when the system is sub-pected to a unit-step input.
b) Given a second order system with the following open loop transfer function where damping ratio, } = 0.707 and natural frequency, Wn= 2.5. wn? G(S) = S2 + 23wns +wn? i. Determine the steady state error to an appropriate input via a calculation method using the transfer function. Compare your answer with the steady state error from the exact frequency response for this system given in Figure Q4(b). (5 marks) ii. Evaluate the difference of the exact frequency response...
A second order mechanical system of a mass connected to a spring and a damper is subjected to a sinusoidal input force mx+cx + kx = A sin(at) The mass is m-5 kg, the damping constant is c = 1 N-sec/m, the spring stiffness is 2 N/m, and the amplitude of the input force is A- 3 N. For this system give explicit numerical values for the damping factor 5 and the un-damped natural frequency Using the given formulas for...
5. For each of the following, determine if the system is underdamped, undamped, critically damped or overdamped ad sketch the it step response (a) G (s) = (c) G(s)-t 2+68+ (d) G (s) = 36 6. The equation of motion of a rotational mechanical system is given by where θ° and θί are respectively, output and input angular displace- ments. Assuming that all initial conditions are zero, determine (a) the transfer function model. (b) the natural frequency, w natural frequency,...
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