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PROBLEMS 26. A system has a transfer function of 100/(s² + s + 100). What will be its natural frequency wn and its damping ratio (? llu damned or quer

PROBLEMS 26. A system has a transfer function of 100/(s² + s + 100). What will be its natural frequency wn and its damping ratio (? llu damned or quer

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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A Q Keau CD Page view Determine how the output will vary with time when there is an input which starts at zero time and then increases at the constant rate of 6 units/s. The initial output is zero. 23. The input x and output y of a system are described by: d²y df² dy +3 +2y=x dx If initially the input and output are zero, what will be the output when there is a unit step input? 24. The input x and output y of a system are described by: d²y dt² +4 dy dx + 3y = x If initially the input and output are zero, what will be the output when there is a unit impulse input? 25. A control system has a forward path transfer function of 2/(s+2) and a negative feedback loop with transfer function 4. What will be the response of the system to a unit step input? INSTRUMENTATION AND CONTROL SYSTEMS PROBLEMS 255 26. A system has a transfer function of 100/(s² + s + 100). What will be its natural frequency wn, and its damping ratio (? 27. A system has a transfer function of 10/(s² + 4s +9). Is the system under-damped, critically damped or over- damped? 28. A system has a transfer function of 3/(s² + 6s +9). Is the system under-damped, critically damped or over- damped? 29. A system has a forward path transfer function of 10/(s + 3) and a negative feedback loop with transfer function 5. What is the time constant of the resulting first-order system? 30. Determine the delay time and the rise time for the following first-order systems: (a) G(s) = 1/(4s + 1), (b) G(s) = 5/(s+1) and (c) G(s) = 2/(s+3). 31. A first-order system has a time constant of 30 s. What will be its delay time and rise time when subject to a unit step input? 32. A first-order system when subject to a unit step input rises to 90% of its steady-state value in 20 s. Determine its time constant, delay time and rise time? 33. Determine the natural angular frequency, the damping factor, the rise time, percentage overshoot and 2% settling time for systems with transfer functions: (a) 100/(s² + 4s + 100) and (b) 49/(s+ 4s +49). 21 Determine the natural anmilar frequency the damning factor the rice time percentage overchont and 2% O Search W
Transcribed Image Text:A Q Keau CD Page view Determine how the output will vary with time when there is an input which starts at zero time and then increases at the constant rate of 6 units/s. The initial output is zero. 23. The input x and output y of a system are described by: d²y df² dy +3 +2y=x dx If initially the input and output are zero, what will be the output when there is a unit step input? 24. The input x and output y of a system are described by: d²y dt² +4 dy dx + 3y = x If initially the input and output are zero, what will be the output when there is a unit impulse input? 25. A control system has a forward path transfer function of 2/(s+2) and a negative feedback loop with transfer function 4. What will be the response of the system to a unit step input? INSTRUMENTATION AND CONTROL SYSTEMS PROBLEMS 255 26. A system has a transfer function of 100/(s² + s + 100). What will be its natural frequency wn, and its damping ratio (? 27. A system has a transfer function of 10/(s² + 4s +9). Is the system under-damped, critically damped or over- damped? 28. A system has a transfer function of 3/(s² + 6s +9). Is the system under-damped, critically damped or over- damped? 29. A system has a forward path transfer function of 10/(s + 3) and a negative feedback loop with transfer function 5. What is the time constant of the resulting first-order system? 30. Determine the delay time and the rise time for the following first-order systems: (a) G(s) = 1/(4s + 1), (b) G(s) = 5/(s+1) and (c) G(s) = 2/(s+3). 31. A first-order system has a time constant of 30 s. What will be its delay time and rise time when subject to a unit step input? 32. A first-order system when subject to a unit step input rises to 90% of its steady-state value in 20 s. Determine its time constant, delay time and rise time? 33. Determine the natural angular frequency, the damping factor, the rise time, percentage overshoot and 2% settling time for systems with transfer functions: (a) 100/(s² + 4s + 100) and (b) 49/(s+ 4s +49). 21 Determine the natural anmilar frequency the damning factor the rice time percentage overchont and 2% O Search W
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Given a second order transfer function

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