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Find the transfer function of the graphical output given to you by the customer, shown below and you are asked to determine the number transfer function. Your answer should be stated as Y(s)/R(s) knowing the canonical 2nd order form. You can read the Precent Overshoot, the time to peak (Tp), the settling time, Ts, and the Mp, maximum amount of overshoot. Assume that there is a Unit step applied to this second order system. You must show all work. Final Answer in Box must follow the standard form, shown for your help. P.O.= 100e-<#//IR G (s) = g2+2(Wn&+w 1.4 T, : 1.2 1.0 4 T, = 47 = 0.8 0.6 0.4 Mp = e-5//1-g2 0.2 니5 Time (s) 2 3. Response

Find the transfer function of the graphical output given to you by the customer, shown below and you are asked to determine the number transfer function. Your answer should be stated as Y(s)/R(s) knowing the canonical 2nd order form. You can read the Precent Overshoot, the time to peak (Tp), the settling time, Ts, and the Mp, maximum amount of overshoot. Assume that there is a Unit step applied to this second order system. You must show all work. Final Answer in Box must follow the standard form, shown for your help. P.O.= 100e-<#//IR G (s) = g2+2(Wn&+w 1.4 T, : 1.2 1.0 4 T, = 47 = 0.8 0.6 0.4 Mp = e-5//1-g2 0.2 니5 Time (s) 2 3. Response

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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Find the transfer function of the graphical output given to you by the customer, shown below, and you are asked to determine the number transfer function. Your answer should be stated as Y(s)/R(s) knowing the canonical 2nd order form. You can read the Percent Overshoot, the time to peak (Tp), the settling time, Ts, and the Mp, maximum amount of overshoot. Assume that there is a Unit step applied to this second order system. You must show all work. Final Answer in Box must follow the standard form, shown for your help. **Formulas:** - Percent Overshoot (P.O.): \( P.O. = 100e^{-\pi \zeta / \sqrt{1-\zeta^2}} \) - Time to peak (Tp): \( T_p = \frac{\pi}{\omega_n \sqrt{1-\zeta^2}} \) - Settling time (Ts): \( T_s = \frac{4}{\zeta \omega_n} \) - Maximum Overshoot (Mp): \( M_p = e^{-\pi \zeta / \sqrt{1-\zeta^2}} \) **Standard Form of Transfer Function:** \[ G(s) = \frac{\omega_n^2}{s^2 + 2\zeta\omega_ns + \omega_n^2} \] **Graph Explanation:** - The graph is a response curve showing the behavior of a second order system over time in seconds. - The x-axis represents time in seconds (Time (s)), ranging from 0 to 5. - The y-axis represents the response level of the system, ranging from 0 to 1.4. - The curve indicates how the system reacts to a unit step input, exhibiting characteristics such as overshoot and settling behavior.
Transcribed Image Text:Find the transfer function of the graphical output given to you by the customer, shown below, and you are asked to determine the number transfer function. Your answer should be stated as Y(s)/R(s) knowing the canonical 2nd order form. You can read the Percent Overshoot, the time to peak (Tp), the settling time, Ts, and the Mp, maximum amount of overshoot. Assume that there is a Unit step applied to this second order system. You must show all work. Final Answer in Box must follow the standard form, shown for your help. **Formulas:** - Percent Overshoot (P.O.): \( P.O. = 100e^{-\pi \zeta / \sqrt{1-\zeta^2}} \) - Time to peak (Tp): \( T_p = \frac{\pi}{\omega_n \sqrt{1-\zeta^2}} \) - Settling time (Ts): \( T_s = \frac{4}{\zeta \omega_n} \) - Maximum Overshoot (Mp): \( M_p = e^{-\pi \zeta / \sqrt{1-\zeta^2}} \) **Standard Form of Transfer Function:** \[ G(s) = \frac{\omega_n^2}{s^2 + 2\zeta\omega_ns + \omega_n^2} \] **Graph Explanation:** - The graph is a response curve showing the behavior of a second order system over time in seconds. - The x-axis represents time in seconds (Time (s)), ranging from 0 to 5. - The y-axis represents the response level of the system, ranging from 0 to 1.4. - The curve indicates how the system reacts to a unit step input, exhibiting characteristics such as overshoot and settling behavior.
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