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5. Derive the transfer function relating input 0; to output 0o. What is the characteristic equation? How many poles does the system have? Block Diagram Desired azimuth angle 0,(s) Potentiometer Power Azimuth Preamplifier Gears angle V(s) + V.(s) Vp(s) K₁ E(s) K₁ 0m(s) 0,(s) K Ks OY000 OF K pot amplifier s+a Potentiometer Motor Kpot and load s(s+am)

5. Derive the transfer function relating input 0; to output 0o. What is the characteristic equation? How many poles does the system have? Block Diagram Desired azimuth angle 0,(s) Potentiometer Power Azimuth Preamplifier Gears angle V(s) + V.(s) Vp(s) K₁ E(s) K₁ 0m(s) 0,(s) K Ks OY000 OF K pot amplifier s+a Potentiometer Motor Kpot and load s(s+am)

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
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### Problem 5: Deriving the Transfer Function **Objective:** - Derive the transfer function relating input \( \theta_i \) to output \( \theta_o \). - Determine the characteristic equation and the number of poles in the system. ### Block Diagram Explanation The block diagram represents a control system designed to regulate the output azimuth angle \( \theta_o(s) \) based on the desired azimuth angle \( \theta_i(s) \). 1. **Input Signal:** - Desired azimuth angle \( \theta_i(s) \) is the input. 2. **Potentiometer:** - The input passes through a potentiometer with a gain \( K_{\text{pot}} \). - The output of the potentiometer is given by \( V_t(s) \). 3. **Error Signal:** - The error signal \( V_e(s) \) is the difference between the reference signal \( V_t(s) \) and the feedback. 4. **Preamplifier:** - Amplifies the error signal \( V_e(s) \) by a constant \( K \). - Output of preamplifier: \( V_p(s) \). 5. **Power Amplifier:** - Takes input \( V_p(s) \) and outputs \( E_a(s) \) through the transfer function \( \frac{K_1}{s+a} \). 6. **Motor and Load:** - The armature is modeled to have a dynamics function \( \frac{K_1}{s(s+a_m)} \). - It converts electrical energy into the mechanical angle \( \theta_m(s) \). 7. **Gears:** - Changes \( \theta_m(s) \) by a gear ratio \( K_g \) producing the final output \( \theta_o(s) \). 8. **Feedback:** - The output \( \theta_o(s) \) is fed back into another potentiometer \( K_{\text{pot}} \) to produce the feedback signal. ### Transfer Function and Characteristic Equation To derive the transfer function, express all the blocks in terms of \( s \)-domain elements and calculate the overall system transfer function from \( \theta_i(s) \) to \( \theta_o(s) \). - Each block contributes to the overall transfer function, which can be calculated by multiplying individual transfer functions and accounting
Transcribed Image Text:### Problem 5: Deriving the Transfer Function **Objective:** - Derive the transfer function relating input \( \theta_i \) to output \( \theta_o \). - Determine the characteristic equation and the number of poles in the system. ### Block Diagram Explanation The block diagram represents a control system designed to regulate the output azimuth angle \( \theta_o(s) \) based on the desired azimuth angle \( \theta_i(s) \). 1. **Input Signal:** - Desired azimuth angle \( \theta_i(s) \) is the input. 2. **Potentiometer:** - The input passes through a potentiometer with a gain \( K_{\text{pot}} \). - The output of the potentiometer is given by \( V_t(s) \). 3. **Error Signal:** - The error signal \( V_e(s) \) is the difference between the reference signal \( V_t(s) \) and the feedback. 4. **Preamplifier:** - Amplifies the error signal \( V_e(s) \) by a constant \( K \). - Output of preamplifier: \( V_p(s) \). 5. **Power Amplifier:** - Takes input \( V_p(s) \) and outputs \( E_a(s) \) through the transfer function \( \frac{K_1}{s+a} \). 6. **Motor and Load:** - The armature is modeled to have a dynamics function \( \frac{K_1}{s(s+a_m)} \). - It converts electrical energy into the mechanical angle \( \theta_m(s) \). 7. **Gears:** - Changes \( \theta_m(s) \) by a gear ratio \( K_g \) producing the final output \( \theta_o(s) \). 8. **Feedback:** - The output \( \theta_o(s) \) is fed back into another potentiometer \( K_{\text{pot}} \) to produce the feedback signal. ### Transfer Function and Characteristic Equation To derive the transfer function, express all the blocks in terms of \( s \)-domain elements and calculate the overall system transfer function from \( \theta_i(s) \) to \( \theta_o(s) \). - Each block contributes to the overall transfer function, which can be calculated by multiplying individual transfer functions and accounting
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