### 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 ExplanationThe 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 EquationTo 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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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)

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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