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Find the plant transfer function

Find the plant transfer function

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 plant transfer function
### Self-Guiding Vehicle's Bearing Angle Control **52. Figure P9.16 is a simplified block diagram of a self-guiding vehicle’s bearing angle control.** #### Explanation of the Block Diagram - **Controller**: Represented by the transfer function \( K \). - **Steering**: Represented by the transfer function \( \frac{50}{s^2 + 10s + 50} \). - **Vehicle Dynamics**: Represented by the transfer function \( \frac{1}{s(s + 5)} \). - **Input**: Desired bearing angle. - **Output**: Actual bearing angle. The block diagram shows a closed-loop system where the controller regulates the steering mechanism based on the desired bearing angle to adjust the vehicle's dynamics and achieve the actual bearing angle. ![Figure P9.16](path-to-image) *Figure P9.16 Simplified block diagram of a self-guiding vehicle’s bearing angle control.* #### Design Task **a) Design a PID compensator to yield a closed-loop step response with 10% overshoot, a settling time of 1.5 seconds, and zero steady-state error.** In this task, you are required to design a Proportional-Integral-Derivative (PID) compensator that optimizes the system performance to meet specified criteria: - **10% overshoot**: This indicates how much the system exceeds the desired response before settling. - **Settling time of 1.5 seconds**: The time taken for the system to remain within a certain percentage (commonly 2% or 5%) of the desired response. - **Zero steady-state error**: Ensures that the system's output will ultimately match the desired input value over time. To achieve this, you need to adjust the parameters of the PID compensator appropriately. The typical form of a PID controller's transfer function is: \[ \text{PID}(s) = K_p + \frac{K_i}{s} + K_d s \] where \( K_p \), \( K_i \), and \( K_d \) are the proportional, integral, and derivative gains, respectively. By tuning these gains, the desired performance characteristics (overshoot, settling time, and steady-state error) can be attained.
Transcribed Image Text:### Self-Guiding Vehicle's Bearing Angle Control **52. Figure P9.16 is a simplified block diagram of a self-guiding vehicle’s bearing angle control.** #### Explanation of the Block Diagram - **Controller**: Represented by the transfer function \( K \). - **Steering**: Represented by the transfer function \( \frac{50}{s^2 + 10s + 50} \). - **Vehicle Dynamics**: Represented by the transfer function \( \frac{1}{s(s + 5)} \). - **Input**: Desired bearing angle. - **Output**: Actual bearing angle. The block diagram shows a closed-loop system where the controller regulates the steering mechanism based on the desired bearing angle to adjust the vehicle's dynamics and achieve the actual bearing angle. ![Figure P9.16](path-to-image) *Figure P9.16 Simplified block diagram of a self-guiding vehicle’s bearing angle control.* #### Design Task **a) Design a PID compensator to yield a closed-loop step response with 10% overshoot, a settling time of 1.5 seconds, and zero steady-state error.** In this task, you are required to design a Proportional-Integral-Derivative (PID) compensator that optimizes the system performance to meet specified criteria: - **10% overshoot**: This indicates how much the system exceeds the desired response before settling. - **Settling time of 1.5 seconds**: The time taken for the system to remain within a certain percentage (commonly 2% or 5%) of the desired response. - **Zero steady-state error**: Ensures that the system's output will ultimately match the desired input value over time. To achieve this, you need to adjust the parameters of the PID compensator appropriately. The typical form of a PID controller's transfer function is: \[ \text{PID}(s) = K_p + \frac{K_i}{s} + K_d s \] where \( K_p \), \( K_i \), and \( K_d \) are the proportional, integral, and derivative gains, respectively. By tuning these gains, the desired performance characteristics (overshoot, settling time, and steady-state error) can be attained.
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