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P6.9 A cassette tape storage device has been designed for mass-storage [1]. It is necessary to control the velocity of the tape accurately. The speed control of the tape drive is represented by the system shown in Figure P6.9. (a) Determine the limiting gain for a stable system, (b) Determine a suitable gain so that the overshoot to a step command is approximately 5%. Power Motor and amplifier drive mechanism K 10 Y(s) R(s) s + 100 (s + 20)² Speeci FIGURE P6.9 Tape drive control.

P6.9 A cassette tape storage device has been designed for mass-storage [1]. It is necessary to control the velocity of the tape accurately. The speed control of the tape drive is represented by the system shown in Figure P6.9. (a) Determine the limiting gain for a stable system, (b) Determine a suitable gain so that the overshoot to a step command is approximately 5%. Power Motor and amplifier drive mechanism K 10 Y(s) R(s) s + 100 (s + 20)² Speeci FIGURE P6.9 Tape drive control.

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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**Title: Control System for Cassette Tape Storage Device** **Overview:** A cassette tape storage device has been designed for mass storage applications. Accurate control of the tape's velocity is crucial for its operation. The system for speed control of the tape drive is represented by the block diagram below in Figure P6.9. **Objectives:** - **(a)** Determine the limiting gain for which the system remains stable. - **(b)** Calculate a suitable gain such that the overshoot in response to a step command is approximately 5%. **Figure P6.9: Tape Drive Control System** **Description of the System:** - **Block Diagram Components:** - **Input \( R(s) \):** Represents the reference input signal for the system. - **Power Amplifier:** This component is modeled as a transfer function \( \frac{K}{s + 100} \), where \( K \) is the gain to be determined. - **Motor and Drive Mechanism:** This is represented by the transfer function \( \frac{10}{(s + 20)^2} \). - **Output \( Y(s) \):** Represents the speed of the tape. - **Process:** - The reference input \( R(s) \) is compared with the feedback to generate an error signal. - This error signal is amplified by the Power Amplifier. - The amplified signal drives the Motor and Drive Mechanism to achieve the desired tape speed \( Y(s) \). **Analysis:** - **Stability and Gain Calculation:** - To achieve system stability and desired performance (5% overshoot), mathematical analysis involving control system principles such as root locus, Nyquist or Bode plots, may be employed. The understanding of this system is critical for maintaining the precision and efficiency required in tape storage devices. Through appropriate gain adjustments, the system can ensure optimal performance with minimal overshoot and high stability.
Transcribed Image Text:**Title: Control System for Cassette Tape Storage Device** **Overview:** A cassette tape storage device has been designed for mass storage applications. Accurate control of the tape's velocity is crucial for its operation. The system for speed control of the tape drive is represented by the block diagram below in Figure P6.9. **Objectives:** - **(a)** Determine the limiting gain for which the system remains stable. - **(b)** Calculate a suitable gain such that the overshoot in response to a step command is approximately 5%. **Figure P6.9: Tape Drive Control System** **Description of the System:** - **Block Diagram Components:** - **Input \( R(s) \):** Represents the reference input signal for the system. - **Power Amplifier:** This component is modeled as a transfer function \( \frac{K}{s + 100} \), where \( K \) is the gain to be determined. - **Motor and Drive Mechanism:** This is represented by the transfer function \( \frac{10}{(s + 20)^2} \). - **Output \( Y(s) \):** Represents the speed of the tape. - **Process:** - The reference input \( R(s) \) is compared with the feedback to generate an error signal. - This error signal is amplified by the Power Amplifier. - The amplified signal drives the Motor and Drive Mechanism to achieve the desired tape speed \( Y(s) \). **Analysis:** - **Stability and Gain Calculation:** - To achieve system stability and desired performance (5% overshoot), mathematical analysis involving control system principles such as root locus, Nyquist or Bode plots, may be employed. The understanding of this system is critical for maintaining the precision and efficiency required in tape storage devices. Through appropriate gain adjustments, the system can ensure optimal performance with minimal overshoot and high stability.
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