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5. , Based on the following unit step response of a sensor, an engineer claims that the sensor acts like a second-order system. (a) Explain how you justify the engineer's claim! (b) Find the static sensitivity of the sensor (c) Find the useful dynamic frequency range of the sensor (within +5% of error) if the time constants are 0.16 and 1.6 seconds. 1 2 4 5 6. Time( sec) 2. 1. temperature (oC)

5. , Based on the following unit step response of a sensor, an engineer claims that the sensor acts like a second-order system. (a) Explain how you justify the engineer's claim! (b) Find the static sensitivity of the sensor (c) Find the useful dynamic frequency range of the sensor (within +5% of error) if the time constants are 0.16 and 1.6 seconds. 1 2 4 5 6. Time( sec) 2. 1. temperature (oC)

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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### Transcription and Explanation **Educational Content: Understanding Sensor Dynamics** --- **Problem Statement:** Based on the following *unit step response* of a sensor, an engineer claims that the sensor acts like a *second-order* system. **Tasks:** (a) Explain how you justify the engineer’s claim. (b) Find the static sensitivity of the sensor. (c) Find the useful dynamic frequency range of the sensor (within ±5% of error) if the time constants are 0.16 and 1.6 seconds. --- **Graph Explanation:** - **Title:** The graph does not have a specific title, but it is a unit step response curve. - **Axes:** - **X-axis (Time):** Measured in seconds, ranging from 0 to 6. - **Y-axis (Temperature):** Measured in degrees Celsius (°C), ranging from 0 to 6. - **Data Points:** The graph shows data points that represent how temperature changes with time after a unit step input is applied to the sensor. - **Trend:** The data points form a curve that begins at the origin (0,0) and rises quickly at first, then gradually levels off as it approaches a steady state around a temperature of 5°C. This suggests a classic asymptotic response typical of a second-order system. **Second-Order System Characteristics:** - **Justification of Engineer's Claim (a):** - The smooth, asymptotic rise to a steady-state value is indicative of a system that may be second-order. A second-order system is often characterized by an over-damped, under-damped, or critically damped response. In this case, the curve suggests an over-damped response without overshoot, supporting the claim of a second-order system. - **Static Sensitivity (b):** - Static sensitivity can be calculated from the steady-state temperature value achieved by the system. Here, the final temperature appears to stabilize around 5°C. Static sensitivity in a linear system is the steady-state gain, which can be determined as the change in output (temperature) per unit change in input. - **Dynamic Frequency Range (c):** - The dynamic frequency range is determined based on the given time constants (0.16 and 1.6 seconds). The bandwidth of a second-order system depends on these time constants, which characterize how quickly the system responds to changes in input.
Transcribed Image Text:### Transcription and Explanation **Educational Content: Understanding Sensor Dynamics** --- **Problem Statement:** Based on the following *unit step response* of a sensor, an engineer claims that the sensor acts like a *second-order* system. **Tasks:** (a) Explain how you justify the engineer’s claim. (b) Find the static sensitivity of the sensor. (c) Find the useful dynamic frequency range of the sensor (within ±5% of error) if the time constants are 0.16 and 1.6 seconds. --- **Graph Explanation:** - **Title:** The graph does not have a specific title, but it is a unit step response curve. - **Axes:** - **X-axis (Time):** Measured in seconds, ranging from 0 to 6. - **Y-axis (Temperature):** Measured in degrees Celsius (°C), ranging from 0 to 6. - **Data Points:** The graph shows data points that represent how temperature changes with time after a unit step input is applied to the sensor. - **Trend:** The data points form a curve that begins at the origin (0,0) and rises quickly at first, then gradually levels off as it approaches a steady state around a temperature of 5°C. This suggests a classic asymptotic response typical of a second-order system. **Second-Order System Characteristics:** - **Justification of Engineer's Claim (a):** - The smooth, asymptotic rise to a steady-state value is indicative of a system that may be second-order. A second-order system is often characterized by an over-damped, under-damped, or critically damped response. In this case, the curve suggests an over-damped response without overshoot, supporting the claim of a second-order system. - **Static Sensitivity (b):** - Static sensitivity can be calculated from the steady-state temperature value achieved by the system. Here, the final temperature appears to stabilize around 5°C. Static sensitivity in a linear system is the steady-state gain, which can be determined as the change in output (temperature) per unit change in input. - **Dynamic Frequency Range (c):** - The dynamic frequency range is determined based on the given time constants (0.16 and 1.6 seconds). The bandwidth of a second-order system depends on these time constants, which characterize how quickly the system responds to changes in input.
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