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Determinc: (a) The process gain K. Give the units. (b) The damping coefficient . (c) The time constant t. Give the units.

Determinc: (a) The process gain K. Give the units. (b) The damping coefficient . (c) The time constant t. Give the units.

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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**Text:** As a new process control engineer with the DMD Chemical Company, you are assigned a unit with an endothermic chemical reactor. In order to learn about the dynamics of the process, you decide to make a step change in an input variable, which is the heating medium flow rate, from 10 gpm to 14 gpm. The reactor is initially at a steady state temperature of 150°F. You obtain the following plot for the reactor temperature. **Graph Description:** - **X-Axis:** Time (minutes), ranging from 0 to 100. - **Y-Axis:** Reactor Temperature (°F), ranging from 150 to 160. - The plot shows the reactor temperature over time after a step change in heating medium flow rate. - The temperature initially spikes above 159°F, then oscillates, gradually stabilizing around 154°F. **Tasks:** Determine: (a) The process gain \( K \). Give the units. (b) The damping coefficient \( \zeta \). (c) The time constant \( \tau \). Give the units. (d) The process transfer function model using the characteristic parameters.
Transcribed Image Text:**Text:** As a new process control engineer with the DMD Chemical Company, you are assigned a unit with an endothermic chemical reactor. In order to learn about the dynamics of the process, you decide to make a step change in an input variable, which is the heating medium flow rate, from 10 gpm to 14 gpm. The reactor is initially at a steady state temperature of 150°F. You obtain the following plot for the reactor temperature. **Graph Description:** - **X-Axis:** Time (minutes), ranging from 0 to 100. - **Y-Axis:** Reactor Temperature (°F), ranging from 150 to 160. - The plot shows the reactor temperature over time after a step change in heating medium flow rate. - The temperature initially spikes above 159°F, then oscillates, gradually stabilizing around 154°F. **Tasks:** Determine: (a) The process gain \( K \). Give the units. (b) The damping coefficient \( \zeta \). (c) The time constant \( \tau \). Give the units. (d) The process transfer function model using the characteristic parameters.
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