A composition sensor is used to continually monitor the contaminant level in a liquid stream. The dynamic behavior of the sensor can be described by a first-order transfer function with a time constant of r in seconds. Consider C and Cm the actual contaminant concentration and the measured value by the biosensor, respectively. The initial (before the change) concentration of contaminant and therefore the sensor reading is CA0 ppm (i.c., the values at t-0). An alarm sounds if the measured value exceeds the environmental limit of 7 ppm. Suppose that the actual contaminant concentration in the liquid stream (i.e. C) gradually increases according to the expression, C(t)= a + bt, where t is expressed in seconds; a and b are constant positive numbers (this is called ramp input which is different from step change). Select all correct statements: The transfer function, G(s) is Cm(s) C(s) Based on the transfer function, the steady-state gain (K₂) of the sensor is 1. steady-state gain (K₂) of a process is defined as 1 TS + 1 where Y and U denote the corresponding steady state values of the output (response) and input (change) variables. C(s)= a + bs In the previous question, in order to find the sensor reading, Cm(s), in the transfer function (G(s)), you need to know the change of actual concentration in the Laplace domain. Which of the following represents the C(s) in the transfer function (Hint: Should C(s) be in a deviation format and in a Laplace domain)? C(s)= a/s + bs Y₂-Y₁ U₂-U₁ C(s)= a/s + b/s² C(s)=b/s² In the previous question, What is the analytical solution of the sensor response with respect to time if: 1. the input, C(t)=5+0.2t 2. sensor time constant is 10 seconds 3. the steady state concentration before change is 5ppm
A composition sensor is used to continually monitor the contaminant level in a liquid stream. The dynamic behavior of the sensor can be described by a first-order transfer function with a time constant of r in seconds. Consider C and Cm the actual contaminant concentration and the measured value by the biosensor, respectively. The initial (before the change) concentration of contaminant and therefore the sensor reading is CA0 ppm (i.c., the values at t-0). An alarm sounds if the measured value exceeds the environmental limit of 7 ppm. Suppose that the actual contaminant concentration in the liquid stream (i.e. C) gradually increases according to the expression, C(t)= a + bt, where t is expressed in seconds; a and b are constant positive numbers (this is called ramp input which is different from step change). Select all correct statements: The transfer function, G(s) is Cm(s) C(s) Based on the transfer function, the steady-state gain (K₂) of the sensor is 1. steady-state gain (K₂) of a process is defined as 1 TS + 1 where Y and U denote the corresponding steady state values of the output (response) and input (change) variables. C(s)= a + bs In the previous question, in order to find the sensor reading, Cm(s), in the transfer function (G(s)), you need to know the change of actual concentration in the Laplace domain. Which of the following represents the C(s) in the transfer function (Hint: Should C(s) be in a deviation format and in a Laplace domain)? C(s)= a/s + bs Y₂-Y₁ U₂-U₁ C(s)= a/s + b/s² C(s)=b/s² In the previous question, What is the analytical solution of the sensor response with respect to time if: 1. the input, C(t)=5+0.2t 2. sensor time constant is 10 seconds 3. the steady state concentration before change is 5ppm
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:A composition sensor is used to continually monitor the contaminant level in a liquid stream. The dynamic behavior
of the sensor can be described by a first-order transfer function with a time constant of t in seconds. Consider C and
Cm the actual contaminant concentration and the measured value by the biosensor, respectively. The initial (before
the change) concentration of contaminant and therefore the sensor reading is CAO ppm (i.c., the values at t = 0). An
alarm sounds if the measured value exceeds the environmental limit of 7 ppm. Suppose that the actual contaminant
concentration in the liquid stream (i.e. C) gradually increases according to the expression, C(t)= a + bt, where t is
expressed in seconds; a and b are constant positive numbers (this is called ramp input which is different from step
change).
Select all correct statements:
The transfer function, G(s) is
Cm(s)
C(s)
G(s)
Based on the transfer function, the steady-state gain (Kp) of the sensor is 1.
steady-state gain (K₂) of a process is defined as Kp =
1
TS + 1
where Y and U denote the corresponding steady state values of the output (response) and input (change)
variables.
C(s) = a + bs
In the previous question, in order to find the sensor reading, C,(s), in the transfer
function (G(s)), you need to know the change of actual concentration in the Laplace
domain. Which of the following represents the C(s) in the transfer function
(Hint: Should C(s) be in a deviation format and in a Laplace domain)?
C(s)= a/s + bs
C(s)= a/s + b/s²
C(s)=b/s²
Y₂-Y₁
U₂-U₁
In the previous question, What is the analytical solution of the sensor response with
respect to time if:
1. the input, C(t)=5+0.2t
2. sensor time constant is 10 seconds
3. the steady state concentration before change is 5ppm
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