Chapter 4    Modelling and Analysis for Process Control
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Check Your Reading             Study Questions             Thought Questions

The questions will be categorized according to the most relevant of the five key concepts.

Laplace Transforms Transfer Functions Block Diagrams
Stability Frequency Response











Check Your Reading

Solidify the Concepts

Which of the following are reasons for using Laplace transforms in process control?

Laplace Transforms



Linearize a non-linear function.


Solve differential equations to determine the dependent variables as a function of time.


Establish key aspects of dynamic behavior from the transfer functions (e.g. stability, damping etc.)

Determine how the steady-state gain depends on equipment design and operating conditions.





Complete the following statement.

Laplace Transforms

"The Laplace transform and its inverse are______ ."


the same




complex numbers













For the following differential equation, select the Laplace transform of the equation.

Laplace Transforms

Differential Equation:



















Select the output response of a process whose only dynamics are a pure dead time to a step input at t = 20 .  We do not know the value of the dead time.

Dead time is like a "plug flow" is a pipe.  

(Click on figure that you select.)

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A transfer function provides a model of:

Transfer Functions


a first order system


the output behavior for any input


the output behavior for any input assuming that all the initial conditions are zero


the output for a specific input using the Laplace transform tables














Complete the following statement: An asymptotically stable system ...




has outputs that approach constant values after all inputs attain constant values.


has poles with positive real parts.


is always underdamped.


has a negative gain.







What can be determined from the following transfer function?

Transfer Functions


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One pole is less than 1; therefore, the system is overdamped.


The gain is negative; therefore, the system is stable.


The system is second order, and it is overdamped.












Complete the following statement:
A block diagram is ...

Block Diagrams




a set of interconnected boxes.


a picture of the connection between transfer function models.


only for dynamic models.


essential for combining several transfer functions into one overall transfer functions.














Frequency response is used in the analysis of dynamic systems because...

Frequency Response




sine inputs occur often in industrial plants.


frequency response is a close approximation to step response.

periodic disturbances (which are not sines) occur often in industrial plants and their effects are analyzed using frequency response.