Chapter 4 SQ

Study Questions

Apply Your Knowledge

4.10
An extension of Textbook Example 4.2

The goal of this model is to predict the behavior of one variable, C_A2. Why do we need two equations?

4.11
An extension of Textbook Example 4.9

Transfer Functions

The transfer function derived in this example for the CSTR's in series is second order. Why?

4.12
A further extension of Textbook Example 4.9

Stability

Is the relationship between C_A0 and C_A2 stable?

4.13
An extension of Textbook Example 4.12

Transfer Functions

Two transfer functions were combined into one overall transfer function, what property facilitated this combination?

	Both individual transfer functions were stable.
	Both models were linear and expressed in deviation variables.
	The gains of both models are positive.
	Neither individual transfer function had a dead time.

4.14
An extension of Textbook Example 4.14

Frequency Response

If the sine had a larger period p (and a smaller frequency, since w = 2p/p) by a factor of 2, what would the new value for the tank volume be? ( w = frequency and p = 3.14159...)

4.15
An extension of Textbook Example 4.15

Frequency Response

What features of the model G(s) = K/(ts+1) were important when we used the "short cut" method for calculating the frequency response (by setting s = jw)?

4.16
A further extension of Textbook Example 4.15

Frequency Response

The amplitude of the sine output (C_A1) decreases monotonically with increasing frequency.

i.	Verify this from the equation.

ii. Explain physically

	the chemical reaction rate is second order
	the gain is second order
	the model involves two dynamic balances

	the model is stable
	the model is linear
	the model gain is 1.0