7/25/2019 Take Home Quiz_Higher Order

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Take Home Quiz: ChE 13-A (Process Dynamics and Control)

Solve the following problems. Show complete solution and box final answers. Use short bond paper

or newsprint.

1.

SECOND-ORDER SYSTEM. Consider a process that is represented by the mathematical model of

which is given by the following ODE. mydt

dy

dt

yd1234.26 2

2

y(0)=y(0)=0;

Find out the standard second order transfer function and answer the following questions for a step

input of size 5.

a. Show that the response of the process is underdamped.

b. Calculate the following values:

i. Rise time

ii. Time to first peak

iii. Percent overshoot

iv. Decay ratio

v. Period of oscillation

vi. Ultimate Value of y(t)

vii. Maximum value of y(t)

2.

ZEROES AND POLES. Consider the transfer function: () =0.7 (+2+2)

+5+234+6

(a) Plot its poles and zeros in the complex plane. A computer program that calculates the roots of

the polynomial (such as the command roots in SCILAB) can help you factor the denominator

polynomial.

(b) From the pole locations in the complex plane, what can be concluded about the output modes

for any input change?

(c) Plot the response of the output to a unit step input. Does the form of your response agree withyour analysis for part (b)? Explain.

3.

PADE APPROXIMATION. The following transfer function is not written in a standard form:

se

ss

ssG

5

)12)(2(

)5.0(2)(

a. Put it in a standard gain/time constant form.

b. Determine the gain, poles, and dead time

c. Determine the response for a unit step change in input.

d. If the time-delay term is replaced by 1/1 Pad approximation, repeat part (b) and (c).

4. HIGHER-ORDER SYSTEM. A process has the block diagram:

Derive an approximate first-order-plus-time-delay (FOPTD) transfer function model using

a. Taylor series expansion

b. Skogestads half rule