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# 1st Assignment in System Identification & Advanced Contr

BE & ME, AUT

David Wilson

1st Assignment in System Identification & Advanced Control

Due Date: 9th August 2013

1st Assignment in System Identification & Advanced Control 代寫

1st Assignment in System Identification & Advanced Control 代寫

1st Assignment in System Identification & Advanced Control

This assignment is part of the overall course assessment. It has 26 points. We expect that you

would need to spend around 20 hours per week for these assignments. I will mark only a sub-set

of the questions.

The assignment is split into two parts. The first part, all students do, the second part is for

he ME students.

The following general points apply to all work handed in for assessment.

• Remember to include your name, student ID, date, course code, and assignment # on your

assignment solutions.

1st Assignment in System Identification & Advanced Control 代寫

1st Assignment in System Identification & Advanced Control 代寫

• I will collect the assignments at the lecture on the due date.

• Type your results, include commented code and Simulink diagrams where necessary, and

make sure your plots have labels, and are numbered.

• You solutions must include all workings to show how you derived the answer. Simply giving

the numerical solutions (as is given in the textbook in the drill exercises) is worthless.

1. 0 pts Make sure you are familiar with the material on the course web page and you have a copy of

the course compendium, Advanced Control using Matlab.

2. 0 pts Make sure you have access to Matlab. You will need Matlab and Simulink to answer the

following questions. There are many books in the library and documents available on the

internet to help you get started using Matlab.

Try some of the following

• www.mathworks.com/access/helpdesk/help/techdoc/learn_matlab/learn_matlab.shtml

• http://www.mech.ubc.ca/ ~ ahodgson/Courses/MECH%20410E/Assignments/matlab.htm

3. 0 pts Make sure that you have access to the Control toolbox, the System Identification toolbox, and

the Symbolic toolbox for Matlab. You can tell which toolboxes are installed by using the

ver command.

4. 0 pts Make sure that have downloaded the Opti toolbox from www.i2c2.aut.ac.nz.

Graded questions for BE and ME

The following questions are for both the BE and ME class.

5. Fig. 1 shows the temperature in a reactor when the input current to an electrical heater was

changed from 0 to 1.5 A.

(a) 4 pts Approximate a dynamic model (transfer function) to the step test data given in Fig. 1.

Note that the shape factor and time constant are related to the decay ratio and the period

by

ζ =

−ln(DR)

√ 4π 2

+ ln(DR) 2

, τ = P

√ 1 − ζ 2

1st Assignment in System Identification & Advanced Control 代寫

1st Assignment in System Identification & Advanced Control 代寫

2π

(b) 3 pts Sketch the response of the temperature assuming the current is i(t) = 0.2sin(2t) for t > 0,

and where t is measured in minutes.

Hint: Think about what happens with negative current.

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1st Assignment in System Identification & Advanced Control 9th August 2013

0 5 10 15 20

30

35

1st Assignment in System Identification & Advanced Control 代寫

1st Assignment in System Identification & Advanced Control 代寫

40

45

50

Temperature [degrees C]

0 5 10 15 20

0

0.5

1

1.5

2

Current [A]

time [min]

Figure 1: Temperature response of a step test. Figure for question 5.

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1st Assignment in System Identification & Advanced Control 9th August 2013

6. We want to approximate the high-order transfer function

G(s) =

−0.3(s − 1)e −s

(s + 1) 2 (s + 0.4)(s + 0.25)

(1)

with simpler models.

(a) 2 pts Approximate Eqn. 1 with a first-order plus deadtime model using the method of areas.

Hint: See algorithm 6.1 in the compendium.

(b) 2 pts Find an approximate second order transfer function with deadtime to Eqn. 1.

Graded questions for Master’s of Engineering only

The following questions are compulsory for those students doing the Master’s course. The

questions are optional for the undergraduate students.

7. 5 pts Read and summarise the paper:

De Nicolao G., System identification: Problems and perspectives, Proceedings of 11th Int.

Workshop on Qualitative Reasoning, Cortona Italy, L. Ironi ed., IAN CNR Pavia n.1036,

379-386, 1997

available from http://www.qrg.northwestern.edu/papers/Files/qr-workshops/QR97/DeNicolao_

tutorial_1997_System_Identification_Problems_Perspectives.pdf

8. Toijala (Waller) and Fagervik developed a model of a 10 plate binary distillation column. The

transfer function is of the form

[

x D

x B

]

= G(s)

1st Assignment in System Identification & Advanced Control 代寫

1st Assignment in System Identification & Advanced Control 代寫

[

u 1

u 2

]

where G(s) is a matrix of transfer functions;

G 1,1 (s) =

0.542

(14.2s + 1)(0.14s + 1)(0.05s + 1)(0.083s + 1)

G 1,2 (s) =

−0.453exp(−0.17s)

(13.4s + 1)(0.13s + 1)(0.167s + 1)(0.083s + 1)(0.05s + 1)

G 2,1 (s) =

0.516

(18.2s + 1)(0.083s + 1) 11 (0.05s + 1)

G 2,2 (s) =

−0.579

(17.4s + 1)(0.167s + 1)(0.05s + 1)(0.083s + 1)

(a) 4 pts Simulate a step response for this system in Matlab or Simulink.

Hint Follow the Wood-Berry multivariable transfer function example in the Compendium.

(b) 6 pts The very high order term G 21 comes from the fast liquid dynamics on each of the 10

trays plus the reboiler. The original authors approximated this term using a first order

plus dead time model with a large time constant

ˆ

G 2,1 =

0.516e −0.5s

(18.2s + 1)(0.4s + 1)(0.05s + 1)

(2)

How good is this approximation, and can you find a better one without using deadtime?

What is the motivation for avoiding deadtime in the approximation?

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1st Assignment in System Identification & Advanced Control 9th August 2013

References

[1] Katsuhiko Ogata. Discrete-Time Control Systems. Prentice–Hall, 1987.

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