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System Identification & Control of Electronic Engineering Systems: Milk Pasteurisation, Exams of Advanced Control Systems

Alliance University Advanced Control Systems

A past exam question from the advanced control module of the bachelor of engineering (honours) in electronic engineering degree at cork institute of technology. It includes instructions for answering four questions related to system identification, modelling, and control of a milk pasteurisation process. The questions involve interpreting diagrams, describing algorithms, designing controllers, and evaluating performance. The document also includes some additional information about pole-placement control, pi controller design, and the least squares algorithm.

Typology: Exams

2012/2013

Uploaded on 03/30/2013

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Cork Institute of Technology

Bachelor of Engineering (Honours) in Electronic Engineering- Award

(NFQ Level 8)

Summer 2007

Advanced Control

(Time: 2 Hours)

INSTRUCTIONS:

Answer any FOUR questions.

All questions carry 25 marks.

Examiners: Dr. T O' Mahony

Prof. G. Hurley

Dr. S. Foley

Q1. The set of data shown in Figure Q1(a) was used to identify two discrete-time transfer

function models using the System Identification Toolbox in MATLAB. The models were

also analysed using the system identification toolbox and the graphical analysis is

illustrated in Figures Q1(b) – Q1(g). Figures Q1(b) – Q1(d) are associated with model 1

while Figures Q1(e) – Q1(g) are associated with model 2. Model 1 is a first-order transfer

function with a delay of 17 samples while model 2 is a fifth-order transfer function with a

delay of 17 samples. The objective of the modelling process is to design a controller for the

system represented by the data shown in Figure Q1(a).

(a) Interpret Figures Q1(b) – Q1(g) and based on your understanding of these diagrams state

which model you would use and support your analysis with reference to each of these

Figures. [15 marks]

(b) The algorithms used in the MATLAB System Identification Toolbox are extensions of the

Least Squares algorithm. In your own words, describe the key concepts that underpin the

Least Squares algorithm. [10 marks]

Discover Exams of Advanced Control Systems Alliance University

Partial preview of the text

Download System Identification & Control of Electronic Engineering Systems: Milk Pasteurisation and more Exams Advanced Control Systems in PDF only on Docsity!

Cork Institute of Technology

Bachelor of Engineering (Honours) in Electronic Engineering- Award

(NFQ Level 8)

Summer 2007

Advanced Control

(Time: 2 Hours)

INSTRUCTIONS:

Answer any FOUR questions.

All questions carry 25 marks.

Examiners: Dr. T O' Mahony

Prof. G. Hurley

Dr. S. Foley

Q1. The set of data shown in Figure Q1(a) was used to identify two discrete-time transfer

function models using the System Identification Toolbox in MATLAB. The models were

also analysed using the system identification toolbox and the graphical analysis is

illustrated in Figures Q1(b) – Q1(g). Figures Q1(b) – Q1(d) are associated with model 1

while Figures Q1(e) – Q1(g) are associated with model 2. Model 1 is a first-order transfer

function with a delay of 17 samples while model 2 is a fifth-order transfer function with a

delay of 17 samples. The objective of the modelling process is to design a controller for the

system represented by the data shown in Figure Q1(a).

(a) Interpret Figures Q1(b) – Q1(g) and based on your understanding of these diagrams state

which model you would use and support your analysis with reference to each of these

Figures. [15 marks]

(b) The algorithms used in the MATLAB System Identification Toolbox are extensions of the

Least Squares algorithm. In your own words, describe the key concepts that underpin the

Least Squares algorithm. [10 marks]

0 100 200 300 400 500 600

0

A

m

pl

uit

de

Output signal

0 100 200 300 400 500 600

0

Input signal

A

m

pl

uit

de

time (seconds)

Figure Q1(a). Input/Output data used in system identification process.

0 100 200 300 400 500 600

0

time (seconds)

A

m

pl

it

ud

e

Output signal versus response of model 1

Output signal Model Response

Figure Q1(b). Validation of model 1 in the time domain.

0 100 200 300 400 500 600

0

time (seconds)

A

m

pl

uit

de

Output signal versus response of model 1

Output signal Model Response

Figure Q1(e). Validation of model 2 in the time domain (the model response is barely distinguishable

from the output signal)

-20 -15 -10 -5 0 5 10 15 20

-0.

0

Autocorrelation of residuals for output y

-20 -15 -10 -5 0 5 10 15 20

-0.

0

Samples

Cross corr for input u1 and output y1 resids

Figure Q1(f). Validation of model 2 via correlation analysis.

10

10 - 10

0 10

1

10

0

A

m

pl

uit

d

e

Frequency response

10

10 - 10

0 10

1

0

Frequency (rad/s)

P

ha

se

(d

e

g)

Figure Q1(g). Validation of model 2 in the frequency domain. The dashed lines represent the 99%

confidence region associated with the model.

Q3. Use the Least Squares algorithm to identify a suitable model from the data provided in

table Q3. Subsequently, design a pole-placement controller for this system. Explain and

justify ALL assumptions and decisions that you make.

k 1 2 3 4 5 6 7

u ( k ) -1 -1 -1 -1 1 1 1

y ( k ) 0 0 0 -1.26 -1.73 -1.90 -1.

Table Q3: Input signal u(k) and response y(k) of a process

[25 marks]

Q4. (a) An air-conditioning duct with the transfer function

z

G (^) P z

is subject to a tonal (i.e. periodic) disturbance. The estimated frequency of the disturbance

is 230Hz and the system is sampled at 60μs. Design a two degree-of-freedom Diophantine

pole-placement controller to reject this disturbance.

[15 marks]

(b) Explain how you would evaluate the performance of this design prior to implementing it on

the actual system. What are the things that you would look for that would suggest that this

might work in practice?

[10 marks]

Q5. Design a cascade controller for the system illustrated in Figure Q4(a) or Figure Q4(b).

Figure Q4(b) is the discrete-time equivalent of Figure Q4(a) where the sampling period is

T = 0.05sec. Again, you may design any type of controller (provided it has a cascade

structure) but you must DEFEND your decision by clearly explaining the advantages it

offers relative to the possible alternatives.

s +

Y 2 (s)

s s

s

D(s)

D(s): unmeasurable disturbance

Y 1 (s): primary process variable, measurable

Y 2 (s): secondary process variable, measurable

Y 1 (s)

U(s)

Figure Q4(a): Block diagram of process model

1

1 0.

z

−

− −

Y 2 (z)

1

1 1

1 1.

(1 0.99 )(1 0.97 )

z

z z

−

− −

−

− −

D(z

D(z): unmeasurable disturbance

Y 1 (z): primary process variable, measurable

Y 2 (z): secondary process variable, measurable

T (sampling period) = 0.05sec

Y 1 (z)

U(z)

Figure Q4(b): Block diagram of process model

[25 marks]

Appendix B: Design abacus for discrete systems

System Identification & Control of Electronic Engineering Systems: Milk Pasteurisation, Exams of Advanced Control Systems

Related documents

Partial preview of the text

Download System Identification & Control of Electronic Engineering Systems: Milk Pasteurisation and more Exams Advanced Control Systems in PDF only on Docsity!

Cork Institute of Technology

Bachelor of Engineering (Honours) in Electronic Engineering- Award

(NFQ Level 8)

Summer 2007

Advanced Control

(Time: 2 Hours)

Q1. The set of data shown in Figure Q1(a) was used to identify two discrete-time transfer

function models using the System Identification Toolbox in MATLAB. The models were

also analysed using the system identification toolbox and the graphical analysis is

illustrated in Figures Q1(b) – Q1(g). Figures Q1(b) – Q1(d) are associated with model 1

while Figures Q1(e) – Q1(g) are associated with model 2. Model 1 is a first-order transfer

function with a delay of 17 samples while model 2 is a fifth-order transfer function with a

delay of 17 samples. The objective of the modelling process is to design a controller for the

system represented by the data shown in Figure Q1(a).

(a) Interpret Figures Q1(b) – Q1(g) and based on your understanding of these diagrams state

which model you would use and support your analysis with reference to each of these

Figures. [15 marks]

(b) The algorithms used in the MATLAB System Identification Toolbox are extensions of the

Least Squares algorithm. In your own words, describe the key concepts that underpin the

Least Squares algorithm. [10 marks]

Figure Q1(a). Input/Output data used in system identification process.

Figure Q1(b). Validation of model 1 in the time domain.

Figure Q1(e). Validation of model 2 in the time domain (the model response is barely distinguishable

from the output signal)

Figure Q1(f). Validation of model 2 via correlation analysis.

Figure Q1(g). Validation of model 2 in the frequency domain. The dashed lines represent the 99%

confidence region associated with the model.

Q3. Use the Least Squares algorithm to identify a suitable model from the data provided in

table Q3. Subsequently, design a pole-placement controller for this system. Explain and

justify ALL assumptions and decisions that you make.

k 1 2 3 4 5 6 7

u ( k ) -1 -1 -1 -1 1 1 1

y ( k ) 0 0 0 -1.26 -1.73 -1.90 -1.

Table Q3: Input signal u(k) and response y(k) of a process

[25 marks]

Q4. (a) An air-conditioning duct with the transfer function

is subject to a tonal (i.e. periodic) disturbance. The estimated frequency of the disturbance

is 230Hz and the system is sampled at 60μs. Design a two degree-of-freedom Diophantine

pole-placement controller to reject this disturbance.

[15 marks]

(b) Explain how you would evaluate the performance of this design prior to implementing it on

the actual system. What are the things that you would look for that would suggest that this

might work in practice?

[10 marks]

Q5. Design a cascade controller for the system illustrated in Figure Q4(a) or Figure Q4(b).

Figure Q4(b) is the discrete-time equivalent of Figure Q4(a) where the sampling period is

T = 0.05sec. Again, you may design any type of controller (provided it has a cascade

structure) but you must DEFEND your decision by clearly explaining the advantages it

offers relative to the possible alternatives.

s +

Y 2 (s)

s s

s

D(s)

D(s): unmeasurable disturbance

Y 1 (s): primary process variable, measurable

Y 2 (s): secondary process variable, measurable

Y 1 (s)

U(s)

Figure Q4(a): Block diagram of process model

Figure Q4(b): Block diagram of process model

[25 marks]