ME603_Assessment4

Master of Engineering
(Industrial Automation)

Master of Engineering (Industrial Automation) 2
ME603_Assessment4_PaperB_v1.1
Assessment Instructions:
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E.g. ME501_Assessment2_SteveMackay_01Aug2019
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Master of Engineering (Industrial Automation) 3

Please complete your answers on the assessment cover page document available on Moodle.
Clearly label your question numbers (there is no need to copy the full question over). Include all working
out.
Instructions:
Complete this exercise using Matlab and Simulink software. You may use the student version (with
the Control Systems Toolbox added on) or access the software from the EIT remote labs.
This practical will be assessed as part of the Class Participation. You can complete each task at your
own pace and submit at the end of the course for assessment.
The exercise requires the student to make use of Matlab tools to evaluate a MIMO system and to
try Statistical Process Control techniques.
The objective of Part A- of this lab exercise is to gain experience with the design of an LQR MIMO
control system for an industrial process. The objective of Part B- is to gain experience with the use
of Statistical Process Control techniques.
Part 1:
In an industrial process, we have two sensors and four actuators. The transfer functions were
obtained by experimentation and they are as follows:
From input 1 to output…
-10
1: ————–
s^2 + 72 s + 9
1
2: ————–
Master of Engineering (Industrial Automation) 4
ME603_Assessment4_PaperB_v1.1
s^2 + 72 s + 9
From input 2 to output…
1
1: ————–
s^2 + 72 s + 9
-12
2: ————–
s^2 + 72 s + 9
From input 3 to output…
0.2
1: ————–
s^2 + 72 s + 9
0.1
2: ————–
s^2 + 72 s + 9
From input 4 to output…
0.1
1: —–
s + 1
0.2
2: —–
s + 1
Question 1: (4 marks)
Master of Engineering (Industrial Automation) 5
Provide the DC gain matrix of the given system.
Question 2: (4 marks)
Apply Singular Value Decomposition on the DC gain matrix and provide the obtained matrices.
Question 3: (4 marks)
You are required to use two actuators only. Which ones you would choose? Update the transfer
matrix to consider the selected actuators. The obtained transfer matrix should be a 2×2 matrix.
Question 4: (4 marks)
Provide the Relative Gain Array of the new system (2×2)
Question 5: (4 marks)
Provide the State-Space model of the new system (2×2)
Question 6: (4 marks)
Design a Linear Quadratic Regulator for the new system (2×2) and provide the optimal gain matrix
and a screenshot of the step response of the corresponding closed loop system.
Part 2:
Question 7: (6 marks)
Before going into production, many manufacturers run a capability study to determine if their
process will run within specifications enough of the time. Capability indices produced by such a
study are used to estimate expected percentages of defective parts.
Master of Engineering (Industrial Automation) 6
ME603_Assessment4_PaperB_v1.1
Capability studies are conducted with the capability function. The following capability indices are
produced:
mu — Sample mean
sigma — Sample standard deviation
P — Estimated probability of being within the lower (L) and upper (U) specification limits
Pl — Estimated probability of being below L
Pu — Estimated probability of being above U
Cp — (U-L)/(6*sigma)
Cpl — (mu-L)./(3.*sigma)
Cpu — (U-mu)./(3.*sigma)
Cpk — min(Cpl,Cpu)
As an example, simulate a sample from a process with a mean of 3 and a standard deviation of
0.005 by typing the following MATLAB code:
rng default; % For reproducibility
data = normrnd(3,0.005,100,1);
Compute capability indices if the process has an upper specification limit of 3.01 and a lower
specification limit of 2.99 by typing the following MATLAB code:
S = capability(data,[2.99 3.01])
Visualize the specification and process widths by typing the following MATLAB code:
capaplot(data,[2.99 3.01]); grid on
Alternatively, you can use R software to obtain the same results by following the instructions
below:
1. Download and install R to your computer: https://cran.r-project.org
2. Download qcc package in R (by adding all dependencies)
3. Load qcc package
4. Launch R and type the following in the console:
data = rnorm(100,3.0,0.005) # generate the random data with mean 3 and std 0.005
Master of Engineering (Industrial Automation) 7
q = qcc(data,type=”xbar.one”) # create an object of type xbar
process.capability(q, spec.limits=c(2.99,3.01)) # produce the capability results with the given
limits
As evidence of completing the practical participation, send the figure of the capability plot.
END OF ASSESSMENT