Reference no: EM132500621

ME603 Advanced Process Control Assignment - Master of Industrial Automation Engineering - Engineering Institute of Technology, Australia

Assessment Task - Practical Participation

Instructions - Complete this exercise using Matlab and Simulink software. 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 a 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 A -

In an industrial process, we have four sensors and four actuators. The transfer functions were obtained by experimentation and they are as follows (attached).

Question 1: Provide the dc gain matrix of the given system.

Question 2: Apply singular value decomposition on the dc gain matrix and provide the obtained matrices.

Question 3: 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 2x2 matrix.

Question 4: Provide the relative gain array of the new system (2 x 2).

Question 5: Provide the state-space model of the new system (2 x 2).

Question 6: Design a linear quadratic regulator for the new system (2 x 2) and provide the optimal gain matrix and a screenshot of the step response of the corresponding closed loop system.

Part B -

Question 7: 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.

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

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

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.

Attachment:- Advanced Process Control Assignment File.rar