p1 rjm 13/03/08for ieee colloquium control education, sheffield © dr richard mitchell 2008 modeling...

p1 RJM 13/03/08 For IEEE Colloquium Control Education, Sheffield© Dr Richard Mitchell 2008

Modeling Project at ReadingDr Richard Mitchell and Dr Will Browne

Cybernetics, School of Systems Engineering

A Part 2 assignment – 15% of a 20 credit Control module – taught to Cybernetics and Electronic Engineering studentsBuilds on Laplace Transforms in Part 1 Engineering Maths. Students find theoretical response to a second order system.Using MATLAB they superimpose the simulated and theoretical responses – to verify the simulation.They generate the block diagram and transfer function of other systems (different each year) and simulate them. Though often considered hard, students say they learn much. We also provide a cut down version of a control toolbox.


HistoryIn 1998 this was introduced in Summer term of year 1 (which

was first term of Part 2) in a unit comprising Laplace Transforms and Modelling

The students were as now required to find theoretical response of second order systems, but the simulation and plotting was done as an exercise in object-oriented programming.

In 2002, MATLAB was introduced to replace O-O prog (which is now part of an exercise for neural networks).

By summer 2003, Reading had more sensible structure – so Laplace Transforms moved to Part 1 Maths, Modelling Project incorporated in Part 2 Control module.

Feedback and Control introduced in Part 1 Cybernetics module.


On the Assignment – from sheetAssignment has Parts A and B.

Part A is 'open book' marked for accuracy. Part B is 'closed book' marked for accuracy, description and uniqueness (i.e. copying anyone else's code is plagiarism)

Derive models of systems using block diagrams.Simulate such systems using MATLAB.Find theoretical step response of first & second order systems.Verify simulation, by superimposing theory and simulation.Utilise MATLAB for system understanding, incl Bode & Nyquist.You will be assessed by a report you write – in the School

Style. Keep a log book: it is good practice and will help the report. Write as many MATLAB functions (m files) as is reasonable. If you need help in part A, ask! Use lecture notes & refs for B.


HintsThe transfer functions you should find can be expressed in one of the following forms, which will help you find the theoretical step response:

2 2 2 2 2K K K K Ks K K

, , , , , ,s+a s(s+a) (s+a)(s+b) (s+a)(s+b)(s+a) (s+a) +b s +a

If you cannot get the transfer function in such a form, you are wrong!

Theoretical response: use commands likethy = 1 - exp(-1.5*t) - (1.5*t.*exp(-1.5*t));

Use '.*' operator to multiply corresponding elements in column vectors (must be the same size)


Tasks to do for Systems in A and B

1. For each system below, draw relevant block diagram(s), and by hand find its transfer function – put in standard form.

2. For each system, using the relevant block diagram, use MATLAB commands to confirm your transfer function.

3. For each system, use Laplace transform techniques to find an expression for the system output as a function of time, when its input is a unit step and initial values are zero. Use only the transforms in the table provided.

4. Use subplot to plot two graphs side by side. The first graph should be the simulated step response, superimposed on to which is the theoretical response. The second graph is the Bode diagram of the system.

5. Utilise MATLAB for system understanding.


On m-files to writeTask 1-4 : Put the code you have written here in an m file

function modelass(sys)% sys specifies system to analyse% function generates the transfer function and plots% simulated & theoretical step response + Bode diagram

Task 5 : Create an input/output viewer that will plot the output signal against time on the same axes as its sinusoid input. Test this viewer with a range of input frequencies applied to the systems. Also plot Nyquist and Bode diagrams:function ioviewer(sys)% where sys specifies the system to analyse% functions produces the transfer function of the system % & plots its input/output relation – simulated or theoretical


Systems in Part AInput position, xi Output position, xoSpring, k

mass mDashpot, F

Object

o

i

xDerive when m = 1 kg and F = 0 and k = 5 N/ m

x

0.5Ω

IL

2F VoVi

1Ω

I1

10H

Vm

Im

Derive the block diagram of the above, reorganise it and then use the inverse transfer function method to find Vo/Vi.

Optional : verify transfer function using two port networks

1

2


Systems in Part B (vary each year)

ControlL: Local

P:PlantScaler

Output,OInput, I S: Pre-

FeedbackM: Main

ControlC:Series

3a - Control of Second Order Plant using PID

O 8 12.5Find when S=1; C=56 96s; L=0; P= ; M=1

I s (1 s3)(1 s4)

3b - Control using Lead Lag and velocity feedback

O 1 s6 12.5

Find when S=1; C=0.5 ; L=0.08s; P= ; M 1I 1 s (1 s3)(1 s4)


4. Wien Bridge for Theremin Oscillators

C1

R1

Vp Vo

R2

C2

+-

RF

R3

Research history, uses and benefits of circuit – cite sources – not wikipedia etc

o2p

V ksShow has f orm

V as +bs+c

Find the resonant frequency ωo when R1 = R2 and C1 = C2

Using skills leant in Part A thoroughly investigate the circuit, noting important features of frequency and time responses. Use values of C = 10nF, R = 10KΩ, RF = 20KΩ and R3= 10KΩ


On MATLAB

MATLAB is introduced in Part 1 – plots, commands and m-files in the Cybernetics module + various practicals (some GUI interface but others involve writing m-files).

At the start of Part 2 all students do an introduction to MATLAB for control practical – learn control toolbox.

The modelling project is done in student’s own time – they can use school PCs which have MATLAB + control toolbox, but also other Uni PCs (or their own) without the toolbox

Hence we have RMControlToolbox that they can download

rmcontrl (help file); rmstep; rmbode; rmtf; rmseries; etc

http://www.personal.reading.ac.uk/~shsmchlr/pof/index.htm


Student’s Comments

Assignment is hard and not worth as many marks as it should.

Many say that it has really helped their understanding.

It is good that it tests a range of topics.

They like the short (ish) exercises on range of systems.

One did project again as a revision aid.

Suggestions for improvements:

Submit Part A and get feedback before doing Part B.

Currently parameter values given … go and search for them.

Have Lab practical afterwards implementing some systems to see techniques in practice.


DiscussionLaplace is taught with Differential Equations in 10 lectures

– and students often ‘ignore’ the Laplace

This assignment helps to get it understood.

Also helps to show material in one module used in others

Control is clearly relevant to Cybernetics, but some Electronic Engineering students are not so clear on its relevance

Hence the modelling assignment has control & electronics.

Helps emphasise ‘systems’ aspect of Cybernetics.

Overall – the project is a good one which has stood the test of time whilst continually evolving.

p1 rjm 13/03/08for ieee colloquium control education, sheffield © dr richard mitchell 2008 modeling...

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