control system

System Response in Time Domain
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	We, by signing this page, declare that the work presented in this report is all work done by us, unless appropriate reference has been made to the work of others. We acknowledge that should this not be the case the report will receive zero marks and due action may be taken.
Lab Number:
Demonstrator
Submitted on
Mark Received

Experiment 1

1.1. Requirements of Experiment 1 Compulsory

A summary of the experiment description provided in the laboratory manual.

(up to ½ page)

1.2. Introduction (Background) Compulsory

An explanation of the underpinning theory, as relevant to this experiment.

(up to 1½ page)

1.3. Solution Description 15 marks

Object transfer function/s, any simplifications needed, transfer function features.

Method your solution used to calculate results.

Brief elaboration on the key aspects of the developed program code

[ensuring that underpinning theory which supports or justifies your solution has been provided in the introduction].

(up to 1½ page)

1.4. Test Results 10 marks

This section of your report should include the following:

· Table of results (using tables provided on the following page);

· Step response plots (showing response characteristics) for both the second order approximation and higher order systems; other response values & equations as outputted by Matlab

· Virtual laboratory responses.

All results should be appropriately labeled, and any inputs or relevant parameter values provided. All plots MUST include:

· labels identifying signals (where multiple signals are shown on 1 plot)

· a figure description directly underneath. This description should include the type of plot, system (e.g. T1(s)), and all parameters associated with generating it (e.g. Kp, Gt, Gp, etc.)

Parameters & Characteristics :	Damping ratio x	Natural frequency (n	Dominant Pole Pair	Settling time Ts (sec)	Peak time Tp (sec)	Percent overshoot %OS	Rise time Tr (sec)
T1(s)	(a) Calculated
	(b) From step response
	(c) Virtual-Lab response
T2(s)	(a) Calculated
	(b) From step response
	(c) Virtual-Lab response
T3(s)	(a) Calculated
	(b) From step response
	(c) Virtual-Lab response

1.5. Discussion & Conclusions 30 marks

Discuss results obtained.

Include a discussion of those expected (e.g. from analytical calculations, or previous results), to those returned by your program.

Compare results calculated by different methods, and justify any assumptions or approximations.

Evaluate and draw conclusions as to the performance / operation of the resulting system.

Your discussion of this experiment should include answers to the following questions :

Q1 : What effect does the increase in Kp have on :

a) transfer function Ti(s) ?

b) natural frequency (n ?

c) damping ratio ( ?

d) pole location?

Your answer should make reference to results in Table 1, expressions for finding the characteristics of second order systems, and the general second order transfer function.

Q2 : How do the characteristics of MATLAB’s simulated step response (row (b) of Table 1) compare to those calculated (row (a) of Table 1)? Explain any differences.

Q3 : How do results of the simulation in MATLAB compare to those found in the ESVL virtual laboratory? What is causing any differences?

Q4 : Describe the effect of increasing natural frequency (n on the resulting step response? Interpret this effect in terms of servo motor operation. What is the effect of increased damping (?

(up to 1½ page)

1.6. References Compulsory

Reference any sources cited in this report.

1.7. Appendix: Compulsory

Printed source code, as implemented in Matlab programming environment (with comments).

Experiment 2

2.1. Requirements of Experiment 2 Compulsory

2.2. Introduction (Background) Compulsory

2.3. Solution Description 15 marks

2.4. Test Results 10 marks

Parameters & Characteristics	(i) - COMPULSORY	(ii) - INCENTIVE
	(a) 2nd order approx. calculated	(b) 2nd order approx. step response	(c) Higher order step response	(a) 2nd order approx. calculated	(b) 2nd order approx. step response	(c) Higher order step response
Damping Ratio x
Natural Frequency (n
Closed-loop Poles
Closed-loop Zeros
Settling time Ts
Peak time Tp
Percent overshoot %OS
Rise Time Tr

2.5. Discussion & Conclusions 20 marks

Your discussion to this experiment should include answers to the following questions.

For each system T1(s) – (COMPULSORY ACTIVITY) and T2(s) – (INCENTIVE ACTIVITY) ,

Q1 : Does pole-zero cancellation result in a valid approximation for this system? Justify the approximation by elaborating on the differences between the actual system and the approximated one.

Q2 : How do results observed in the virtual laboratory compare to those of Matlab, and what may be causing any differences?

Q3 : What may be the consequences of using this approximation in system design? Relate your discussion to the servomechanism.

2.6. References Compulsory

2.7. Appendix Compulsory

NOTES:

1.

Marks assigned to compulsory activities total 100.

2.

Incentive activities, altogether, bring an additional 10% marks, if all performed successfully.