Basic Control Theory: Part I

March 24, 2015 in General, MATH6037 | Leave a comment

This is the first in a series of posts that are an attempt by me to understand why my Industrial Measurement and Control students need to study the Laplace Transform.

Consider a black box model that takes as an input signal a function x(t) and produces an output signal y(t). For reasons that are as of yet not clear to me, we can take all of the derivatives of y(t) (and x(t)) to vanish for t=0.

Definition

The transfer function of a black box model is defined as

\displaystyle H(s)=\frac{Y(s)}{X(s)},

where Y(s) and X(s) are the Laplace Transforms of y(t) and x(t).

Note we have the Laplace transform of a function f(t) is a function F(s) defined by

F(s)=\mathcal{L}\{f(t)\}=\int_{0}^\infty f(t)e^{-st}\,dt.

Poles of H(s) are complex numbers z such that X(z)=0. For example, for an input signal x(t)=e^t, the transfer function has a pole at s=1 as

\displaystyle F(s)=\frac{1}{s-1}.

If the coefficients of x(t) are real, then in general the poles of the transfer are real or come in conjugate root pairs.

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MATH7021: Week 7

March 23, 2015 in MATH7021 | Leave a comment

I am emailing a link of this to everyone on the class list every week. If you are not receiving these emails or want to have them sent to another email address feel free to email me at jpmccarthymaths@gmail.com and I will add you to the mailing list.

Catch-up Classes

We will have one more catch-up class on Thursday at 12:00 in B187.

Assignments 1 & 2

The corrections are now done and the results sent to you.

You will not receive the second Assignment until after Easter. The hand-up date will be the Monday of Week 11 — when you really will be quite busy.

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MATH6040: Week 7

March 23, 2015 in MATH6040 | Leave a comment

I am emailing a link of this to everyone on the class list every week. If you are not receiving these emails or want to have them sent to another email address feel free to email me at jpmccarthymaths@gmail.com and I will add you to the mailing list.

Catch Up Classes

We will have catch up classes on Wednesdays at 10:00 in C236 in Weeks 9 and 10 (after Easter). That is an extra MATH6040 lecture on

  • 15 April 2015
  • 22 April 2015

Academic Learning Centre Question

Question 2, P.73.

Week 7

We have been looking at determinants.

Week 8

We will finish off Cramer’s Rule and start the third chapter with a revision of differentiation.

Study

Please feel free to ask me questions about the exercises via email or even better on this webpage.

Student Resources

Please see the Student Resources tab on the top of this page for information on the Academic Learning Centre, etc..

MATH6037: Week 7

March 23, 2015 in MATH6037 | 4 comments

I am emailing a link of this to everyone on the class list every week. If you are not receiving these emails or want to have them sent to another email address feel free to email me at jpmccarthymaths@gmail.com and I will add you to the mailing list.

Continuous Assessment

You are identified by the last four digits of your student number unless you are winning the league. The individual quiz marks are out of 2.5 percentage points. Your best eight quizzes go to the 20% mark for quizzes. The R % column is your running percentage (for best eight quizzes), MPP is your Maple Percentage Points and the GPP is your Gross Percentage Points (for best eight quizzes and Maple). Most of the columns are rounded but column six, for quiz five, is correct.

S/N Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 R % QPP MPP GPP
Kelliher 3 3 3 3 2.3 98 12.3 4.5 16.8
8335 2 3 2 3 2.5 98 12.3 4.5 16.8
3281 2 3 3 3 2.1 96 12.0 4.5 16.5
5527 2 3 3 3 2.5 94 11.9 4.5 16.4
7878 2 2 2 2 2.1 85 10.6 4.5 15.1
8416 2 1 2 3 2.5 84 10.5 4.5 15.0
8478 2 2 2 2 0 82 8.2 4.5 12.7
1864 1 2 3 2 1.24 76 9.5 4.5 14.0
8403 2 1 2 3 1.3 76 9.5 4.5 14.0
4198 0 1 2 3 1.7 74 7.4 4.5 11.9
6548 2 1 2 3 1.6 71 8.9 4.5 13.4
8603 1 2 2 2 0 67 6.7 3 9.7
8556 1 1 2 2 0 66 6.6 4.5 11.1
2567 2 2 2 1 1.8 65 8.2 4.5 12.7
1852 1 1 2 2 2.1 57 7.1 4.5 11.6
2859 2 1 0 1 1.6 55 5.5 4.5 10.0
5546 0 0 1 1 1.9 53 4.0 4.5 8.5
7950 0 0 1 0 1.8 52 2.6 3 5.6
9464 1 1 2 1 1.24 46 5.7 4.5 10.2
7209 2 1 2 1 0.16 44 5.5 4.5 10.0
8455 0 1 1 1 1.9 38 4.8 4.5 9.3
4775 1 0 1 0 0.4 22 2.2 4.5 6.7
5553 0 1 0 0 0.1 17 1.3 4.5 5.8

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MATH7021: Week 5

March 6, 2015 in MATH7021 | Leave a comment

I am emailing a link of this to everyone on the class list every week. If you are not receiving these emails or want to have them sent to another email address feel free to email me at jpmccarthymaths@gmail.com and I will add you to the mailing list.

Week 6

We will have catch-up classes on Thursdays at 12:00 in B187 in

  • Week 7 — 19 March
  • Week 8 — 26 March

Assignment 1

This must be handed up before 5 pm today. Make sure to email me your Excel file.

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MATH6040: Week 5

March 6, 2015 in MATH6040 | Leave a comment

I am emailing a link of this to everyone on the class list every week. If you are not receiving these emails or want to have them sent to another email address feel free to email me at jpmccarthymaths@gmail.com and I will add you to the mailing list.

Test 1

Please find the results below. You are identified by the last four digits of your student number unless you excelled.

The average of the students with one attendance warning was 70. This average drops by 10 percentage points for each attendance warning.

As I mentioned at the start of the semester, this chapter is arguably the most straightforward and the easiest way to pass this module is to do well in the vectors test and exam question. Those of us who are attending class and still performing poorly need more help than the tutorials alone. The students in this category need to start attending the Academic Learning Centre to boost their performance.

I handed out and corrected a Quick Test with suggestions. I would advise poorly performing students to bring this Quick Test with them to the Academic Learning Centre. Furthermore I am going to put up one problem per week that poorly performing students should bring to the ALC and try with the help of the maths lecturers there.

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MATH6037: Week 5

March 5, 2015 in MATH6037 | 10 comments

I am emailing a link of this to everyone on the class list every week. If you are not receiving these emails or want to have them sent to another email address feel free to email me at jpmccarthymaths@gmail.com and I will add you to the mailing list.

Continuous Assessment

You are identified by the last four digits of your student number unless you are winning the league. The individual quiz marks are out of 2.5 percentage points. Your best eight quizzes go to the 20% mark for quizzes. The R % column is your running percentage (for best eight quizzes), MPP is your Maple Percentage Points and the GPP is your Gross Percentage Points (for best eight quizzes and Maple). Most of the columns are rounded but column five, for quiz four, is correct.

S/N Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 R % QPP MPP GPP
Kelliher 3 3 3 2.5 100 10.0 3 13.0
3281 2 3 3 2.5 99 9.9 3 12.9
8335 2 3 2 2.5 98 9.8 3 12.8
5527 2 3 3 2.5 94 9.4 3 12.4
7878 2 2 2 1.9 85 8.5 3 11.5
1864 1 2 3 2.1 83 8.3 3 11.3
8403 2 1 2 2.5 82 8.2 3 11.2
8478 2 2 2 2.4 82 8.2 3 11.2
8416 2 1 2 2.5 80 8.0 3 11.0
4198 0 1 2 2.5 76 5.7 3 8.7
6548 2 1 2 2.5 73 7.3 3 10.3
8603 1 2 2 2.4 67 6.7 3 9.7
8556 1 1 2 2.2 66 6.6 3 9.6
2567 2 2 2 1.28 64 6.4 3 9.4
7209 2 1 2 0.5 54 5.4 3 8.4
2859 2 1 0 0.5 52 3.9 3 6.9
1852 1 1 2 1.5 50 5.0 3 8.0
9464 1 1 2 0.9 45 4.5 3 7.5
5546 0 0 1 1 42 2.1 3 5.1
7950 0 0 1 0 32 0.8 1.5 2.3
8455 0 1 1 0.7 29 2.9 3 5.9
5553 0 1 0 0 24 1.2 3 4.2
4775 1 0 1 0 24 1.8 3 4.8

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MATH6040: Week 4

February 26, 2015 in MATH6040 | Leave a comment

I am emailing a link of this to everyone on the class list every week. If you are not receiving these emails or want to have them sent to another email address feel free to email me at jpmccarthymaths@gmail.com and I will add you to the mailing list.

Test 1

The test will be on the TUESDAY of Week 5 at 11:00 in B214.

We will have an extra tutorial for all students at 17:00 on Monday in B240 where I will go through the sample and answer any questions.

Week 4

We looked at how to do matrix multiplication and did some examples of matrix arithmetic. We looked at Matrix Inverses — “dividing” for Matrices.

Week 5

We will see full examples of 3×3 inversion using the Gauss-Jordan Algorithm and then look at Matrix Equations.

Week 6

I will be away in Week 6 (9 – 13 March) so you have no maths that week.

We will have catch up classes on Tuesdays at 14:00 in C236 in Weeks 8, 9 and 10. That is an extra MATH6040 lecture on

  • 24 March 2015
  • 14 April 2015
  • 21 April 2015

Study

Please feel free to ask me questions about the exercises via email or even better on this webpage.

Student Resources

Please see the Student Resources tab on the top of this page for information on the Academic Learning Centre, etc..

MATH7021: Week 4

February 26, 2015 in MATH7021 | Leave a comment

I am emailing a link of this to everyone on the class list every week. If you are not receiving these emails or want to have them sent to another email address feel free to email me at jpmccarthymaths@gmail.com and I will add you to the mailing list.

Week 6

I will be away in Week 6 (9 – 13 March). We will have catch-up classes on Thursdays at 12:00 in B187 in

  • Week 5 — next week, 5 March
  • Week 7 — 19 March
  • Week 8 — 26 March

Assignment 1

If you are having problems get onto me ASAP. Please read the instructions carefully. The deadline is Friday 6 March.

Please find the first assignment here. Please change the c_1 and c_2s in Question 1.1. to k_1 and k_2s please.

You also need to download these files:

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MATH6037: Week 4

February 26, 2015 in MATH6037 | 2 comments

I am emailing a link of this to everyone on the class list every week. If you are not receiving these emails or want to have them sent to another email address feel free to email me at jpmccarthymaths@gmail.com and I will add you to the mailing list.

Continuous Assessment

You are identified by the last four digits of your student number unless you are winning the league. The individual quiz marks are out of 2.5 percentage points. Your best eight quizzes go to the 20% mark for quizzes. The R % column is your running percentage (for best eight quizzes), MPP is your Maple Percentage Points and the GPP is your Gross Percentage Points (for best eight quizzes and Maple). The first two columns are rounded figures but the third, for quiz three, is correct.

The solutions to the last quiz may be found in the notes.

S/N Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 R % QPP MPP GPP
Kelliher 3 3 2.5 100 7.5 1.5 9
3281 2 3 2.5 98.7 7.4 1.5 8.9
8335 2 3 2.4 97 7.275 1.5 8.775
5527 2 3 2.5 92 6.9 1.5 8.4
7878 2 2 2.25 88 6.6 1.5 8.1
1864 1 2 2.5 82.7 6.2 1.5 7.7
8478 2 2 2.15 76.9 5.77 1.5 7.27
8403 2 1 2.45 76 5.7 1.5 7.2
8416 2 1 2.2 73.3 5.5 1.5 7
2567 2 2 2.05 68 5.1 1.5 6.6
7209 2 1 1.75 64.7 4.85 1.5 6.35
6548 2 1 2.25 64 4.8 1.5 6.3
8556 1 1 2.4 58 4.35 1.5 5.85
NR 1 2 1.85 56.7 4.25 1.5 5.75
9464 1 1 1.5 48 3.6 1.5 5.1
1852 1 1 1.6 46.7 3.5 1.5 5
2859 2 1 0 68 3.4 1.5 4.9
4198 0 1 2 64 3.2 1.5 4.7
8455 0 1 1.05 28.7 2.15 1.5 3.65
4775 1 0 1 24 1.8 1.5 3.3
5553 0 1 0 24 1.2 1.5 2.7
5546 0 0 1.1 44 1.1 1.5 2.6
7950 0 0 0.8 32 0.8 0 0.8

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