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Automated Flight Summary

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  • June 17, 2020
  • 37
  • 2019/2020
  • Summary

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AMSTERDAM
UNI ERSIT OF
APPLIED SCIENCES
ACA C A 2019-2020
A ED
A
FLIGH




A ED
FLIGH
A




A

, AMSTERDAM UNIVERSITY OF APPLIED SCIENCES


Course Overview

Week Subject
1 General introduction in automated flight, basics in complex numbers.
2 Historical developments; Laplace transform.
3 Control Theory; Laplace transform and Partial fraction expansion.
4 Control Theory; Partial Fraction expansion, mass spring system.
5 Control Theory; Block Diagrams and Stability
6 Control Theory; Stability, Poles, System Response and Block Diagrams
7 Control Theory: Proportional Control and Root Locus
8 Control Theory: PID Controllers




AUTOMATED FLIGHT SUMMARY 2

, AMSTERDAM UNIVERSITY OF APPLIED SCIENCES


Week 1: General Introduction and basics in Complex Numbers
Control Theory
System A set of connected things or devices that operate together.




input C System output

Summing Point
feedback Branch Point



= Closed-Loop System (+feedback)
= Open-Loop System

Closed-Loop A system that utilizes a measurement of the output and makes a comparison with
the desired output.

Open-Loop A system that uses a device to control the process without using feedback. The
output of the system does not affect the signal necessary to control the system.

Feedback A signal from the output of the system that is applied as feedback to control the
system.
Feedback control can be:
- Positive Feedback; Regenerative Feedback
Output signal is fed back, so it adds to the input signal.
- In phase with input;
- Increase oscillatory motion.
- Negative Feedback; Degenerative Feedback
Output signal is fed back, so it subtracts to the input signal.
- Out of phase with input;
- Improves stability.
When feedback is used in a system, a controller is needed to rectify the input [ C ].

Summing Point where signals come together.
Point

Branch Point Point where signals divert.

SISO Single Input – Single Output

SIMO Single Input – Multiple Output

MISO Multiple Input – Single Output

MIMO Multiple Input – Multiple Output


AUTOMATED FLIGHT SUMMARY 3

, AMSTERDAM UNIVERSITY OF APPLIED SCIENCES


Complex Numbers
A complex number is a number that can be expressed in the form a + bj, where a and b are real
numbers. For the complex number a + bi, a is called the real part, and b is called the imaginary part.

Cartesian notation
Complex numbers expressed in their Cartesian form are written as:

𝑧 = a + bj

Where a is the real part and b the imaginary part.

Complex Conjugate
The conjugate of a complex number is the expressed by changing the sign + or – of the
imaginary from + to –, or vice versa.

If z = a + bj, its complex conjugate, denoted by 𝑧, is

𝑧 = a − bj

Operations
If 𝑧1 = 𝑎1 + 𝑏1 j and 𝑧2 = 𝑎2 + 𝑏2 j

Sum Adding two complex numbers together;
𝑧1 + 𝑧2 = 𝑎1 + 𝑎2 + (𝑏1 + 𝑏2 )j

Multiply Multiplying two complex numbers;
𝑧1 ∙ 𝑧2 = 𝑎1 ∙ 𝑎2 − 𝑏1 ∙ 𝑏2 + (𝑎1 ∙ 𝑏2 + 𝑎2 ∙ 𝑏1 )j
𝑧1 ∙ 𝑧1 = 𝑎2 + 𝑏2

Divide Dividing two complex numbers;
𝑧1
𝑧2
= 𝑎(𝑎1 ∙2𝑎)22 ++ 𝑏(𝑏1 ∙2𝑏)22 + (−𝑎(𝑎12∙ )𝑏22 + 𝑎2 ∙ 𝑏1 )
+ (𝑏2 )2
j

To multiply and divide complex numbers it is easier to re-write the cartesian complex number
to its Polar Form.

Argand Diagram

The complex number z = a+bj can be plotted as a
point with coordinates (a, b). Because the real part of
z is plotted on the horizontal axis, we often refer to
this as the real axis. The imaginary part of z is plotted
on the vertical axis and so we refer to this as the
imaginary axis. Such a diagram is called an Argand
diagram.




AUTOMATED FLIGHT SUMMARY 4

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