Control - 2 - Analysis of Linear Systems

Question 1

Lag vs Delay

Answer 1

Lag is the exponential response of a first order system;

Delay is a period of time when nothing happens.

Question 2

What is a deadband?

Answer 2

• A deadband (sometimes called a neutral zone or dead zone) is a band of input values in the domain of a transfer function in a control system or signal processing system where the output is zero (the output is ‘dead’ - no action occurs).

Question 3

What property do linear systems have?

Answer 3

Linear systems have the property of superposition

Question 4

Why linearity and superposition are useful

Answer 4

• Allows you to break down the complicated input into a sum of simple basis signals (e.g. Fourier analysis uses sine and cosine)
• output is the sum of the responses to the broken-down inputs

Question 5

Laplace Transform of this exponential:

Answer 5

Question 6

Apply laplace transform:

Answer 6

Question 7

What is a transfer function? And why is it used?

Answer 7

• A transfer function is an s-plane description of a linear system.
• It replaces solution of a differential equation (hard) by an (easy) multiplication.

Question 8

LT of the first derivative:

Answer 8

Question 9

LT of the second derivative:

Answer 9

where dx/dt(0) is the initial value of dx/dt when t = 0.

Question 10

Invert this 2x2 matrix

Answer 10

Question 11

If you keep on increasing the superscript variable n in t, how does the fourier transform change?

Answer 11

Question 12

Do the inverse LT of this function

Answer 12

Question 13

What is the Final value theorem?

Answer 13

Method to find the final steady value of a signal as t → ∞

Question 14

Final value theorem for time signal function

Answer 14

If the final value is steady, the derivatives are zero.

Question 15

Final value theorem for s-plane function

Answer 15

Question 16

In Final value theorem questions what should you not forget?

Answer 16

Question 17

What respective roles do zeros and poles play in transfer functions?

Answer 17

• Zeros influence the magnitudes and signs of the signals
• Poles determine which signals are present;

Question 18

Laplace transform of a time delay

Answer 18

Question 19

Moment of a force and tangential velocity equations

Answer 19

Question 20

voltage-current characteristics for linear components:

Answer 20

Question 21

Equivalent variables for rotational dynamics when compared to translation

Answer 21

Question 22

Newtons Second Law for rotational dynamics

Answer 22

Question 23

Laminar versus turbulent flow

Answer 23