Control - 2 - Analysis of Linear Systems Flashcards
Lag vs Delay
Lag is the exponential response of a first order system;
Delay is a period of time when nothing happens.
What is a deadband?
- 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).
What property do linear systems have?
Linear systems have the property of superposition
Why linearity and superposition are useful
- 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
Laplace Transform of this exponential:
Apply laplace transform:
What is a transfer function? And why is it used?
- A transfer function is an s-plane description of a linear system.
- It replaces solution of a differential equation (hard) by an (easy) multiplication.
LT of the first derivative:
LT of the second derivative:
where dx/dt(0) is the initial value of dx/dt when t = 0.
Invert this 2x2 matrix
If you keep on increasing the superscript variable n in t, how does the fourier transform change?
Do the inverse LT of this function
What is the Final value theorem?
Method to find the final steady value of a signal as t → ∞
Final value theorem for time signal function
If the final value is steady, the derivatives are zero.
Final value theorem for s-plane function
In Final value theorem questions what should you not forget?
What respective roles do zeros and poles play in transfer functions?
- Zeros influence the magnitudes and signs of the signals
- Poles determine which signals are present;
Laplace transform of a time delay
Moment of a force and tangential velocity equations
voltage-current characteristics for linear components:
Equivalent variables for rotational dynamics when compared to translation
Newtons Second Law for rotational dynamics
Laminar versus turbulent flow
