Blog Marco - Signals and Systems

What is frequency response?

Mon, 29 May 2006 03:27:47 -0700

When a system is in the steady state, a sinusiondal input generates a sinusoidal output at the same frequency but the two sinusoids differ in amplitude and phase angle. The differences are a function of frequency.

Sinusoids can be represented by phasors. One part magnitude, one part phase.

Phasors can be represented in three ways: Polar form, Rectangular form and the Exponential form from Euler's Formula.

You can plot a phasor in two ways: As a function of frequency and on a polar plot. Usually when the magnitude or phase is plotted against frequency it is converted to decibels by taking the log (base 10) and multiply by 20 and plotting it on a log scaled frequency plot - i.e. bode plot.

From Control Systems Engineering by Norman S. Nise

System Design Using MATLAB rltool

Fri, 19 May 2006 06:12:56 -0700

I was in a laboratory tutorial this morning learning how to play around with MATLAB to obtain the controller specs from knowing the transfer function of the plant i.e. the Maze Rover (from which the transfer function was obtained experimentally from a step response as well as a series of input and output magnitude and phase measurements to form a bode plot, which in turn would give the means to the derivation of the transfer function for the maze rover.

Assume that the transfer function you derived from your plant or maze rover was:
0.5
---------
s^2 + 2 s

System Design Lab # 6

Fri, 19 May 2006 04:48:14 -0700

Today we formally finished all our formal lectures for Signals and Systems and it also marks the first day to begin our group project - a.k.a "lab #6". The objectives of the lab are:

"1) To obtain an s-domain block diagram model of the maze rover – that is, to synthesize its transfer function of observing its input/output behaviour."

What does that mean? We need to make up a transfer function (out/in) in the frequency domain (s-domain) into a block diagram model given some design constraints. We would obtain the transfer function of the back box – i.e. the maze rover (a little motorized car with a controller/plant setup) by testing out input / output behaviour. (By feeding specified inputs, measuring output then plotting a bode plot)