SYSLAB - Dynamic Systems Virtual Lab

INPUT SIGNALS

Description of the lab

In this lab you can learn about the most common test signals that are used as inputs to physical systems under test, or to simulated systems. The following signals are offered:

  • Pulse
  • Step
  • Ramp
  • Sinus

Aim of this lab

The aim is to develop both a quantitative and a qualitative understanding of the different input signals.

Motivation for this lab

In most situations where you are to analyse a dynamic system (e.g. a control system, a thermal system, a lowpass filter) you do the analysis under the assumption that the system is excited by some input signal. This lab covers the most typical signals. For example, the dynamic properties of a system is often expressed in terms related to the time response after a step input to the systems. One such term is the time constant, which is defined from the step response, and the gain, which is also defined from the (stationary part of) the step response. Furthermore, the frequency response of a dynamic system is calculated under the assumption that the input signal is sinusoidal.

Review of theory for this lab

In the following each of the signals are treated individually.

Pulse signal

The pulse signal is implemented as a square pulse of amplitude or height H at time t0 with duration dt. Thus the area (under the curve) or strength of the signal is A=Hdt. This square pulse is and one of several possible approximative realizations of the ideal impulse function (which has infinite amplitude and zero duration). The latter can be represented by

y(t) = Ad(t-t0)    (Eq. 1)

Step signal

The step signal is given by the time-function

y(t) = US(t-t0)    (Eq. 2)

where U is the step amplitude. S(t) is the unit-step function, which has value 0 for t < 0, and value 1 for t >=0. Thus, y(t - t0) is a step of amplitude U at time t0.

Ramp signal

The ramp signal is given by the time-function

y(t) = KR(t-t0)    (Eq. 3)

where K is the slope. R(t) is the unit ramp function starting with the slope at t=0. Thus, R(t-t0) denotes a ramp starting at time t0.

Sinus

The sinus signal is given by the time-function

y(t) = Asin(wt) = Asin(2pft)    (Eq. 4)

where A is the amplitude, w is the frequency [radians per second], and f is the frequency [Hertz]. The period of the sinus signal is

Tp = 1/f [sec or time units]    (Eq. 5)

Signals often have a bias!

It is quite common that the above signals varies about a bias B, which is a constant signal. This is the case in most physical experiments. For example, a sinusoidal power input to a thermal plant must in fact be a sinus added to a bias, since otherwise the negative values of the sinus would mean negative power! With the bias, the signal becomes

y(t) = y0(t) + B    (Eq. 6)

where y0(t) is the unbiased signal as defined in the sections above. In the lab, the bias can be added and adjusted separately.

Suggested exercises

Note: The equality sign "=" in the following text can be regarded as "approximately equal to" (so you do not have to enter exact numeric values into the lab panel).

  1. Pulse: Run the lab while adjusting the pulse amplitude H (try both positive and negative values), and duration dt, and observe how these two parameters influate the time-signal. And what is the meaning of t0? And what is the effect of adjusting the bias? Conclude!

  2. Step: Run the lab while adjusting the step amplitude U (try both positive and negative values), and the step time t0, and observe how these two parameters influate the time-signal. And what is the effect of adjusting the bias? Conclude!

  3. Ramp: Run the lab while adjusting the ramp slope K (try both positive and negative values), and the ramp start-time t0, and observe how these two parameters influate the time-signal. And what is the effect of adjusting the bias? Conclude!

  4. Sinus: Run the lab while adjusting the sinus amplitude A (try both positive and negative values), and the frequency f, and observe how these two parameters influate the time-signal. Choose one specific value of f, and check on the plot that the period actually has the value as indicated in the numeric display. And what is the effect of adjusting the bias? Conclude!

How to download and run the lab

This lab can be run on the following PCs:

  • On a PC having the LabVIEW system installed.
  • On a PC having just LabVIEW Run-Time Engine (LVRTE) installed. The installer for LVRTE is available for free (via for example the web browser) at the address below.

    ftp://ftp.ni.com/support/labview/runtime/windows/6.1/LVRunTimeEng.exe

    (The file size is approximately 14 MB.) You can download and run it, thereby installing LVRTE. You need to install LVRTE only once on your PC. If you work on a PC on which LabVIEW is installed, you do not have to install the LVRTE.

The exe-file which constitute the simulator for this SYSLAB lab is input_signals.exe. You can download it to the directory (folder) you want, and run it to start the simulator.

[SYSLAB]

Updated September 1, 2002. Developed by Finn Haugen. E-mail: finn@techteach.no. Homepage: http://techteach.no/adm/fh.asp