Example: Ball and Beam Experiment - PID Control

Problem setup

For the detailed description of the problem setup, have a look at http://www.engin.umich.edu/group/ctm/examples/ball/ball.html
You will find there also all the steps of the paper-and-pencil procedure necessary for the equation formulation and transformation
before MATLAB can be used to compute the open-loop response.

Modeling using DYNAST

When using DYNCAD, you need not to deal with any equations at all. You can easily set up the system model in graphical form
from a kit of dynamic elements. Open the following system model in DYNCAD and see its Help for more details.


Step response computation

To compute the open-loop step response of the system using DYNCAD

  1. pull-down the menu DYNAST
  2. click Compute analysis
DYNCAD will send the request across the Internet to DYNAST - a simulation package based on a server in the Czech Technical University in Prague.
In a while, an applet should display the following response on your screen.


Transfer function computation

DYNAST can also provide linearization and semisymbolic analysis of the system model. To see the following list of poles and zeros of the system transfer function(s)

  1. pull down the menu Results in DYNCAD
  2. click Textual
You can even find in the listing the following semisymbolic expression for the step response


Analog PID controller design

You can use the transfer function computed above to design a PID controller for the plant following the procedure given on http://www.engin.umich.edu/group/ctm/examples/ball/bbPID.html

To avoid copying the transfer function data manually it is posibble to export the data in an M-file for MATLAB sent to you by e-mail. To recieve it

  1. log in yourself in the pull-down menu File after clicking Login
  2. click New account if you have not set yet your private account in DYNCAD
  3. click Export-Matlab in the pull-down menu File
Design verification

Add the designed PID control loop to the plant to form the following model of the controlled system.

To verify the designed system by computing its step response, click Compute analysis in the DYNAST pull-down menu in DYNCAD



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