Experimental Analysis of Inverted Pendulum System
(ECP Systems-Model: 505)
Procedures
A. Controller set up and stabilization
1. Enter the Utility menu and Reset the controller.
2. Place the sliding rod in its approximate center of travel.
3. Balance the pendulum rod so that it remains vertical. Be sure to keep your head
clearly away from the mechanism and out of the plane of action of the sliding
rod.
4. Enter the Setup menu and choose Setup Control Algorithm option. You should
see the sampling time Ts = 0.00884 seconds. Discrete time control, and the
General Form button selected.
5. Now select Setup Algorithm and you should see the following gains: To=O.48,
So=24.61, S124.OO, Ho=l,O lo=l٠8427, 11 1.76, Eo=O.35, and G1O.5. This
controller was designed using the linear quadratic regulator (LQR) technique
with all error weighting on encoder #1 (the pendulum angle encoder). In
addition, a low pass filter was included (Gi coefficient) to reduce quantization
noise.
6. Exit this dialog box and, with the pendulum in the vertical position and the
sliding rod in its middle "T" position, select Implement Algorithm. The control
law is now downloaded to the real-time Controller.
7. Very gently push the pendulum rod with the ruler to verify that control action
is in effect. If you do not notice any motor power, use the ruler to move it back
to the vertical position and then, click on the Implement Algorithm button
again until you notice the servo loop closed.
8. Now select Algorithm, then Upload General Form and Setup Algorithm. You
should see the same coefficients uploaded back from the real-time controller
to the Executive program. Note that the general form algorithm is the only
structure that actually runs in real-time. AH other structures (e.g. PID... etc.) are
translated to the general form by the Executive prior to implementation.
B. Step response
1. Enter the Data menu and select Setup Data Acquisition. In this box make sure
that the following four items are selected: Commanded Position and Encoders
1.2. & Control effort. Data sample period should be 5 which mean that data
will be collected every fifth servo cycle (in this case every 5*0.00884 seconds).
Now exit this menu.
2. Enter the Command menu and select Trajectory. In this box select Step and
then Setup. You should see step size = 300 counts, dwell time =4000 ms and
no. of repetitions: 1.
3. Exit this box and go to the Command menu. This time select Execute and with
the Sample Data box checked run the trajectory. You should have noticed a step
move of 300 counts, a dwell of 4 second and a return step move.
4. Wait for the data to be uploaded from the real-time Controller to the Executive
