Industrial Emulator
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ARO 322L
Equipment
Industrial Emulator
Experiment 2 – Industrial Emulator
Submitted by:
Joseph Anthony
Submitted: November 2, 2001
Executive Summary
The purpose of the System Identification Industrial Emulator Experiment was to determine the transfer function of the drive disk by finding the inertia, gain, and damping of various systems through measurements of their effects on the system response characteristics. The calculated
Table of Contents
Title
Page
Executive Summary
Table of Contents
Objectives
Procedures
Results and Discussion
Summary
Appendices
Objectives
The objectives of this experiment were to use known parameters of the industrial emulator system and experimental data from accelerating the disk and inducing an underdamped response to calculate the damping ratio and polar moment of inertia of the system. Through additional analysis the damping constant was to be calculated and evaluated as a negligible or influential term.
Procedures
Gain Measurement Procedures:
This step will describe how to measure the hardware gain, khw by accelerating the disk and using closed loop feedback.
Be sure to have the units set to counts.
The control algorithm should have a settling time of Ts = 0.002652.
The trajectory should be bidirectional and an Open Loop Step with a step size of .5 volts, 200ms duration, and 2 repetitions. This actually gives a 2.0V input to the servo amplifier.
To acquire data, encoder #1 should be selected as data to be acquired with data being sampled every 5 cycles.
Measure khw using data taken from the velocity and acceleration plots and known relationships between Torque and moment of inertia seen below
and khw = kckaktkeks
where acceleration is acquired from the data and J is as follows
Inertia Measurement:
For this part of the experiment, the load disk inertia can be found by using an underdamped response.
Begin with setting up the control algorithm with kp set to 0.25 and kd set to 0.001.
Execute a Closed Loop Step with a step size of 1000 counts for 1000 ms and 1 repetition and graph the results.
Measure the amplitude of the initial cycle and the last cycle from the graph, as well as the number of cycles to obtain Xo, Xn, and n respectively. From here, calculate the value of ζ.
(Eqn. 1)
Divide the number of cycles, n, by the time it takes to complete them (tn-to) and convert it to frequency to get the damped frequency, ωd, which is related to the natural frequency, ωn, by the following equation:
(Eqn. 2)
Use the value of khw found in the Gain Measurement along with Eqn. 2 to find the experimental value of Jdd.
Results and Discussion
Gain Graph Results and Discussion- Matt
Figure 1 – Gain Graph – Counts/s vs Time (Velocity)
Figure 2 – Gain Graph – Counts/s/s vs Time (Acceleration)
Figure 1 shows the Open Loop response. By dividing the change in counts over the change in time, the acceleration can be found. With the acceleration, along with the voltage and total inertia of the moving parts, the hardware gain, khw can be calculated as follows:
a = 550,000 counts/s¬¬2
From Figure 1
Jmotor = 3.8*10-5kg-m2
Given
Jdrive disk = ρπr4h
= 7.62*10.4kg-m2
J = Jmotor + Jdrive disk
= 3.8*10-5kg-m2 + 7.62*10-4kg-m2
= 7.997*10-4kg-mg2
kaktke = (J*a)/(2V)
=109.9 (kg-mg2-counts/s2V)
kc = 10V/32,768 DAC counts
ks = 32 (controller input counts/encoder input counts)
khw = kckaktkeks
= (109.9 kg-mg2-counts/s2V)*(10V/32,768 DAC counts)*32 (controller input counts/encoder input counts)
= 1.073 N-m/rad*(controller input count)/(DAC count)
Figure 2 shows the acceleration vs. time plot