Motion Control for Packaging Machines
Vibration analysis through Vibration analysis through
motion control-motor-load motion control-motor-load
interactioninteraction
Motion Control for Packaging Machines
Example of Motion Control-motor-load
PID Controller
Motor
Transmission
Load
Motion Control for Packaging Machines
250 Hz
PID Controller bandwidth measure
The controller bandwidth has been experimental found.In particular has been applied a TORQUE STEP to the pulley.
Torque step (signal)
PID bandwidth (FFT)
Motion Control for Packaging Machines
Torque step
The torque step is an approximation of a Dirac impulse thus a infinite frequency generator. The Torque step excite the mechanical system with a very wide band.
Only for certain control system it’s possible to apply a software Torque step.
If it isn’t available a software Torque step, we can obtain a similar result with a quick hammer hit on the pulley. The tangential hammer hit on the pulley has the effect of a Torque step on the motor shaft.
Motion Control for Packaging Machines
The software torque step is a better approximation of a Dirac impulse. It has a wider harmonic content (it contains higher frequencies and so excites the system at higher frequencies.
Torque Step
-5000
-4000
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-1000
0
1000
2000
1.455 1.955 2.455
4096 =
stall to
rq
ue =
60N
m
250 Hz
Software
Torque step
Hammer
Torque step
Motion Control for Packaging Machines
Motion control response to Torque step
The controller reacts to the pulley displacement, with a correction signal which has all the available frequencies and shows his bandwidth.
The 2 types of torque step has been applied on 2 different control system with different bandwidth.
It’s however useful to observe the Torque step responses of 2 different control system.
Motion Control for Packaging Machines
Frequency analysis of software Torque step response
Frequency analysis of hammer test response
We can see multiple peaks with 6-7 Hz width. This behaviour is the FFT of a step; it shows the forcing action on the system (Torque step) that has an effect on the output (controller response).
Std P Gain Torque Step Response
0
20
40
60
80
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120
1 13
25
37
49
61
73
85
97
10
9
12
1
13
3
14
5
15
7
16
9
18
1
19
3
250 Hz
Motion Control for Packaging Machines
Link between bandwidth and PID parameters
The controller bandwidth depends on PID gains. We can obtain the bandwidth from transfer function (mathematical model) of the controller in which appear PID gains.
In particular if we increase the PROPORTIONAL gain, the control becomes much ready, it reacts quicker to errors and his bandwidth increases.
The sinusoidal signal with high frequency has a quicker rise and then correct errors in a short time (of position, velocity or torque depending on PID structure and which gain has been modified).
Motion Control for Packaging Machines
In the picture below we can see that increasing proportional gain the bandwidth increases.
We can see 3 different great peaks due to many PID that interacts. We can also see that the area below the 2 curves is equal; it depends on drive’s energy that is constant (it depends from the input voltage). In High P-gain case we have higher amplitude at high frequencies because the bandwidth “cover” the resonance frequency of the system and ignite a vibration.
High (red) and Std (yellow) P Gain Torque Step Response
0
20
40
60
80
100
120
140
1 11
21
31
41
51
61
71
81
91
10
1
11
1
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1
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1
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1
15
1
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1
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1
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1
19
1
First Peak Second Peak Third Peak
Motion Control for Packaging Machines
Vibration analysis
After a vibration problem on servomotors we have elaborated a model to simulate the group motion control-motor-load.
The vibration analysis has been divided in:• ignite of vibrations on motor+load; • experimental measures;• result analysis through FFT (Fast Fourier Transform).
Motion Control for Packaging Machines
Ignite of vibrations
The vibrations have been ignited increasing position proportional gain. The bandwidth increases and “cover” the resonance frequency of motor+transmission+load.
The vibration is visible on Torque feedback and position error(lag error) signals.
Tests has shown that the causes of vibrations are:• bandwidth wide enough (high gains);• profile point with jerk impulse.
Motion Control for Packaging Machines
• BANDWIDTH WIDE ENOUGHThe bandwidth has been widen increasing proportional gain.
In this way we “cover” the resonance frequency of motor+transmission+load.
To obtain a vibration during the movement it would be necessary to further increase the proportional gain, with the risk to ignite too great vibrations.
High P Gain Torque Step Response
0
20
40
60
80
100
120
140
1 13
25
37
49
61
73
85
97
10
9
12
1
13
3
14
5
15
7
16
9
18
1
19
3
S o c a p e lP I D B a n d w i d t h
Resonance peak
Motion Control for Packaging Machines
• PROFILE POINT WITH JERK IMPULSE
From the tests we have seen that , with high P-gain the vibration at natural frequency of motor+transmission+load, happens when there is a jerk sudden peak in the profile.
The jerk impulse is similar to the Dirac impulse and, as the Torque step, excites the system natural frequency and ignite the vibration.
Motion Control for Packaging Machines
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0
1000
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3000
4000
Jerk impulse i.e. excitement of natural frequencies
Natural frequency of motor+transmission+load at 100 Hz
Jerk impulse and vibration
Motion Control for Packaging Machines
Frequency analysis
It’s necessary to underline that the theoretical Fourier transform is an integral on a infinite time interval of a continuous function.
Acquired signals, instead, are digital and so discrete. We can’t use the Fourier transform but the FFT (Fast Fourier Transform) which can be applied to discrete signal with finite length.
Considering that , the max computable frequency is related to minimum period and so to sample time.
Tf
1
Motion Control for Packaging Machines
3D FFT GRAPH
The Fourier Transform is born for periodic signal. The real signals aren’t periodic because they become from measures.
The Fourier Transform (called in this case STFT Short Term Fourier Transform) is then different if we consider a part of signal or another.
If we have a signal of 10s, for example, if we analyse the first or the eighth second is different. If we analyse all the 10 seconds we obtain all the characteristic frequencies each other superimposed.
Motion Control for Packaging Machines
If we have elaborated mechatronic system, with complex motion profiles, the geometric configuration and the mass and forces distribution changes during the movement.
For the jaw system of Filling Machine A3/Flex, for example, the load (the mass) is distributed on the 4 axis in a different way if we have closed or opened jaws.
It’s important to understand if only certain frequencies becomes resonant only in certain profile points and why.
Motion Control for Packaging Machines
Motion Control for Packaging Machines
To do the FFT in time of a signal, we take windows (which can be of different types) and we do FFT in each window.
Placing side by side the results of the windows we obtain a 3D graph which has:• amplitude on z axis• frequency on x axis• time on y axis
Torque vibration
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0
1000
2000
3000
4000
0 1 2 3 4 5 6 7 8
x
z
y
Motion Control for Packaging Machines
Some examples
0
6.9
36
41
61
85
13
.87
28
32
37
20
.80
92
48
55
27
.74
56
64
74
34
.68
20
80
92
41
.61
84
97
11
48
.55
49
13
29
55
.49
13
29
48
62
.42
77
45
66
69
.36
41
61
85
76
.30
05
78
03
83
.23
69
94
22
90
.17
34
10
4
97
.10
98
26
59
[0.000,0.138]
[0.830,0.969]
[1.661,1.799]
[2.491,2.630]
[3.322,3.460]
[4.152,4.290]
[4.982,5.121]
[5.813,5.951]
[6.643,6.782]
0
50
100
150
200
250
Frequencies
Time intervals
Amplitude
Motion Control for Packaging Machines
0 100 200 300 400 500Frequency [Hz]
0.00
0.05
0.10
0.15
0.20
0.25
Accelerazione [g]
0
10
20
30
40
C8 (M) Slow inching high pgain 45 secondi Verticale Motore [g] FFT(C2) 1 Y Peak
Motion Control for Packaging Machines
Example of a FFT of a mechatronic system with belt
pos lag High P-Gain(torque step response) from 40 Hz
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
PAM 250Hz
Bandwidth
Motor+Transmission+load resonance
peak Belt axial natural frequency at 300
Hz (as found by the model)
Motion Control for Packaging Machines
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