Motion Control for Packaging Machines Vibration analysis through motion control-motor-load interaction

Motion Control for Packaging Machines

Vibration analysis through Vibration analysis through

motion control-motor-load motion control-motor-load

interactioninteraction


Example of Motion Control-motor-load

PID Controller

Motor

Transmission

Load


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)


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.


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

-3000

-2000

-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 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.


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

100

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


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).


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

12

1

13

1

14

1

15

1

16

1

17

1

18

1

19

1

First Peak Second Peak Third Peak


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).


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.


• 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


• 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.


-4000

-3000

-2000

-1000

0

1000

2000

3000

4000

Jerk impulse i.e. excitement of natural frequencies

Natural frequency of motor+transmission+load at 100 Hz

Jerk impulse and vibration


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


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.


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.



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

-4000

-3000

-2000

-1000

0

1000

2000

3000

4000

0 1 2 3 4 5 6 7 8

x

z

y


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


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


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)


Documents

Motion Control for Packaging Machines Vibration analysis through motion control-motor-load interaction