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

2. Motion Control for Packaging Machines Summary Motion Control-motor-load Bandwidth PID Controller PID bandwidth measure Vibration analysis

3. Motion Control for Packaging Machines Example of Motion Control-motor-load PID Controller Motor Transmission Load

4. Motion Control for Packaging Machines MOTION CONTROL The motion control includes all the hardware devices and software applications that contribute to make the motor rotate. The control chain depends on applications and suppliers. We consider 2 different devices: PLC DRIVE

5. Motion Control for Packaging Machines PLC The PLC manage the communication with the machine and with TPOP through bus and I/O Rockwell Automation PLC includes the controller which generates motion profiles with a defined coarse update.

6. Motion Control for Packaging Machines DRIVE The drive receive the motion profile from the controller at course update rate and the position transducer feedback. The position transducer can be: ANALOGIC (resolver) that needs a A/D converter (Resolver to digital Converter RDC) DIGITAL (encoder) The drive provide, through a PID controller, for generating the current reference (which becomes torque) for the motor.

7. Motion Control for Packaging Machines MOTOR The motor is brushless with SINCOS encoder (digital position transducer with high precision which has angular position sin and cos as output). The motor receive the current profile as input and gives torque on motor shaft as output. On motor shaft is mounted a pulley which transmit the motion to the load. The encoder read the shaft position and gives the feedback signal to the drive.

8. Motion Control for Packaging Machines LOAD In the Filling Machine A3/Flex the transmission is direct drive (without gear) and the linear movement is generated by a belt system. The belt is made of polyurethane and, even if it has stainless steel internal wire, introduces elasticity in the transmission chain.

9. Motion Control for Packaging Machines Motion control-motor –load interaction All kinematic chain elements has natural frequencies. The natural frequencies are higher than the rotation frequency of the motor (few tenth of Hertz). The motion control nevertheless has frequencies that may excite system natural frequencies. With the introduction of electrical cam and of complex control system, has been introduced an interaction between motion control and mechanical devices (transmission+load) and electrical devices (motor).

10. Motion Control for Packaging Machines BANDWIDTH It’s important to know which frequencies (bandwidth) are used by control system. Every physical system is a low pass filter, it has some frequencies which transmit while it filters the others (to transmit all the frequencies it might have infinite energy). In this way it’s possible to understand if the control system may excite motor, transmission or load natural frequencies. It’s possible to calculate the motion control bandwidth from its mathematical model. But even a good model is approximate, reason why we used a experimental approach.

11. Motion Control for Packaging Machines CONTROLLORI PID Rockwell automation PID is a series PID.

12. 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)

13. 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.

14. 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. 250 Hz Software Torque step Hammer Torque step

15. 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.

16. 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). 250 Hz

17. Motion Control for Packaging Machines Fourier Transform of an impulse The Fourier transform change the signal from the time domain to the frequency domain ( ). For a signal f(t) we have t1t1

18. Motion Control for Packaging Machines For an impulse with amplitude Y and length (of time) 2t 1 centred in the origin Considering that and

19. Motion Control for Packaging Machines The Fourier transform of is t1t1

20. Motion Control for Packaging Machines The absolute value of the transform for positive pulse is The peaks’ width is

21. Motion Control for Packaging Machines For an impulse of 0.2s length the peaks’ width is 5Hz Whereas for an impulse of 0.1s length is 10 Hz

22. 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).

23. 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. First PeakSecond PeakThird Peak

24. 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).

25. 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.

26. Motion Control for Packaging Machines BANDWIDTH WIDE ENOUGH The 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. S o c a p e l P I D B a n d w i d t h Resonance peak

27. 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.

28. Motion Control for Packaging Machines Jerk impulse i.e. excitement of natural frequencies Natural frequency of motor+transmission+load at 100 Hz Jerk impulse and vibration

29. Motion Control for Packaging Machines Experimental measures Several tests in different condition has been done. Torque feedback and lag error signal has been acquired from the motor. The Torque signal is measured by a sensor who measures the current on the motor; lag error signal is measured by a position transducer (resolver o encoder). We pass from the time domain to the frequency domain to study vibration phenomenon.

30. 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.

31. Motion Control for Packaging Machines From Shannon theorem sample frequency must be at least double of maximum signal frequency. Starting with a digital signal with a certain sampling rate, the maximum frequency that we can obtain from FFT is We can deduce that to obtain FFT with high frequency are necessary accurate acquisition and sample.

32. 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.

33. 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

34. 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 x z y

35. Motion Control for Packaging Machines A type of window is the Hanning window: the part of the signal considered has been weighed with a cosine curve which has value zero at the ends. In this way the first and the last point of the part of signal considered, are zero the signal becomes periodic. If we correctly superimpose the windows we can exactly rebuild the signal.

36. Motion Control for Packaging Machines Some examples

37. Motion Control for Packaging Machines

38. Example of a FFT of a mechatronic system with belt 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