1. Control of Voice coil transducers
Design and implementation of a Motional Feedback
Loudspeaker Woofer
Thanks
Welcome to MFB
Will take 30 minutes
Time for wuestions

2. Overview Introduction to loudspeakers Objective Setup 1 Results 1
Conclusion
Questions
The presentation is divided into several parts
First I will give you an introduction to loudspeaker woofers and the corresponding problems
I will set a research objective
Then I will discuss the design and testing of the initial setup
I will discuss the second setup
After testing the second setup, the results are avaluated
Opportunity for questions

3. Introduction to loudspeakers
This is an example of a loudspeaker
The goal of a loudspeaker is to transform electrical power into sound.
The loudspeaker is just one link in the chain from a CD with sound information to the sound that is heard
Many other links determine the performance of the chain, but the loudspeaker is one that has a lot of influence
If we look at the loudspeaker, you can see that it consists of multiple components
The component this research is on, is the woofer, that takes care of the low frequency sound, or bass.

4. Introduction to loudspeakers
This is a crosssection of a woofer
There are four main components in the figure
The frame of the woofer
This is used for mounting all the components and mounting the entire woofer in the cabinet
The Lorentz actuator
This is used to translate an electrical current to a force
The cone
A large body that can move and can compress the air
The suspension
This is used to keep the moving parts aligned properly and creates a seal between the pressure in the cabinet and the environment.
The spider and the surround behave much like a spring and a damper.

5. Introduction to loudspeakers
So what I can do is run current through the voicecoil. This creates a force that pushes on the cone.
As soon as the cone starts to move, the spring and damper have a force on the cone too, depending on the motion.
In other words, the motion of the cone is determined by the sum of all the forces
We also know that the motion of the cone compresses en decompresses the air close the cone.
If the cone moves up and down, this creates pressure waves that we can hear.
Therefore, the motion of the cone determines the radiated sound.

6. Introduction to loudspeakers
If the components can put forces on the cone would be linear to the motion of the cone,
The transfer from electrical current in the Lorentz actuator to the motion of the cone would be linear
If that is the case, the transfer from electrical current in the Lorentz actuator to the sound waves near the cone would be lineair too
That would mean that I can change the sound to my taste by applying linear correction like tuning an equaliser
However, the Lorentz actuator, spring and damper do not have a fully linear behaviour.
This means that the transfer from electrical current to measured sound is non-linear

7. Introduction to loudspeakers
To illustrate what in practice happends, I have made a measurement of a tone of 20 Hz.
If the transfer between the current and the motion of the cone would be lineair, the measured motion would be just the 20 Hz sinewave
You can clearly see that the figure is not showing just 20 Hz, but other signals too, that deform the signal.
This deformation can be heard and is not present in my CD sound signal

8. Introduction to loudspeakers
When you measure that signal and look at what frequencies are in it, you can see the peak at the original 20 Hz.
There are however other frequencies in the signal too that are there because of non-linearities
There are clear peaks at 40, 60, 80 and 100 Hz.
These peaks indicate that there is a measured motion that is not equal to the 20 hz signal
Since I wanted to move the cone at 20 hz, all deviations from that signal are unwanted disturbances.

9. Introduction to loudspeakers
PACSYS
There is another phenomenon that is of interest
The moving cone is not at all times the same shape.
At certain frequencies, the outer ring of the cone and the centre of the cone do not move the same
This means that at certain frequencies, the cone can be deforming

10. Introduction to loudspeakers
PACSYS
Here you can see that the cone no longer is moving as a rigid body.
This casues peaks and dips in sound pressure levels around the frequency of this breakup

11. Objective Suppress disturbances due to non-linearities
Reduce the cone break-up
One of the objectives of this research is to suppress the unwanted disturbances
In the 1970s, Philips developed loudspeakers that used feedback to accomplish this target.
The system worked, but suppressed the disturbance only by a factor 3.5
The other objective is to increase the control bandwidth of a feedback loop in order reduce the cone breakup
Because electronics have become more advanced and cheaper since the 1970,
I believed, that by the use of modern, more flexible, digital signal processors I could accomplisch better results If

12. Setup 1
I made a test setup in order to evaluate woofer dynamics and to implement feedback that would reduce the non linear disturbance
The woofer chosen is a 6.5 inch diameter woffer from Peerless
The reason this woofer is chosen is because of a very interesting peak and dip in the sound pressure level over frequency plot

13. Setup 1
Here you can see the sound pressure level generated by the woofer over frequency.
When looking at the 3 lines that are close to eachother, you can see a peak and dip
The frequency at the peak and dip is around 600 Hz to 800 Hz
A peak and dip like this can only occur when the cone is breaking up.
In that case, the centre of the cone and the outer ring of the cone are moving in opposite directions
The pressure levels at that frequency are canceled out due to this motion, resulting in a dip in sound pressure level
The fact that this woofer has breakup behaviour of such impact makes in interesting to use as a test subject since one of the objectives is to reduce this breakup

14. Setup 1 What I want to do with this woofer is apply feedback.
In short, a feedback loop like in the picture is constructed from several parts
There is a reference, r. This is the desired motion I want the woofer to have
I have a controller, the C block. This consists of a transfer function. This function is a linear function that I can design
There is the plant, the P block. This in my case is the relationship between a signal I send to an amplifier, u, and the resulting motion I measure, y.
Then the error, e, that is the difference between the desired reference signal and the measured signal
If a loop like this is implemented well, the motion of the woofer is a closer match to the reference because the non lineair disturbances should be reduced.

15. Setup 1 Reference signal Implementation of controller
Measure the motion of woofer
In order to implement the loop I need a couple of things
I need the reference signal. This is available either from the CD or from a signal generator
I need to implement the controller transfer function. I use a dSpace computer for that.
This enables me to design a transfer function in Matlab and implement that transfer function in a DSP that is part of the dspace computer
Finally I have to measure the motion of the cone.
The acceleration of the cone is the motion that needs to be measured.
I could use a microphone, laser or acceleromter for that purpose. I have used an acceleromter.

16. Setup 1
In order to design the controller, I need to know more about the plant
Therefore, I need to make a model of the transfer from the input of my power amplifier to the measured acceleration of the cone.
By exciting a lot of frequencies by a sine sweep, a linear representation of the plant can be estimated.

17. Setup 1
From the transfer function estimation, I built a model dat captures most of the dynamics.
This model is a close match to the measurement from 30 Hz to 2 kHz

18. Setup 1
After designing the controller, the controller, multiplied by the plant looks like the bode figure.
There are two crossover frequencies of 0 dB, both at 30 Hz and at 500 Hz
This is required to guarantee closed loop stability

19. Setup 1
The controller I designed is not very complex, but hard to design with analuque circuitry.
This is one of the advantages of using a DSP based setup

20. Setup 1
If I want to predict the suppression of non linear disturbance, I can use the sensitivity function
This describes the suppression of the error measured by the sensor.
This bode plot shows that between 40 Hz and 400 Hz, the disturbance is reduced
The suppression of disturbances between 75 Hz and 130 Hz is 20 dB, a factor ten in magnitude
Now I need to implement the controller and close the loop on the real setup
In order to test the actual performance, I first measured the reduction of a manually introduced disturbance

21. Setup 1
I introduced the disturbances at different frequencies and measured the amount of suppression by the controller.
This is a match to the predicted suppression
In other words, the controller works.
Now I need to test the actual disturbance suppression instead of the manually introduced disturbance.
So I used a 40 Hz signal and did a reference measurement

22. Setup 1 This is the reference measurement
In all of these tests, I look at the change in magnitude of the fundamental frequency and second and third harmonic distortion cause by the non-linear behaviour
In this figure I have a measured fundamental frequency at 15 dB and the secoind and third harmonic distortion close to -20 dB
If the controller works, the second and third harmonics distortions at 80 Hz and 120 Hz should be reduced by 20 dB, when the controller is implemented

23. Setup 1
After implementing the controller and running an identical test,
We can evaluate the suppression of the distortion
It is clear that the fundamental frequency is unchanged in magnitude,
while the second and third hamonid distortion is reduce by 20 dB
This means that the contribution of harmonic distortion is reduced by a factor 10
In other words, the controller works well and the reduction of distortion is good

24. Setup 1
Ok, now I expect that the same holds for the acoustic reduction of distortion
Again I take a measurement as a reference
It is clear that there is a fundamental frequency at 40 Hz and the distortion at 80 and 120 Hz
The distortion is measured to be 55 dB and 53 dB
Now the controller is implemented

25. Setup 1 I can see that the fundamental frequency is unchanged
However, the harmonic distortion now is at 47 dB and 43 dB
The reduction is 10 dB and 7 dB
This is less than the reduction measured on the accelerometer
In other words, the sensor does not give a good representation of the acoustic increase of performance
I believe that this is caused by the choice of woofer
I chose a woofer that had a dominant breakup behaviour. This means that the outer ring of the cone is very dominant when breakup occurs
When I apply feedback, I only control the centre of the cone.
If the outer ring of the cone is still radiating distortion, the distortion reduction by the controller is not as large on the microphone as it is on the accelerometer
To test this, I measured on several location on the cone, to get an impression of the local reduction of distortion

26. Setup 1
This figure shows the distortion profile without feedback, with the microphone close to the center
Now if the theory holds, the distortion profile measure on the outer ring of the cone, should have a different profile

27. Setup 1 This is a measurement close to the outer ring of the cone
It is clear that the second harmonic distortion is not identical to that of the centre of the cone
In other words, the outer ring of the cone is radiating distortion that is not radiated by the centre.
If I only compensate for the motion in the centre of the cone, I reduce only a part of the distortion, which is confirmed by the acoustic measurements made earlier

28. Setup 1 Outer ring of cone still add distortion
“Better” cones gain more from a feedback loop
This observation leads to the theory, that the increase in performance is reduced by the outer ring of the cone
This means that depending on the woofer, the implementation of feedback can be less effective
If that would be true, a woofer with a more uniform distortion profile should have more benefit from a feedback loop.

29. Setup 1 Suppress disturbances due to non-linearities
Reduce the cone break-up
In order to design the controller, I need to know more about the plant
Therefore, I need to make a model of the transfer from the input of my power amplifier to the measured acceleration of the cone