Confused about PID controller for current control with PMW

In summary, the PID controller with a PMSM works by controlling the voltage of the motor, rather than the current. The speed is controlled by the frequency of the sinusoidal waveforms, which adapt automatically depending on the torque needs.
  • #1
mechamania
16
0
Hi,
I'm looking into the control of a PMSM (permanent magnetics synchronous motor) motors using H-briges and PWM (puls width modulation).

I'v seen motor controllers that use a PID controller for speed regulation. The output of the PID controls the PMW. This makes sense to me because the PMW controls the voltage of the motor phases and this is proportional to the speed. The speed is measured and feed back into the PID.

But now I want to regulate the torque, thus the current. I have seen implementations that use a PID controller with current inputs (reference and sensed phase current) and again the output of the PID controlling the PMW. So essentially the same setup as for speed control.
I do not understand this. The output of the PID should control the motor current. But it controls the voltage. The current will increase or decrease because of the voltage and inductance. So there is an extra integration going on. How is it possible such a PID loop works?
 
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  • #2
You can regulate either speed or torque but not both at the same time. The motor controllers I have worked with, control the speed, increasing the torque as needed until the torque limit is exceeded. At that point the speed is reduced to keep the torque (or current) from exceeding its set limit. Sometimes the torque is limited on startup to keep the motor from accelerating too rapidly.

If on the other hand you need constant torque, then the speed must be free to change in order to deliver that torque.
 
  • #3
I understand that I can not control both torque and speed at the same time.
The point is that I do not understand how the torque regulation is done using the described PID controller with PMW.

The PID has current value inputs but controls the voltage of the motor. And the voltage of the motor is not proportional to the current because of the indictance. So how does this work?
 
  • #4
I'm sorry, I didn't notice before you mentioned that it is a synchronous motor. I believe the speed of a synchronous motor is controlled by the frequency, not the voltage. Why would you want to use a PID controller with a synchronous motor?
 
  • #5
I agree that the speed can be controlled by the frequency of the sinusoidal waveforms.
But in that implementation the motor position was used to generate the correct sinusoidal phases. And the PID output controlled the amplitude of the sinusoidal waveforms. So the
speed is indeed controlled by the voltage. The frequency adapts automatically.

My question still stands. How can a PID controller work when it compares current values as input and when it controls the PWM with its output. Because this PMW corresponds to voltage control. The current will increase or descrease because of the voltage. This is an extra integration.

I want a PID because I want to control the torque.
 
  • #6
mechamania said:
I agree that the speed can be controlled by the frequency of the sinusoidal waveforms.
But in that implementation the motor position was used to generate the correct sinusoidal phases. And the PID output controlled the amplitude of the sinusoidal waveforms. So the
speed is indeed controlled by the voltage. The frequency adapts automatically.

My question still stands. How can a PID controller work when it compares current values as input and when it controls the PWM with its output. Because this PMW corresponds to voltage control. The current will increase or descrease because of the voltage. This is an extra integration.

I want a PID because I want to control the torque.

Can you provide the model or block diagram of both (voltage control and current control) PID systems? Often times you can use conversion factors to derive one from the other. You have an electrical transfer function or model that describes the motor components, right?
 
  • #7
i saved a Powerpoint presentation from TI that's pretty exhaustive
you might see if it's still available
title is
TI_MotorControlCompendium_2010.ppt

and once upon a time it could be downloaded here
from a post in February:
See if you can open the powerpoint presentation here -
( you need Microsoft's free powerpoint reader )

i think you'll like it.

http://focus.ti.com/docs/training/catalog/events/event.jhtml?sku=OLT210201


http://focus.ti.com/download/trng/docs/c2000/TI_MotorControlCompendium_2010.ppt

hope it helps..

edit see around slide 165
i think it requires measuring rotor position and controlling "quadrature" current
which would to me mean phase, which becomes frequency...
so a pid on phase of stator voltage relative to shaft position ought to work,
isn't that power angle?

probably you're ahead of me aready.
 
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  • #8
@DragonPeter
I have no models yet. I just want to understand how it works first.

@jim hardy
Thanks. Found it. Looks very interesting. Will take some time to study it ;-)
 
  • #9
mechamania said:
@DragonPeter
I have no models yet. I just want to understand how it works first.

In that case, forgive me if I am thinking too simply or ignorantly here, but if you apply a voltage to a motor's terminals with any load whatsoever, then you will also have a current. Much like in a circuit you will have a current and a voltage with a load. If I tell you the voltage and resistance of a resistor circuit, you will be able to tell me the current with Ohm's law, and if I told you to increase the current by 10%, you could simply increase the voltage by 10% if R is constant. So if you can sense and control voltage, you indirectly are controlling current and vice versa because you know the inductance and resistance of the windings and the Km and Kt constants. You simply use a conversion factor to switch between the two. In a control system block diagram, you can tap between blocks to get the specific output,input, or variable you want to consider, but the system is still a closed loop.

For example, if a motor normally runs 600 RPM from an applied voltage of 50V, you already know what the torque will be at for a known load at that operating point. If you apply 50V, and the motor is running slower than 600 RPM, you know that the current has increased because the back EMF has dropped. The RPM that you're measuring is related to voltage by the motor constant, but indirectly you still know that the current has increased through the known relationship. So, you can lower the voltage in that case til the motor speed drops to a lower value, and for that value to correspond to the desired current by the known relationship.

That is how you could control torque indirectly from a voltage PWM/RPM measurement, but you could also have a shunt resistor to measure current semi-directly (but you could still control it with voltage by the relationship). If I'm off here, please explain to me why, because I will have a misunderstanding myself.
 
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  • #10
@DragonPetter:

Thanks for your answer.
I agree for a pure resistor the voltage control is equal to current control.
But we have a lot of inductance here.
I also agree that I could calculate the needed voltage given the motor speed and motor
parameters (like back emf and inductance).
But the PID regulator does not use al this extra information.
That is why I do not understand that the PID controller works properly. The PID outputs a voltage only given the sensed current and wanted current. No speed sensing, no motor parameters are used.

I found a picture in the document jim pointed me to (see attached pdf file). It is from a FOC controller, but it shows that currents values are used as PID inputs and the output is a voltage. But a voltage to an inductor results in a current change, thus an extra integration. I do not understand this PID loop can work properly.

@ jim hardy:
I did read the document. Very interesting. Thanks again. I attached a page from it that shows my point. See above.
 

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  • #11
dont forget the loop gets closed by rotor position.
 
  • #12
jim hardy said:
dont forget the loop gets closed by rotor position.

I found a better picture of a FOC controller.
Here you see the inner PID loops, controlling current.
And the outer PID loop controlling speed.
The rotor position is needed for the transformations.

The output of the inner PIDs control the PMW, thus controls the voltage on the motor windings. The voltage is propotional to motor speed, not motor current.
So why is the current feedback and not the speed?
 

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  • #13
I found a better (much simpler) controller diagram to explain my question.
See attachment again.

Here the torque (is current) is controlled by a PI controller. The output is a voltage.
The PMW makes sure this voltage is applied to the motor.
But the motor current is feedback to the PI controller!

I do not understand this.
The voltage on a motor is more or less proportional to the motor speed. So it makes more sense to me to feedback the speed. The voltage will increase or decrease the current because the motor is an inductor. So the voltage gets mathematically integated. How can a PI controller work with this (integrated) feedback?
 

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  • #14
In your DC motor example, most recent post, ...

why can't two integrators be cascaded?

just their time constants need to be separated ..

and - feeedback is measured current and is compared to desired so error will be forced to zero
so far as the control system is concerned, output is measured current
and motor's transfer function is just one more term
motor coild be moved inside yellow block

try thinking of the motor as a first order lag instead of an integration
because it really does have an L/R time constant so will not integrate for very long.

any help?
 
  • #15
@jim

Thanks for you answer.
I'm afraid the PID want work stable enough when cascading two integrators.

So what you are saying is that you can control the motor current by controller the voltage in a more or less proportional way. And the integrattion will not disturb the PID controller?
 
  • #16
As you see in the example you provided, the PI controller block diagram has the conversion built into it.
 
  • #17
mechamania said:
I do not understand this.
The voltage on a motor is more or less proportional to the motor speed. So it makes more sense to me to feedback the speed. The voltage will increase or decrease the current because the motor is an inductor. So the voltage gets mathematically integated. How can a PI controller work with this (integrated) feedback?

Applied voltage is not directly related to motor speed. It is proportional, but the actual speed is dependent on other factors too - the current/mechanical load.

It is the back-EMF that you need to think about. And the back EMF is the parameter that is dependent on the angular velocity of the rotor. It fights with your applied voltage as an inherent negative feedback, and when the motor is producing higher torque, the back EMF has decreased for the same applied voltage. Your current relationship comes into play here, as this back-emf reduction causes a larger voltage drop across the windings -> more current through them. The parameters are all related by equations, so it is not magic that you can control the current with the voltage.

Saying the motor is an inductor really does not have much importance with the current/voltage relationship other than the back EMF effect. The inductor aspect is more important for understanding electrical transient behavior of the motor, about just as relevant as the internal resistance of the motor as far as your original question goes.

The answer to your question really boils down to following the units conversions in the block diagram path. Like I said, it is a conversion factor that is built into the closed loop somewhere that translates an applied voltage to the motor's current.
 
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  • #18
And the integrattion will not disturb the PID controller?

first i don't think the inductance truly integrates because it isn't a pure inductor. it has a time constant so is a frst order lag

1/s isn't same as 1/(s+a)

second - cascading controllers is tricky but commonly done.
look up three element feedwater control.
drawing courtesy of this fellow: http://www.controlguru.com/wp/p44.html

LC and FC are both p+i 's, and boiler integrates the flow error...
here's an image that looks more like my feedwater control system
G2 and G3 in cascade

1-s2.0-S0307904X07000686-gr3.jpg

courtesy of this fellow: http://ars.els-cdn.com/content/image/1-s2.0-S0307904X07000686-gr3.jpg

here's a nuts&bolts explanation i use for my guys:
since flow measurement Wf and Ws into flow controller G3 is imperfect, level controller G2 will force level to desired with whatever offset in reported flows W makes system settle.

observe there's a boiler closing the loop, it integrates the true flow mismatch. so i see a 3 integrator closed loop.

any help ?

if someone well versed in motor controllers is reading, please chime in. my interest in them is purely hobby level.
 
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  • #19
my interest in them is purely hobby level.
that sounds dismissive and rude, in retrospect, which was not my intent at all

i should have said "My interest in them is from natural curiosity ; i never worked on them so am not expert."

sorry if the remark offended.
 
  • #20
jim hardy said:
that sounds dismissive and rude, in retrospect, which was not my intent at all

i should have said "My interest in them is from natural curiosity ; i never worked on them so am not expert."

sorry if the remark offended.

I read it just as you being your normal humble self haha. That brings up something I've wondered for a while now, is where to draw the line behind hobby and professional work being valid. I think a professional experienced engineer can do hobby work that is much better than a beginning engineer's professional work. Also, some amateurs can have designs that are useful in professional areas.
 
  • #21
Thank you both very much for explaining all this stuff.

I think I start to understand now why you can control the current by applying a voltage calculated by the PID that has current values as input.

I found an example where a measured speed is used to compensating for the back-emf by adding some value (depending on speed) to the voltage output of the PID. So that the voltage will be incremented automatically at higher speeds to compensate the back-emf.

This way the PID does not have to deal with the back-emf (or has to deal less with it).
Do you think this is a good idea?

I found this in the following (very interesting) document:
ABOUT COMMUTATION AND CURRENT CONTROL METHODS FOR BRUSHLESS MOTORS
When you put this title in the Google search bar it will be one of the first hits.

Figure 4.2 shows the compensation. It is part of a (FOC) Field Oriented Control controller (called Synchronous Regulator in this document). I understand the FOC mechanisme and I understand most of figure 4.2.

But figure 4.2 also shows 2 other compensations, which I do not understand:
ωLd and ωLq. Any idea why this is?
 
  • #22
here's the only line i saw that leapt out at me.

For better dynamic performance, crosscoupling
terms (ωLdId and ωLqIq) may also be compensated as in Fig. 4.2.

and w is commutation frequency

and this was above on page 7
Traditionally, the commutation function generates balanced 3 phase sinusoidal or
trapezoidal current commands with angles synchronized to the rotor position. With this
implementation, analog current regulator is implemented for each phase. The same commutation and current control can be realized by a microprocessor-based digital control, although different current regulation schemes such as synchronous regulator are becoming popular. For drives with phase current regulator, phase current command waveforms on the motors are sinusoidal (or with harmonics for some motors) with the commutation frequency proportional to the speed of the motor. For high speed variable motors with a large number of pole-pairs, maximum commutation frequency (fc) may be several hundred Hz or even higher. Since current regulators on AC motors should produce negligible magnitude and phase errors at all operating frequencies in order to produce desired torque, current regulator bandwidth must be high. In general, it is desirable to have the current loop bandwidth (fbw) at least 4 - 5 times the maximum electrical frequency and phase lag should be compensated by means of “phase advancing technique” [2] at the current command stage.

and ref [2] is us patent 4447771
which only says phase is adjusted " to control torque and back emf constants... by some adequate system parameter." second page of text, lower right...

So i am guessing here that it's a small commutaion angle trim to account for an L/R time constant, perhaps even the motor's leakage reactance.

But that's a guess.

These complex monsters are in our washing machine motors these days - so i have stashed away several old induction motors, and a '68 Ford pickup.
This rate-of-change of complexity can't last, can it?

In India they're reprinting turn of the century EE textbooks..
i have my original of this one, printed in 1901

51UY9-IZVvL._SL500_AA300_.jpg

https://www.amazon.com/dp/B006FNDPG2/?tag=pfamazon01-20

Back to the Future!

old jim
 
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  • #23
Figure 4.2 shows the basic structure for field oriented control of the stator currents of a PMS machine with back-emf decoupling added.

It won't make much sense unless you understand the reference frame transformation (Park's transformation) that produces that particular model from a PMSM model expressed in phase quantities.

The terms they add/subtract to/from the output of the controllers are the nonlinear back-emf terms that act as disturbances in the sense of classical control. It is feedforward compensation to decouple the two first order systems that produce the direct and quadrature current components, respectively.

Edit:
Your feedback controllers will have some degree of disturbance rejection (depending of course on how well you designed them), so you don't strictly have to use decoupling as shown in Figure 4.2. It's a good idea though since you usually measure the stuff that goes into the back-emf terms anyway and it's extremely simple to add in your DSP/microprocessor code (it was literally two terms in a couple of lines of C-code for a TI 28335 DSP when I was doing FOC at uni).

You also see this type of feedforward compensation for the back-emf when controlling DC-motors, it's just much less important in that case since the back-emf term only depends on the angular speed of the motor (which changes very slowly compared to the current in the armature windings) and any compensator with integral action will be very effective at rejecting it.
 
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  • #24
jim hardy said:
So i am guessing here that it's a small commutaion angle trim to account for an L/R time constant, perhaps even the motor's leakage reactance.

But that's a guess.


old jim

So do I understand correctly that the two terms ωLdId and ωLqIq together result in a angle adjustment/change?
 
  • #25
milesyoung said:
Figure 4.2 shows the basic structure for field oriented control of the stator currents of a PMS machine with back-emf decoupling added.

It won't make much sense unless you understand the reference frame transformation (Park's transformation) that produces that particular model from a PMSM model expressed in phase quantities.

The terms they add/subtract to/from the output of the controllers are the nonlinear back-emf terms that act as disturbances in the sense of classical control. It is feedforward compensation to decouple the two first order systems that produce the direct and quadrature current components, respectively.

Edit:
Your feedback controllers will have some degree of disturbance rejection (depending of course on how well you designed them), so you don't strictly have to use decoupling as shown in Figure 4.2. It's a good idea though since you usually measure the stuff that goes into the back-emf terms anyway and it's extremely simple to add in your DSP/microprocessor code (it was literally two terms in a couple of lines of C-code for a TI 28335 DSP when I was doing FOC at uni).

You also see this type of feedforward compensation for the back-emf when controlling DC-motors, it's just much less important in that case since the back-emf term only depends on the angular speed of the motor (which changes very slowly compared to the current in the armature windings) and any compensator with integral action will be very effective at rejecting it.

So what would the result of this compensation be? Or better, what is the problem when I do not have this compensation?
 
  • #26
well you're certainly beyond my experience base here.

This link is a quick introduction to the FOC method
http://www.ti.com/lit/an/bpra073/bpra073.pdf
and is my first exposure to it
but it helps.

Let me talk completely through my hat here and be honest about it.

--------------- Start thinking out loud------------------

Now - i noticed those terms wLqIq and wLdId in eq's 3.1 and 3.2, near this statement
Eqs.3.1-3.2 also
indicates that two current-loop are coupled together.

d(Iq)/dt = (1/Lq)[ -Rs Iq - ω Ld Id - ω λm + Vq ] (3.1)
d(Id)/dt = (1/Ld)[ -Rs Id + ω Lq Iq + Vd ] (3.2)

Now why on Earth is Ld Id in the Iq formula 3.1, and and vice versa?

let's rearrange 3.1 and 3.2

(3.1) Lq * d(Iq)/dt = [ -Rs Iq - ω Ld Id - ω λm + Vq ]

(3.2) Ld *d(Id)/dt = [ -Rs Id + ω Lq Iq + Vd ]

well now , Ldi/dt is a voltage
and w L I is a voltage
so we have in the quadrature axis voltage formula a direct axis voltage term wLdId
and we have in the direct axis voltage formula a quadrature axis voltage term wLqIq
looks to be criss-crossed, but in sinewaves physical displacement and phase are equivalent

can it be this simple:
direct and quadrature axes are 90 physical degrees apart
and there's only one current, sum of direct and quadrature
so direct axis current Iq through direct axis inductance Lq makes a voltage 90 deg out of phase with Iq but in phase with Id ? And in phase with Vd, if Vd is direct component of counter-emf Vs i think ??
observe signs are swapped in 3.1 and 3.2 and on fig 4.2 as well, inferring a physical displacement on the rotatin frame


guys that's in the spirit of a question from a struggling student not an assertion of fact.
I sure don't have my brain around FOC yet


So do I understand correctly that the two terms ωLdId and ωLqIq together result in a angle adjustment/change?
seems to me it'd affect amplitude of both d and q current components according to machine constants Lq and Ld, so probably tweaks phase and amplitude both.

As best i recall there's not a lot of crosstalk between direct and quadrature fluxes in an ordinary machine so maybe that's why author says on page 8 it's an optional performance enhancement

For better dynamic performance, crosscoupling
terms (ωLdId and ωLqIq) may also be compensated as in Fig. 4.2.

----------------------end thinking out loud--------------



Thanks for indulging me - i feel better about FOC now.

If i keep hanging out with you guys i may not be so intimidated by wife's new washing machine!
 
  • #27
Wow!
I wish I could 'think out loud' this way. I'm not really a math person. Although I understand some. I have to study your 'thinking' more closely.
I always want to understand what I'm doing in a practical way. When I tweak parameters or change algorithms I want to be able to predict the result. I want to be able to explain what is going on in a none mathematical manner. Than I can work and play with it.

The way I see FOC is that it is a nice transformation such that the motor can be controlled more like a DC brushed motor. The big advantage is that the PID controllers operate on a DC level (for a steady state). They do not have to track the sinusodial phase voltages. The rotor position is needed to transfer to and from the rotating coordinate system.

But I do not understand yet what these ωLdId and ωLqIq terms do. But I will study your 'thinking' more closely.

My conclusion so far (please correct me if I'm wrong):

I think my question equally applies to a brushed DC motor as a FOC controlled brushless motor (and others).

Suppose I want to control a (brushed) DC motor. I can use a PID for speed control like in figure A below. This works because the motor voltage is more or less proportional to the motor speed. This is mainly because of the back-emk. Higher speed means higher back-emk, thus the voltage need to be higher.

speedandtorquecontrol.jpg


But I could also implement torque control by sensing the current like in figure B above. This works because the motor is not a pure inductor. The resistor part is also strongly present.
But the voltage still has to overcome the back-emk. Am I correctly when saying that the Integrator part of the PID controller will take care of this? It will change the motor voltage (integrating the error) until the bacl-emk is compensated?

To improve the control loop you could compensate for this back-emk like in figure C above.
Will this make the PID faster because we do not have to wait for the integration to compensate the back-emk (and the integrator is only used to make the torque error smaller)?

I hope my conclusions are correct so far.
 
  • #28
There's no problem with not using decoupling - in fact, it is far more common to not use it and just throw in a couple of PI's to control the d and q current components, respectively, which you can easily tune (lock the rotor, back-emf terms are zero, tune one loop and apply the same gains to the other).

Now, let's say you want to design the controllers instead so you can make them adhere to some performance specifications. Using classical linear control theory, you'll quickly realize that the d and q systems are simply just a couple of low pass filters - but only if you use decoupling!

By using decoupling you are effectively linearizing the systems you're trying to control, by which you can make linear controllers (like PI/PID's) more effective, i.e. get a better dynamic response.
 
  • #29
But the voltage still has to overcome the back-emk. Am I correctly when saying that the Integrator part of the PID controller will take care of this? It will change the motor voltage (integrating the error) until the bacl-emk is compensated?

Yes, this is correct. Look at the back-emf term though, notice the only time-varying part of it is the angular velocity of the motor. This velocity changes veeeery slowly compared to the current. The PID effectively sees the back-emf as a disturbance which is constant in time over the period in which the current changes. Even a poorly tuned PID will be very effective at rejecting this, so you shouldn't expect much of a gain in performance when adding compensation for it.

On the other hand, notice how the d and q components of the back-emf in the case of the PMS motor depend on more than just the angular velocity of the motor - specifically, notice they include current components. You're trying to control currents and you have disturbances that change as fast as what you're trying to control, which is usually bad. Adding compensation here is a much more viable option than in the DC case.
 
  • #30
i think i'd best defer to someone better versed . This is my first foray into FOC

Wasn't it Mark Twain quipped "Tis better to remain quiet and be thought a fool than to speak out and remove all doubt." ?
i already missed one chance to remain quiet. From here on i'll learn FOC from you fellows.


old jim
 
  • #31
I feel I should try to offer a bit of intuition with regards to those voltage terms I labeled as 'back-emf terms'.

I'll just restate the PMSM voltage equations for reference purposes:
Vq = R Iq + Lq d(Iq)/dt + ω Ld Id + ω λm
Vd = R Id + Ld d(Id)/dt - ω Lq Iq

- Left hand side of these equations should be clear, they're the dq-components of the stator terminal voltages.
- First terms on the right hand side are the resistive drops.
- Second terms are transient drops - zero in steady state.

Now, these third terms represent dq-components of an inductive voltage drop. The Id current will produce a voltage drop leading the d-axis by 90 deg. It will thus be on the q-axis, which is what the q-component equation reflects.

Same thing goes for the d-component equation. The Iq current will produce a voltage drop leading the q-axis by 90 deg, which will place it in the negative direction on the d-axis, which is what the minus sign reflects in the d-component equation.

- The fourth term in the q-component equation is the true back-emf term - it leads the d-axis by 90 deg, as it must.

The third and fourth terms on the right hand side are commonly known collectively as the speed voltages.

I hope this helps, I think it's is as much as I can explain without going mathy.

Edit:
Ok so I have a bit more as to the origin of the third terms. Me calling them back-emf terms is really very misleading, I just want to make that clear - they have nothing to do with the back-emf (the rotor flux should influence them if they did, but the rotor flux is only part of the fourth term).

If you consider the steady state case where the dq current components and the angular velocity of the rotor is constant, then the stator current must be producing a rotating magnetic field. The motor has inductance so this changing stator current must produce an inductive voltage drop. Where is this reflected in the dq-component equations? It's the third terms.
 
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  • #32
milesyoung said:
I feel I should try to offer a bit of intuition with regards to those voltage terms I labeled as 'back-emf terms'.

I'll just restate the PMSM voltage equations for reference purposes:
Vq = R Iq + Lq d(Iq)/dt + ω Ld Id + ω λm
Vd = R Id + Ld d(Id)/dt - ω Lq Iq

- Left hand side of these equations should be clear, they're the dq-components of the stator terminal voltages.
- First terms on the right hand side are the resistive drops.
- Second terms are transient drops - zero in steady state.

Now, these third terms represent dq-components of an inductive voltage drop. The Id current will produce a voltage drop leading the d-axis by 90 deg. It will thus be on the q-axis, which is what the q-component equation reflects.

Same thing goes for the d-component equation. The Iq current will produce a voltage drop leading the q-axis by 90 deg, which will place it in the negative direction on the d-axis, which is what the minus sign reflects in the d-component equation.

- The fourth term in the q-component equation is the true back-emf term - it leads the d-axis by 90 deg, as it must.

The third and fourth terms on the right hand side are commonly known collectively as the speed voltages.

I hope this helps, I think it's is as much as I can explain without going mathy.

Thank you very much for trying! It I learn a lot from these kind of explanations.

So all three components (ω.Ld.Id, ω.Lq.Iq and ω.λm) are neede for a correct back-emk compensation. I was thinking the ω.λm was the only one needed for back-emk compensation and the other two are for another improvement.

What is not clear to me is why there is an inductive voltage drop because of the rotor speed. Does the back-emk consist of 2 components? One depending only on rotor speed and one depending on motor speed and phase current?
If so, then a quick calculation gives me a much higher value for the ω.λm component compared to the ω.Ld.Id and ω.Lq.Iq components. I quess the last two are still (more) important because of the higher frequency component (currents change faster then speed).
 
  • #33
Look up my edit in my previous post, I think that clears some of it up.

There is only one back-emf term, the fourth term on the right hand side in the q-component equation. The third terms must be there regardless of the back-emf.

When adding decoupling, you add compensation for both the back-emf and the coupling terms. This is different from the DC case.
 
  • #34
Ok Thanks

I see now you explain it in the last sentence. Sorry I overlooked it.

Is it correct that these third terms are usually much smaller then the back-emk (fourth term of Vq) term? And did I understand correctly that these third terms are still important because they change faster then the back-emk (current changes faster than speed)?
 
  • #35
The coupling terms can be considerable in magnitude compared to the back-emf but it's difficult to say in general as it depends on the parameters of the machine you're working with.
And did I understand correctly that these third terms are still important because they change faster then the back-emk (current changes faster than speed)?

You don't really care about the back-emf term since it changes so slowly compared to the current component - any controller with integral action will reject it (same as in the DC case). As you say, due to the high frequency content of the third terms, these are the important terms to compensate for.

But really, if you use decoupling, you're mostly doing it to simplify the design procedure using linear control theory. The performance without decoupling can be very good.
 
<h2>1. What is a PID controller?</h2><p>A PID (Proportional-Integral-Derivative) controller is a feedback control system that is used to regulate a process or system. It calculates an error signal based on the difference between the desired setpoint and the actual output, and uses this error signal to adjust the control input in order to minimize the error.</p><h2>2. How does a PID controller work?</h2><p>A PID controller uses three components - proportional, integral, and derivative - to calculate the control input. The proportional component adjusts the control input in proportion to the error signal, the integral component integrates the error signal over time to eliminate any steady-state error, and the derivative component predicts the future trend of the error signal and adjusts the control input accordingly.</p><h2>3. What is the purpose of a PID controller in current control with PWM?</h2><p>In current control with PWM (Pulse Width Modulation), a PID controller is used to regulate the amount of current flowing through a system. The controller adjusts the duty cycle of the PWM signal to maintain a desired current level, based on the error signal between the setpoint and the actual current.</p><h2>4. What are the advantages of using a PID controller for current control with PWM?</h2><p>A PID controller offers several advantages for current control with PWM, including precise and accurate control, fast response to changes in the system, and the ability to adjust for disturbances or changes in the system. It also allows for easy tuning and can be implemented in a variety of systems.</p><h2>5. Are there any limitations to using a PID controller for current control with PWM?</h2><p>While PID controllers are effective in many systems, they do have some limitations. They may not perform well in systems with large time delays, nonlinear dynamics, or significant disturbances. Additionally, they require proper tuning to achieve optimal performance, which can be challenging in some systems.</p>

1. What is a PID controller?

A PID (Proportional-Integral-Derivative) controller is a feedback control system that is used to regulate a process or system. It calculates an error signal based on the difference between the desired setpoint and the actual output, and uses this error signal to adjust the control input in order to minimize the error.

2. How does a PID controller work?

A PID controller uses three components - proportional, integral, and derivative - to calculate the control input. The proportional component adjusts the control input in proportion to the error signal, the integral component integrates the error signal over time to eliminate any steady-state error, and the derivative component predicts the future trend of the error signal and adjusts the control input accordingly.

3. What is the purpose of a PID controller in current control with PWM?

In current control with PWM (Pulse Width Modulation), a PID controller is used to regulate the amount of current flowing through a system. The controller adjusts the duty cycle of the PWM signal to maintain a desired current level, based on the error signal between the setpoint and the actual current.

4. What are the advantages of using a PID controller for current control with PWM?

A PID controller offers several advantages for current control with PWM, including precise and accurate control, fast response to changes in the system, and the ability to adjust for disturbances or changes in the system. It also allows for easy tuning and can be implemented in a variety of systems.

5. Are there any limitations to using a PID controller for current control with PWM?

While PID controllers are effective in many systems, they do have some limitations. They may not perform well in systems with large time delays, nonlinear dynamics, or significant disturbances. Additionally, they require proper tuning to achieve optimal performance, which can be challenging in some systems.

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