Simulation result of the example model: "Frequency Response Estimation of PMSM Using Field-Oriented Control"

Hello Everyone,

the simulation result from the example model is for me somehow confusing: Frequency Response Estimation of PMSM Using Field-Oriented Control - MATLAB & Simulink Example - MathWorks Deutschland

Because the fact that, the motor has the same Ld and Lq, I would expect that the both Id-Plant and Iq-Plant should have the same bode plot, right? And we should see R-L behavior: (1 / (R+L*s)), what we actually can see for Id-Plant above. But for Iq-Plant, it is somehow a strange bode plot for me ?!

Could anyone please help regarding this? Any help is really appreciated!

Thanks in advance!

Tony

Answer 1

[Ananth kumar]

Please find the PMSM equation above.

Both Vd/Id and Vq/Iq are not same.

[Tony]

Hello Kumar,

many thanks for your reply!

In fact, the last terms in your equation above are disturbances.

For the frequence response estimation from Vd to Id (and from Vq to Iq), the result should be only the plant-behavior (RL-plant).

What should be the expected analytical transfer function from Vq to Iq ?

I find another example model : Frequency Response Estimation for Power Electronics Model Using Pseudorandom Binary Signal - MATLAB & Simulink - MathWorks Deutschland

You see that the estimated result matches to the analytical result:

Many thanks!

Kind regards.

Tony

[Ananth kumar]

Hi Tony,

1. It is not recommended to treat the cross-coupling factor and permanent flux-linkage as disturbances. If you want to validate the frequency response estimator, use known plant model like impedance or DC motor.
2. For online frequency response estimator, you can use either Sine-stream or PRBS as shown in the figure below.

In PMSM example, online frequency estimation is compared with simulation and physical hardware (using sine-stream for perturbation).

In Voltage Booster example, frequency estimation is compared with simulation of sinestream and PRBS perturbation with analytical method.

PRBS takes less time and recommended. You can use sine-stream or PRBS in your hardware testing or simulation.

[Tony]

Hi Kumar,

for your point-1 above: "It is not recommended to treat the cross-coupling factor and permanent flux-linkage as disturbancesIt is not recommended to treat the cross-coupling factor and permanent flux-linkage as disturbances" : what do you mean? Could you please share the source said that?

The fact is, the decoupling between d-q is state of the art:

With the FRE of the plant (Idq), the designer could design e.g. his PI-controller with bode diagram of open-loop and to compare with the expected analytical result. So with a correct PRE of the plant, you can see some saturation effects, if it is avaiable under loaded motor...

What do you need result from the example model for? Just only to compare with the physical HW calculation without understanding the expected analytical result, does not help to design some controllers (PID, or other..)

Kind regards

Tony

[Ananth kumar]

Hi Tony,

This sounds interesting.

You are considering decoupling in your algorithm but in the shipped example decoupling is not included. With proper decoupling, I agree with your expectation on frequency response. You given me a thought to improve this example further by adding appropriate decoupling algorithm. Thanks.

In a way, this example shows the plant model which includes cross-coupling effect.

This example solves two objectives, (1) from plant frequency response in simulation and in hardware you can validate your plant modeling. You can estimate motor parameters using instrumented test and create a plant model. Using Frequency Response Estimator workflow, you validate your estimated parameters with the hardware plant frequency response (2) second objective is to demonstrate the usage of frequecy response date (frd) to estimate the control gains which is a common use-case.

You may find many examples for Frequency response estimation for Boost converter and Motor control simulations, this example particulary focuses on hardware deployment of the algorithm in a DSP. This can be extended for any black-box plant model.

Thanks for your interesting conversation.

[Tony]

Hi Kumar,

regardign your second objective "(2) second objective is to demonstrate the usage of frequecy response date (frd) to estimate the control gains which is a common use-case"

I think, with the result of FRE above, we could not be able to design control gain.

Because, even in example models of Motor-control-blockset, DQ-current PI control gains (Ki; Kp) are designed based on the well-known Magnitude Optimum Criterion.

For that, the motor dq-plants are assumed as PT1-Plants (also RL-Plant)

So our team thinks, for now the Mathworks Motor-Control-Blockset is not good enough for our motor control devolopment.

Many thanks !

Tony

[Ananth kumar]

I am very sorry to hear your comments.

I recommend you go through the below experiments and comments.

1Comparing the frequency response of d-current and q-current loop. You could observe more deviations in frequency less than 100 Hz. This is due to the fact, when perturbation is applied in Iq, speed distortion is observed, and this affects the frequency estimation in lower frequency. Online frequency estimation is applicable for SISO.

Figure 1Different frequency response is observed for Id and Iq current loop. When perturbations is applied in Iq, speed distortion is observed this affects the plant frequency response.

2. To exclude the influence of speed in Iq perturbation, better couple a motor with dyno and spin in constant speed or brake the motor to zero speed. You can find the attached example, demonstrated to run for d-current control loop and q-current control loop with a braked motor (speed is 0, irrespective of Iq perturbations).

Figure 2 Brake the motor and inject constant Id and Iq. Run the frequency estimation and this shows same frequency response for Id and Iq control loop

In this case, you could observe both the frequency plots are overlap each other.

3. I repeat the exercise with Lq=2*Ld and observe the below behaviour, which is expected,

Figure 3 Same as experiment 2, but change the motor parameter as Lq=2*Ld.

1. Recommendation:
2. Step 1: With motor coupled to dyno (constant speed) or brake (zero), run frequency estimation for d-current control and q-current control.
3. Step 2: use PI tuner App for tuning control gains for Id and Iq control loops. Update the controller gains in d and q loop.
4. Step 3: Change the motor from speed mode to torque mode (disengage from brake or coupled dyno).
5. Step 4: Include speed control loop and repeat the exercise for speed -loop frequency response.

We are happy to assist you on your queries. Please reach out us through MathWorks customer support or through sales team for quick response.

[Tony]

Hi Kumar,

yes, you are right, the issue should be the speed distortion...

Many thanks for your attached fix-model! It is working fine. But we see somehow the estimated plant (for the default case Ld = Lq) is not that close to the expected transfer function (for the magnitude at low frequency / DC)

Expected at DC / low frequency: 20 * log10 (1/((pmsm.Rs + inverter.R_board))) = 8.7dB

What we see above estimated: 5dB

We run your fix-model and edited the script : mcb_pmsm_freq_est_plot.c

So that, only the dq-plant is shown and included the expected dq-transfer functions in bode plot.

What do you think? What would you expect from FRE-results?

Many thanks!

Tony