2MTR-DYNO: Units of measure for controlling through Simulink

Hi Veronica,

Welcome to the world of fixed point in embedded systems. You may learn fixed point representation of numbers & IQMath by TI's resources separately. To keep it simple: We are using a ‘per-unit’ representation of signals applied to embedded systems. This helps in generating optimized code, especially when working with fixed-point data types. Also, the signals represented in PU system range from -1 to +1, as against a large number for an equivalent SI unit. You can use the following formula to convert signals from PU to SI units and vice-versa.

quantity expressed in PU = (quantity expressed in SI units)/(base value)

OR, as per your requirement:

quantity expressed in SI units = quantity expressed in PU × base value

The base values used for speed, current and position signals in the example mentioned by you are given below:

• Base speed, Speed_base = 1200 rpm
• Base current, I_base = 19.3 A
• Base position, Theta_e = 2*pi (radians)

Now coming to your questions: 

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1) The Speed Demand from 0.2 to 0.7 means per-unit speed w.r.to. base speed.

The variable ‘Speed_per_unit_scaler’ in MATLAB workspace represents the base value of speed.

You may use the above described formula, to convert these signals from PU system to SI units. If you wish, you may change the base speed to maximum speed of the motor by updating the workspace variables.

These variables are initialized when the Simulink model is loaded. You may access the initialization script by going to model properties-->Callbacks.

Alternately, you may also type ‘edit c28377pmsmfoc_data’ at MATLAB command window to open this models’ initialization script.

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2) Regarding the load torque demand: 

The load torque in this example is PU value for q-axis current of the load motor. You may use the base value for current to convert this into amperes. Then, you may use the following conversion to get torque in Newton-meter (NOT Newton-per-meter):

Tem = (3/2)*(polePairs)*(FluxPM_weber)*Iq_amps

 about the plots: Current

As for the current signal: What is being displayed is the output count of ADC. Inside the algorithm on the target, it is converted into per-unit by following approach:

Ia_PerUnit = (Ia_ADC_Count – ADC_Offset)*AdcVoltsPerCounts*AmperePerVolt*(1/I_base)

Where,

• Ia_ADC_Count = Signals you see on the host model
• ADC_Offset = 2300 (approx.) // This is ADC Count at zero current (~1.65V at ADC for this example)
• AdcVoltsPerCounts = (1.65/2048)
• AmperePerVolt = (19.3/1.65)
• Base current, I_base = 19.3 A

Similar calculations are used for Ib. You may convert the currents from per-unit to amperes using the base current mentioned above.

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3) What about speed, duty cycle and position?

Unit of measure for speed is PU. As explained, you may multiply by base speed and convert to RPM. This can further be converted to any other units (e.g. rad/s) 

Duty cycles: These are counts for ePWM block. The variable ‘PWM_Counter_Period’ in MATLAB workspace describes equivalent count for 100% duty cycle. You may convert the duty cycles accordingly.

Position is per-unit representation of 2*pi radians. You may multiply by 2*pi and convert to radians. Or convert to any other units (e.g. degrees) of your choice.

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“Because I don't find any connection between that value and the plotted signal of speed.”

Thanks for pointing this out. We are coming up with much better documentation for Motor Control examples in R2020a. 

Hope this was helpful.

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Darshan Pandit | MathWorks

Hi Veronica,

One thing I missed in the post above is: The target model converts the signal data-types to uint16 before sending them over serial. This happens at following subsystem inside the target model: ‘c28379Dpmsmfocdual_cpu1_ert/FOC Alogrithm Motor/Data Logging’. Let’s call this signal data-type conversion as signal conditioning for briefness of the discussion here. This is explained below, prior to the solution you are looking forward to.

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Signal Conditioning:

The signal conditioning is not needed for duty cycles and ADC counts for currents, as these signals are already of ‘uint16’ datatype. However, the data-types of speed and position signals inside the target are fixdt(1,32,15) and fixdt(1,32,16) respectively. Hence, these signals require signal conditioning.

The signal conditioning is implemented via representing last 16 bits of a fixed point as stored integer, and then, sending this as a 'uint16' data-type. The fixed point representation of the value 0.2 in given datatype, when seen as stored integer (uint16), corresponds to 6554 - which is around the average value of 4000 to 9000 you are observing in the scope. Similarly, the fixed point representation of 0.45, when seen as stored integer (uint16), corresponds to 14746. This again, is around the average of 1.3x10^4 to 1,63 x 10^4 as observed by you . To explore these, type the following at your MATLAB command prompt:

a = fi(0.2,1,32,15);

a.Value

a.storedInteger

The first command above stores the value 0.2 as a fixed point representation with Signedness = 1, WordLength= 32 bits, FractionLength = 15 bits. The second and third displays their value and stored integer representation respectively.

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To get to the solution required:

You’d have to modify the data-types of received signals in the host model. These would be different for speed and position respectively. The attached image would guide you better on this.

Having done signal conditioning, you’d see the signals as expected by you: Per-Unit Speed (signal1) & Position (signal2).

Once you can see these signals clearly for your hardware, you may start working towards solving problems such as tuning of PI controllers, Sliding Mode Oberserver, etc in the model.

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Which is the value of FluxPM_weber and Iq_amps??

Iq_amps is the q-axis current represented in amperes. As explained in previous post, the per-unit value of Iq is same as the torque demand (entered by you) in the host model. We need to convert it's value from per-unit to amperes, in order to compute the torque in N-m using the relationship provided.

FluxPM_weber: is the value of permanent magnet flux represented in webers. This would be different for each motor. For the pmsm available with you, this can be computed by either back-emf constant (Ke) or torque constant (kt) using the following relationships:

FluxPM = (Ke)/(sqrt(3)*2*pi*1000*polePairs/60); %PM flux computed from Ke

OR

FluxPM = (Kt)/((3/2)*polePairs; %PM flux computed from Kt

Where,

• Ke = back-emf constant with units as 'Vline_peak/krpm' (Vline = Vab)
• Kt = toque constant with units as 'N-m/Amp'
• polePairs = Number of rotor pole pairs of the pmsm

Have a good day!

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Darshan Pandit | MathWorks

Welcome.

The base voltage is decided by maximum phase voltage the inverter can generate using given PWM dutycycles:

• For Sinusoidal Modulation, this is Vdc/2
• For Space Vector Modulation, this would be Vdc/sqrt(3)

SI Units =  Internation System of Units

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Darshan Pandit | MathWorks

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