This update calculates battery current, motor current and electrical wattage targets for control loop implementation. Please note there are presently 2 throttle variations of efficiency control - watt control throttle & motor current control throttle (both variations updated here). In BLDC / block commutation mode the motor current target probably makes the most sense to use for a control loop. In FOC mode, I envision the battery current or electrical wattage target being used for the control loop.

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Efficiency Control

Watt Control Throttle Variation

Control Loop Targets

Settings:

M= 100% = Throttle % Setting

K= 90% = Desired Efficiency % Setting

L= 500w = Desired Min Watts Available Setting

P= 4500w = Desired Max Watts Available Setting

Y= 120a = X*(sqrt(3)/2) = Max Motor Amps BLDC

X= 138.56a = Y/(sqrt(3)/2) = Max Motor Amps FOC

Z= 95% = Max Duty Cycle %

Observables:

G= 48.2v = Battery Voltage

D= 16.94v = Back EMF Voltage

F= 0.025ohm = Winding Resistance Ohms

Control Loop Targets:

A= XX.XXXa = Battery Amps

B= XX.XXXa = Motor Amps (BLDC)

W= XX.XXXa = B/(sqrt(3)/2) = Peak Phase Current FOC

H= XX.XXXw = Throttled Wattage

N= XX.XXXw = Desired Full Throttle Wattage

C= XX.XXX% = Duty Cycle

E= XX.XXXv = Effective PWM Voltage

N=L

&

if D>((sqrt(F)*K*sqrt(L))/(10*sqrt(100-K))) then N=(-1)*((100*(D^2)*(K-100))/(F*(K^2)))

&

if N>P then N=P

&

if Y<((sqrt((D^2)+(4*F*N))-D)/(2*F)) then N=Y*(D+(F*Y))

&

if Z<((50*(sqrt((D^2)+(4*F*N))+D))/G) then N=(G*Z*(G*Z-(100*D)))/(10000*F)

&

C=10*((sqrt((25*(D^2))+(F*M*N))/G)+((5*D)/G))

&

E=G*(C/100)

&

B=(E-D)/F

&

H=B*E

&

A=H/G

&

repeat

Therefore:

Instantaneous Control Loop Targets:

A= 29.400a = Battery Amps

B= 75.264a = Motor Amps (BLDC)

W= 86.90a = B/(sqrt(3)/2) = Peak Phase Current FOC

H= 1417.10w = Throttled Wattage

N= 1417.10w = Desired Full Throttle Wattage

C= 39.049% = Duty Cycle

E= 18.821618v = PWM Effective Voltage

------------------------------

Efficiency Control

Motor Current Control Throttle Variation

Control Loop Targets

Settings:

M= 100% = Throttle % Setting

K= 90% = Desired Efficiency % Setting

L= 500w = Desired Min Watts Available Setting

P= 4500w = Desired Max Watts Available Setting

Y= 120a = X*(sqrt(3)/2) = Max Motor Amps BLDC

X= 138.56a = Y/(sqrt(3)/2) = Max Motor Amps FOC

Z= 95% = Max Duty Cycle %

Observables:

G= 48.2v = Battery Voltage

D= 16.94v = Back EMF Voltage

F= 0.025ohm = Winding Resistance Ohms

Control Loop Targets:

A= XX.XXXa = Battery Amps

B= XX.XXXa = Motor Amps (BLDC)

W= XX.XXXa = B/(sqrt(3)/2) = Peak Phase Current FOC

H= XX.XXXw = Throttled Wattage

N= XX.XXXw = Desired Full Throttle Wattage

C= XX.XXX% = Duty Cycle

E= XX.XXXv = Effective PWM Voltage

Where:

N=L

&

if D>((sqrt(F)*K*sqrt(L))/(10*sqrt(100-K))) then N=(-1)*((100*(D^2)*(K-100))/(F*(K^2)))

&

if N>P then N=P

&

if Y<((sqrt((D^2)+(4*F*N))-D)/(2*F)) then N=Y*(D+(F*Y))

&

if Z<((50*(sqrt((D^2)+(4*F*N))+D))/G) then N=(G*Z*(G*Z-(100*D)))/(10000*F)

&

H=(M*((-1)*D*(M-100)*sqrt((D^2)+4*F*N)+((D^2)*(M-100))+(2*F*M*N)))/(20000*F)

&

C=((50*(sqrt((D^2)+(4*F*H))+D))/G)

&

E=G*(C/100)

&

B=(E-D)/F

&

A=H/G

repeat

Therefore:

Instantaneous Control Loop Targets:

A= 29.400a = Battery Amps

B= 75.264a = Motor Amps (BLDC)

W= 86.90a = B/(sqrt(3)/2) = Peak Phase Current FOC

H= 1417.10w = Throttled Wattage

N= 1417.10w = Desired Full Throttle Wattage

C= 39.049% = Duty Cycle

E= 18.821618v = PWM Effective Voltage

———————-

For Illustration:

classical settings: 100% throttle, 300a battery amp limit, 300a motor amp limit, 33.2v battery, 850kv 0.0135ohm motor, 120mm tire diamter, 4:1 gear reduction, 2 motors

efficiency control settings: 100% throttle, 300a battery amp limit, 300a motor amp limit, 87.5% desired efficiency setting, 200w minimum electrical wattage setting, 9960w maximum electrical wattage setting, 33.2v battery, 850kv 0.0135ohm motor, 120mm tire diamter, 4:1 gear reduction, 2 motors

## "Peak Efficiency" Control Mode?

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