MICROFORUM

I'm looking at how to control the speed of a BLDC motor between zero and 10,000 rpm

Potemkin, check here:

SPEED CONTROL OF BLDC MOTOR
Speed control of BLDC motor is essential for making the motor work at desired rate. Speed of a brushless dc motor can be controlled by controlling the input dc voltage / current. The higher the voltage more is the speed.
Many different control algorithms have been used to provide control of BLDC motors. The motor voltage is controlled using a power transistor operating as a linear voltage regulator. This is not practical when driving higher-power motors. High-power motors must use PWM control and require a microcontroller to provide starting and control functions.
The control algorithm must provide three things:

PWM voltage to control the motor speed
Mechanism to commutate the motor
Method to estimate the rotor position using the back-EMF or Hall Sensors

Pulse-width modulation is used to apply a variable voltage to the motor windings. The effective voltage is proportional to the PWM duty cycle. When properly commutated, the torque-speed characteristics of the BLDC motor are identical to a dc motor. The variable voltage can be used to control the speed of the motor and the available torque.
The commutation of the power transistors energizes the appropriate windings in the stator to provide optimum torque generation depending on the rotor position. In a BLDC motor, the MCU must know the position of the rotor and commutate at the appropriate time.

source: https://www.mathworks.com/matlabcentral ... bldc-motor

look here https://www.renesas.com/eu/en/applicati ... ards__kits

one link more https://www.microchip.com/en-us/solutio ... dc-motors#
Let us know more details about your motor (voltage, power...)

I have Maxon EC motor Type 136206. That's brushless 150 watt, 48V, rpm 8960 with a tacho.

This motor requires sufficient power and has an encoder that returns speed. The best way is PWM control with a microcontroller.