Closed Loop control of a propeller

Question

Hello I'm trying to control the velocity of the propeller with the pitch angle. I have a diagram from the factor cp over J and phi (see image: Draw.io diagram), but not a analytical formula.

J = v*60/(nDpi), v: wind velocity, n: rotational speed, D: diameter of the propeller.

I get a motor torque and a rotational speed as setpoint. I should control the propeller speed by changing the pitch angle phi.

My question is, how do I calculate the controller to control the rotational speed?

My first approach was to invert the formula "Propeller Momentenstrecke". So I get the image below, but this is only valid if the Time Tphi is so small, that in this timeinterval the rotational speed changes less. There is a problem, if the rotational speed is very slow, so the output of the 3rd block become very big.

Do anybody knows, how I can control this system, which approach do I have to use? Do anybody know some papers?

edit: I'm talking about a small aircraft with one propeller in front. The maximum speed of the motor is 2500rpm mechanical, its a permanent magnet synchrone machine with 6 pole pairs.

Answer 1

It makes no sense to change the pitch angle within a rotation cycle, you would get a helicopter-like translational force on the rotor then. If you need exactly that, you better stick to a pure mechanical solution, a swashplate.

To avoid that, the pitch angle has to be controlled over at least one rotation cycle, for all practical purposes many more. Simply filter the rotational speed through a low-pass.

Answer 2

edited

1. Scrap your design and this question** A better question has specs with niputs, outputs and stability criteria ..not how to solve a block diagram...
2. ALWAYS define better specs FIRST.
3. What are your real goals? define each block

4. When you discover new parameters, update your design spec.
   a) optimum thrust control at optimal efficiency? stability margin?
   b) what are the disturbances, what is the allowed error to be ignored?
   c) divide each goal into finer goals,
   d) have you completed your design spec.? not yet?
   e) then start with defined transfer functions for each block with PID feedback where necessary.
   f) then solve the compensation feedback with Nyquist, Root Locus or Bode Methods.
   g) How fast does thrust (prop pitch) need to change? ( BW, error tolerance (overshoot, steady state)
   ( 10~90% slew rate and bandwidth are related f=0.35/t) in slew rate depends on environmental swings ( disturbances) What is your error spec? h) What is your stability criteria? i) Is there a deadzone for power applied to a gear ratio motor to control pitch? These should all be in your specs in block diagrams or transfer functions.

   j) Do you start with a transfer function of each block or a model (from the shoulders of giants)
   k) Synthesize it. Solve it using Control Theory methods that work. Bode, Nyquist, Root Locus etc... l) then realize it? build it, test it m) write a test plan (DVT), verify the specs. Write a simple DVT report ( 1 page per test with fig. photo and results)

You may end up PMDC Motor RPM/n poles with pitch control being some other planatary gear motor with some kV/RPM spec range and power spec and holding torque spec for a hybrid. or magnetic holding for a pure PM Stepper. - Thrust can be varied with Prop Pitch control with an efficiency curve with some actuator.

• Driver depends on cost, power, size, characteristics

Most efficient is a 3 phase PMDC with Field Oriented Control (FOC) aka Space Vector Control ( Re-search it)

• 8 equal shifted phases with PWM with sine and 6 of 8 logic vectors) (aka V/F RPM control) voltage to the 3 phase motor using 6 vectors out a possible 8 to create a net sinusoidal force. But not the only solution.

end edit

I would expect inputs for Prop. Rotor position is connected to motor with a gear ratio and motor has multiphase voltage and current sensing.

RPM is best derived by rotation position sensor or EMF filter. In order to have a faster system response time, it dictates the number of poles per Prop rotation are needed.

Velocity is then the derivative (D) of position so PID control constants should work well with other system constraints.

Motor Current indicates torque and expected changes in velocity by integration (I) but leads to more phase shift and overshoot but this can be used if demand power is less than supply and Prop angle can be increased with output PWM supply power to match demand. ... Generally if is best to control a system with 1st order feedback with high portional gain, since the system has integral inertia like internal compensation for an Op Amp is an integrator for gain control is stable with 1st order slope. But often Lead-lag phase filters are needed to optimize gain phase margin at unity loop gain.

Since this question is beyond the scope of this forum

Research more here

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