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Tethered DC motor with propeller modelling (vertical movement) problem

Hi,

is it possible to design a SISO model of a system consisting of a tethered DC motor with propeller, considering the gravitational force as well? I'm thinking of the easiest possible scenario, where we'd control the altitute having the thrust force as input. No motor time constant assumed. The motor moves only up and down, vertically. The equation I've derived is:

a(t) = d^2h(t) / dt^2 = F_thrust(t) / m - g

The gravitational acceleration is messing around. I don't understand how to cope with that, to be able to calculate a transfer function from thrust force to altitude. Or maybe it's a MIMO system already, with gravity as the second input? Or should I use the state space?

I wanted to use some simple techniques to design the controller, like the root locus. I've also read about a technique called 'succesive loop closure' once, but I don't know how to use that here as well.

Regards and thanks for any help in advance.

Reply to
terster
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In most environments accessible to earthbound humans, gravity exerts a constant force downward. (Definition of /down/.) If thrust force is up, gravity subtracts directly. Wake up!

Jerry

Reply to
Jerry Avins

Does it mean, there is an error in the equation I've derived? Otherwise, I still don't know, how your answer should help me solve my problem. As I modelled the system, the Laplace transform of the equation of motion assuming zero initial conditions would be:

s^2*H(s) = F_thrust(s) / m - g,

where the minus sign before the gravity constant means an opposite direction. Is the equation wrong? How do I calculate the transfer function from thrust to altitude?

Reply to
terster

What are the units of m? Of g? Do they match? If not, you can't add or subtract them. Maybe I misconstrue your implied parentheses.

Are Laplace transforms really appropriate for such a simple system?

Jerry

Reply to
Jerry Avins

You separate your bias thrust from incremental. You set your bias thrust equal to the apparent force of gravity; what's left over fits nicely into a SISO system.

Note that lots of interesting things happen between the drive to the motor and the thrust -- in the end you'll have to model that, too.

Reply to
Tim Wescott

=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF= =AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AFTJerry, that wasn'= t very helpful

There is an error or omission in your model in that it isn't complete.

Heed what Tim said, there is no way you can change the thrust instantly. The rotor or propeller has inertia and resistance.

This system may have several states. I bet you end up with one for vertical velocity and elevation, and another for rotor speed at least. Here is a model for the DC motor

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can see the DC motor model adds a current state too.

Is thrust linear with rotor speed?

Peter Nachtwey

Reply to
pnachtwey

There is an error or omission in your model in that it isn't complete.

Heed what Tim said, there is no way you can change the thrust instantly. The rotor or propeller has inertia and resistance.

This system may have several states. I bet you end up with one for vertical velocity and elevation, and another for rotor speed at least. Here is a model for the DC motor

formatting link
can see the DC motor model adds a current state too.

Is thrust linear with rotor speed?

Peter Nachtwey

OP will be lucky if the system linearity is sufficient for a linear transform approach (although I have seen techniques for dealing with simple nonlinear systems using laplace). It'll depend on what range of operation the model has to accommodate, and whether it happens to be working close to any discontinuities such as stall.

I get the feeling that this could be a fair challenge, unless a lot of simplifying assumptions are made, which are likely to seriously compromise the fit.

Reply to
Bruce Varley

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯TJerry,

I dunno -- if the thing is lifting the engine then it should be at a fairly linear portion of the thrust vs. motor voltage (or thrust vs. motor torque) curve.

I've got a control systems trainer that I'm (oh so slowly) developing that basically consists of a motor on a stick, and sees fairly good linearizion just by driving the motor with the direction * square root of the desired thrust.

Reply to
Tim Wescott

Thanks for all the answers. Sorry for my late tnanks, I've been out.

Reply to
terster

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