## Rocket pitch and yaw control question : is is decoupled from roll control?

## Rocket pitch and yaw control question : is is decoupled from roll control?

(OP)

Hello,

I'm designing a controller for rocket Pitch and Yaw control (aim is for rocket to remain upright, so zero pitch and yaw angles). I'm having trouble developing the dynamic equations and can't find existing material corresponding to my needs elsewhere. I've got the following non-linear dynamic equations:

I'm trying to get a transfer function so I need to linearize these. This is where my problem comes in.

The actuator that I will implement will be unable to roll-stabilize the rocket so the rocket is free to spin, and I want pitch and yaw angles to remain 0==> ψ=0 and θ=0. The problem is then that if I linearize around an equilibrium position where roll angle φ=0 and roll rate P=0, then the linear set of equation that I get is:

These contain no information about roll! Can you confirm that effectively pitch and yaw control is decoupled roll control in rockets?

Best,

Danylo.

I'm designing a controller for rocket Pitch and Yaw control (aim is for rocket to remain upright, so zero pitch and yaw angles). I'm having trouble developing the dynamic equations and can't find existing material corresponding to my needs elsewhere. I've got the following non-linear dynamic equations:

I'm trying to get a transfer function so I need to linearize these. This is where my problem comes in.

The actuator that I will implement will be unable to roll-stabilize the rocket so the rocket is free to spin, and I want pitch and yaw angles to remain 0==> ψ=0 and θ=0. The problem is then that if I linearize around an equilibrium position where roll angle φ=0 and roll rate P=0, then the linear set of equation that I get is:

These contain no information about roll! Can you confirm that effectively pitch and yaw control is decoupled roll control in rockets?

Best,

Danylo.

## RE: Rocket pitch and yaw control question : is is decoupled from roll control?

That said, taking a step back from differential equations...

The only way for the fins to induce a rolling moment would be if they are actuated in opposite directions. If they're adjusting for pitch/yaw, they are are not doing this. Minus tolerances.

Ditto gimbaled engines.

## RE: Rocket pitch and yaw control question : is is decoupled from roll control?

needto have some info about the rocket's current roll angle and rate, otherwise the controller actuating the fins will have no idea about roll and hence, as in the situation described in the first few sentences of this post, the rocket will quickly go haywire.In doing some reading, it seems that ever author is allowing him/herself to decouple pitch and yaw from roll, and from each other even, just as you described because they assume that the rocket is roll-stabilized so the situation of "super fast roll rate" will never arrive. In my situation, it is a model rocket and I have no interest in adding additional mass for an internal inertia wheel for roll control. I will work more on my problem and post back results. Meanwhile, if anyone has suggestions for attitude control of

roll uncontrolledrockets reading (I've found none), please drop in a word.Cheers,

Danylo.

## RE: Rocket pitch and yaw control question : is is decoupled from roll control?

It sounds like you are trying to control the rocket like a model airplane with visual feedback. Then you have to design the rocket like a model airplane, using large fins (wings) and trim tabs to minimize roll. It has to be stable enough to fly using only visual feedback. Generally, rockets are too fast for manual control to work.

## RE: Rocket pitch and yaw control question : is is decoupled from roll control?

## RE: Rocket pitch and yaw control question : is is decoupled from roll control?

## RE: Rocket pitch and yaw control question : is is decoupled from roll control?

notroll-stabilized rocket, or does that create huge complications? Today I successfully wrote the in-plane 2D rocket flight simulation and I imagine that that would suffice for a roll-stabilized case (as pitch and yaw are decoupled and for my rocket the moments of inertia about pitch and yaw axes is the same).## RE: Rocket pitch and yaw control question : is is decoupled from roll control?

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## RE: Rocket pitch and yaw control question : is is decoupled from roll control?

## RE: Rocket pitch and yaw control question : is is decoupled from roll control?

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## RE: Rocket pitch and yaw control question : is is decoupled from roll control?

I cannot say that the rocket has an equilibrium at 0 roll angle, 0 roll rate. For all I know, the roll angle one second after lift-off may be 270° offset from the at-launch roll angle (which we may define as 0). Another second later, this roll angle may become 570°! You see, I can't say anything about roll angle or rate. The linearized equations in my original post are effectively linearized around 0 roll angle and 0 roll rate and, as you can see, have become decoupled ==> this is why roll angle is no longer present in them as, for small roll angles and roll rates (as would be assured by a roll controller), pitch and yaw may be considered independently from each other and from roll. But sincemyrocket hasnoroll controller, the linearized equations are simply not true and I'm looking for whether someone knows how to handle this kind of situation without recurring to non-linear control. I'm pretty sure it's possible without going into non-linear control because, as you can see in this video the Apollo-era Little Joe rocket handled the no-roll-control situation rather well (and I'm sure they didn't have non-linear controllers back in the day??).## RE: Rocket pitch and yaw control question : is is decoupled from roll control?

Most, if not all, later boosters incorporated roll control via either thrust vectoring from a pair of gimballed engines, or by attitude control thrusters, or by aero control surfaces, or some combination of the three.

## RE: Rocket pitch and yaw control question : is is decoupled from roll control?

## RE: Rocket pitch and yaw control question : is is decoupled from roll control?

2. In a model rocket, roll instability is compounded by the higher likelihood of aero surface misalignment causing a roll rate proportional to forward speed, and due to a low roll-direction mass moment of inertia, both in relative terms to full-scale orbital boosters.

Given 1 and 2, it is even more likely that an attempt to control yaw and pitch via ailerons, on a typical model rocket, is doomed from the start given the assumption that theta-dot remains below a threshold that causes the instability.

Do look at the "AIM 9" and/or "rolleron" entry in wikipedia, and/or search google images for the term rolleron. They are a pretty low-mass, self-actuated solution to the problem.

## RE: Rocket pitch and yaw control question : is is decoupled from roll control?

I don't quite understand what you mean after the "given the assumption that theta-dot..." as it seems to me like that very assumption is what would ensure that the control system works (given that we mean theta-dot is the roll rate).

## RE: Rocket pitch and yaw control question : is is decoupled from roll control?

So I've re-written the dynamic equations and simulated them in MATLAB. I attached a PDF of the equations as well as the 2 Matlab files you need to run the simulation. They seem to work well, but disclaimer : this is work in progress!

Now comes the linearization step, which I will report on once I do it. In the PDF of the equations, the notation is:

x,y,z = coordinates of rocket CG with x the roll axis, y the pitch axis and z the yaw axis. If the rocket is drawn upright on paper then x is up, y is right and z is into the paper, with the origin at the c.m. (Center of Mass).

ψ,θ,φ = yaw, pitch, roll Euler angles executed in that order.

V = rocket velocity

U = air velocity

W = velocity of rocket with respect to the air, which in the body axes computes as vec(U_B)-vec(V_B)

Anything with subscript "B" ==> means "in the body axes frame of reference".

I plan to write a paper with the step by step development once I am done. I will publish the paper here.

## RE: Rocket pitch and yaw control question : is is decoupled from roll control?

## RE: Rocket pitch and yaw control question : is is decoupled from roll control?

## RE: Rocket pitch and yaw control question : is is decoupled from roll control?

Read the whole sentence, which starts with "Given 1 and 2", 2 being a statement that (for two independent reasons) in a model rocket, theta-dot is extremely unlikely to remain a small value once the fire gets lit.

## RE: Rocket pitch and yaw control question : is is decoupled from roll control?

## RE: Rocket pitch and yaw control question : is is decoupled from roll control?

You might find these useful, this topic..

MIL-HDBK-762 DESIGN OF AERODYNAMICALLY STABILIZED FREE ROCKETS http://quicksearch.dla.mil/

AIAA ARC may have downloadable tech reports on [AIAA Journal, papers, etc] articles on Missile stability http://arc.aiaa.org/action/doSearch?AllField=

AIAA Education Series http://arc.aiaa.org/series/4.es

Regards, Wil Taylor

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