I've been working on rocket stabilization for my graduation project similar to this video: Roll gyro stabilized rocket with automatic control system.
I used a low cost MEMS sensor (MPU-6050) and was able to find accurate roll, pitch & yaw of the rocket using a kalman filter and sensor calibration. Later I installed some servo motors on the body to control movable fins, similar to the video. I built an air tunnel to test "making fast air flow directly to the rocket."
My goal is to set a specific pitch and yaw angle to the PID controller so that it moves the fins and makes the rocket stable within it (like the video). What I'm unable to determine is the transfer function that will translate the desired pitch to an action by the motor to make the rocket compensate for deviations and stay stable.
For example, I want pitch = 30 degrees.
The sensor reads 35, thus I have a 5 degree error, which is propagated to the PID controller .
The PID will then output a value that will be translated to a motion by the servo connected to the fins that control the pitch.
How do I find this equation, taking into consideration speed and other dependencies.