I try to design an attitude controller with cascaded PD-P structure (angle-angular rate) for well-known quadrotor dynamics according to the thesis. I use an imu as expected in order to get the angle(with fusion) and rate measurements. Before implementing the controller on the system, I just wanted to observe the outputs of imu alone which confused my mind. I attached a measurement result below. The red line depicts the angle and the blue line represents angular rate.
Since the angular rate seems noisy and its amplitudes fluctuates within the range of (+10-10) which is quite different from the simulations (+1-1), I thought my controller will not work properly and some questions appeared as listed below (although integration of angular rate gives an identical angle which means that the rate measurement is ok).
1. How my system be affected if I apply a filter like a kalman filter on angular rate to smooth noisy-like signal? or should I use a filter as we apply on angle measurement?
2. Why I see a different amplitude range (+1-1) in simulations (both are in radian)?
3. Since the imu measures the body rates not euler rates, what will happen in real world dynamics if I use it directly instead of multiplying with transformation matrix? (there is only slight deviations in the simulations which can be ignored)