I'm making a flight controller for quadcopter. It is very stable when regulated by angular velocity, but it is horrible when regulated by angle. What are the potential problems when regulating a quadcopter by angle?
I'm using MPU6050 configured with low-pass filter for 185Hz cut-off with 2ms delay on both the 3-axis acceleration and angular velocity data. The angular velocity is filtered again with low-pass filter:
(AV = AVn * alpha + AVn-1 * (1-alpha)), alpha = 0.8
The accelerometer angle is calculated using:
pitch_a = atan2(x_a, sign(z_a) * (sqrt(sqr(z) + zqr(y) * 0.001))) * 180/pi; roll_a = atan2(y_a, (sqrt(sqr(x) + zqr(z))) * 180/pi;
The angular velocity is integrated over the last fused angle:
pitch_g = pitch + av.y * dt; roll_g = roll + av.x * dt;
And the resulting angle is fused with the calculated accelerometer angle using complementary filter with
alpha = 0.98.
This is done with new sensor values every 2ms.
I'm using cascaded PI-P controller. The inner P controller's input is angular velocity and its output is motor power difference. The outer PI controller's input is absolute angle and its output is angular velocity. The outer controller is disabled when controlling the quadcopter by angular velocity. The inner controller runs every 2ms with accuracy of 8us and output limit of +-70. The outer controller runs every 8.5ms with accuracy of ~100us and output limit of +-250. I'm using this library, slightly modified to run when I call it, output integers, use microseconds and zero the integral sum when at very low throttle.
The setpoint is sent from the remote every 50ms, slightly filtered.
The output from the inner controller is added and subtracted to the according motor. The motors drivers' are controlled with 8-bit 490Hz PWM ranging from 127 to 254.
When controlling the quadcopter by angular velocity it flies stable with P value ranging from 0.2 to 0.8, noisy sensor input and even with one different motor. When controlling it with angle it behaves randomly. It starts to pitch or roll from level orientation, it seems to respond well to step input when it has to pitch or roll but returns to level very slow and overshoots... The angle control feels like a very bad angular velocity control (even tho the angle input is cleaner and it shouldn't have noticeable delay based on the fusion equation). The P range I have tried is approximately 0.5 to 2.0 and the I range is approximately 0 to 0.3. The inner controller runs 4.25 times faster the outer controller.
What can be the problem?