Hi,

I changed the attitude control loop a little bit to achieve more stability. Rate control with a PID(T1) instead of a PI controller. Here I present the necessary changes in the code to do this.

Pro:

1. Much more attitude stability
2. Much faster response on disturbances or new setpoints

Con:

1. You need to tune the control loop again after this change
2. This change is experimental, it works for me but you do it on your own risk ;)

I'm starting from Software AC 2.1. First I modified the library "PID" to save calculating time. I saved the following floating point operations per call to "get_pid": 2 x division, 4 x multiplication. You can download the modified library here. Unzip it and put the folder "PID_fast" in the "libraries" folder.

In file "ArduCopter.pde":

Add this line to the includes:

#include <PID_fast.h>            // PID library

For the following 4 blocks, I post it like the diff you get in GIT. The "-" means that you should look for this line and remove it. Replace it with the following lines starting with the "+". Of cause, the lines in the code have no "-" or "+". It's just to show what to remove and what to add instead.

-                g.pi_rate_roll.reset_I();
-                g.pi_rate_pitch.reset_I();
+                g.pid_rate_roll.reset_I();
+                g.pid_rate_pitch.reset_I();

-            g.pi_rate_roll.kP(tuning_value);
-            g.pi_rate_pitch.kP(tuning_value);
+            g.pid_rate_roll.kP(tuning_value);
+            g.pid_rate_pitch.kP(tuning_value);
 
-            g.pi_rate_roll.kI(tuning_value);
-            g.pi_rate_pitch.kI(tuning_value);
+            g.pid_rate_roll.kI(tuning_value);
+            g.pid_rate_pitch.kI(tuning_value);
 
-            g.pi_rate_yaw.kP(tuning_value);
+            g.pid_rate_yaw.kP(tuning_value);

In file "Attitude.pde":

In function "get_stabilize_roll(int32_t target_angle)":
 
-    rate         = g.pi_rate_roll.get_pi(error, G_Dt);
+    rate         = g.pid_rate_roll.get_pid(error, G_Dt);

In function "get_stabilize_pitch(int32_t target_angle)":

-    rate         = g.pi_rate_pitch.get_pi(error, G_Dt);
+    rate         = g.pid_rate_pitch.get_pid(error, G_Dt);

In function "get_stabilize_yaw(int32_t target_angle)":

-        rate     = g.pi_rate_yaw.get_pi(error, G_Dt);
+        rate     = g.pid_rate_yaw.get_pid(error, G_Dt);

-    rate         = g.pi_rate_yaw.get_pi(error, G_Dt);
+    rate         = g.pid_rate_yaw.get_pid(error, G_Dt);

In function "get_rate_pitch(int32_t target_rate)":
 
-    target_rate = g.pi_rate_yaw.get_pi(error, G_Dt);
+    target_rate = g.pid_rate_yaw.get_pid(error, G_Dt);

In file "Parameters.h":

Increase the number after "static const uint16_t k_format_version" by one. Warning: This will make the APM erase your EEPROM and Log after flashing the new compiled firmware. So save your settings first! After this, you have to reload your settings and level the copter again.

Later on in the file:

-    k_param_pi_rate_roll = 235,
-    k_param_pi_rate_pitch,
-    k_param_pi_rate_yaw,
+    k_param_pid_rate_roll = 235,
+    k_param_pid_rate_pitch,
+    k_param_pid_rate_yaw,

-    APM_PI        pi_rate_roll;
-    APM_PI        pi_rate_pitch;
-    APM_PI        pi_rate_yaw;
+    PID_fast    pid_rate_roll;
+    PID_fast    pid_rate_pitch;
+    PID_fast    pid_rate_yaw;

-    pi_rate_roll        (k_param_pi_rate_roll,            PSTR("RATE_RLL_"),    RATE_ROLL_P,        RATE_ROLL_I,        RATE_ROLL_IMAX * 100),
-    pi_rate_pitch        (k_param_pi_rate_pitch,            PSTR("RATE_PIT_"),    RATE_PITCH_P,        RATE_PITCH_I,        RATE_PITCH_IMAX * 100),
-    pi_rate_yaw            (k_param_pi_rate_yaw,            PSTR("RATE_YAW_"),    RATE_YAW_P,            RATE_YAW_I,            RATE_YAW_IMAX * 100),
-
+    pid_rate_roll        (k_param_pid_rate_roll,            PSTR("RATE_RLL_"),    RATE_ROLL_P,        RATE_ROLL_I,        RATE_ROLL_D,        RATE_ROLL_IMAX * 100),
+    pid_rate_pitch        (k_param_pid_rate_pitch,        PSTR("RATE_PIT_"),    RATE_PITCH_P,        RATE_PITCH_I,        RATE_PITCH_D,        RATE_PITCH_IMAX * 100),
+    pid_rate_yaw        (k_param_pid_rate_yaw,            PSTR("RATE_YAW_"),    RATE_YAW_P,            RATE_YAW_I,            RATE_YAW_D,            RATE_YAW_IMAX * 100),

In file "config.h":

You have to add a few lines. Lines to add are indicated by "+". Other lines are for reference to find the right place.

 #ifndef RATE_ROLL_I
 # define RATE_ROLL_I         0.0
 #endif
+#ifndef RATE_ROLL_D
+# define RATE_ROLL_D         0.0
+#endif

 #ifndef RATE_PITCH_I
 # define RATE_PITCH_I        0 //0.18
 #endif
+#ifndef RATE_PITCH_D
+# define RATE_PITCH_D         0.0
+#endif

 #ifndef RATE_YAW_I
 # define RATE_YAW_I     0.0
 #endif
+#ifndef RATE_YAW_D
+# define RATE_YAW_D     0.0
+#endif

In file "system.pde":

-    Log_Write_Data(12, g.pi_rate_roll.kP());
-    Log_Write_Data(13, g.pi_rate_pitch.kP());
+    Log_Write_Data(12, g.pid_rate_roll.kP());
+    Log_Write_Data(13, g.pid_rate_pitch.kP());

Now, all changes are done. Now save your current settings of the APM, compile and load the code... You will find 3 new parameters (RATE_RLL_D, RATE_PIT_D and RATE_YAW_D) you can edit like any other mavlink parameter. These are the D-Terms for all rate control loops.


Testing and tuning:

Be really carefull, propellers are dangerous!  I do the tuning of the control loops while I hold the copter in my hand and try if it compensates the disturbances without overshot or oscillation. You should decide for yourself if cou can hold your copter in one hand while you throttle up and test the stability. Even small propellers can harm your fingers! If you want to proceed, I do it like this:

1. Reload your last setup and level the copter.
2. Set all parameters for stabilize STB_***_P and STB_***_I to zero.
3. Set all parameters for rate control RATE_***_P, RATE_***_I and RATE_***_D to zero.
4. Hold the copter with one hand, throttle up until it becomes weightless, then turn it. Nothing should happen, because all control loop parameters are zero. You have just manual throttle control.
5. Increase the D-Terms and test again while holding the copter in your hand. Remember, it can't fly with most parameters set to zero. Increase the D-Term and test again, until you got some oscillation. Let's call the value you found 100 percent. Now reduce it to 50..70 percent. Do this for ROLL and PITCH.
6. Proceed with the P-Terms. Increase and test until it gets unstable. Then reduce it to 50..70 percent of the original value.
7. Set the I-Terms to 30..50 percent of the P-Terms. Test again. If it is unstable, reduce P and I and maybe D a little bit.
8. Now go to the STABILIZE control parameters. Increase the P-Term. Now the copter should return to level position automatically. Increasing of the P-Term will lead to a faster return to level position after disturbance or also to a fast respond to the desired angle by pilot input. Find a value where the copter returns fast from a disturbance without overshot or oscillation.
9. Always leave the STABILIZE I-Term STB_***_I zero in this controller configuration!
10. For YAW you can leave the D-Term zero and use your previous settings for STABILIZE and RATE control. Or you tune it, but I didn't try it at YAW yet.
11. If everything works well and the copter returns to level position after disturbance or pilot input without overshot or oscillation, then you can try to hover and fly carefully. Not before!
    
    

Here are some controller parameters from my Tricopter (80 cm from motor to motor, 1440 g in flight weight), the D-Terms are quite small:

STB_PIT_I,0
STB_PIT_IMAX,1500
STB_PIT_P,9
STB_RLL_I,0
STB_RLL_IMAX,1500
STB_RLL_P,9
STB_YAW_I,0
STB_YAW_IMAX,1500
STB_YAW_P,4

RATE_PIT_D,0.015
RATE_PIT_I,0.02
RATE_PIT_IMAX,1000
RATE_PIT_P,0.09
RATE_RLL_D,0.012
RATE_RLL_I,0.02
RATE_RLL_IMAX,1000
RATE_RLL_P,0.09
RATE_YAW_D,0.004
RATE_YAW_I,0.002
RATE_YAW_IMAX,500
RATE_YAW_P,0.5

It would be really nice, if other people try this modification. For me, it was a significant increase in stability.

Regards, Igor