Roy Vegard Ovesen wrote:
På 29.09.2005 00:47 CEST skrev Hans-Georg Wunder
Behaviour with delta_u_n = 0 and an input jump function of 0.6
Saturation at the beginning
o Time, reference,input,output
21:56:54,0,0,0
21:56:55,0,0,0
21:56:56,0,0,0
21:56:57,0,0,0
21:56:58,0,0,0
21:56:59,0,0.6,0.02549 Here the P-part is missing There
has to be a jump to u_max
You should not set the input to 0.6. You should set the reference to 0.6.
The input is the process value, and the reference is the set point. You
can not set the process value directly. If you could then you would not
need a controller at all ;-).
The test is done in an open loop configuration. The only difference
between the input value and the reference value is the sign.
Here the test results with the step response of the reference
Same test with change of the reference value.
Time, reference,input,output
08:51:03,0,0,0
08:51:04,0,0,0
08:51:05,0,0,0
08:51:06,0,0,0
08:51:07,0.6,0,-0.0195 Jump to 0.6 into saturation,
output is negative due to Kp=-1
08:51:08,0.6,0,-0.08006P-Part ist missing
08:51:09,0.6,0,-0.14050001
08:51:10,0.6,0,-0.2011
08:51:11,0.6,0,-0.26150002
08:51:12,0.6,0,-0.32250002
08:51:13,0.6,0,-0.3833
08:51:14,0.6,0,-0.44350003
08:51:15,0.6,0,-0.4994
08:51:16,0.6,0,-0.4994
In your example here it does not matter, results would have been similar
if you set the reference to 0.6. But you have to remember this when you
use live values with your controllers.
The patch committed by Erik:
http://cvs.flightgear.org/cgi-bin/viewcvs/viewcvs.cgi/source/src/Autopilot/xmlauto.cxx.diff?r1=1.19r2=1.20cvsroot=FlightGear-0.9
should fix this. This is what would happen when you set
delta_u_n = u_max - u_n_1 :
delta_u_n (u_max - u_n_1)
0.6 (0.5 - 0.0) : true
delta_u_n = u_max - u_n_1 = 0.5 - 0.0 = 0.5
u_n = u_n_1 + delta_u_n = 0.0 + 0.5 = 0.5
and at the next time step let's assume that delta_u_n
is still 0.6:
0.6 (0.5 - 0.5) : true
delta_u_n = 0.5 - 0.5 = 0.0
u_n = 0.5 + 0.0 = 0.5
u_n jumps to u_max and stays there as long as delta_u_n
is positive.
With this patch, the controller gets out of sync. Here the test results.
But only, when the windup is used.
Sorry, that it is so long.
Behaviour with delta_u_n =u_max - u_n_1 (Patch fromj Erik) and an input
jump function on the reference input of 0.2. Not Saturation at the
beginning
Time, reference,input,output
08:50:46,0,0,0
08:50:47,0,0,0
08:50:48,0,0,0
08:50:49,0,0,0
08:50:50,0,0,0
08:50:51,0.2,0,-0.2088 P-Part
08:50:52,0.2,0,-0.2291667 Integrator-Part
08:50:53,0.2,0,-0.24983339
08:50:54,0.2,0,-0.27016668
08:50:55,0.2,0,-0.2904
08:50:56,0.2,0,-0.31116659
08:50:57,0.2,0,-0.33133323
08:50:58,0.2,0,-0.35149986
08:50:59,0.2,0,-0.37216648
08:51:00,0.2,0,-0.39266644 Here the reference
value changed from 0.2 to 0
08:51:01,0,0,-0.21149975 There the P-Part = 0
ond we only the the I-Part
08:51:02,0,0,-0.21149975
08:51:03,0,0,-0.21149975
08:51:04,0,0,-0.21149975
08:51:05,0,0,-0.21149975
08:51:06,0,0,-0.21149975
08:51:07,0,0,-0.21149975
08:51:08,0,0,-0.21149975
08:51:10,0,0,-0.21149975
08:51:11,0,0,-0.21149975
08:51:12,0,0,-0.21149975
08:51:13,0,0,-0.21149975
08:51:14,0,0,-0.21149975
08:51:15,0,0,-0.21149975
08:51:16,0,0,-0.21149975
08:51:17,0,0,-0.21149975
08:51:18,0,0,-0.21149975
08:51:19,0,0,-0.21149975
08:51:20,0,0,-0.21149975
08:51:21,-0.2,0,-0.0061664115 Here the reference value change
from 0 to 0.2
08:51:22,-0.2,0,0.014166921The P-Part is added to
the output value
08:51:23,-0.2,0,0.034500255The I-Part is added to
the output value
08:51:24,-0.2,0,0.054833595
08:51:25,-0.2,0,0.075333593
08:51:26,-0.2,0,0.095666916
08:51:27,-0.2,0,0.11616691
08:51:28,-0.2,0,0.13683358
08:51:29,-0.2,0,0.15716694
08:51:30,-0.2,0,0.17766697
08:51:31,-0.2,0,0.19833365
08:51:32,-0.2,0,0.21866701
08:51:33,-0.2,0,0.23900037
08:51:34,-0.2,0,0.25966703
08:51:35,-0.2,0,0.2832
08:51:36,-0.2,0,0.30016693
08:51:37,-0.2,0,0.32083356
08:51:38,-0.2,0,0.34100019
08:51:39,-0.2,0,0.36150015
08:51:40,-0.2,0,0.38200011
08:51:41,-0.2,0,0.40266674
08:51:42,-0.2,0,0.4231667
08:51:43,0,0,0.2318Here the reference
value change from -0.2 to 0
08:51:44,0,0,0.2318The P-Part is
subtracted and we have only the I-Part
08:51:45,0,0,0.2318
