There are several methods to keep the stability of system such as
Doyle's method, output feedback, or H-infinity method, etc. I tried to

apply the output feedback method to the system which has some
deviations between the model and actual system in the following site:
http://139.134.5.123/tiddler2/digital/digital.htm

Pretty good. This did take some effort. You should have some example
values for P and P*. Most people will not know what values to place in the
P arrays. I didn't see any so I used some from my text book and my results
look very close to your first examle. The slide controls do not permit
enough resolution to allow me to enter precisely the numbers from my text
book. I would also make the sample time a little smaller.
It isn't obvious that y is velocity and not positions. It make be easier
for the user to enter a gain and an exponential frequency in the continuous
domain and you convert the numbers to discrete time and fill out the P
arrays. This would allow you to use the same scheme for entering numbers
but now you can calculate the values of the P arrays to a greater precision
than would is currently available.
The numbers I used for P and P* are:
1 .01
0 .91
The .01 could not be changed and still get resonable results.
for q I used:
0
1
Someday I will have to really learn java so I can do the same type of thing
Peter Nachtwey

Thank you for nice suggestions! As you know the conversion of system
matrix from analogue to digital is a bit awkward work. Since my aim on
the simulator was to estimate the effect of output feedback for the
roughly designed(!) digital controlling system, I omitted the process
of the conversion from analogue to digital in the webpage. However as
you indicated rightly the software for that purpose should be added to
the simulator to use it on the design work because the real system
will be described physically and consequently it is an analogue
system.

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