🚀 go-pugleaf

In article 289, Guoqiano Lu asked some questions about simulink.
From the description of the problem, I guess that the problem system belong to
one of two cases:
 
(1) The system has fast transient feature, or the system is a bang-bang
control style caused by reseting parameters in self-tuning control.
If the problem is bang-bang control system, the peaks may be the feature
of the system.
(2) The system contains both continuous time and discrete time models.
 
One should not be surprised if some crazy peaks appeared if the "max
step size" in the integration is as large as 10 as default value in simulink
parameters.
 
As pointed out by Mike Stoughton in article 291, some integration
parameters need to be set up before the simulation.
 
As a rule of thumb, one shoul set the "max step size" to be less or equal to
half of minimum sample time among all of discrete time models in the system.
"min step size" should be less or equal to "max step size"/1000.
Generally, a simulation integration algorithm starts the step size from "max
step size", comparing the integration result with a smaller step size. If the
error between these two are smaller than the tolerance value (which is 
resetable by the user in simulink), then the result is accepted. Otherwise, 
take a step size samller than the "smaller step size" in the previous 
computation and compare the result again. The procedure goes on and on until
the minimum step size is reached. Considering the computation procedure, 
setup the parameters before simulation is very important.
 
For a stiff system, gear method or linsim method will be better. However,
the computation is more complex than Euler or Runge-Kutta method. It is a good
idea to switch between different algorithms and compare the results. One can
choose the computation algorithms in the parameter window in simulink.
 
Weizheng Wang
wang@bode.usc.edu
wang@hot.caltech.edu