Simulation of observer control

[Tomoya Ito]

Hello LVers,

I am trying to make a simulation program on LV for control
using "order reduced observer".
Now, I am standing at the stage how to solve one dimensional
differential equation as follows:

dx(t)/dt = A*x(t) + B*u(t) + K*i(t) (1)
y(t) = D*x(t) + H*i(t) (2)

where A,B,K,D and H are scalar values.
u(t) and i(t) are functions possibly expressed in sin curve.

I can use Matlab to immediately solve it, but in order to
look in or estimate the method itself it will be better
to be build from a source code and also a wired diagram.

Does anybody have experienced such trial ?
Every kind actions might be eagerly acceptable for me.
Sorry for a question a little out of topic(--;)

Thanks in advance
Tom
--Tomoya
ITO
--ito@rd.fujitec.co.jp

[Rado Miklavcic]

Tomoya Ito wrote:
>
> Hello LVers,
>
> I am trying to make a simulation program on LV for control
> using "order reduced observer".
> Now, I am standing at the stage how to solve one dimensional
> differential equation as follows:
>
> dx(t)/dt = A*x(t) + B*u(t) + K*i(t) (1)
> y(t) = D*x(t) + H*i(t) (2)
>
> where A,B,K,D and H are scalar values.
> u(t) and i(t) are functions possibly expressed in sin curve.

Hi,

Sorry for a delayed reply. Try converting the differential equation
which describes your sistem to the state-space coordinates. You can find
a description of the state-space representation of the system in any
decent book about control, but since you are writing about observers, I
am sure you already know it.

Then you can easily simula
te the system, using the approximation:

x(T) = x(0) + A*x(0)*T + B*u(0)*T
x(2T) = x(T) + A*x(T)*T + B*u(T)*T
..
..
.. etc

Where T stands for a time sample (T = 0.01, 2T = 0.02 ... for example),
x(t) is a value of state vector at a given time interval, A is the
system matrix and B is the input vector. This method is simple to use in
LV and I use it all the time to simulate simple proceses.

Best wishes,

Rado