[Scilab-users] Question syslin

[Tim Wescott]

On Tue, 2014-12-16 at 11:01 +0100, Andreas Ladanyi wrote:
> Hi,
> 
> i am reading the help of scilab to understand the syslin function. In 
> the help i can see 3 options for the dom parameter. There is an option 
> for a sampled system 'n'.
> 
> In this help there is no example for a sampled system. So what is the 
> difference between a discrete system and a sampled system ? What is the 
> difference between an discrete system d and an sampled system n for syslin ?
> 
> In the most examples i read in the web syslin is called with dom='c'.

Hey Andreas:

Domain = 'c' is for a continuous-time system, where the system is
defined as

dx/dt = A * x + B * u,
y = C * x + D * u

This is a normal continuous-time linear state-space system description.

Domain = 'd' is for a discrete-time system where the sampling interval
is left undefined for whatever reason (in my case, it's usually because
I'm being lazy, but sometimes it's because the sampling interval isn't
constant, or because there's no meaningful "sampling interval" in the
problem).

It defines the sampled-time system:

x{k} = A * x{k-1} + B * u{k}
y{k} = C * x{k-1} + D * u{k}

(Note the mixed time indexes on the input and state variables on the
right-hand side of these equations.  You'll sometimes see this expressed
differently, so if you're trying to implement something from an article
or book, pay attention!)

Domain = n is for a discrete-time system where the sampling interval is
defined.  It works exactly like domain = 'd', except that things that
depend on the real-world frequency, like Bode plots, will come out
right.

When I am doing control system design this is usually the form that I
use, because by the time I'm down to this level of detail I've usually
established the sampling rate, and I'm working at tuning the system to,
or verifying it against, some real-world criteria that must be expressed
in the frequency domain.

-- 

Tim Wescott
www.wescottdesign.com
Control & Communications systems, circuit & software design.
Phone: 503.631.7815
Cell:  503.349.8432