For continuous time linear systems, I use rung-kutta 4th order
integration approach for analysis purpose with proper integral
Can I adopt the same approach for real-time digital control
applications with out discretizing the given linear system?
What is the difference between these two? and where will I face
difficulty if I go with rung-kutta integration.
RK methods can still be used with a discrete-continuous system, but
because you now have a "mixed" system, the simulation has to align the
continuous-time values (state variables, inputs etc) with the correct
values at the sampling instants. If you are using something like
Simulink, then this will be handled for you if you set it up correctly.
I re-read your question and hopefully have a better answer. When doing
in discrete time, you will normally have a model of the system which is
valid at the sampling instants as you have to produce the correct
actuation at those instants. That is, you will have a model of the
system and controler in the Z domain (or the delta domain if you
RK4 is mainly for simulation purposes.
Which is better, to use discrete model or Runge Kutta 4th order?
The answer depends on type of manipulated variable u have, continuous
time or discrete time!!!
When we convert continuous system to discrete system, It is exact
integration (and it will give answer without approximation if ur input
is truely discrete time). When we use RungeKutta, we are approximating
So if your manipulated variable in continuous time then it is better to
use Runge Kutta for simulation.
But if u have discrete manipulated variable then it is better to use
discrete model with sampling time = switching time of manipulated
variable. This will give you an exact answer (without approximation).
if your simulation is not a control example then your manipulated
variable is INDEPENDENT variables u may be changing during simulation.
If you are not changing any variables then definitely using discrete
time model will give u a true solution.
Hope this helps
Fred Stevens wrote:
If you mean can you use the Runga-Kutta integration approximation for
the integrator in a digital control application?
Well, you could, but it would be using excess processing power and
getting a performance degradation in return.
Ultimately what you care about is that your digital controller needs a
certain transfer function in the z domain -- using fancy integration
approximations will only get in your way.
Yes, I want to implement RK4 for digital control application in real
Why poor performance? I am expecting better performance for RK4
compared to a discretized system as this is a two-point difference
Define performance, and tell us where you're using the RK algorithm.
If you're using RK to implement the integrator in your controller (you
haven't said, even though I included this 'if' in my prior post), then
the best you can do is an approximation for an integrator that's 3rd
order. That's one pole for the integrator, and two extraneous poles
that you can't otherwise control because you're stuck on using something
that you can call 'RK'.
If you use a 1st-order integrator, then an entire PID controller will
only be 2nd-order, will likely have less delay than your 'RK'
integrator, and will _certainly_ give you full control over the
If your optimal controller _does_ have four poles, it's very unlikely
that two of them will be at the values forced on you by calling your
integrator 'RK' -- so you'll have to add extra poles to get close to
optimal. The extra poles will decrease performance, and being close to
(instead of at) optimal will degrade performance.
"srinivas" wrote in news:1165383626.612288.138430
I'm confused. What's the two-point difference approximation? If the
signal you're integrating is a two-point difference--i.e., a derivative,
you must already have access to the integrated signal, and don't need to