# doubt

• posted

For continuous time linear systems, I use rung-kutta 4th order
integration approach for analysis purpose with proper integral
sampling.
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.
Thanks
srinivas
• posted
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.
Fred
• posted
I re-read your question and hopefully have a better answer. When doing control 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 prefer). RK4 is mainly for simulation purposes.
Fred.
• posted
Hi, 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 the integral.
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
Rahul Gandhi
Fred Stevens wrote:
• posted
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.
• posted
Yes, I want to implement RK4 for digital control application in real time applications.
Why poor performance? I am expecting better performance for RK4 compared to a discretized system as this is a two-point difference approximation.