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.
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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.
Reply to
Fred Stevens
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.
Reply to
Fred Stevens
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:
Reply to
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.
Reply to
Tim Wescott
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.
Please clarify.
Thanks srinivas
Reply to
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 controller poles.
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.
Reply to
Tim Wescott
"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 integrate.
Reply to
Scott Seidman

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