# Simulating a PID in a DAE - how to simulate a DDAE?
**URL:** https://discourse.julialang.org/t/simulating-a-pid-in-a-dae-how-to-simulate-a-ddae/111320
**Category:** Modelling & Simulations
**Created:** [March 7, 2024, 7:53pm UTC](https://discourse.julialang.org/t/simulating-a-pid-in-a-dae-how-to-simulate-a-ddae/111320 "2024-03-07T19:53:03Z")
**Posts on this page:** 5
**Page:** 1
### Author:  [@lpz18](https://discourse.julialang.org/u/lpz18)
#### Post date: [March 7, 2024, 7:53pm UTC](https://discourse.julialang.org/t/simulating-a-pid-in-a-dae-how-to-simulate-a-ddae/111320/1 "2024-03-07T19:53:03Z")
I would like to run a PID controller with a nonlinear set of ODEs with 6 continous variables.
I thought I could do this with delay differential algebraic equaions, since in DelayDiffEq.jl it says
> Covers neutral and retarded delay differential equations, and differential-algebraic equations.
I haven’t been able to find any tutorials for how to write a DDAE system, could someone point me in the right direction?
Or even better, suggest another way to simulate a PID controller with a set of DAEs
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### Author:  [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)
#### Post date: [March 7, 2024, 10:40pm UTC](https://discourse.julialang.org/t/simulating-a-pid-in-a-dae-how-to-simulate-a-ddae/111320/2 "2024-03-07T22:40:16Z")
What have you tried? If you just define a DDAE in mass matrix form it should work. There’s tests on this.
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### Author:  [@lpz18](https://discourse.julialang.org/u/lpz18)
#### Post date: [March 8, 2024, 10:28pm UTC](https://discourse.julialang.org/t/simulating-a-pid-in-a-dae-how-to-simulate-a-ddae/111320/3 "2024-03-08T22:28:02Z")
Thanks Chris!
So I see this [example](https://github.com/SciML/DelayDiffEq.jl/blob/master/test/interface/mass_matrix.jl), which is very useful and resolves how to simulate a DDAE.
I still don’t know how to simulate a [PID controller](https://en.wikipedia.org/wiki/PID_controller) which requires an integral term. The example above has a constant lag, and I’d be looking to compute an integral/sum over a fixed window of time into the past.
I can do this by sampling at a discrete number of constant lag points, but my solver is already relatively slow, and I was wondering if there is a more elegant way solving the problem
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### Author:  [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)
#### Post date: [March 9, 2024, 1:37pm UTC](https://discourse.julialang.org/t/simulating-a-pid-in-a-dae-how-to-simulate-a-ddae/111320/4 "2024-03-09T13:37:18Z")
A PID controller is commonly simulated just by created in an integrated state, i.e. add the ODE `Ix' = x` and then `Ix = Integral(x)`.
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### Author:  [@lpz18](https://discourse.julialang.org/u/lpz18)
#### Post date: [March 11, 2024, 6:16pm UTC](https://discourse.julialang.org/t/simulating-a-pid-in-a-dae-how-to-simulate-a-ddae/111320/5 "2024-03-11T18:16:45Z")
I used the example of the SIR model I linked above and a vector of constant lags summed over like in [this example](https://discourse.julialang.org/t/integro-differential-equations-with-differentialequations-jl/19265)
I am not sure what you mean by `Ix = Integral(x)`. I searched in the DifferentialEquations docs and github page and can’t find anything like that. The closest thing I found was Integrals.jl, but it doesn’t seem to have any examples that use DEs.
If you meant something specitic, then I would appreciate clarification. Otherwise, I have a working solution now.
thanks for your help