Using Discrete PID Significantly Slows Down Simulation

Hello,

I am currently modeling a complex system with numerous joints and motors (from sim mechanics) and I ran into an issue while trying to discretize the system. To start, I modeled my PID controllers as continuos (I have 12 of them). I now wish to turn them into discrete-time PIDs.

However, when I switch the PID's to discrete, the simulation that used to take a couple of minutes to run now takes hours. Furthermore, as the simulation goes on, it only gets slower. When I switched the PID's back to continous, the simulation ran in minutes as it did before. I even tried to switch only one of the 12 PID controllers into discrete to see what effect it would have and the same thing ended up happening - the simulation would take hours. I tried this with two different solver types (ode15s and ode23t) and tried to reduce the solver's relative tolerance from 1e-3 to 1e-2 but it did not help.

Initially I used a PID sample time of 0.001 but this ran way too slow so i switched it to 0.01 and it started running faster but the simulation would still take hours.

Is there a reason why this is happening? And is there a way to get around this?

Thanks!

Answer 1

[David Balbuena]

This is most likely happening because you have a discrete controller driving a continuous variable-step plant. As mentioned in this documentation page,

https://www.mathworks.com/help/releases/R2020a/simulink/ug/solver-resets.html#mw_85fe4463-d903-444c-8420-7d15196bf1b9

this scenario will trigger Solver Resets every time the discrete signal changes, which can impact the performance of your model. In R2019b, there was a new "First Order Hold" block added for this specific use-case (discrete controller driving continuous plant):

https://www.mathworks.com/help/releases/R2020a/simulink/slref/firstorderhold.html

This block is introduced in greater detail in this blog post:

https://blogs.mathworks.com/simulink/2020/01/17/a-new-first-order-hold/?s_tid=srchtitle

If you are in R2019b or later, feel free to give the First Order Hold block a try and see how that works.