Algebraic loop: PID control DC motor in Simscape

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InducibleWolerines
InducibleWolerines 2017-10-11
回答： Francisco J. Triveno Vargas 2024-7-9
I am trying to add a PID controller to the elec_motor_dc_pwm.slx DC motor Simscape example:
Original model:
My model:
However, Simscape complains about an algebraic loop in the feedback path.
This answer says models shouldn't contain both "physical signal to simulink" and "simulink to physical signal" converter blocks. (My picture does.) But then how do you design a feedback controller?
This Simscape help page suggests replacing the "PS-to-S" blocks with blocks like "PS Subtract" and "PS Gain". However, there is not a "PS Derivative" block, which would be needed for a PID controller.
Here is a link to these two models.
Thanks for your help.

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Sebastian Castro
Sebastian Castro 2017-10-11
Check out this blog post -- I think it sums up pretty well how to address algebraic loops with continuous dynamics (like that PID block):
https://blogs.mathworks.com/simulink/2015/07/18/why-you-should-never-break-an-algebraic-loop-with-with-a-memory-block/
- Sebastian
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Sebastian Castro
Sebastian Castro 2017-11-17
You're right that this approach is a numerical "hack" IF the controller is an analog/continuous-time controller like in your model.
If you're implementing such a continuous-time derivative fully in Simscape, you should be able to do it using the Simscape Language. The equations have a "der" keyword so you can probably create a block that takes in the signal u and its integral uIntegral and then use a component equation like:
output == Kp*u + Ki*uIntegral + Kd*u.der;
The other option is to move the "hack" into the computation of the derivative, in that you can calculate a filtered derivative instead of a perfect one.
For practical applications, your PID controller will likely be discrete. At that point, you can break the loop with a Unit Delay block (at the same sample time of the controller) to mimic the delay in getting a sensor reading into the controller at the following time step.
- Sebastian

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Francisco J. Triveno Vargas
Only is necessary include the memory block to cancel the algebric loop.

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