How to tune PI controllers of MIMO system?

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chandu 2021-5-20

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编辑： Musa Maxhera 2024-8-13，20:01

How to tune the PI controllers for this kind of MIMO system as shown in the picture? Any resources regadring this would be appreciated.

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Mathieu NOE 2021-5-21

hello

this control scheme works if the MIMO system is diagonal dominant (i.e. the transfer function from input 1 to output 1 is greater than to output 2 , and transfer function from input 2 to output 2 is greater than to output 1 )

if this is not the case , no "simple" PID logic shown above will give good results...

you can start by tuning each PID by considering the SISO model extracted from the MIMO model

so PID 1 tuned with SISO model based on input1 / output1 of the MIMO model

there are plenty of tools available around for PID tuning

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Answer 1

Raghava S N 2024-5-24

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Hello Chandu,

A workflow to tune a MIMO Control System for Specified Bandwidth using PI controllers can be found in the MathWorks Documentation. I have attached it here for your reference - https://www.mathworks.com/help/control/ug/tune-a-mimo-control-system-for-a-specified-bandwidth.html.

The documentation provides a detailed example of how to tune a MIMO control system to achieve a specified bandwidth using the MATLAB function looptune. The documentation for looptune can be found here - https://www.mathworks.com/help/control/ref/dynamicsystem.looptune.html?s_tid=doc_ta.

The workflow describes tuning a control system with an example plant model to achieve set loop crossover frequencies. The controller used is a PI controller, using the function tunablePID. The MathWorks documentation can be found here for your reference - https://www.mathworks.com/help/control/ref/tunablepid.html. The inputs to the controller are through a tunableGain block. The gains can be set to 1 to arrive at the control system attached in the post. The MathWorks documentation for the tunableGain block can be found here - https://www.mathworks.com/help/control/ref/tunablegain.html.

The plant is a two-input, two-output model with a specific transfer function, based on the plant for a Decoupling Controller for a Distillation Column. You can find more details about the plant here - https://www.mathworks.com/help/control/ug/decoupling-controller-for-a-distillation-column.html.

The tuning process is explained in detail in the documentation. The result of the tuning process is a controller model with optimized PI coefficients and decoupling matrix gain values.

The documentation also describes how to display the tuned controller parameters and evaluate the system's performance through time-domain and frequency-domain responses. The step response plot and loopview function are used to analyze how well the tuned system meets the design requirements, including tracking performance and crosstalk minimization. The documentation for loopview can be found here - https://www.mathworks.com/help/slcontrol/ug/sltuner.loopview.html

Hope this helps!