What is the best free tool available to do tuning procedure to the PID controller system below

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If you already have Simulink, then you can tune the gains by hand or download something free from the file exchange. MathWorks offers PID Tuning tools in Simulink Control Design and Robust Control Toolbox. For a MIMO system like yours the best choice is Robust Control Toolbox, as explained in this example , which appears similar to your application.

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You can use Siso Tools.

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Many thanks to you Danilo , but please could give more details because I am a new user to control systems.

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