Why do these methods to obtain the simulink model transfer function... (2024)

Thank you Paul for taking the time and giving me this comprehensive and most helpful answer - that helped me to understand the difference. In the provided example from the manual without feedback gain, the tf are identical and since it just spoke about 'the closed loop transfer function' I went to conclusions too fast.

With 'ripping apart' largely I meant the need to place a gain of 1 following the closed loop, and place the open-loop output behind this, so the feedback is not opened by the linearizer. Or would placing the open-loop output behind the sum of the PI yield the same result as in the second example above?

As a side note, I think the feature of just building a model with variable parameters and obtaining an analytical transfer function for further calculations etc. might be a huge time saver especially for students or beginners who are not that versed with the symbolic math toolbox.

You're quite welcome.

For this problem there is no need to use open-loop input and open-loop output analysis points. Instead, use the input perturbation and the output measurement analysis points. The former goes on the output of the Constant block, like you already have, and the latter would go at the output of the PI sum block. This way there is no need for the additional gain block at the input to the scope.

The open-loop analysis points are useful when you want to get the TF for only a portion of the model. For example, if you want the TF of only the PI you could put an open-loop input on the output of the sum block that forms the error signal and an open-loop output at the output of the PI sum block.

Unfortunately, neither Simulink, Simulink Control Design, nor the Control System toolbox offer any facility for analytical, rather than numeric, analysis. The closest they come is being able to represent parameterized models, but the parameterization is always for specific numerical values. You can submit an enhancement request to MathWorks if you feel strongly about it.

The Symbolic Math Toolbox isn't that hard to learn and use for basic problems such as this. Sometimes it takes a bit of effort to wrangle results into simpler forms. Let's assume your feedback gain is K_f

For our specific case

I've often wondered how hard it would be to build a toolbox that provides basic control system analysis functionality for commands like feedback, et. al. and other basic functions for symbolic representations of linear systems. Maybe there's something out there already on the File Exchange. I know that there are threads on this forum that show how to convert symbolic objects, like H(s), into lti objects for use with Control System Toolbox.