Similar results in type-1 and type-2 fuzzy logic controller applying in MIMO systems

For doing comparative analysis, why I got similar results when comparing both type-1 and type-2 fuzzy logic controller for applying MIMO systems?

What is the solution for the above questions?

Is there any mistakes in rule base or Simulink structures?

Answer 1

[Sam Chak]

Hi @F. Paul

• The reason for the similarity lies in the fact that the performance of the Type-2 fuzzy logic controller behaves akin to a Type-1 fuzzy logic controller within certain conditions. However, without detailed information about your system's design, input data, or specific metrics being analyzed, pinpointing the exact reason for this similarity is challenging. It's worth noting that this observation doesn't necessarily indicate a technical problem.
• As for a solution, it's contingent upon identifying any technical issues related to the fuzzy control design that may be contributing to the observed similarity. Typically, exploring potential factors that could influence the results from the perspective of a fuzzy system design expert can enhance the performance of both types of fuzzy controllers.
• In fuzzy rule design, there's no definitive right or wrong approach, as it largely depends on the designer's interpretation of logical reasoning in accommodating uncertainty. However, conducting thorough validation and verification procedures, such as simulation testing with various scenarios, can help uncover any potential human errors and ensure the robustness of the design.

[F. Paul]

How to fix the issue in MATLAB Simulink?

Or, we want to implement the type-1 and interval type-2 fuzzy logic controller in other software?

[Sam Chak]

Returning to this question after nearly a year. 😅

There is no issue to begin with, as you were lucky to have designed a Type-2 fuzzy logic controller that performs comparably to the Type-1 fuzzy logic controller. In the absence of uncertainties, Type-1 controllers typically perform better than Type-2 controllers in the aspect of reference tracking. In fact, you can refer to this example for its similarity to your case. Additionally, both MATLAB and Simulink can handle both types of fuzzy logic controllers.

https://www.mathworks.com/help/fuzzy/fuzzy-pid-control-with-type-2-fis.html

Of course, it is possible to intentionally redesign the Type-2 fuzzy logic controller to significantly degrade its performance by adjusting the footprint of uncertainty for the input membership functions. However, I don't recommend this due to research integrity. In the eyes of a fuzzy logic expert reviewer, it is generally not possible to "cheat" or conceal shortcomings. Some papers in the field have claimed that their Type-2 fuzzy logic controller is superior, but such evaluations often result from the authors not having properly designed their Type-1 fuzzy logic controller.

By the way, the Type-1 FLC in the example is, in fact, a simple PD controller (see the flat control surface of the Type-1 FIS). It is entirely possible to redesign a nonlinear Type-1 FLC that significantly outperforms the Type-2 FLC. 😎