Fuzzy logic gains appear nonlinearly in the control action. Multiple things like normalization/denormalization, fuzzy-proportional/derivative/integral gains, etc. may be dependent on the same gains. So you need to have your own expertise knowledge about how your gains are affecting the system stability and performance. One good approach is to study the [error-derivative of error] phase plane analysis, i.e. how your change in the gains are affecting the convergence of the error phase plane trajectory either at origin or near origin. 

In my opinion, Increasing the gains can give you good response time. You can get better results while changing the gains using simple head and trail rule.

Hi Ms. Ibtissam,

It is assumed that the desired preliminary response is achieved when tuning the gains for the PI controller. After replacing the PI controller with the fuzzy controller, the fuzzy controller (before fine-tuning) is expected to perform as good as the PI controller.

Now, instead of tuning the fuzzy gains, you may try adjusting the shapes of the fuzzy INPUT membership functions (MFs) around the equilibrium point until a better response is obtained. It is advisable to replace the triangular MFs with Gaussian MFs because of the flexibility they offer.

Hi Ms. Ibtissam,

Here are additional remarks on the design of Fuzzy PI controller. There are several variants of a Fuzzy PI controller. The approach in my previous post is suitable for one variant (with the linear PI gains fixed), while other variants may require adjustments on the Fuzzy gains.

Could you identify the type of variant that you use to replace the Linear PI controller? 

Reshaping the fuzzy control surface (from linear to nonlinear) is necessary in order to improve the response of the closed-loop system. This can be done either by

• modifying the If-Then rules,
• gradually altering the shapes of the membership functions, or
• increasing the range of operation within the universe.