**5. Annex**


Manny industrial processes are nonlinear and thus complicate to describe mathematically. However, it is known that a good many nonlinear processes can satisfactory controlled using PID controllers providing that controller parameters are tuned well. PID controller and its different types such as P, PI and PD controllers are today basic building blocks in control of various processes. In spite their simplicity; they can be used to solve even a very complex control problems, especially when combined with different functional blocks, filters (compensators or correction blocks), selectors etc. One of the ways to improve the traditional PID controllers is to use fractional order controllers with non integer derivation and integration parts. However, the difficulties of designing Fractional Order PID (FOPID) is relatively higher because these controllers include derivative order and integer order in comparison with traditional PID controllers. As for a linear system, if the dynamic characteristics are basically the same using either integer-order PID controller or FOPID controller, the result of using FOPID controller may provide a better robustness. We get the

optimal control with a FOPID than a conventional PID controller.

Fig. 9. Nichols diagrams

**4. Conclusions** 

**5. Annex** 


Table 2. Approximation of 1/ Sv for different v values
