**6. Conclusion**

In this chapter, there were analyzed some digital controller, based on fuzzy blocks with Mamdani structure and PID dynamics.

A pseudo-equivalence of them with linear PID controllers was made, based on the inputoutput transfer characteristics of the fuzzy block, obtained by digital computer calculation.

The design of the fuzzy controller is based on the linearization of the fuzzy block around the origin, for the permanent regime. There is used the gain in the origin obtained as a limit in origin of the gain function, obtained from the translated SISO transfer characteristic.

For this type of controllers, the design relations were demonstrated. There was made an analysis of these design relations. There were also presented some observations related to the influences of the scaling coefficients.

The results presented in this chapter are important in the practice design of the control systems based on PID fuzzy controllers. This method for equivalence is valid for all kind of fuzzyfication and defuzzification methods, all types of membership functions, all inference methods, because it is based on analytic transfer characteristic, which may be obtained using computer calculations.

**Part 5** 

**Discrete Intelligent PID Controller** 

If there is a designed linear PID controller for a process control, we may use the equivalent fuzzy PID controller in its place in order to control the process with better control quality criteria. Based on the above notice, the method may be used also for tuning the fuzzy PID controller in a control system.

The term of "pseudo-equivalence" is used because there is no direct equivalence between the nonlinear digital fuzzy PI controller, with linearization only in the origin, and a linear analogue PI controller.

The theory presented in this paper is used and proved by the author in practical control applications, as speed control of electrical drives for dc motors, synchronous and induction motors.
