Fig。 2: Mapping of the data set X to the real numbers 

However, not using a mathematical model of the process is also a source of uncertainty。 For example, the many degrees of freedom in designing fuzzy systems can be a disadvantage。 

 The following overview provides the advantages and disadvantages of fuzzy control (Siemens,2003): 

 Simple implementation of verbally expressed rules (if 。。。, then。。。) on a computer to solve a problem。 

The behaviour of the fuzzy system is understandable to human beings。 

 Avoids the costly development of a mathematical description when compared with conventional methods。 ſ Possible to use for processing complicated and involved processes。 ƀ Task definitions with not enough knowledge of the system and little or very imprecise knowledge of the system behaviour results in bad, possibly unusable fuzzy solutions。 ƀ Usually no adaptability and learning capability if the system behaviour changes。 

 Design of a system requires experience because of the many degrees of freedom。 

The following figure (figure 3) illustrates the components of the fuzzy controller and its functional principle。 Fuzzy control is based on a collection of rules, known as the rule base 。 

Fig。 3:  The components of the fuzzy controller and its functional principle 

The functional principle is pided into the following steps: 

Fuzzification - The degrees of fulfilment for the linguistic values (degrees of membership of the fuzzy sets) of the linguistic variables are assigned to the non-fuzzy input values。 

Inference - For each rule of the rule base, the degree of fulfilment of the THEN part is formed from the degree of fulfilment of the IF part by a certain method。 This process is also called implication。 The degree of fulfilment of the THEN part is equivalent to the degree of fulfilment of the rule, which is also called the rule intensity。 All these inpidual rule evaluations put together result in one membership function for the output signal, which is also termed composition。 The resulting membership function describes a "fuzzy control command"。 When the IF part contains a combined statement "IF。。。。 AND。。。" --- (THEN。。。。), the fuzzy logic AND operation is executed first and the degree of fulfilment is used in the overall rule evaluation。 All these statements together are often called aggregation。 

Defuzzification - The most representative numeric (nonfuzzy) output value is calculated for the control variable from the fuzzy control command (in the form of the resulting membership function)。 Based 

3。  THE SERVOMECHANISM 

3。1  Mathematical description of the servomechanism 

The plant is represented by a servomechanism (figure 4) consisting of two identical motors which are connected by a mechanical clutch。 The first motor is used for the control of the rotation speed or the shaft angle。 The second one, further called generator, is used for a simulation of load torque。 It contains A/D–D/A converters, digital input/output channels and an incremental encoder input channel (Amira)。 

The manipulated signals are the tachogenerator signal and the control signal for the servo amplifier of the motor。 

Fig。 4。 The servomechanism (Petr Chalupa)。 

A general diagram of the equipment is shown in figure 5。 

Fig。 5。 General diagram of the servomechanism (Luis J。 de Miguel)。 

The equivalent electrical circuit of the permanently excited DC motor is shown in figure 6。 Equation (1) is obtained from 

this circuit, where 

UA: armature voltage。 

E: electromotive force。 

IA: armature current。