RA: armature resistance。 

  LA: armature inductance。 

 Ω: armature frequency 

The electromotive force E is proportional to the rotational speed of the motor Ȧ; as equation (2) shows, where C is the motor constant and F is the constant magnetic flux。 The magnetic exitation ĭ is related to Ȧ (rad/s) by equation (3): 

Fig。 6。 Equivalent electrical circuit of the DC motor。 

The torque M generated by the motor is proportional to the armature current IA, as shown in equation (4): 

M=KMIA                             (4) 

3。2  The identification of parameters and the computing of the fuzzy controller 

The fuzzy controller implemented for the process has the structure, shown in figure 7。 

Figure 7: The structure of the fuzzy controller 

The following names are chosen for the fuzzy variables: 

x: Acceleration 

y: SpeedError 

z: ControlSignal 

The actual transfer function of the fuzzy controller kernel is   z = f(x,y), where the function f defined by fuzzy sets, fuzzy variables and fuzzy rules is arbitrary。 The method "Center of Area" (coa) is used by our fuzzy controller for defuzzyfication。 A single fuzzy set always has the same center of area independent of its weighting by the Max-Prodmethod。 Therefore the value of a fuzzy output variable with only one fuzzy set is always equal to the value of the constant center of area of this fuzzy set。 So the output value is: 

out = coa( set ) = const。         (5) 

If, in contrast, the fuzzy output variable has two sets, its value can only be between the two center of areas of both sets depending on the weighting of each set。 In the extreme case the weighting of one of the two fuzzy sets of the variable is zero, which leads to a value of the output variable equal to the center of area of the other fuzzy set。 So the output value is: 

out  [ coa( set1 ), coa( set2 ) ]                                                (6) 

If, however, the desired performance of the speed control is considered, it is recommended to significantly restrict the above mentioned intervall。 The value of a fuzzy set at the limits of the definition range of a fuzzy variable is continued to the infinity。 If for instance the above mentioned intervall is restricted to the range r1000 and the input value is +6000, the input variable behaves just as if the input value would be +1000。 

The definition range of x is limited by the maximum y deviation during a sampling period。 To calculate this value, the maximum control signal 10V is assumed。 

represents the mechanical time constant of the system。 The result is: 

Therefore the definition range of x is:   

The control signal of the controller is limited to the range of  -10V to +10V。 The integrator following the fuzzy controller kernel cannot operate with greater values。 The definition range of the output variable directly affects the loop amplification and therefore determines the dynamic of the closed loop to an extent。 In case the control signal range of 20V is to be passed in n sampling periods of 5 ms, the maximum output value of the fuzzy controller kernel is determined by: 

with n=20 it follows zmax=200V, the definition range of z is then: