using DTC and fuzzy logic with duty ratio.

Figure 3.1 Simulink model for direct torque control of induction motor.

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A Simulink model above was developed to study the performance of the conventional DTC and fuzzy controller for 4 poles induction motor to reduce the high ripple torque in the motor. After the field work experiment, the error of the torque, flux linkage and position of stator flux linkage were used in the simulation and the data generated are in table 3.1 below.
• To determine the error in the torque of the induction motor that causes vibration which lead to backlash that result in the production of less standard products.
The errors in the electromagnetic torque of the induction motor were determined using the torque ripple test apparatus.
Because we want to know the actual error in the induction motor that causes the high ripple torque in the motor.

Figure3.2Torque ripple test apparatus
An induction motor with torque ripple of 0.9N-m was connected to the shaft of the motor and with a load torque sensor that can measure the vibration or ripple of the shaft and will equally give the vibrational result of the motor then a DC voltage was supplied to the motorand observed a peak to peak torque equal to 0.9N-m. The formula for torque ripple calculation was used.
Tr = Torque ripple
Peak to peak value of the ripple = 0.9Nm, 0.15Nm
Average output of the ripple = 0.15Nm
In table 3.1 below, actual torque equal 0.15N-m, measured torque equal to 0.9N-m, error in torque is equal to 0.75N-m.
Tr = Peak – to -peak x 100
Average output

Tr = (0.9 – 0.15) x 100 = 5 ÷ 0.15 = 13.33%

0.15
• To determine the stator flux linkage error in the induction motor that also causes vibration.
The errors in the stator flux linkage of the induction motor were determined.
To help us to know the actual flux linkage error that contributed to the high ripple torque in the motor.

Figure 3.3Stator motor
The induction motor was dismantled and the flux meter was used to measure the coils in the slots of the stator of the induction motor, when the flux meter probe that have indicator at the end where it will indicate the amount of flux linkage at any instant were placed on top of the coil in the slot, it will indicate the amount of flux linkages.
At the end of the whole slot, we got approximately 170wb while the standard value is 150wb, as stated in table 3.1 below.
• To determine the position of the stator flux linkage space vector in the poles of the induction motor.
The positions of the stator flux linkage space vector were determined.
Because we want to know the position of the flux linkage in the different poles of the induction motor.
In figure 2 above, the flux meter was used to measure the flux linkages in the different poles of the electric motor, in order to know the position of the flux linkage space vector of the motor. With the measurement, we observed that the flux linkage is varies per poles in the table 3.1 below.
Table 3.1 Result obtained after the analysis
Actual value Measured value Error
Torque 0.15Nm 0.9 Nm 0.75 Nm
Position of the flux linkage 0.5? 5? 4.95?

Figure 3.4 Simulink model for fuzzy logic with duty ratio of induction motor.

The Simulink model were simulated and the result are in the table 4.1, 4.2, and 4.3, below.
Direct torque control (DTC) and fuzzy logic with duty ratio model were designed.
Because we want to control the induction motor drives in order to reduce the high ripple torque of the motor.
In the principles of direct torque control of induction motor, the ripples in the motor can be reduced if the errors of the torque and the flux linkage and the angular region of the flux linkage are sub-divided into several smaller sub-section then the errors should be pick and compared in other to select voltage vector with less ripples, in doing so, a more accurate voltage vector is being selected in the switching of the system hence the torque and flux linkage errors were reduced.
In the conventional DTC a voltage vector is applied for the entire switching period, and this causes the stator current and electromagnetic torque to increase over the whole switching period. Thus for small errors, the electromagnetic torque exceeds its reference value early during the switching period, and continues to increase, causing a high torque ripple. This is then followed by switching cycles in which the zero switching vectors are applied in order to reduce the electromagnetic torque to its reference value.
The ripple in the torque and flux can be minimize by applying the selected inverter vector for a complete switching period, as in the conventional DTCinduction motor drive, but only for a part of the switching period. The time for which a non-zero voltage vector has to be applied is selected just to increase the electromagnetic torque to its reference value and the zero voltage vector was applied for the rest of the switching period.
During the application of the zero voltage vector, no power was consumed by the machine, and thus the electromagnetic flux is almost constant, it was only decreases slightly.Theaverage input DC voltage to the motor during the application of each switching vector was?Vdc. By adjusting the duty ratio between zero and one, it is possible to apply voltage to themotor with an average value between 0 and Vdc during each switching period. Thus, the
Torque ripple will be low compared to when the full DC link voltage was applying for the completeswitching period. This increases the demand of the voltage vector, without an increase in thenumber of semiconductor switches in the inverter.
The duty ratio of each switching period is a non-linear function of the
Electromagnetic torque error, stator flux-linkage error, and the position of the stator fluxlinkagespace vector. Therefore, by using a fuzzy-logic-based DTC system, it is possible to perform fuzzy-logic-based duty-ratio control, where the duty ratio is determined during each switching cycle. In such a fuzzylogic system, there are three inputs, the electromagnetic torque error,the stator flux-linkage space vector position (??) within each sector assigned with the voltage vectors and the flux error where the output ofthe fuzzy-logic controller is equal to the value of duty ratio.
There are various types of fuzzy logic controller for this particular application. A Mamdani-type fuzzy logic controller, which contains a rule base, a fuzzifier,and a defuzzifier, is selected. Fuzzification is performed using membership function. The inputs and the output of the fuzzy controller are assigned Gausian membership functions. The universe of discourse for the torque error and the duty ratio is variedusing simulations to get acceptable torque ripple reduction.
The attention in the fuzzy rule is to reduce the torque ripple. Generallythe duty ratio is proportional to the torque error, since the torque rate of change isproportional to the angle between the stator flux and the applied voltage vector, the duty ratio depends on the position of the flux within each sector. The use of two fuzzy sets isthe fact that when the stator flux is greater than its reference value a voltage vector that advance the stator flux vector by two sectors is applied which result in a higher rate of change for the torque compared to the application of a voltage vector that advance the stator flux vector byone sector when the stator flux linkage is lower than its reference value.
The duty ratio is selected proportional to the magnitude of the torque error so that if the torque error is Small, Medium or Large THEN the duty ratio is Small, Medium or Large respectively. The fuzzy rules are then adjustedto reflect the effects of theflux error, torque error and position of the space vector error. If the torque error ismedium and the stator flux lies in sector with magnitude greater than its reference value then the voltage vector Vk+2 isselected. If the flux position is small, that means there is a large angle between the flux andthe selected voltage vector that makes the selected vector more effective in increasing thetorque so that the duty ratio is set as small rather than medium, the fuzzy rule is stated as IF (torque error is medium) AND (flux position is small) THEN (duty ratio is small)IF (torque error is large) AND (flux position is small) THEN (duty ratio is medium).
Using the above reasoning and simulation to find the fuzzy rules, the two sets of fuzzy rulesare summarized in Table 3.2 below.

Table 3.2 Rules for the duty ratio fuzzy controller
Flux Torque error dT=k1 Small Medium Large
Negative
d?=0 Small Small Small Medium
Large Small Medium Large
Positive
?d=1 Small Small Medium Large
Medium Small Medium Large
Large Medium Large Large

Fuzzy logic toolbox was used in the implementation of theduty ratio fuzzy controller. The Graphic User Interface included in the toolbox wasused to edit the membership functions for the inputs (the torque error and the flux position),the output (the duty ratio). The membership functions and the fuzzy rules were adjusted using thesimulation until an acceptable torque ripple reduction was achieved.
• Simulate the model above in the Simulink environment and validate the result.

The model that will reduced the high ripple torque in the induction motor were developed.
To enable us study the performance of the conventional direct torque control and fuzzy logic with duty ratio controller for four (4) pole induction motor torque control and also to simulate for the same and verified for the purpose of reducing the high torque ripple in the induction motor drive.
3.2 The motor parameters

Definition of terms
Pa = Active power per phase
Qa = Phase reactive power
Ia = Phase current
Va = phase voltage
Rs = Stator winding resistance
Rr = Rotor winding resistance
Lm = Magnetizing inductance per phase
Xis = Stator leakage reactance
Lis = Stator inductance per phase
Xir = Rotor leakage reactance
Lir = Rotor leakage inductance per phase
Dc = Direct current
Rdc = Resistance in direct current
X = Reactance
Xm = Magnetizing reactance
Xn = Total reactance

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