## Figure 2

Figure 2.3.Stator flux vector locus and different possible switching Voltage vectors. FD: flux decrease. FI: flux increase. TD: torque decrease.
TI: torque increase.
Table 2.1.General Selection Table for Direct Torque Control, “k” being the sector number.
Voltage vector Increase Decrease
Stator flux Vk,Vk+1, Vk-1 Vk+2,Vk-2, Vk+3
Torque Vk+1, Vk-1 Vk+2, Vk-2

This can be tabulated in the look-up Table 2.1 (Takahashi look-up table).
Finally, the DTCclassical look up table is as follows:
Table 2.2 conventional DTC look up table
Flux errorD? Torque error
DT S1 S2 S3 S4 S5 S6

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1 1 V2 V3 V4 V5 V6 V¬1
0 V0 V7 V0 V7 V8 V7
-1 V6 V1 V2 V3 V4 V5

0 1 V3 V4 V5 V6 V1 V2
0 V0 V7 V0 V7 V0 V7
-1 V5 V6 V1 V2 V3 V4

2.3 DTC SCHEMATIC:

Figure 2.4 Direct Torque control scheme
A schematic of Direct Torque Control is shown. As it can be seen, there are two different loops corresponding to the magnitudes of the stator flux andtorque. The reference values for the flux stator modulus and the torque are compared with theactual values, and the resulting error values are supplied into the twolevel and three-levelhysteresis blocks respectively. The outputs of the stator flux error and torque error hysteresisblocks, together with the position of the stator flux are used as inputs of the look up table. The inputs to the look up table are given in terms of 1,0,-1 depend on whether torque and flux errors within or beyond hysteresis bands and the sector number in whichthe flux sector presents at that particular moment. In accordance with the figure 1.2, the statorflux modulus and torque errors tend to be restricted within its respective hysteresis bands.
From the schematic of DTC it is cleared that, for the proper selection ofvoltage sector from lookup table, the DTC scheme require the flux and torque estimations.
2.3.1 Techniques for Quantifications of Stator Flux in DTC:
Accurate flux quantifications in Direct Torque controlled inductionmotor drives is necessary to ensure proper drive operation and stability. Most of the flux estimation methods proposed was based on voltage model, current model, or the combination ofboth. The estimation based on current model normally applied at low frequency, and stator current and rotor mechanical speed or position. Insome industrial applications, the use of incremental encoder to get the speed or position of therotor is undesirable since it reduces the robustness and reliability of the drive. It has been generally known that even though the current model has managed to remove the sensitivity tothe stator resistance variation. The use of rotor parameters in the estimation introduced errorat high rotor speed due to the rotor parameter variations. So in this present DTC controlscheme the flux and torque are quantified by using voltage model which does not need a position sensor and the only motor parameter used is the statorresistance. (Oghanna, 2011)
2.4 INTRODUCTION OF FLC
Fuzzy logic has become one of the most successful of today’s technology fordeveloping sophisticated control system. With it aid, complex requirement may be implemented in simply, easily and inexpensive controlling method. Theapplication ranges from consumer products such as cameras,camcorder, washing machinesand microwave ovens to industrial process control, medical instrumentation and decision supportsystem .many decision-making and problem solving tasks are too complex to be understand quantitatively however,people succeed by using knowledge that is imprecise rather than precise. Fuzzy logic is all about the relative importance of precision. It has two different meanings. In a narrow sense,fuzzy logic is a logical system which is an extension of multi valued logic,but in wider sense fuzzy logic is synonymous with the theory of fuzzy sets. Fuzzy set theory is originally introduced by LotfiZadeh in the 1960s, resembles approximate reasoning in it use of approximate information and uncertainty togenerate decisions.
Several studies shows, both in simulations and experimental results, that Fuzzy Logiccontrol yields superior results with respect to those obtained by conventional controlalgorithms thus, in industrial electronics the FLC control has become an attractive solutionin controlling the electrical motor drives with large parameter variations like machine toolsand robots. However, the FL Controllers design and tuning process was often complex because several quantities, such as membership functions, control rules, input and output gains, etc.must be adjusted. The design process of a FLC can be simplified if some of the mentionedquantities are obtained from the parameters of a given Proportional-Integral controller (PIC)for the same application. (Lotfizabeh, 2011).
2.5 Why fuzzy logic controller (FLC)
• Fuzzy logic controller was used to design nonlinear systems in control applications.The design of conventional control system is normally based on the mathematical model. If an accurate mathematical model is available with known parameters it can be analyzed and controller can be designed for specific performances, such procedure is time consuming.
• Fuzzy logic controller has adaptive characteristics. The adaptive characteristics can achieve robust performance to system with uncertainty parameters variation and load disturbances.
The main principles of fuzzy logic controller.
The fuzzy logic system involves three steps fuzzification application of fuzzy rules and decision making and defuzzification. Fuzzification involves mapping input crisp values and decision is made based on these fuzzy rules. These fuzzy rules are applied to the fuzzified input values and fuzzy outputs are calculated in the last step, a defuzzifier coverts the fuzzy output back to the crisp values. The fuzzy controller in this thesis is designed to have three fuzzy input variables and one output variable for applying the fuzzy control to direct torque control of induction motor. There are three variable input fuzzy logic variables. The stator flux error, electromagnetic torque error, and angle of the flux in the stator.