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1.1 BACKGROUND OF THE STUDY
The problem our thesis work will solve is to reduce backlash in induction motor. Backlash is described as a mechanical form of dead band that can lead to error on hole location, if the motion required to machine the holes causes a reversal in axis direction it also lead to loses of motion between input and output shafts, making it difficult to achieve accurate center in equipment such as machines tools etc. The main problem are vibrations from motor as a result of high ripple torque in the motor.
The motor is a kind of an AC machine in which alternating current is supplied to the stator directly and to the rotor by induction from the stator. Induction motor can appear in a single phase or a poly phase. (Toufouti, et al, 2013).
In construction, the motor has a stator which is the stationary portion consisting of a frame that houses the magnetically active angular cylindrical structure called the stator lamination. It stack punched from electrical steel sheet with a three phase winding sets embedded in evenly spaced internal slots.
The rotor which is the rotatory parts of a motor is made up of a shaft and cylindrical structure called the rotor lamination. It stack punched from electrical steel sheet with evenly spaced slots located around the periphery to accept the conductors of the rotor winding (Ndubisi, 2006).
The rotor can be a wound type or squirrel cage type.
in a poly phase motor, the three phase windings are displaced from each other by 120 electrical degrees in space around the air-gap circumference when excited from a balanced poly phase source, those windings (stator winding) will produce a magnetic field in the air-gap rotating at synchronous speed as determine by the number of stator poles and the applied stator frequency (Bimal, 2011).
In the controlling of electrical motor; the introduction of micro-controllers and high switching frequency semiconductor devices, variable speed actuators where dominated by DC motors.
Today, using modern high switching frequency power converters controlled by micro-controllers, the frequency phase and magnitude of the input to an AC motor can be changed and hence the motor’s speed and torque can be controlled. AC motors combined with their drives have replaced DC motors in industrial applications because they are cheaper, better reliability, less in weight, and lower maintenance requirement. Squirrel cage induction motors are most generally used than all the rest of the electric motors as they have all the advantages of AC motors and they are easy to build.
The main advantage is that motors do not require an electrical connection between stationary and rotating portion of the motor. Therefore, they do not need any mechanical commutators to the fact that they are maintenance free motors. The motors also have lesser weight and inertia, high efficiency and high over load capability. Therefore, they are cheaper and more robust, and less proves to any failure at high speeds.
Furthermore, the motor can be used to work in explosive environments because no sparks are produced.
Taking into account all the advantages outlined above, induction motors must be considered as the perfect electrical to mechanical energy converter. However, mechanical energy is more than often required at variable speeds, where the speed control system is not a trivial matter. The effective way of producing an infinitely variable motor speed drive is to supply the motor with three phase voltage of variable amplitude.
A variable frequency is required because the rotor speed depends on the speed of the rotating magnetic field provided by the stator. A variable voltage is required because the motor impedance reduces at low frequencies and the current has to be limited by means of reducing the supply voltage. (Schauder, 2013).
Before the days of power electronics, a limited speed control of the motors was achieved by switching the three stator windings from delta connection to star connection, allowing the voltage at the motor windings to be reduced. Induction motors also available with more than three stator windings to allow a change of the number of pole pairs.
However, a motor with several windings is very costly because more than three connections to the motor are needed and only certain discrete speeds are available. Another method of speed control can be realized by means of a wound rotor induction motor, where the rotor winding ends are brought out to slip rings (Malik, 2013). However, this method obviously removes the main aim of induction motors and it also introduces additional losses by connecting resistor or reactance in series with the stator windings of the motors, poor performance is achieved.
With the enormous advances in converters technology and the development of complex and robust control algorithms, considerable research effort is devoted for developing optimal techniques of speed control for the machines. The motor control has traditionally been achieved using field oriented control (FOC). This method involves the transformation of stator currents in a such manner that is in line with one of the stator fluxes. The torque and flux producing components of the stator currents are decoupled, such that the component of the stator current controlling the rotor flux magnitude and the component controls the output torque will differ (Kazmier and Giuseppe, 2013).
The implementation of this system however is complicated. The FOC is also well known to be highly sensitive to parameter variations. It also based on accurate parameter identification to obtain the needed performance.
Another motor control techniques is the sensor less vector control. This control method is only for both high and low speed range. Using the method, the stator terminal voltages and currents estimate the rotor angular speed, slip angular speed and the rotor flux. In this case, around zero speed, the slip angular velocity estimation becomes very difficult.
Motivation for the work
When we were on training in machine in our office, we are told gave us a drawing to produce a machine shaft. During the process, when we feed in a cut of 10mm to the machine, it would cut 9.5mm and when we wanted to drill a hole at the center of the job, it would drilled it off centered, we called on our supervisor after we have wasted much time, power and materials. Surprisingly, after his supervision, he told us that backlash in the machine is responsible for that and he instructed us to use another machine which we did and got what we need immediately. Therefore, that ugly experience motivated us to research on how to reduce high ripple torque in induction motor which is the main causes of vibrations that lead to the backlash in the industrial machine.

1.2 STATEMENT OF THE PROBLEM
• The statement of the human problem our research work will solve is to reduce backlash in industrial machine.
• Explanation of the problem

BACKLASH
Backlash can be defined as the maximum distance or angle through which any part of a mechanical system may be moved in one direction without applying appreciable force or motion to the next part in mechanical sequence and is a mechanical form of dead band. More so, it is any non-movement that occurs during axis reversals. For instance, when x – axis is commanded to move one inch in the positive direction, immediately, after this x – axis movement, these x-axis is also commanded to move one inch in the negative direction if any backlash exists in the x-axis, then it will not immediately start moving in the negative direction and the motion departure will not be precisely one inch.
So, it can cause positioning error on holes location, if the motion required to drill the holes causes a reversal in axis direction, it also causes loses ofmotion between reducer input and output shafts, making it difficult to achieve accurate positioning in equipment such as machines tools etc.
The main cause of this problem electrically is vibrations from electric motor as a result of high ripple torque in the induction motor.

• Benefits of solving the problem
1. High quality products will be produce.
2. Productivity will increase because adjustment and readjustment of machine feeding handle or feeding screw to eliminate backlash have been reduced.
3. Operational cost will reduced.
4. Greater efficiency will be guaranteed.
5. Greater accuracy and precision of product will be guaranteed.
6. Wasting of materials will be highly reduced.
1.3 RESEARCH OBJECTIVES
1. To develop a model that will control the error to achieve stability using DTC and fuzzy logic with duty ratio.
2. To determine the error in the torque of the machine that causes vibration which lead to backlash that result in production of less standard products.
3. To determine the position of the stator flux linkage space vector in the poles of the induction motor.
4. To determine the stator linkage flux error in the induction motor that also causes vibration.
5. To simulate the model above in the Simulink environment and validate the result.

1.4 SCOPE AND LIMITATION OF THE WORK
This project work is limited to the use of fuzzy logic controller with duty ratio to replace the torque and stator flux hysteresis controllers in the conventional DTC techniques. The controllers have three variable inputs, the stator flux error, electromagnetic torque error and position of stator flux linkage vector. The inference method used was the Mamdam fuzzy logic inference system. The deffuzzification method adopted in this work is the maximum criteria method.

1.5 SIGNIFICANCE OF THE WORK
The importance of this work in industry where induction motor drives are mainly in application cannot be over emphasis.
As earlier noted, induction motors because of their ruggedness simple mechanical structure and easy maintenance; electrical drives in industries are mostly based on them.
Also, a wide range of induction motor applications require variable speed, therefore induction motor speed, if not accurately estimated will affect the efficiency of the overall industrial processes. Equally, the harmonic losses if not put in check will shorten the life span and efficiency of the motor inverter.
Based on the above, it is aimed at reducing the principle causes of the inefficiency in the DTC induction motor and improves the performance of the system.
1.6 ORGANIZATION OF THE WORK
The work is organized into five chapters. Various control techniques were discussed in chapter two, in chapter three, we discusses the methodology, design and implementation of the direct torque control of induction motor using fuzzy logic with duty ratio controller.
Chapter four discusses data collection, analysis and the simulated results showing the system using conventional method of control and the proposed fuzzy logic with duty ratio method of control under applied load torque conditions.
Conclusion, recommendations and suggestion for further work are mentioned in chapter five.
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CHAPTER TWO
LITERATURE REVIEW
Due to power electronic switches, variable speed of motor drive system using various control system have been generally used in many applications, such as direct torque control.
DIRECT TORQUE CONTROL:
Efficiency and low sensitive to parameter variation have been generally accepted in the control of motor speed widely in all industrial applications because of its technique.
Despite its importance, it has a major setback associated with it. That is the large torque and flux ripple at steady state operation of the motor. These ripples can affect the accuracy of speed consideration of motor.
Effort have been made using the space vector modulation and the multi-level inverter methods to reduce these ripples. These methods when used though, achieved some degree of success in reducing the ripples but they are difficult and costly to implement.
In this chapter, a lot of control techniques are deeply treated, the work done in reducing the torque and flux ripples using direct torque control method is highlighted. The proposed fuzzy logic with duty ratio control is equally treated in detail.
In DTC drives, the uncoupling of the torque and flux components are Source Inverter (VSI).achieved by using hysteresis comparators which compares the actual and considered values of the electromagnetic torque and stator flux. The DTC drive consists of controller, torque and flux calculator, and a Voltage
2.2 Principle of direct torque control of induction motor:
In a direct torque controlled induction motor drive, it is possible to control directly the stator flux linkage (s?) or the rotor flux (r?) or the magnetizing flux (m?) and the electromagnetic torque by the selection of an optimal inverter voltage vector. The selection of the voltage vector of the voltage source inverter is made to restrict the flux and torque error within their respective flux and torque hysteresis bands and to get the fastest torque response and highest efficiency at every instant. DTC enables both quick torque response in the transient operation and reduction of the harmonic losses and acoustic noise.
The Benefits of using DTC include the following:
1 No need for motor speed or position feedback in 95% of applications. Thus, installation of costly encoders or other feedback devices can be avoided.
2DTC control is available for different types of motor including permanent magnet and synchronous reluctance motors.
3Accurate torque and speed control down to low speeds, as well as full startup torque down to zero speed.
4 Excellent torque linearity.
5 High static and dynamic speed accuracy.
6 No preset switching frequency optimal transistor switching is determined
2.2.1 Voltage Source Inverter
A six step voltage source inverter provides the variable frequency AC voltage input to the induction motor in DTC method. The DC supply to the inverter is provided either by a DC source like a battery, or a rectifier supplied from a three phase or single phase AC source. Fig. 2.2 shows a six step voltage source inverter. The inductor L is inserted to limit short circuit through fault current. A large electrolytic capacitor C is inserted to stiffen the DC link voltage.
The switching devices in the voltage source inverter bridge must be capable of being turned OFF and ON. Insulated gate bipolar transistors (IGBT) are used because they can offer high switching speed with enough power rating. Each IGBT has an inverse parallel-connected diode. This diode provide alternate path for the motor current after the IGBT, is turned off.

Figure 2.2 Voltage Source Inverter
Each leg of the inverter has two switches one connected to the high side (+) of the DC link and the other to the low side (-); only one of the two can be ON at any moment. When the high side gate signal is ON the phase is assigned the binary number 1, and assigned the binary number 0 when the low side gate signal is ON. Considering the combinations of status of phases a, b and c the inverter has eight switching modes(Va,Vb,Vc=000-111) V2 (000) are zero voltage vectors V0 (000) and V7 (111) where the motor terminals are short circuited and the others are nonzero voltage vectors V1 to V6
The six nonzero voltages space vectors will have the orientation, and also shows the possible dynamic locus of the stator flux, and its different variation depending on the VSI states chosen. The possible global locus is divided into six different sectors signaled by the discontinuous line. Each vector lies in the center of a sector of width named S1 to S6 according to the voltage vector it contains.
It can be seen that the inverter voltage directly force the stator flux, the required stator flux locus will be obtained by choosing the appropriate inverter switching state. Thus the stator flux linkage move in space in the direction of the stator voltage space vector at a speed that is proportional to the magnitude of the stator voltage space vector. By selecting one after another the appropriate stator voltage vector, is then possible to change the stator flux in the required method. If an increase of the torque is required then the torque is controlled by applying voltage vectors that advance the
same sector depending on the stator flux position.

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 DTC classical 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

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 and torque. The reference values for the flux stator modulus and the torque are compared with the actual values, and the resulting error values are supplied into the two level and three-level hysteresis blocks respectively. The outputs of the stator flux error and torque error hysteresis blocks, 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 which the flux sector presents at that particular moment. In accordance with the figure 1.2, the stator flux 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 of voltage 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 induction motor 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 of both. The estimation based on current model normally applied at low frequency, and stator current and rotor mechanical speed or position. In some industrial applications, the use of incremental encoder to get the speed or position of the rotor 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 to the stator resistance variation. The use of rotor parameters in the estimation introduced error at high rotor speed due to the rotor parameter variations. So in this present DTC control scheme 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 stator resistance. (Oghanna, 2011)
2.4 INTRODUCTION OF FLC
Fuzzy logic has become one of the most successful of today’s technology for developing sophisticated control system. With it aid, complex requirement may be implemented in simply, easily and inexpensive controlling method. The application ranges from consumer products such as cameras, camcorder, washing machines and microwave ovens to industrial process control, medical instrumentation and decision support system .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 to generate decisions.
Several studies shows, both in simulations and experimental results, that Fuzzy Logic control yields superior results with respect to those obtained by conventional control algorithms thus, in industrial electronics the FLC control has become an attractive solution in controlling the electrical motor drives with large parameter variations like machine tools and 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 mentioned quantities 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.

Figure 2.5. Block Diagram of Fuzzy logic controller.
The membership functions of these Fuzzy sets are triangular with two membership function N and P for the flux-error, three membership functions N, Z, P for the torque-error, six membership variables for the stator flux position sector and eight membership functions for the output commanding the inverter. The inference system contains thirty six Fuzzy rules which is framed in order to reduce the torque and flux ripples. Each rule takes three inputs, and produces one output, which is a voltage vector. Each voltage vector corresponds to a switching state of the inverter. The switching state decides the pulse to be applied to the inverter. The Fuzzy inference uses MAMDANI’s procedure for applying Fuzzy rules which is based on minimum to maximum decision. Depending on the values of flux error, torque error and stator flux position, the output voltage vector is chosen based on the Fuzzy rules. Using Fuzzy Logic controller the voltage vector is selected such that the amplitude and flux linkage angle is controlled. Since the torque depends on the flux linkage angle the torque can be controlled and hence the torque error is very much reduced.
2.6. Fuzzy logic controller (FLC)
Fuzzy logic expressed operational laws in linguistics terms instead of mathematical equations. Many systems are too complex to model accurately, even with complex mathematical equations, therefore traditional methods become impracticable in these systems.
However fuzzy logics linguistic terms provide a possible method for defining the operational characteristics of such system.
Fuzzy logic controller can be considered as a special class of symbolic controller. The configuration of fuzzy logic controller block diagram is shown in Fig.2.6

Figure 2.6 Block diagram for Mamdani type Fuzzy Logic Controller
The fuzzy logic controller has three main components
1. Fuzzification.
2. Fuzzy inference.
3. Defuzzification.
2.6.1. Fuzzification
The following functions:
1. Multiple measured crisp inputs first must be mapped into fuzzy membership function this process is called fuzzification.
2. Performs a scale mapping that transfers the range of values of input variables into corresponding universes of discourse.
3. Performs the function of fuzzification that converts input data into suitable linguistic values which may be viewed as labels of fuzzy sets.
Fuzzy logic’s linguistic terms are often expressed in the form of logical implication, such as IF-THENrules. These rules define a range of values known as fuzzy membership functions.
Fuzzy membership function may be in the form of a triangle, a trapezoidal, and a bell as shown in Fig. 2.7

Triangle Trapezoid

Bell

Figure 2.7. (a) Triangle, (b) Trapezoid, and (c) BELL membership functions.
The inputs of the fuzzy controller are expressed in several linguist levels. As shown in Fig.2.8 these levels can be described as positive big (PB), positive medium (PM), positive small (PS), negative small (NS), negative medium (NM), and negative big (NB). Each level is described by fuzzy set below.

Figure.2.8.Seven levels of fuzzy membership function

2.6.2. Fuzzy inference
Fuzzy inference is the process of draw up the mapping from a given input to an output using fuzzy logic. The mapping then provides a basis from which decisions can be made. There are two types of fuzzy inference systems that can be implemented in the Fuzzy Logic Toolbox: Mamdani-type and Sugeno-type. These two types of inference systems vary to some extent in the way outputs are determined.
Fuzzy inference systems have been successfully applied in fields such as automatic control, data classification, decision analysis, expert systems, and computer vision. Because of its multi-disciplinary nature, fuzzy inference systems are associated with a number of names, such as fuzzy-rule-based systems, fuzzy expert systems, fuzzy modeling, fuzzy associative memory, fuzzy logic controllers, and simply, fuzzy Mamdani’s fuzzy inference method is the most commonly seen fuzzy methodology.
Mamdani’s method was among the first control systems built using fuzzy set theory. It was proposed in 1975 by Ebrahim Mamdani as an attempt to control a steam engine and boiler combination by arranging a set of linguistic control rules obtained from experienced human operators. Mamdani’s effort was based on LotfiZadeh’s 2011on fuzzy algorithms for complex systems and decision processes.
The second phase of the fuzzy logic controller is its fuzzy inference where the knowledge base and decision making logic reside .The rule base and data base from the knowledge base. The data base contains the description of the input and output variables. The decision making logic evaluates the control rules .the control-rule base can be developed to tolerate the output action of the controller to the inputs.
2.6.3. Defuzzification
The output of the inference mechanism is fuzzy output variables. The fuzzy logic controller must convert its internal fuzzy output variables into crisp values so that the actual system can use these variables. This conversion is called defuzzification.
2.7: Fuzzy Direct Torque Controller
The fuzzy direct torque control technique consists of inverter, induction motor, torque controller, flux controller, flux estimator, torque estimator and clarke’s transform. The fuzzy logic technique which is based on the language rules, is used to solve this nonlinear issue. In a three phase voltage source inverter, the switching commands of each inverter leg are matched. For each leg a logic state Ci (I = a,b,c) is defined, thatCi is 1 IF the upper switch turned ON and zero IF the lower switch turned OFF. IFCi is 0 THEN it means that the lower switch is ON and upper switch is turned OFF. Since three are independent there will be eight different states, so eight different voltages.
To study the performance of the developed DTC model, a closed loop torque control of the drive is simulated using MATLAB/Simulink simulation package. The torque error and flux errors were compared in their respective hysteresis band to generate their respective logic state as (ST) and (S?). The sector logic state (S?) is used as the third controlling signal for referring the DTC switching table. These three controlling signals are used to determine the instantaneous inverter switching voltage vector from three dimensional DTC switching lookup table. The simulation results are implemented for conventional DTC scheme and proposed fuzzy based DTC scheme. There are three non-zero voltage vectors and two voltage vectors.

Figure2.9Block Diagram of fuzzy logic DTC
The DTFC on induction motor drives is designed to have three fuzzy input variables and one output control variable to achieve fuzzy logic based DTC of the induction machine. Its functional block diagram is as shown in fig. 2.9 the three input variables are the stator flux error, electromagnetic torque error and angle of stator flux. The output was the voltage space vector. The DTF Cconsist of fuzzification, rule base, data base, decision making and defuzzification.
The input variable (?T) and (?) are fuzzified using fuzzy functions over the respective domains. The output of DTFC was also fuzzified, the all possible fuzzy rules are stored in fuzzy rule base.
DTFC takes the decision for the given input crisp variables by firing this rule base.

Figure2.10 DTC functional Block Diagram

2.8 SUMMARY
With the principle of direct torque control (DTC)of induction motor, the high ripple torque in the motor have being reduced to above 65% in the reviewed work.
These controls have being one of the best controls for driving induction motor because of its principles. Though DTC strategy is popular and simpler to implement than the flux vector control method because voltage modulators and coordination transformations are not required.
Although, it introduces some drawbacks as follows:
1. High magnitude of torque ripple
2. Torque and small errors in flux and torque are not distinguished. In other word, the same vectors are used during start up and step changes and during steady state.
3. Sluggish response in both start up and step changes in either flux or torque.
In other to overcome the mentioned drawbacks, there are difference solution like fuzzy logic duty ratio control method. In this work fuzzy logic with duty ratio control is proposed to use with direct torque control to reduce this high ripple torque and realized the best DTC improvement.