3.1 DTC and fuzzy logic with duty ratio.

3.1 METHOD Develop a model that will control the error to achieve stability using DTC and fuzzy logic with duty ratio. Figure 3.1 Simulink model for direct torque control of induction motor.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 magnetic torque of the 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 A 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 motor and observed a peak to peak torque equal to 0.9N-m. The formula for torque ripple calculation was used.

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Tr = Torque ripplePeak to peak value of the ripple = 0.9Nm, 0.15NmAverage output of the ripple = 0.15NmIn 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 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 Themotor was dismantled and the flux meter was used to determine the coils in the slots of the stator of the 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 NmFlux linkage 150wb 170wb 10wbPosition 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 DTC induction 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. The average 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 the motor with an average value between 0 and Vdc during each switching period. Thus, theTorque ripple will be low compared to when the full DC link voltage was applying for the complete switching period. This increases the demand of the voltage vector, without an increase in the number of semiconductor switches in the inverter.The duty ratio of each switching period is a non-linear function of theElectromagnetic torque error, stator flux-linkage error, and the position of the stator flux linkage space 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 fuzzy logic 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 of the 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 varied using simulations to get acceptable torque ripple reduction.The attention in the fuzzy rule is to reduce the torque ripple. Generally the duty ratio is proportional to the torque error, since the torque rate of change is proportional 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 is the 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 by one 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 orLarge respectively. The fuzzy rules are then adjusted to reflect the effects of the flux error, torque error and position of the space vector error. If the torque error is medium and the stator flux lies in sector with magnitude greater than its reference value then the voltage vector Vk+2 is selected. If the flux position is small, that means there is a large angle between the flux and the selected voltage vector that makes the selected vector more effective in increasing the torque 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 rules are summarized in Table 3.2 below.Table 3.2 Rules for the duty ratio fuzzy controllerFlux 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 the duty ratio fuzzy controller. The Graphic User Interface included in the toolbox was used 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 the simulation 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. The motor parameters Definition of termsPa = Active power per phaseQa = Phase reactive powerIa = 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 phaseXir = Rotor leakage reactance Lir = Rotor leakage inductance per phase Dc = Direct current Rdc = Resistance in direct currentX = Reactance Xm = Magnetizing reactance Xn = Total reactance DETERMINATION OF INDUCTION MOTOR PARAMETERSThe motor is a three phase 158-W, 240-V induction motor (Model 295 Bodine Electric Co.

)The motor is Y-connected with no access to the neutral point. DC Resistance Test: To determine R1; Connect any two stator leads to a variable voltage DC power supply. Adjust the power supply to provide rated stator current. Determine the resistance from the voltmeter and ammeter readings.As shown in figure 3.7, a DC voltage VDC is applied so that the current IDC is close to the motor rating.

Because the machine is Y-connected: RS = Rdc/2 = (VDC/IDC)/2.From measurement, VDC = 30.6V, IDC = 1.05A.Hence, RS = RDC = (31.5/1.

04) = 15.14?/phase. 2 2 Figure 3.7 Circuit for DC resistance test.BLOCKED – ROTOR TESTTo determine X1 and X2 Determine R2 when combined with data from the DC test.

Block the rotor so that it will not turn. Connect to a variable voltage supply and adjust until the blocked – rotor current is equal to the rated current.NO LOAD TESTTo determine the magnetizing reactance, Xm and combined core, friction, and wind age losses. Connect as in block rotor test below. The rotor is unblocked and allowed to run unloaded at rated voltage and frequency. The set up for no load test and blocked rotor test is shown in the figure below: Figure 3.8 Circuit for no load and locked rotor test.With the motor running at no load, measure V, I and P to find the machine reactance Xn =Xis+XmTable 4.

3 Measured valueFrequency (Hz) 50Voltage (V) 230Current (A) 1.32Real power (W) 158At no load the per-unit slip is approximately zero, hence the equivalent circuit is as shown in figure 3.9 below. Figure 3.9 Equivalent circuit of three phase induction motor under no load test.The real power P represents, Hysteresis and Eddy current losses (core losses) Friction and wind age losses (rotational losses) Copper losses in stator and rotor (usually small as no load)Phase voltage: Va =V = 220 = 132V ?3 ?3Phase current: la = 1.

32APhase real power: Pa = Pa/3 = 138.2 ÷3 = 46.1WPhase reactive power:Q_a = ??(VaIa)2-P2a= ?(((137 x 1.32)2)-(46.1)2)=174.

86VAr?_Xn = Qa=174.86 =100.36? I2a 1.322Since S ~ 0,Xn~ Xls +Xm3. Locked rotor testWith the rotor locked, the rotor speed is zero and per- unit slip is equal to unity. The equivalent circuit is as shown in Figure 3.10 or Figure 3.

11. Figure 3.10 Equivalent circuit of three phase induction motor under locked rotor test.

Figure 3.11 Simplified equivalent circuit of three phase induction motor under locked rotor rest. Table 4.4 the tested valueFrequency (Hz) 50Voltage (V) 68.

52Current (A) 1.3Real power (W) 105.33Phase voltage: Va =V = 68.

52 = 39.56V ?3 ?3Phase current: la = 1.3AActive power per phase Pa = P = 105.33=35.1W 3 3 Reactive power phaseQ_a = ??(VaIa)2-P^2 a= ?(((35.

56 x1.3)2)-(35.1)2)=30.08VAr?_For a class C motor. Xls = 0.3 x Qa= 0.3 x 30.

08 = 5.34? I2a 1.32Xlr = 0.7 xQa = 0.7 x 30.

08 = 12.46?12a 1.32From the no – load test, Xn = 100.36?, soXm = Xn – Xls = 100.

36 – 5.34 = 95.02?R = Pa = 35.1 = 20.77? 12a 1.32From figures 3.11, R2 = R – Ris= 20.77 – 5.

34 = 1 5.43?Comparing figures 3.10 and 3.11, R2 + jX2 = (Rr + jXir) x jXm (Rr + jXir) + jXm R2 =Rr X2m Rr + (Xlr + Xm)2 Rr = R2 x (Xir + Xm)2 = 15.43 x (12.46 + 95.

02)2 = 19.74? Xm 95.02Summarizing, Stator winding resistance Rs = 15.14?/phase Rotor winding resistance Rr = 19.74?/phase Magnetizing reactance Xm = 95.

02?/phaseThe magnetizing inductance per phase is Lm = Xm = 95.02 = 0.3024H 2?f 2? x 50 Stator leakage reactance Xls= 5.34?/phase The stator inductance per phase is Lls = Xls= 5.34 = 0.0169H. 2?f 2nx50 Rotor leakage reactance Xlr = 12.

46?/phase,The rotor leakage inductance per phase is Llr = Xlr =12.46 = 0.0396H. 2?f 2?x50 Table 4.5: Motor parameters Rated voltage 240VMaximum torque 1.5N-mPoles 4Rated speed 1440rpmStator resistance 15.14?Rotor resistance 19.

74?Stator leakage inductance 0.0169HRotor leakage inductance 0.0396HMutual inductance 0.3024H3.3 IMPLEMENTATIONMATLAB fuzzy logic tool box was used in the implementation of the duty ratio fuzzy controller. The graphic user interface included in the tool box was used to edit the membership functions for the inputs (the torque error and the flux position), the output (the duty ratio). A Mamdani type fuzzy inference engine was used in the simulation. The membership functions and the fuzzy rules were adjusted using the simulation until a particular torque ripple reduction was achieved.

To know the performance of the duty ratio controller, the simulation was run at switching frequency of 5KHz. The difference between the conventional DTC and DTC with duty ratio fuzzy control was clearly realized by monitoring the switching behavior of the stator voltage and the electric torque. The selected voltage vector is applied for the complete sampling period and the torque keeps increasing for the complete period, then a zero voltage is applied and the torque keeps decreasing for the complete sampling period and these results in high torque ripple. The selected voltage vector is applied for part of the sampling period and removed for the rest of the period.

As a result, the electric torque increases for part of the sampling period and then starts to decrease. By adjustment of the duty ratio, the desired average torque may be continuously maintained. The duty ratio controller smoothly adjusts the average stator voltage.

3. family structure has developed an important

3. Discuss the role of ‘the family’ in reproducing social inequalities.

Introduction
Family structure is an important instrument for the reproduction of class, race, gender and sexual inequalities. Income inequality has increased, and family structures have diversified. We can reason that family structure has developed an important apparatus for the reproduction of class, race and gender inequalities. With the review into studies of income inequality and the more modern family structure changes we can find a wide range of estimates of the correlation between family structure and its link to reproducing social inequalities. How does income affect single mothers and fathers?
Families and raising children
Families are the primary establishment for raising children and family experiences play an important role in the art of influencing children’s life likelihoods. It’s the first few vital years of a child’s life that play a vital role in how they are shaped in the world. In 1960, only six percent of children in the united states lived with a single parent, it’s a sign of the period that they lived in it reflects the mind-set of the people of that period it was looked down to have a broken marriage or have a child out of matrimony (Percheski, 2008) . Nowadays over fifty percent of all children are expected to spend some time in a single parent family home before the age of eighteen, it’s become a societal norm now as the majority of parents are unmarried. Single parent families typically a single mother is the more common, ‘Families have transformed dramatically since 1960, from widowed mothers to divorced mothers and most recently never married’ (Percheski, 2008). Since 1960, single motherhood and income disparity among families have been amplified. ‘Through the 1960’s, income disparity declined reaching historically low levels in 1969. After 1970, income inequality increased steadily through the 1970’s, levelled off in the late 1980’s increased rapidly again in the early 1990’s and levelled off at the end of the 1990’s. in contrast, single motherhood advanced continuously after 1960 (Percheski, 2008) . Palpably showing the link between social inequality and the rise of single mothers in society during the periods.
Single mothers in society
Increases in income inequality may lead to increases in single motherhood, particularly among the less educated women in society. Single motherhood in turn decreases intergenerational economic mobility by affecting children’s material resources, and the parenting they experience. The level of family structure transformation goes well outside the increase in single motherhood, with modification within as well as amongst the categories of single mothers and married parents. ‘Single mother families, as measured by census data, include lone mothers and cohabiting couples. By two thousand almost fifty percent of all nonmarital births were to a cohabiting mother’ (Percheski, 2008). Between one quarter and two fifths of children were expected to experience parental cohabitation during childhood another new scenario being introduced into the upbringing of children. Two parent married couple families have also become more diverse. ‘Between 11% of children now live with a step parent at some point during childhood’ (Percheski, 2008). Variations in family structure have not arose consistently across population subgroups instead there are perceptible modifications by race and education with growths in single motherhood most apparent among the most underprivileged groups. ‘Unmarried mothers account for nearly two in three births to mothers without a high school education but only nine percent of births to mothers with a high school education’ (Percheski, 2008). These educational variances in non-marital birth rates combined with modifications in divorce and remarriage rates produce a scenario in which children with mothers in the bottom educational quartile are almost twice as likely to live with a single mother at some stage during their life cycle as a child as children with a mother in the top quartile. Extremely strong relationship between low educational attainment and the likelihood of becoming a never-married lone mother (Lunn, Fahey and Hannan, 2009).

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parents
A large body of research indicates that living apart from a biological parent (typically the father) is associated with a host of negative outcomes that are expected to affect children’s future life affect children’s future life chances or ability to make up the income ladder. Children that grow up apart from their biological fathers score lower on standardized testing, report lower grades and view themselves as having less academic potential than children who grow up with both biological parents. Income inequality has led to delays in marriage among both advantaged and disadvantaged women, which should increase nonmarital childbearing all else being equal. It can also be argued that income inequality has led to delays in childbearing among advantaged women but not among disadvantaged women contributing to a separation of marriage and child bearing among the latter. Research shows that women experience earrings losses because they take time off work to care for the children and are penalized for this in the labour market. In contrast the evidence suggests that men either benefit or experience no charge in employment based on their parental status. Changes in family structure may contribute to the reproduction of gender inequalities in two ways. First, parenthood affects the employment of earnings much more strongly for woman than it does men. When parents live in the same house-hold, these changes in earnings and employment may off-set each other. Nevertheless, when they live in different households’ women lose only potential benefits from this type of knowledge. Despite the considerable changes in family structure since 1960, the share of single parents who are men has remained virtually the same. (Percheski, 2008)

Caretaking responsibilities for children also differ by family structure fathers spend less time with their children if they do not live in the same household with them leaving mothers in single-mother families, with more responsibility. This uneven distribution has two effects. Firstly, single mothers have less time available for work or leisure and more stress in coordinating and providing care for their children. Secondly, non-resident fathers miss out on the benefits of living with their children. Its also considered that men without children in the home are more likely to engage in risky behaviour, work less and have much lower incomes.
Unequal childhoods
It’s common to hear that childhood itself is a 20th-century construct, and up to this point children were perceived as ‘little adults’, there previously was no distinction between adults and children. Children were expected to contribute to the household income and to the family. Historians like Professor Hugh Cunningham have sought to disprove this notion, demonstrating that childhood was seen as a distinct period of time from the Middle Ages on. However, there is a clear demarcation between the treatment of children today and those in, say, Victorian Britain. Childhood only existed for those from wealthy parents during the industrial time. It was only in recent times that emerged with compulsory schooling and eventual child labour laws, A hundred years ago, writes historian Heather Montgomery, it would have been acceptable for a child to work in a factory. Today the factory owner and parents would be prosecuted. She adds that children in the 21st century have fewer responsibilities than ever.

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