Al-Fatih journal

Praise be to God, Lord of the worlds, and may God’s prayers and peace be upon the righteous Imam, our Master Muhammad, and upon his family, companions, and those who follow them in kind until the Day of Judgment.
And after:
The science of financial and banking transactions is still developing and renewing in line with the tremendous progress witnessed by dealing systems in various parts of the world, which created new images for us that we have not left from previously known contracts such as Salam and Istisna'a and companies except their names, after the combined contracts entered them, which required searching for Imagine her and find out her judgment.
Among these embodied contracts that need to be discussed: the parallel peace contract and its role in economic development, and this is what is studied through two topics:
As for the first topic: it includes nudity complicating the traditional peace, indicating evidence of its legitimacy, and mentioning the most important conditions related to peace.
In the second topic: the parallel or parallel ladder contract was introduced, with scholars' opinions on it to arrive at its legal ruling, in addition to a statement of economic feasibility in contemporary financial transactions.
The research problem: Explaining the development of the inherited jurisprudential concepts, and linking them to the emerging image that modern life requires, which indicates modernity and contemporary, and the validity and reform of Islamic jurisprudence for every time and place.
Research objectives: Presenting the legal alternative to holding peace that is known in our original jurisprudence, in ways that are appropriate for our time, with an emphasis on being a proposed method for filling the state's working budget deficit.
We ask Allah to help and guide

The current research aims at setting a boundaries of the mind preparatory school students in Mosul City, in order to achieve this, the two researchers reviewed some studies and literature, and the mental boundaries test was prepared according to Hartmman's theory. The test consists of (63) items distributed on (8) fields (dimensions): (boundaries related to thoughts and emotions, (perceptual boundaries, memory boundaries, physical boundaries, boundaries related to identity
(gender identity), boundaries among individuals, boundaries related to organizing oneself, boundaries related to opinions and rules). As it was relied upon after the approval of experts and arbitrators in education and psychology, the sample was chosen randomly from preparatory school students on both coasts of Mosul City. The two researchers carried out validity, consistency and discrimination procedures for preparing the test, as the number of its items became (75) items, thus achieving the goal of the research in preparing the mental boundaries test, and a number of recommendations and proposals were made.

The current research aims to design a guiding program according to the technique of Socratic questions in reducing psychological delusions among intermediate school students, and for the purpose of achieving this, the two researchers set (13) guiding sessions covering the dimensions of the scale of psychological delusions, which are (the illusion of persecution, the illusion of jealousy, the illusion of sex) that the two researchers set and the validity of the program was calculated, and the research sample included (10) intermediate school students in the city of Mosul for academic year (2019-2020). The period of each session took (40-45) minutes, and by this, the research aim was achieved, and a number of recommendations and proposals were formulated

Introduce and document the information of sports families in the city of Mosul, from their number, role and institutions, which take care of them or work in it that interact with main classifications :
1- The famous families with more team games as there divisions (male players families, female players families and mixed families).
2- Famous players in soccer, basketball, handball and volleyball .
The researchers used historical curriculum, the research community includes sports families in the city of Mosul, one of their members while male or female players were practiced or famous in one team game or more, and for achieving the aims of the research, the research depends on making meetings with families of sport players in research community, or with their friends, or from messages from them .
The researchers reached the most important conclusions :-
1- The city of Mosul contains (24) sport families their members practiced more than one team game (18) families of male players, one of female family sport, and (5) mixed families.
2- There are (16) sport families specialized in soccer, their players were from Mosul Club, the institutions in the governorate of Mosul had an important role in improving their sport level .
3- (11) sport families were specialized and famous in basketball, and there was clear care from Mosul Club to their number and some institutions had special role in improving them .
4- (6) sport families were specialized and famous in handball from Al-fttwa Club and Ninavah Education Administration and in improving their sport abilities .
There were (4) sport families were specialized and famous in volleyball the attention tended to Al-fttwa Club compared with Mosul Club, Also some social institutions had an effective role in improving them.

The research aims to (build a guide for Arabic language teachers and teachers to teach the expression at the primary level). The researchers adopted the descriptive approach to achieve the goal of research, adopting the Model Hilda Taba in building the curriculum for its compatibility and aim of building the guide, and following the following steps:
1. Identifying the needs and aspects of the behavior to be developed.
2. Formulating the general objectives of the guide:
3. Choose directory content.
4. Identify an appropriate education strategies and methods.
5. Prepare typical plans.
6. Select the appropriate calendar methods.
7. Organize content.
8. Choose educational experiences.
9. Organizing educational experiences.
10. Determine what it will do and how to evaluate it.
The research was limited to:
1. Teacher's guide built by the researchers.
2. Arabic teachers and teachers.
3. The subject of expression for the primary stage
4. Taba'sModel1962.
5. School year 2020-2021..
The research tool was based on the questionnaire built by the researchers and distributed to the research sample, while the researchers used the statistical program (APSS) to process research data and extract its results, and the results of the research resulted in the selection of eleven topics that were most important from the point of view of the research sample to be placed in the guide to be built. In light of the results, the researchers came up with a number of conclusions, recommendations and proposals.

The aim of this study is to identify the degree of the spread of irrational thoughts, and the level of Covi-19 panic spread among Arab young people in Egypt, Iraq and Palestine. The study also aims to specify the nature of the relationship between irrational thoughts and this panic among the members of the study sample. In addition, the study aims at identifying the nature of the differences in the degree of the spread of irrational thoughts about this Pandemic, and the level of panic among the youth due to their gender, nationality and their level of education.
The sample consists of 303 Egyptian, Iraqi and Palestinian young people. The researchers have used both the irrational thoughts measurement, and the Pandemic panic measurement. The results have revealed that the degree of the spread of irrational thoughts is of three levels: low (29.73%), intermediate (31.77), and high (38.50%). The study has also shown that the spread of panic is also of three levels: (18.21%), (32.29%), (49.50). It has also shown that there is no significant statistical correlation between the irrational thoughts and panic. In addition, there are no significant statistical differences between the irrational thoughts and panic due to the gender, nationality and level of education of the study sample

The Carrent research aims at setting apassion for Learning measuring For intermediate school stadents in Mosul city in order to achieve this, the two researcher reviewed some studies and literature, boundaries measuring passion for Learning consists of (51) items distributed on (6) Fields: (congnitive curiosity, Folw, Engagment, Learning Motivation, self- efficacy- presererance) as it was relied upon after the approval of experts and arbitrators in education and psychology, the sample was chosen randomly for: intermediate school students on both casts of Mosul city. The two researchers carried out Validity, consistency and consistency and discrimination procedures for preparing the test as the number of the items becam (49) items, thus achiering the goal of the research of recommendations and proposal weremade.

The aim of the research is to shed light on the nature of the third place in terms of definition and concept, and to clarify the relationship, characteristics and functions of the third place with sustainable development and information institutions and libraries, and to define the functions of the third places and their relationship to sustainable development, and to clarify the facts that make information institutions and libraries a third place that is not ephemeral. As for the research method, the researchers used the analytical documentary method in this research, as it is the most appropriate to the nature of the research and its requirements. The most important conclusions are: The third place is a public place other than the home and the workplace where people can gather and meet without restrictions and conditions, and the third place works in accordance with the call for sustainable development for the sustainability of cities and communities and thus achieves the third place as part of the sustainable development goals, sustainable cities And the ones that are suitable for peaceful coexistence are those cities that give their citizens an opportunity to spend beautiful or happy times outside the home and workplace, and this is what the third place works on. The characteristics of the third place are identical to libraries in total and in detail

The current research aimed to build a measure of higher thinking skills. The basic research sample consisted of (68) teachers who were deliberately selected from schools for the displaced in Erbil, for the academic year (2019-2020), distributed among (4) primary schools, and to achieve the research objectives, the The research tool to measure the higher thinking skills of the teachers, and the tool consisted of (8) skills containing (43) paragraphs, and in its final form of (40) paragraphs. , Retesting and its coefficient of stability was (0.81) and the second method using the alpha-Cronbach equation whose value was (0.88). The data were statistically treated using the simple correlation coefficient and the (t) test for one sample, and the (t) test for the significance of the correlation coefficient. The results showed that the level of higher-order thinking skills was low among the respondents in general. In light of the research results, a number of conclusions, recommendations and suggestions were drawn up.

The aim of this research is to determine the list of critical thinking skills to be available in the science book for the fifth grade at primary school.
The research community represented the content of the science book for the fifth grade at primary school approved by the Ministry of Education for the academic year (2019-2020) fourth edition. It included the introduction of the book and six units by two chapters per unit with a total number of pages of the book (228) pages. The sample of the study included (119) pages after excluding the introductions of each unit and the questions of the chapters and the use of the descriptive analytical method. The researcher looked at a set of literature related to critical thinking skills and collected information and evidence and interpreted the content of the science book for the fifth primary grade. The critical thinking skills questionnaire was built as a research tool for analyzing the content of the science book for the fifth primary grade. The tool included five main skills: conclusion, assumption knowledge, discussion evaluation, interpretation, and inference), under these five main skills include sub-indicators of twenty-five sub-indicators.
The research tool was presented to a group of experts and specialists in the field of teaching methods, curricula and statistics about (20) experts to find the validity of the analysis and then presented them with the model of analysis.
To find the stability of the analysis, (20 percent) from the content of the science book for the fifth primary grade was analyzed, which included four pages of each of the six units in the book on 14 February 2021, which is the first analysis of critical thinking skills. Then the researcher conducted the second analysis of critical thinking skills on 1/3/2021, and the percentage of fixed analysis using the Holisty equation was calculated at (0.94%).
The same sample (20%) was then displayed from the science book for the fifth grade of primary school on two other arbitrators to analyze it. The first holds a bachelor's degree in science and the second holds a master's degree in general teaching methods, and when using the Holisty equation the fixed ratio between the analysis of the researcher and the first analyst was (0.83%), between the researcher's analysis and the second analyst was (0.77%), between the first analysts and the second analyst was (0.93 percent). The average stability (test) reached (86.75). To treat the data of research the researcher used repetitions, percentages, and Holisty equation, and finding the stability of analysis among analysts average stability (test), and the content of the science book for the fifth primary grade was analyzed where the number of critical thinking skills were (843) skill.

Results reached by the researcher: Availability of assumption knowledge skill (33.09%), availability of conclusion skill (26.2%), availability of interpretation skill (17.67%), availability of inference skill (12.93%), availability of discussion evaluation skill (10%).
The percentages of sub-indicators were calculated in the light of each major skill, and the researcher referred to the conclusions, recommendations, and suggestionsd in the fourth chapter of the research.

The current research aims to investigate using participatory learning among teachers of Social Studies (History and Geography) in the intermediate academic stage from the teachers' point of view. The researchers relied on the descriptive approach. The research population consisted of teachers of social subjects (history and geography) and consisted of (725) teachers of History and Geography in the averages in the center of the cities of Mosul and Hillah. A random sample of (110) teachers of History and Geography is selected from teachers in the city center of Mosul and Hillah. The researchers have prepared a questionnaire. It includes (58) items distributed among eight areas: (the field of educational objectives according to participatory learning, the field of lesson planning according to participatory learning, the field of implementing the lesson according to participatory learning, the field of employing teaching methods and educational aids according to participatory learning and the field of using electronic applications in participatory learning, the field of human relations and classroom management according to participatory learning, the field of the scientific aspect and professional growth in participatory learning, the field of evaluation according to participatory learning). The validity and reliability have been verified.
The following statistical means are used: the percentage, the Pearson correlation coefficient, the Spearman Brown coefficient, the weighted average, and the percent weight. After analyzing the data statistically, the results show that: there is a weakness among teachers of social studies (History and Geography) in the methods of participatory learning, in the formulation of behavioral objectives, in the employment and use of electronic applications, in the use of examples and current events, and in encouraging students to extracurricular activities and the use of educational methods and evaluation methods in participatory learning . The researchers reached a number of conclusions, including: the weakness of Social Studies teachers in the methods of modern electronic participatory learning, and the lack of experience among social teachers using participatory learning and the educational methods and techniques that are used in participatory learning. Based on this, a number of recommendations are made, including: Social Studies teachers (History and Geography) should have training courses in participatory learning and the necessity for the preparation and training unit in the cities of Mosul and Hillah to train History and Geography teachers on the use of participatory learning platforms and how to prepare and design electronic educational aids. A number of suggestions have been put forward, including: The reality of participatory learning among History and Geography teachers in middle school from their point of view and its relationship to the variables of gender and specialization.

the use of distance learning - Corona table - moral intelligence - parents - secondary school students

The target of the current search is to know the impact of the Rothkopf method on the achievement of art education students in the subject of Art Elements. To achieve the goal of the research, teaching plans were designed according to the Rothkopf method. Accordingly, the researchers prepared an achievement test that measures the level of information-theoretical-cognitive information for a subject. The researchers also identified the community and sample of the current research for first-year students / Department of Art Education / in the College of Basic Education / Al-Mustansiriya University / morning study. The number of students were (133). They were distributed over four classrooms including class No. (3) which was chosen randomly, the number of its students were (32) to represent the experimental group, and class no. (4), whose number of students (31) was chosen to represent the control group. The researchers excluded the three failing students, two of whom were from Classroom No. (3) and (1) from Classroom No. (4). In order to avoid the impact of previous experience due to their failure last year, which may affect the results of the total number of students which were (60) for both the groups, the experimental method was used because it is suitable for the research procedures.
The study reached a set of results, the most important of which are:
There are significant differences at the level of 0.05 in favor of the experimental group that was studied according to the Rothkopf method in the subject of Art Elements.
In light of the findings of the research, researchers recommend using the Rothkopf method in teaching the Elements of Art for the first stage in the Department of Art Education, College of Basic Education, because of its effective impact on increasing the achievement and organizing the material among students

The current research aims to find out the effect of the Fink model on developing reflective thinking and cognitive motivation among fifth-grade literary students. The researcher used the experimental design with partial control and the pre and post tests for the experimental and control groups. The study sample consisted of (60) female students, including (30) female students for the experimental group that taught according to the Fink model, and (30) female students for the control group that taught in the usual way. The two groups were rewarded in the variables: (the chronological age of the students calculated in months, the scores of the IQ test, the pretest for reflective thinking, and the pre-test for cognitive motivation). The experiment spanned (12) weeks from the second course of the academic year (2018-2019). After the end of the experiment, the reflective thinking test and the cognitive motivation scale were applied, and the validity and reliability of the two tools were verified. By using the appropriate statistical means to process the data, the results showed that the students of the experimental group that studied according to the Fink model outperformed the students of the control group in the test of reflective thinking and the measure of cognitive motivation. In light of the findings of the researcher, she developed a set of conclusions, recommendations and proposals.

This study aimed to identify the role of socialization among Arab Palestinian families in the areas occupied in 1948 in belonging to the Palestinian national identity as seen by students of the Arab American University,
Where the study population consisted of all 1948 students studying at the Arab American University, in the year 2019/2020. The study sample consisted of (70) students from the study population
The researcher used the questionnaire as a research tool, which included (36) items within two main areas: the cultural field and the social field. The researcher used the descriptive and analytical approach, which was considered an appropriate approach to the nature and objectives of this study.

Among the most important findings of the study were:
* It was found that the role of socialization in belonging to the Palestinian identity of the Arab family in the areas occupied in 1948, as their children see students of the Arab American University in the cultural field, was great.
And in the social sphere it was great.
It was found that there are no statistically significant differences at one level about the role of socialization in belonging to the Palestinian identity in the Arab family in the areas occupied in 1948, as seen by their children, students of the Arab American University, due to variables: (school year, gender, and college variable)
Finally, the researcher recommended the following:
The need for the Arab family in the territories occupied in 1948 to use the Arabic language at home.
The need for the family to participate in drawing targeted pictures expressing patriotism and pasting them on the walls of the house.
The need for the family to constantly provide its children with the principles of patriotism and defend it with the pen and tongue.
- The need for the family to instill in the hearts of its children a love of volunteer work and involvement in civil institutions.
- The need for parents to devote family sessions to discuss matters related to the homeland، which develops the student's national identity.

The aim of the research is to identify the effect of using the self-inquiry strategy in providing fourth-scientific students with the physical concepts and developing their visual thinking.
The research sample consists of (70) students from Abd Al-Rahman Al-Ghafiqi preparatory school in the city of Mosul, and it has been divided into two groups, the first experimental of (37) students studied according to the strategy of self-inquiry, and the second control of (33) students studied according to the traditional method . In order to achieve the goal of the research, the researcher prepared two multiple-choice tests: the first conceptual consisting of (30) items, and the second for visual thinking consisting of (20) items, and they were characterized by validity, reliability and psychometric properties. The researcher conducts the experiment for a whole semester, after which the two research instrument have been applied at the end of the second semester on (5-6 / 5/2019). The collected data has been analyzed statistically using the t-test for two independent samples and two correlated samples. The researcher concludes the following results:

1- There is a statistically significant difference at the level of (0.05) between the means of the acquisition of the experimental group students and the control group students of the physical concepts in favor of the experimental group.
2-There is a difference of statistical significance at the level (0.05) between the means of the growth of visual thinking among students of the experimental and control groups and in favor of the experimental group.
3-There is a statistically significant difference at the level (0.05) between the mean scores of visual reasoning in the pre and post applications among the members of the experimental group and in favor of the post application. In the light of the results above, the researcher came up with a number of conclusions, recommendations and suggestions.

The current research includes the subject of (curiosity and its relationship to competition among Riyadh children), the first chapter included the definition of research from the problem of research ((Is there a relationship between curiosity and competition and curiosity is one of the means of compatibility with the ongoing changes in contemporary society, as it is one of the means of The curiosity is an internal self-motivation directed by the individual to what must be satisfied, and to achieve the satisfaction of this motivation, the individual feels confident and pushes him towards further polling. People differ in their behaviors from one person to another, which is natural and clear, but different behaviors of children in stages First From age makes us confused about the distinction between normal and abnormal behaviors. From the perspective of parents, it may be something natural, but teachers and those around them see something unreasonable in society that generates competition.
Its importance is that curiosity promotes cognitive development through exposure to diverse experiences through which learning takes place, that it is a means of gathering information about the environment and its objects, especially the unknown, and that it facilitates various mental and cognitive functions such as attention, distinction, innovation and information operation. And raise the level of expertise and access to a distinct level of public and private understanding, and it helps the individual to solve the problem, and competition exists in all societies, regardless of their cultural levels, or social nature, as we find that individuals compete for access to social status and take over Kza prestigious among their peers, and this has a significant impact in the progress and prosperity and breeding elite))
The research objectives include:
1 - Recognize the level of curiosity among the children of Riyadh.
2 - identify the level of competition among children in Riyadh.
3 - Is there a relationship between curiosity and competition among children in Riyadh.
The second chapter includes the theoretical framework and includes the most important literature and theories and previous Arab and foreign studies of the first variable (curiosity) and the second variable (competition), while the third chapter includes the research methodology of the research community of the children of Riyadh to raise Diyala and the adult research sample (60 A child and one of the children of Riyadh to raise Diyala were selected randomly simple method, and research tools adopted by the researcher from the scales (Dr. Elham, 2017) and (Dr. Mayada, 2018), which consists of (41) paragraph, the stability of the measure has reached The method of re-testing was the value of stability First (0.81) and (0.84), the value of the stability of the second measure, which is acceptable for the stability of the value of the two measures, the researcher has reached the following conclusions:
1-Children have curiosity.
2. Children have a clear competition.
3. There was a positive correlation between curiosity and competition.
Recommendations:
From the above procedures and research results the researcher can make the following recommendations:
1_ enriching the school environment with pictures and curricula that contribute to building general concepts.
2 - Training teachers and provide them with tests and measures of the special abilities of children to help them to stand aspects that they need to develop.
3_ Awareness and training of Riyadh teachers to make the competition outlet where the child gains fun and satisfaction in an atmosphere of love, kindness and encouragement.
4_ Competition must be preceded by a purposeful and systematic educational process based on respect for opinion, the other opinion, freedom of expression and collective action.
Suggestions:
In light of the research results, the researcher suggests the following:
1- Study the development of competition and its relationship to cognitive independence in children
2 - Conducting a study dealing with curiosity and its relationship to some variables such as (sense of self, cognitive style)
3 - conducting a correlative study between the curiosity and the personality of the child.

The research aims to find out the effectiveness of Swom's strategy in innovative thinking among first-average students in mathematics To verify the goal of the research, the hypothesis was formulated (there is no statistically significant difference at a significance level of (0.05) between the mean scores of the students who study according to the SWOM and the grades of students who study according to (the usual method) in the innovative thinking test) The research sample consisted of (60) female students distributed into two groups, one of which was the experimental, the number was (30) female, while the other was a control, the number was (30) female The first group was taught according to the SWOM strategy, while the second group was taught according to the usual method of teaching The two research groups were rewarded with a number of variables. The two researchers prepared a test for innovative thinking, which consisted of (25) paragraphs of the essay type Its authenticity has been verified, and its reliability factor was calculated. The experiment was implemented in the first semester of the academic year (2019-2020) The data were processed by using the SPSS program and the results showed a statistically significant difference in the innovative thinking test as a whole and in all its capabilities in favor of the experimental group. In the light of the results, the researcher recommends a number of recommendations and proposals.

The research aims to use the technical learning method in learning the preparation skill of the second stage students of the College of Physical Education and Sports Sciences, University of Baghdad in volleyball. To know the effect of the artistic learning method in the acquisition and retention of the preparation skill among the individuals of the research sample, the experimental approach was chosen by the method of equal groups experimental and control For its convenience to the nature of the research problem. The research sample was chosen from students of the second stage of the College of Physical Education and Sports Sciences / University of Baghdad for the academic year 2019/2020. (F) as an experimental group and Division II (g) as a control group. The number of students of the second (and) experimental group was (25) female students and (26) female students for the control group, and those who failed from the last year and who had previous experience in volleyball were excluded from among the players of clubs and university teams who submitted a requests for postponement for the academic year 2019/2020. Also students are frequently absent, and the final number of students who underwent the experiment was (20) students for the experimental group and (20) students for the control group.

The study aimed to identify the training needs of science teachers in middle and high school in Riyadh in the use and activation of virtual classes through the platform of my school, and to achieve the purpose of the study, the researcher followed the descriptive analytical approach, where the community consisted of science teachers in Riyadh, and a random sample of (87) teachers was taken. The results of the study showed: that the level of science teachers ’acquisition of computer skills in the intermediate and secondary levels is an average of 69%, and that the level of science teachers’ acquisition of skills in the intermediate and secondary levels of skills to deal with the Madrasati platform is an average of 72.4%, Also, there are no statistically significant differences in the degree of science teachers' acquisition of skills in using the Madrasati platform due to variables (years of service - academic qualification - number of courses in the computer field - number of courses in the field of e-learning - number of courses in the field of using the Madrasati platform) .
The study recommended the importance of using the Madrasati platform in the educational system, especially in light of distance education, in addition to the necessity of holding training workshops for science teachers in intermediate and secondary levels in Riyadh on how to use and activate virtual learning classes through the Madrasati platform.

This work aim to study the transient stability of a 3- phase induction motor controller.
A simulation based analysis is depended. stator current electromagnetic torque and rotor speed has been studied, a mathematical model and FFT analysis also presented for the transient response, parameters effect stability margin was discussed.

Introduction:
Transient stability of a system refers to the stability when subjected to large disturbances such as faults and switching of lines [1]. Hence linearized analysis is not applicable and the nonlinear equation of the system have to be solve in stability evaluation checking transient stability is only one of the many objectives of running a simulation program which can give lot more information such as predict the dynamic performance of the system involving low frequency transient.

Mathematical formulation:
Consider a continuous time system of equation [2].
X=f(x,t)…………………………………………………..1
The solution of the above equation can expressed as
X(t)=∅t (x0,t0)…………………………………………….2
Where x0 is the initial value of x at time t=t0
The integration algorithms generate a sequence of points x0,x1,x2,…..at time t0,t1,t2,……with approximation
XK= ∅tk(x0,t0)……………………………………………..3
It is usually assumed that the points are uniformly spaced with size h>0,that is .
TK=t0+hk for k=0,1,2,3…… …………..4
In the forward Euler method f is approximated as constant evaluated at time tk .
Thus xk+1 can be calculated from
Xk+1=xk+hf (xk,tk)………………………………………5
By applying forward Euler method ,xk+1 can be expressed as
Xk+1=[1+Ah]xk=[F]xk……………………………………6
For numerical stability, the eigen value (λj,j=1,2,3,…….n) of the matrix [F] must satisfy | λj| <1.
And using trapezoidal rule of integration:
Xk+1=xk+(h/2)[f(xk,tk)+f(xk+1,tk+1)]………………………..7

Induction motor modeling:
The equivalent circuit for an induction motor shown in fig. (1). And the motor is assumed to


Fig.(1) equivalent circuit of an induction motor.
Be driven by the stator voltage given by (3):
V ⃗1=jθ (t) Lkik0 exp[jθ(t)]………………………………………8
And the corresponding magnetizing current i0 is assumed to be represented by :
i0= i0 exp{j(θ + ∅0)}……………………………………………..9
And as shown in (3) the following are derived :
Te=K L0 Ti02(∅0+θ-ωr)…………………………………………..10
(J/n) ωr=Te-Tsh……………………………………………………11
And taking into account the small deviation in the state variables (i0, ∅0,ωr) from an equilibrium point (i00, ∅00,ω00) as
i0= i00+∆ i0→ i0=∆ i0.......................................................................12
∅0= ∅00+∆ ∅0→ ∅0=∆ ∅0……………………………………….13
ωr= ωr0+∆ ωr→ ωr= ∆ωr…………………………………………..14
Substituting, and neglecting the higher order terms, the linearized equation are derived as follows (3):
[A||∆i0,∆ό0,∆ώr]=0……………………………………………….15
[A]=[aij] (I,j=1̴ 3)
where:
a11=a22=α11p2+β11 p+γ11 a12=-a21=-α12 p-β12
a13=β13 a23=-α23 p – β-β23
a31=β13 a32=-k2p
a33=p+k2
α11=L1T0 β11=r1T0+L1
γ11={L1 T0θ(θ -ωr0)ω} α12=L1T0 (2 θ -ωr0)
β11=r1T0(θ -ωr0) β13=L1T0 θ
α23=L1T0 β23=r1T0 p=a/dt

Stability analysis:
Following the induction motor model for the voltage source type inverter ,H can derived (4) that the stator current error will satisfy the following equation :
e1=G(s)pjλ̑r(ω̑m-ωm)………………………………………16
G(s)= -s/€ [s2I+s(Xi+yj)+Mi+Ni]-1
=[■(G11&G12@G21&G22)] …………………………………….17
Where:
m=[Rr/Lr(h1+Rs/σ Ls+h3/€)-pωm(h2+h4/€)]
n=[Rr/Lr(h2+h4/€)-pωm(h1 –R s σ Ls- h3/€)]
x=[h1+Rs/σ Ls+Rr/σ Lr] y=[h2-pωm]
H1=[■(h1&-h2@h2&h1)] H2=[■(h3&-h4@h4&h3)]………18

H1,H2 are the observers gains and " " denotes the estimated value it should be noted that equation (16) and (17) are the general form of error equation for most model _ adjustment based speed estimators. And form these equation we can composed the output error transfer function G(s) together with PI speed estimator as shown in fig (2)




e1
+
-
-Ф -ωm
PJλre
+
PJλr ωm


Fig (2) Blok diagram of output error in adaptive observer

To carry out the stability analysis easily we will transfer the estimation error system from the stator frame (α-β) to rotor flux frame (d-q) [4].and then simplify the error system considering also measurement noise as shown in fig (3).
ωm Ƞ ωm






Fig(3) Blok diagram of SISO error system on rotor flux frame


G22(s) is calculated to be
G22(s)=(s^(2 )+xs^(2 )+(〖ω0〗^2+m)s+〖ω0〗^2 x+ω0n)/(-ε [(s^(2 )+xs^ -ω0y+m)^2+((2ω0+y)s+ω0x+n)^2])……………………..19
Where ω0 is the angular frequency of the estimated rotor flux:
ω0> ωc=-n/x (critical frequency)………………………………………20
x>0……………………………………………………………………..21
ω0n Where m,n and x depend on motor parameters and feedback gain H1, H2 as given in equation (18).
The boundary for stability is the point when ω0, ωc, considering that:
ω0=p ωm+ ωse .......................................................................................23
ωc=p ωm/1+τ…………………………………………………….…….24
When τ can be changed by feedback gain h3,we can find that the stability boundary is given by:
ωm = ((1+Ƞ)Rr)/(Ƞp|λr|^2 ) Tm………………………………………………...25

From the condition equ(20) and equation (18),(25) we can compare conceptually the unstable region on the torque – speed plane for the system with and without error feedback.
Simulation Results:
This research use the block diagram shown in fig (4) to simulate the induction motor with electrical drive.