# Robustness High Performance Of Induction Motor Derives Computer Science Essay

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Applications of fuzzy logic controller to induction motor drives are on the rise. The paper presents an overview of high performance and robustness indirect field-oriented control (IFOC) of IM drives with the focus of hybrid fuzzy with self-tuning FLC - PI controller plus PI speed controller. After that, it presents the overview of design of this controller and effective factors on its robustness and high performance.

Keywords: self-tuning, indirect field oriented, fuzzy logic, speed control, induction motor

## 1-Introduction

Electric drives for motion control must have a fast torque response, four quadrant operation capability and controllability of torque and speed over a wide range of operating conditions [1].High performance electric motor drives are considered an essential requirement for modern industrial applications. In the past, dc motors have been widely used for this purpose. However, large size, heavy weight and frequent maintenance requirements make dc motors an expensive solution. Moreover, mechanical commutator-brush assembly cause undesired sparking, which is not allowed in certain applications. These inherent drawbacks of dc motors have prompted continual attempts to find out a better solution for the problem. Numerous attempts have been made to use induction motors instead of dc ones since they have many advantages like simplicity, reliability, low cost and virtually maintenance-free. However, the high nonlinearity and time-varying nature of an induction motor drive demands fast switching power devices and a large amount of real-time computation [2].

In the past decades, induction motors were controlled using scalar control methods like the volt-hertz control [3, 4] . Here the magnitude and frequency of the stator voltages are determined from steady-state properties of the motor, which leads to poor dynamic performance. The various variable frequency control methods for induction motor are shown in Figure . In scalar control only magnitude and frequency of voltage, current and flux linkage vectors are controlled. This scheme acts only under steady state condition. In vector control the magnitude, frequency and instantaneous position of voltage, current and flux linkage vector are controlled and valid for steady state as well as transient conditions. Thus, the vector control method is better option than to the scalar control to obtain the dynamic performance [3]. Control technique, which is developed upon the field orientation principle proposed to simplify the speed control of induction motors and has been implemented in a wide range of industrial applications. This method gives elegant way of achieving high performance control of induction motor drives. The primary advantages of this approach are the decoupling of torque and flux characteristics and easy implementation. So induction motor can be controlled like a separately excited dc machine. In addition to, the advent of recent power semiconductor technologies and various intelligent control algorithms, an effective control method based on vector control technology can be fully implemented in real-time application. Because of these facilities, vector-control based High-performance IM drives have occupied most of the positions that were previously stationed by dc motor drives [5-7].

This paper attempts to make a summary review high performance and robustness IFOC of IM drives with the focus hybrid fuzzy with self-tuning FLC - PI plus PI speed controller. It is briefly described, an overview of vector control of IM in section1 , structure of speed controller in section2 , hybrid fuzzy controller and its design in section3,4.

Figure1: Control methods for induction motor

## 2- Induction motor model and basic vector control equations

## 2.1 Dynamic model

A dynamic model developed either with the concept of space phases [8, 9] or d-q [10] representations may be utilized to develop the basic machine equations for implementation of vector control. We like to use the latter for convenience and familiarity. The d-q axes model of an induction motor with reference axis rotating at synchronous speed has shown in Equation ()

(1)

Where

(2)

The electromagnetic torque developed by a 3-phase, P-pole, induction motor is

(3)

Where

(4)

(5)

The field orientation implies that the stator current components obtained be oriented in Phase (flux component) and in quadrate (torque component) to the flux vector which can be either stator flux (), air gap or mutual or magnetizing flux (), or rotor flux ( as shown in the equivalent circuit in Figure [1]. The orientation of the stator current with respect to the stator, rotor and air gap flux has been examined and the relative merits and developments of the schemes have been reported [11, 12]. It has been shown that the rotor flux orientation alone provides natural decoupling, fast torque response and all round stability. The stator flux and air gap flux orientation, however, are attractive due to ease of flux computation and for the purpose of wide range of field weakening operation [13] but need decoupled network. A new strategy has been developed which decouples flux and torque in an arbitrary flux reference frame [14]. Rewriting the rotor voltage equations in (1)

(6)

(7)

1.jpg

Figure 2: Conventional stator referred induction motor equivalent circuit showing different

Where

(8)

For rotor flux orientation control, the rotor flux axes are locked with the synchronously rotating reference system such that the rotor flux is entirely in the d-axis,

(9)

(10)

Substituting (9) & (10) in (6) & (7) yields

(11)

(12)

For the range of operation below the base speed, the flux is kept constant, when

(13)

From (5) & (10),

(14)

Above equation shows a direct equilibrium relation between the torque component current and the rotor current. The torque equation is

(15)

Above equation shows the desired property of providing a torque proportional to the torque command.

During flux changes in the transient, and from (12)

(16)

Combining (16), (5) & (10), yields the equation relating flux Command and the flux as shown in (17),

(17)

This in the steady state is

(18)

The close parallel to the dc machine is now clearly visible. With the flux command held

Constant, a change in is followed instantly by corresponding change in . While with a change in flux command, a transient rotor current is induced subsequently decays with the rotor open circuit time constant as shown in (17).

## 2.2 Steady state model

A convenient steady-state equivalent circuit model of the field -oriented induction motor as shown in figure 3 can be obtained from the conventional equivalent circuit (figure 1) by using a referral ratio in lieu of the common choice of the stator to rotor turns ratio [15]. With adoption of this ratio, the stator current is seen to be subdivided into the orthogonal components (flux component) and (torque component), equivalent toand referred in the dynamic model, and the slip relation (11) can be obtained by equating the voltages across the parallel branches as

(19)

Equation (19) expresses the co-ordination between the slip and the current components required to attain correct field orientation. The torque expression is obtained from the air gap power as

(20)

Which shows the desired torque control via current components and.

a.jpg

Figure 3: Derived steady-state equivalent circuit for rotor flux orientation scheme

Where

(21)

## 2.3 Induction motor vector control implementation

The implementation of vector control requires information regarding the magnitude and the position of the flux vector (stator, rotor or mutual, as the case may be) and fast control of stator current in both magnitude and phase. Depending upon the method of flux acquisition, there are essentially two general methods of field oriented control. The first one is called the direct method [5] and the other one is known as the indirect method [6]. The universal field oriented controller developed [14] is applicable to both these field orientation schemes and the generalized approach [16] to indirect control of induction and synchronous motors.

## 2.3.1 Direct field orientation

In the direct method, also known as flux feedback method, depends on generating unit vector signals, the air gap flux is directly measured with the help of sensors such as Hall probes, search coils or tapped stator windings [17], or estimated/observed from machine terminal variables such as stator voltage, current and speed [18]. Since it is not possible to directly sense rotor flux, it is synthesized from the directly sensed air gap flux using equations (22, 23)

(22)

(22)

A variety of flux observers can be employed to estimate and improve the flux response with less sensitivity to machine parameters as detailed [19, 20]. A major drawback with the direct orientation schemes is their inherent problem at very low speeds to measure the air gap flux is difficult. Closed-loop stator flux observers based on the motor current, voltage and the measured rotor position have been found to obviate this difficulty [18, 21].

## 2.3.2 Indirect vector control

An alternative to direct measurement or estimation of the flux position for application of vector control to the induction motor without flux sensors is the indirect field oriented method uses the rotor speed and the slip angular frequency derived from the rotor dynamic equations to generate the unit vector signals to achieve flux orientation [1]. Although Indirect field orientation method is very sensitive to variations of motor parameters, such as rotor time constant, it is generally preferred than the direct one. This is because direct method requires a modification or a special design for the machine. Moreover the fragility of flux sensors often degrades the inherent robustness of an induction motor drive [22].Indirect vector method decouples the motor current components by estimating the slip speed which requires a proper knowledge of the rotor time constant. The accuracy of this model depends very much on the accuracy of motor parameters, especially the rotor time constant which in turn depends on the accuracy of the rotor resistance and the inductance [23].The rotor time constant is defined as the ratio of rotor inductance over rotor resistance [23-25]. However, changes in the rotor time constant , often cause field-orientation detuning and degrade system performance, especially for large high-efficiency induction machine systems. A deviation between the instrumented and the actual motor values is said to "detune" when detuning occurs, the efficiency and torque capability of drive are greatly reduced in steady state. Furthermore, due to the inverter current limits, torque/ampere capability of the drive is significantly less, resulting in unsatisfactory drive performance, particularly for fast dynamic speed commands [26, 27]. In addition, the drive performance will also be affected by other disturbances, such as load Torque, rotor inertia and unmodeled dynamics, etc [24, 28].

## 2.4 Vector control techniques

Progress in the field of power electronics and digital signal processing (DSP) and microelectronics enables the application of induction motors for high-performance drives where traditionally only DC motors were applied. Thanks to sophisticate control methods, induction motor drives offer the same control capabilities as high performance four-quadrant DC drives. A major revolution in the area of induction motor control was invention of field-oriented control (FOC) or vector control in the late1960 [29].

The conventional vector control methods have been replaced by the new dynamic microprocessor based control techniques [30-32]. The advancement of microprocessor technology has followed a rapid pace since the advent of the first 4-bit microprocessor in 1971. From simple 4-bit architecture with limited capabilities, microprocessors have evolved towards complex 64- bit architecture in 1992 with tremendous processing power. A microprocessor based slip frequency and flux control scheme was implemented by using Motorola 6800 microprocessor for induction motor and results were supported by the experimental setup[33]. As the fast changes in the technology of microprocessor, a newly developed 32-bit microprocessor-based fully digital control system has been implemented to control the nonlinear dynamic induction motor. The high-performance microprocessor based vector control schemes for induction have been presented in [34, 35] and the controller performance was check and verified experimentally. Digital signal processors (DSPs) began to appear roughly around 1979 and today advanced (Digital Signal Processors), RISC (Reduced Instruction Set Computing) processors, and parallel processors provide ever more high computing capabilities for most demanding applications. With the great advances in the microelectronics and very large scale integration (VSLI) technology, high performance DSP's can be effectively used to realize advance control scheme. High performance Vector control of an induction motor drive has done by DSPs in [36-38].

## 3. Structure of speed controller

Since speed controller is evaluated with a conventional PI controller, literature review will start with PI controller.

## 3.1 PI controller

The conventional PI controller (CPIC) is one of the most common approaches for speed control in industrial electrical drives in general [39, 40], because of its relatively simple structure, which can be easily understood and implemented in practice, its simplicity, and the clear relationship existing between its parameters and the system response specifications and it is also the basis for many advanced control algorithms and strategies [41-43] that many sophisticated control strategies, such as model predictive control, are based on it. In spite of its wide spread use there exists no generally accepted design method for the controller [44].structure control of IFOC IM has shown in Figure .

aaFigure 4: Structure control an IFOC IM

Most industrial processes exhibit nonlinear dynamics, and this places additional complexity on the modeling procedure used. In practice, many nonlinear processes are approximated by reduced order models, possibly linear, which are clearly related to the underlying process characteristics. However, these models may only be valid within certain specific operating ranges. When operating conditions change, a different model may be required to be used or the model parameters may need to be adapted. System model is necessary for tuning controller coefficients in an appropriate manner (e.g., percent overshoot, settling time). Because of neglecting some parameters, the mathematical model cannot represent the physical system exactly in most applications. That's why, controller coefficients cannot be tuned appropriately. It is well known that fixed-gain controllers may be insufficient to deal with systems subjected to severe perturbations and may perform well under some operating conditions but not all because the involved processes are in general complex, time variant, with non-linearity and model uncertainty [40, 45, 46]. In fact, PI controller main drawbacks are the sensitivity in performance to the system parameters variations and inadequate rejection of external perturbations and load changes and robustness to inertia increasing and rotor resistance variations in the case of an indirect rotor flux oriented machine [47, 48]. Thus, the controller parameters have to be continually adapted according to the current trend of the system [24, 49].

The PI speed controller is initially tuned by the Ziegler-Nichols method based on stability boundary [50, 51]. It is subsequently tuned through simulations in order to obtain satisfactory responses. The saturation of the controller is avoided by adding a correction of the integral term (Kc) [50]. This method has good load disturbance attenuation but shows unsatisfactory performance, with a large overshoot and long settling time. The structure of this controller is shown in Figure 5.

Figure 5: Pi controller with anti windup correction term

There are several adaptive control techniques for tuning of coefficient PI controller such as model reference adaptive control (MRAC) [52], sliding-mode control (SMC) [53], variable structure control (VSC) [54] , and self-tuning PI controllers [55], etc. The design of all of the above controllers depends on the system exact mathematical model. For some of these techniques the motor parameters and load inertia must be calculated in real time, so there is a high processing requirement for the used processors [56]. Although they have been developed to deal with this issue, but due to their complexity, only a few have been implemented in IFOC IM drives, e.g. [53, 55, 57].

However, it is often difficult to develop an accurate system mathematical model due to unknown load variation, unknown and unavoidable parameter variations due to saturation, temperature variations, and system disturbances [45]. Many of the recent developed computer control techniques are grouped into a research area called Intelligent Control, that result from the integration of fuzzy-logic techniques within automatic control systems. The tuning of electric drive controller is a complex problem due to the many non-linearity of the machines, power converter and controller [58]. In the conventional controller design process, heuristics enter into the implementation and tuning of the final design. Consequently, successful controller design can in part be attributable to the clever heuristic tuning of a control engineer. An advantage of fuzzy logic control(FLC) is that it provides a method of manipulating and implementing a human's heuristic knowledge to control such a system [57].

## 3.2 FLC controller

The mathematical tool for the FLC is the fuzzy set theory introduced by Zadeh [57]. Over the past three decades, the field of fuzzy controller applications has broadened to include many industrial control applications, and significant research work has supported the development of fuzzy controllers. In 1974, Mamdani [59] pioneered the investigation of the feasibility of using compositional rule of inference that has been proposed by Zadeh [60], for controlling a dynamic plant. A year later, Mamdani and Assilian [61] developed the first fuzzy logic controller (FLC), and it successfully implemented to control a laboratory steam engine plant.

Mamdani's pioneering work also introduced the most common and robust fuzzy reasoning method, called Zadeh-Mamdani min-max gravity reasoning. Also, a significant number of in-depth theoretical and analytical investigations related to this structure have been reported in [62-66]. Takagi and Sugeno [67] introduced a different linguistic description of the output fuzzy sets, and a numerical optimization approach to design fuzzy controller structures.

As compared to the conventional PI, PID, and their adaptive versions, the FLC has some advantages such as: 1) it does not need any exact system mathematical model; 2) it can handle nonlinearity of arbitrary complexity; 3) sometimes they are proved to be more robust than conventional controllers [15, 68]; 4) control are performance robustness against plant parameter variation, load disturbance effects, independence of mathematical model information of the plant and satisfactory performance with imprecision signals from the sensors [69] , and 5) it is based on the linguistic rules with an IF-THEN general structure, which is the basis of human logic [70]. FL control has its critics, particularly among the conventional control theorists. Commonly mentioned weakness includes the lack of a formal design and analysis methodologies, including the difficulty in obtaining stability and robustness indices [71] . However, the application of FLC has faced some disadvantages during hardware and software implementation due to its high computational burden [72]. To minimize the real-time computational burden of an FLC, a method based on simple MFs and rules has been implemented in [45]. A conventional FLC is shown in Figure 6.

Figure 6: Conventional fuzzy logic controller block diagram

Generally, In standard FLCs, the scaling factors of the fuzzy controller are fixed and selected under nominal conditions, in which attention cannot be simultaneously given to both dynamic and steady-state performances of a drive system with wide speed range, namely, short rising time, rapid settle time and little overshoot under dynamic state, and small error under steady state [73].Figure 7 shows standard FLC in control circuit.

Figure : Standard fuzzy logic controller in control circuit

FLC has emerged as a complement to conventional strict methods. Design objectives that are mathematically hard to express can be incorporated into FL controller (FLC) by linguistic rules. Recent literature has paid significant attention to the potential of FLC for the speed control of ac drives [45, 47, 74-78]. FLC have been developed and can be divided into two groups [79].

The first group focuses in improving the design and performance of the standard FLC [45, 76, 77, 80-82]. The second group of approaches combines the advantages of FLC and those of conventional adaptive techniques. In the early years, most FLCs were designed by trial and error. Since the complexity of a FLC will increase exponentially when it is used to control complex systems, it is tedious to design and tune FLCs manually for most industrial problems like motors control. That is why, the conventional nonlinear design method [74] was adopted in the fuzzy control area, such as fuzzy sliding control [25, 83], fuzzy gain scheduling [75], Fuzzy SMC-PI control [84], robust self-tuning PI- type FLC (STFPIC) [85] ,Various forms of self-tuning and self-organizing FLCs [86-89],and adaptive fuzzy control [28], in order to alleviate difficulties in constructing the fuzzy rule base and improve the performance of the drive under severe perturbations of model parameters and operating conditions.

Also To achieve more improved performance and increased robustness, recently neural networks and genetic algorithms are being used in designing such controllers [90-97]. Moreover, FLC is used to compute the individual PI, PID coefficients for industrial and process applications requiring high performances, regardless any load disturbances, parameters variations, and any model uncertainties, several self-tuning controllers based on adaptive and optimal control techniques, or artificial intelligent methods, were proposed in order to improve the control robustness [41, 43, 82, 86, 98-108]. Extensive adaptive self-tuning PI algorithms were exposed in the literature for this purpose, such as those presented in [42, 43, 46, 98, 100, 101, 104, 109, 110], for example.

## 3.3 hybrid fuzzy controllers

For most control systems especially motors control , error signals and their first derivative are assumed to be available to the controller if the reference input is piecewise continuous. Analytical calculations show that a two-input FLC employing proportional error signal and velocity error signal is a nonlinear proportional-integral (PI) or proportional-derivative (PD) or proportional-integral -derivative (PID) as shown in figure 8,9 [111, 112].

Among the various types, proportional integral (PI), proportional derivative (PD), and proportional-integral derivative (PID) of FLC's, just like the widely used conventional PI controllers [113] in process control systems, PI-type FLC's are most common and practical. Because proportional (P) and integral (I) actions are combined in the proportional-integral (PI) controller to take advantages of the inherent stability of proportional controllers and the offset elimination ability of integral controllers. The performance of PI-type FLC's is known to be quite satisfactory for linear first-order systems. But like conventional PI-controllers, performance of PI-type FLC's for higher order systems, with integrating elements or large dead -time, and also for nonlinear systems may be very poor due to large overshoot and excessive oscillation. Such systems may be ultimately uncontrollable [114]. PD-type FLC's are suitable for a limited class of systems [115]. And they are not recommendable in presence of measurement noise and sudden load disturbances. Since they do not have integral mechanism, the associated system is with significant steady state error [116]. PID-type FLC's are rarely used due to the difficulties associated with the generation of an efficient rule base and the tuning of its large number of parameters [117].

Due to the popularity of PID controllers in industrial applications, most of the development of fuzzy controllers revolves around fuzzy PID and PI or P or D controllers in the past decade [116, 118-123]. To emphasize the existence of conventional controllers in the overall control structure, they are called hybrid fuzzy controllers [124] as shown in Figure 10. In [116] is shown that Hybrid fuzzy controller with PI type fuzzy plus PI controller is robust to load disturbance and with fast response , low overshoot , and less steady state error in very wide speed range.

Figure 8: Block diagram of a PI-type and PD-type fuzzy logic controllers

Figure 9: Block diagram of PID-type fuzzy logic controllers

11.jpg

Figure 10: Block diagram of PI- type fuzzy plus PID controlled system

## 4. Design hybrid fuzzy controller

There are some difficulties that prevent the design of hybrid fuzzy controllers from being systematic [124].

First, the choice of the overall control structure is the first problem faced by many designers. Each conventional nonlinear design method has its own merits and drawbacks. The design of hybrid fuzzy controllers can be viewed as using conventional control methods to facilitate FLCs design or incorporating FLCs into conventional control structure so as to enhance the power of conventional design method. In either point of view, the contradiction between conventional functions and fuzzy systems has to be solved in order to integrate the design. Second, Partitioning the control space or the fuzzification problem consists of three aspects, namely what kind of MFs should be used, where the MFs should be located and how many MFs should be used. There are no standard answers to the first two questions. However, for control problems in control system, the reference trajectory may guide us to a fairly good fuzzification of signals. As to the third question, it is common sense that the more MFs and rules are used, a better fuzzy controller will be obtained. Theoretically, by firing a very large number of fuzzy rules, a fuzzy system can be viewed as a universal approximator on a compact set of arbitrary accuracy [125] and an FLC can generate perfect control actions for any dynamic systems. Obviously, such kind of design is impractical due to either the tuning problem of design parameters or limitations of hardware implementation. Construction of a fuzzy rule base by using a limited number of rules to approximate the input-output relationship of a FLC with a high degree of accuracy is always a challenging task.

In a hybrid fuzzy controller, not only parameters of the FLC need to be designed, but also the gains of the conventional controller need to be tuned. A self-tuning PI-type fuzzy plus PI can be developed by applying a tuning algorithm to directly adjust the following: 1) the rules; 2) the MFs; and/or 3) the scaling gains. Techniques to tune the scaling gains in real time have received the highest priority in literature due to the influence of the gains on the performance and stability of the system [63, 126].The real-time tuning of the scaling gains is necessary in order to maintain the desired performance of the drive. In order to satisfy both dynamic and static state performances, a supervised MRAS-based STFC is implemented in [79], and self-tuning gain fuzzy PI controller scheme with conditional integration is proposed in [47].

## 4.1. Design PI-type FLC

Typically, the design of a FLC starts with a linguistic description of the control strategy, in the form of IF (condition) THEN (action) rules, that relate some process states (e.g., error and error change) to the appropriate control action. The next step consists in deriving a quantitative description of the linguistic variables, in the form of fuzzy sets. The design procedure is completed by selecting an inference method that defines how the set of control rules (rule base) is evaluated to yield the control action for a particular process state [71].

The design of fuzzy controller essentially consists of knowledge base design that includes formulation of membership function (MF) shape and its distribution for the fuzzy variables, the rule matrix design, and number of linguistic rules. It can be shown that MFs play important role in the performance of fuzzy control system. It is well-known that fuzzy control design essentially embeds the behavioral nature of the plant that is evidenced by the experience and intuition of a plant operator, and sometimes those of a designer and/or researcher of the plant. Therefore, fuzzy controller design is somewhat heuristic, i.e., depends on trial-and-error procedure [69]. Unfortunately, optimal design of fuzzy controller by such heuristic procedure may become time-consuming. A number of techniques have been suggested in the literature to alleviate this problem [127-132].

Unfortunately, such elegant techniques are complex that tend to mask the simplicity of fuzzy control and contribute time delay when attempted for real-time control. By far, the majority of applications yet use manual trial-and-error design of the fuzzy controller. Of course, if mathematical model of the plant is available, the system can he simulated on computer and the control design can be iterated by using tools, such as MATLAB based Fuzzy Logic Toolbox [133].

## 4.2 Selecting MFs and scaling gains

Figure 11 shows the block diagram two-dimensional fuzzy PI controlled induction motor drive with indirect vector control. The speed control loop of the drive generates two control signals for the fuzzy control, i.e., the loop error (E) and change in error (CE) by differentiating the E signal. These signals are then converted to per unit (pu) signals e and ce by dividing with the respective scale factors GE and GC. The per unit (pu) or normalized defination of universe of discourse has the advantages that the design is simple and intuitive, and the same fuzzy control algorithm is applicable for all the scaled systems except that the gain factors GC, GE and GU require modification in individual case. The IM magnetization and starting procedures are used in [74] to select the best scaling gains of an FLC. However, if subjected to severe perturbations, the control may require online tuning of its parameters.

A priori determination of membership function shape and its optimum distribution is the best for fast, simple and effective design of fuzzy controller [69]. Triangular type MF is the best for fuzzy controlled drive system [69, 134]. Symmetrical distribution of MFs with number of fuzzy sets (N=7) is the optimal case and asymmetrical distribution of MFs with both convergent and divergent type asymmetry is optimal when the loop error (e) signal MFs has high degree of convergence, the error rate (ce) MFs has medium degree of convergence and the output signal (du) MFs has divergence. All the fuzzy variables (e, ce and du) may not necessarily use the same membership functions [69]. However, Conventional triangular membership functions used in fuzzy inference systems can be modified for improving the system performance [135].

Figure 11: Fuzzy logic controlled induction motor drive with indirect vector control

## 4.3 Selecting rules type and defuzzification method

The well-known Mamdani type fuzzy inferencing method has been used in all the cases [69]. A special design of fuzzy rule base is proposed in [76] with rather promising results. The fuzzy rule base for the PI fuzzy controller with 49 rules as shown in table1 can be selected and the fuzzy inference used is Mandani type using max- min composition [59]

Table 1: fuzzy PI rule base with 49 rules

The defuzzification method used in the system is based on center of area (COA) method [136] rather than center of heights (COH) [137] or center average defuzzification [138] that was used in [62, 64, 139]. The COH method is a convenient way to obtain output solution with least number of expressions. However, the COH method ignores the effect of fuzziness [140] associated with the output linguistic variables and is equivalent to taking fuzzy singleton functions. On the other hand COH is better for obtaining piece wise linearity. For high degree of nonlinearity, it requires a large number of rules. This particular characteristics has been exploited to obtain the nonlinear function approximations [138], but at the expense of larger number of rules. However the COG method is difficult to analyze for a highly nonlinear rule bases. The fuzzy controller output is denormalized and integrated to establish the active current of the vector-controlled drive as shown in Figure 4.

## 5. CONCLUSIONS

This paper has reviewed vector control methods and techniques for induction motor drives. Basic principles and the recent developments in these control schemes have been discussed systematically in this paper. Recently most of the speed controllers of IM drives have been designed by hybrid fuzzy. Therefore this report reviews the methods trends of electric drive control that relate to speed controller and its design to having high performance and robustness of induction motor derives. As the performance of the vector control scheme of induction drive is sensitive to parameter variation different new control techniques like the PI-type fuzzy plus PI with adaptive methods offer interesting perspective for the future research which is robust to parameter variation. At present, these new techniques are alternative solution to the conventional control techniques.