# Design Simulation Of Takagi Sugeno FLC Computer Science Essay

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In this chapter, a novel design of a Takagi-Sugeno based fuzzy logic control scheme for controlling some of the parameters, such as speed, torque, flux, voltage and current, etc. of the induction motor is presented.

Fuzzy logic based controllers are considered as potential candidates for the control of industrial drives. In this context, a novel fuzzy logic controller is developed based on the Takagi-Sugeno principles. This method yields excellent results compared to the other methods such as the PI method or the Mamdani based FLC method. Hence, this TS based FL control design becomes a hybrid method of control approach for the control of IM. Such a hybrid combination leads to a more effective control design with improved system performance.

Due to the usage of the Takagi Sugeno concepts in the design of the fuzzy controller in closed loop with the plant, the dynamic characteristics of the AC drive increases. The developed strategy does not require the mathematical model of the controller unlike that of the conventional electrical drive controller, which uses the mathematical model. The sudden fluctuation/ change/ variation in speed from one value to another & its effect on the various parameters of the dynamic system are also considered, thus exhibiting the robustness behavior.

The designed controller not only takes care of the sudden perturbations in speed, but also brings back the parameters to the reference or the set value in fraction of seconds. In other sense, the designed controller is robust to parametric variations. The closed loop speed control of the induction motor using the above technique thus provides a reasonable degree of accuracy which can be observed from the simulation results depicted at the end of this chapter.

The structure of the work presented in this chapter is organized in the following sequence. An introduction about this chapter is given in section 6.1. A brief review of the Takagi-Sugeno based FLC & its design is presented in section 6.2. Controller design is presented in section 6.3. The section 6.4 shows the development of the Simulink model for the speed control of the induction motor. The graphical results of the simulation & the discussion are presented in section 6.5 Further, the justification of robustness is dealt with in greater detail in section 6.6. This is followed by the conclusions in the section 6.7.

## 6.1 Introduction

The design and implementation of industrial control systems often relies on quantitative mathematical models of the plants (say, induction motors, generators, DC motors, etc), the controllers, etc. Induction motors (type of AC motor) play a vital role in the industrial sector especially in the field of electric drives & control and are used in the work undertaken in this chapter. Without proper controlling of the speed, it is virtually impossible to achieve the desired task for a specific application. AC motors, particularly the squirrel-cage induction motors (SCIM), enjoy several inherent advantages like simplicity, reliability, low cost and virtually maintenance-free electrical drives.

However, for high dynamic performance industrial applications, their control remains a challenging problem because they exhibit significant non-linearity and many of the parameters, mainly the rotor resistance, vary with the operating conditions [Error: Reference source not found]. Many times, various problems are encountered during the controller design process and if the order of the designed controller is very high, then it may become very difficult to implement it in real time and hence it becomes more expensive. Sometimes, it becomes very difficult to obtain a mathematical model of the controller. In addition, usual computation of system mathematical model is difficult or impossible.

To obtain the exact mathematic model of the system, then one has to do some identification techniques such as the system identification & obtain the plant model. In such cases, it is often necessary to observe human experts or experienced operators of the plants or processes and discover rules governing their actions for automatic control [Error: Reference source not found] using AI based techniques. In this context, the fuzzy logic concepts play a very important role in developing the controllers for the plant as this controller uses only some set of rules. Consequently, performance deteriorates and a conventional controller such as a PID is unable to maintain satisfactory performance under these conditions. Recently, there has been observed an increasing interest in combining artificial intelligent control tools with classical control techniques [Error: Reference source not found].

Fuzzy logic concept was introduced by Lotfi. Zadeh in 1965. Many researchers used this FLC concept developed by Zadeh to develop controllers for their applications, which had yielded good results. Thus, this FLC concept remained as a popular control scheme in the control world even today. The recent years have witnessed rapidly growing popularity of fuzzy control systems in engineering applications. The numerous successful applications of fuzzy control have sparked a flurry of activities in the analysis and design of fuzzy control systems [Error: Reference source not found]. In the last few years, fuzzy logic has met a growing interest in many motor control applications due to its non-linearity handling features and independence of the plant modeling.

Fuzzy Logic control (FLC) has proven effective for complex, non-linear and imprecisely defined processes for which standard model based control techniques are impractical or impossible[Error: Reference source not found]. Fuzzy Logic, deals with problems that have vagueness, uncertainty and use membership functions with values varying between 0 and 1 [Error: Reference source not found]. This means that if the reliable expert knowledge is not available or if the controlled system is too complex to derive the required decision rules, development of a fuzzy logic controller become time consuming and tedious or sometimes impossible.

If the expert knowledge of the system is available, then the fine-tuning of the controller might be time consuming process. Of course, this fine tuning might yield excellent result [Error: Reference source not found]. Furthermore, an optimal fuzzy logic controller cannot be achieved by trial-and-error. These drawbacks have limited the application of fuzzy logic control [Error: Reference source not found].Some efforts have been made to solve these problems and simplify the task of fuzzy control [Error: Reference source not found]. These approaches mainly use adaptation or learning techniques drawn from artificial intelligence.

However, there is no systematic method for designing and tuning the fuzzy logic controller & one has to design using some trail & error using the IF-THEN-ELSE rules. Since, the induction motor is a complex non-linear system, the time-varying parameters entail an additional difficulty during the controller design [Error: Reference source not found].

A brief review of the research works done by various authors using scalar control, vector or field-oriented control (FOC), direct torque and flux control, PI control, PID control, sliding mode control, and the adaptive controls was discussed in chapter 1 along with their advantages & disadvantages. A sincere attempt is made to overcome some of the drawbacks & difficulties which were encountered while designing the controllers as observed in the previous paragraphs by various researchers using the Takagi-Sugeno based fuzzy concepts. Here, we have formulated a novel control strategy using the Takagi-Sugeno based fuzzy scheme for the speed control of IM, which has yielded excellent results [Error: Reference source not found], which is the main contributed work of this chapter. The results of our work have shown a very low transient response and a non-oscillating steady state response with excellent stabilization.

## 6.2. Review of Takagi- Sugeno fuzzy control

In this section, a brief review of the Takagi and Sugeno control strategy to control various system parameters of the plant is presented.

Takagi and Sugeno [Error: Reference source not found],[Error: Reference source not found],[Error: Reference source not found] proposed a new type of fuzzy model (TS model) which has been widely used in many of the industrial applications, especially in the control of dynamical systems, such as AC motors, DC motors, etc [Error: Reference source not found],[Error: Reference source not found]. This fuzzy model is described by IF-THEN fuzzy rules which represent local linear input-output relations of a non-linear system.

The main feature of a Takagi-Sugeno fuzzy model is to express the local dynamics of each fuzzy implication (rule) by a linear system model. The overall fuzzy model of the system is achieved by fuzzy "blending" of the linear system models. These TS models use fuzzy rules with fuzzy antecedents and functional consequent parts, thereby qualifying them as mixed fuzzy or non-fuzzy models [Error: Reference source not found]. Such models can represent a general class of static or dynamic non-linear mappings via a combination of several linear models.

In short to say, the TS model represents a general class of non-linear systems & is based on the fuzzy partition of input space and can be viewed as a expansion of piecewise linear partitions. The whole input space is decomposed into several partial fuzzy spaces and each output space is represented with a linear equation [Error: Reference source not found].

Hence, this class of fuzzy models should be used when only performance is the ultimate goal of predictive modeling. In this context, the TS control model which is being used by us to design the controller for the speed control of induction motor is explained as follows. In general, TS models are represented by a series of fuzzy rules of the form [Error: Reference source not found]

Fuzzy models relying on such rules are referred to as singleton fuzzy models [Error: Reference source not found]. This class of fuzzy models can employ all the other types of fuzzy reasoning mechanisms, because they represent a special case of each of the above-described fuzzy models. Parameter varying systems which possess m working state characteristic variables, q inputs and single output can be described by the TS fuzzy model consisting of R rules, where the ith rule can be represented as [Error: Reference source not found].

where, R is the number of rules in the TS fuzzy model, zj(j = 1, 2, 3, Î»,â€¦..,m) is the jth characteristic variable, which reflects the working state of the systems and can be selected as input, output or other variables affecting the parameters of the system dynamics. Here, xl(l = 1, 2, 3, Î»,.â€¦.., q) is the lth model input and yi is the output of the ith rule. For the ith rule, is the fuzzy sub-set of zj. Here, is the coefficient of the consequent terms & rj is the fuzzy partition number of zj.

For simplicity of induction, we let rj = r, and r is determined by both the complexity and the accuracy of the model. Once a set of working state variables (z10, z20,.. Î».., zm0) and the model input variables (x10, x20, ..Î»,..xq0) are available, then the output of the TS model under such working states can be calculated by the weighted-average of each yi as [Error: Reference source not found]

Where yi is determined by consequent equation of the ith rule. The truth-value Î¼i of the ith rule can be calculated as [Error: Reference source not found].

Furthermore, Eq. (6.3) can be rewritten as [Error: Reference source not found].

Which is nothing but the final output of the system and is the weighted average of all the rule outputs (from i to R). From Eq. (6.1), one can see that the TS fuzzy model can be expressed as an ordinary linear equation under certain working states, since the truth-value Î¼i is only determined by the working state variables. As Î¼i varies with the working state, TS fuzzy model becomes a coefficient-varying linear equation. For all possible varying ranges of the various parameters, the TS fuzzy model reflects the relationships between these model parameters and the working states. Thus, the global dynamic characteristics of the parameter varying systems can be represented using the TS fuzzy approach [Error: Reference source not found].

In chapter 5, the design of controllers using Mamdani based FLC was presented, whereas in this section the design of controller using the Takagi-Sugeno based FLC is presented. The main differences between the controller presented in chapter 5 & the one that is presented in this chapter is that the TS output membership functions are either linear or constant, whereas in Mamdani, it is non-linear in nature. Also, the difference lies in the consequents of their fuzzy rules, and thus, their aggregation & de-fuzzification procedures differ suitably. The number of the input fuzzy sets and fuzzy rules needed by the TS fuzzy systems depend on the number & locations of the extrema of the function to be approximated.

In TS method, a large number of fuzzy rules must be employed to approximate periodic or highly oscillatory functions. The minimal configuration of the TS fuzzy systems can be reduced & becomes smaller than that of the Mamdani fuzzy systems. TS controllers usually have far more adjustable parameters in the rule consequent & the number of parameters grows exponentially with the increase of number of input variables.

Far fewer mathematical results exist for TS fuzzy controllers than do for Mamdani fuzzy controllers, notably those on TS fuzzy control system stability. Mamdani's approach of designing controller for the plant is easy compared to the TS method. For Mamdani fuzzy models the de-fuzzification process may be time-consuming and systematic fine tuning of the parameters is not easy [Error: Reference source not found].

For TS based fuzzy logic controllers, it is hard to assign appropriate linguistic terms. Readability and performance thus appear as antagonist objectives in fuzzy rule-based systems. Because the TS model is more compact and computationally efficient representation than a Mamdani system, it lends itself to the use of adaptive techniques for constructing more complicated fuzzy models. These adaptive techniques can be used to customize the membership functions so that the fuzzy system best models the data.

## 6.3. TS Based Controller Design

In this section, the design of the controller is presented. Note that it can be a hardware or a software unit (or both) which controls each & every operation in the system making decisions. From the control system point of view, it is bringing stability to the system when there is a disturbance, thus safeguarding the equipment from further damages. In this context, the development of the control strategy for control of various parameters of the induction machine such as the speed, flux, torque, voltage, current is presented, the designed control strategy using the concepts of Takagi-Sugeno based fuzzy control scheme, the block diagram of which is shown in the Fig.6.1.

To start with, we design the controller using the TS scheme based FL controller. Fuzzy logic is one of the successful applications of fuzzy set in which the variables are linguistic rather than the numeric variables. Linguistic variables, defined as variables whose values are sentences in a natural language (such as large or small), may be represented by the fuzzy sets. Fuzzy set is an extension of a `crisp' set where an element can only belong to a set (full membership) or not belong at all (no membership). Fuzzy sets allow partial membership, which means that an element may partially belong to more than one set.

A fuzzy set 'A' of a universe of discourse X is represented by a collection of ordered pairs of generic element xÎµX and its membership function Î¼: Xâ†’[0 1], which associates a number Î¼A: Xâ†’ [0 1], to each element x of X. A fuzzy logic controller is based on a set of control rules called as the fuzzy rules among the linguistic variables. These rules are expressed in the form of conditional statements. Our basic structure of the fuzzy logic coordination controller to control the speed of the IM consists of 3 important parts, viz., fuzzification, knowledge base-decision making logic (inference system) and the de-fuzzification, which are explained in brief in further paragraphs.

The inputs to the FLC, i.e., the error & the change in error is modeled using the Eqs.(6.6)& (6.7) as

e(k) = Ï‰ref - Ï‰r, (6.6)

âˆ† e(k) = e(k) - e(k - 1), (6.7)

where Ï‰ref is the reference speed, Ï‰r is the actual rotor speed, is the e(k) error and âˆ†e(k) is the change in error.

The internal structure of the fuzzy coordination unit with the TS control scheme is shown in the Fig.6.1. The necessary inputs to the decision-making unit blocks are the rule-based units and the data based block units. The fuzzification unit converts the crisp data into linguistic variables. The decision making unit decides in the linguistic variables with the help of logical linguistic rules supplied by the rule base unit and the relevant data supplied by the data base. The output of the decision-making unit is given as input to the de-fuzzification unit and the linguistic variables are converted back into the numeric form of data in the crisp form.

The decision-making unit uses the conditional rules of `IF-THEN-ELSE', which can be observed from the algorithm mentioned in the algo for developing the fuzzy rules below. In the fuzzification process, i.e., in the first stage, the crisp variables, the speed error & the change in error are converted into fuzzy variables or the linguistics variables. The fuzzification maps the 2 input variables to linguistic labels of the fuzzy sets. The fuzzy coordinated controller uses the linguistic labels. Each fuzzy label has an associated membership function which can be observed in the fuzzy editor tool box window. The inputs are fuzzified using the fuzzy sets & are given as input to fuzzy controller.

The same rule base shown in the table 5.1 in chapter 5 in section 5.2, which was used for the Mamdani based FLC for the decision-making purposes is used in this chapter for the decision making purposes for designing of the TS based FL controller 5.2. Also, the developed TS based fuzzy rules (7Ã-7 = 49) included in the fuzzy coordinated controller is shown in the form of an algorithm in chapter 5 in section 5.2. The same 49 rules can be used here for the control purposes & is not shown here for the sake of convenience.

The control decisions are made based on the fuzzified variables. The inference involves a set of rules for determining the output decisions. As there are 2 input variables & 7 fuzzified variables, the fuzzy logic coordination controller has a set of 49 rules for the fuzzy logic based TS controller. Now, the 49 output variables of the inference system are the linguistic variables and they must be converted into numerical output, i.e., they have to be defuzzified. In our work, we use the centre of gravity (CG) method for the de-fuzzification process.

The output of the de-fuzzification unit will generate the control commands which in turn is given as input (called as the crisp input) to the plant through the inverter. If there is any deviation in the controlled output (crisp output), this is fed back & compared with the set value & the error signal is generated which is given as input to the TS-fuzzy controller, which in turn brings back the output to the normal value, thus maintaining stability in the system. Finally, the controlled output signal, i.e. y is given by Eq. (6.5).

This controlled output y is nothing but the final output of the controller and is the weighted average of all the rule based outputs. From Eq. (6.5), one can see that the TS fuzzy model can be expressed as an ordinary linear equation under certain working states since the truth-value Î¼i is only determined by the working state variables. The main advantage of designing the TS based fuzzy coordination scheme in this paper is to control the speed of the IM to increase the dynamic performance & to provide good stabilization.

## 6.4 Development of the Simulink model

The block model of the induction motor system with the controller was developed using the power system, power electronics, control system, signal processing toolboxes & from the basic functions available in the Simulink library in MatLab/Simulink & is shown in the Fig. 6.2. In this section, plots of voltage, torque, speed, slip, current, load & flux, etc are plotted as functions of time with the controller and the waveforms are observed on the corresponding scopes after running the simulations.

The IM system is modeled in Simulink along with the controller. The developed Simulink model is a closed loop feedback control system & consisting of the plants, controllers, samplers, comparators, feedback systems, constants, the mux, de-mux, summers, adders, gain blocks, multipliers, clocks, sub-systems, integrators, state-space models, the output sinks (scopes), the input sources, etc. The specifications of the SCIM used for simulation purposes are given in the chapter 7.3.

## 6.5 Simulation results & discussions

Simulink model with the controller for the speed control of IM was developed in Matlab 7 as shown in the Fig. 6.2 In order to start the simulations, the fuzzy rule set has to be invoked first from the command window. Initially, the fuzzy file where the rules are written with the incorporation of the TS algorithm is opened in the Matlab command window, after which the fuzzy editor (FIS) dialogue box opens.

The .fis file is imported using the command window from the source file & then opened in the fuzzy editor dialog box using the file open command. Once the file is opened, the TS-fuzzy rules file gets activated as shown in the Fig. 6.3.

Further, the data is exported to the workspace & the simulations are run for a specific amount of time (say 2 to 3s). The fuzzy membership function editor is then obtained using the view membership command from the menu bar and this is shown in the fig 6.4. The written 49 TS-fuzzy rules can be viewed from the rule view command. The rule viewer for the 2 inputs and 1 output can also be observed pictorially in the fuzzy editor tool box.

The surface plot for the error in speed & change in error with the output is shown in the Fig. 6.5.

Now, after viewing all the preliminary steps, the simulations are run for a period of 3 seconds in Matlab 7 with a reference speed of 100 rads / sec rpm & with a load torque of 2 N-m. While the simulation is run, the 2 fuzzy inputs are then given to the controller (Takagi-Sugeno-fuzzy) as shown in the Fig. 6.3, where the controller output is obtained thereafter. Note that in this TS based fuzzy controller (which consists of 3 basic blocks viz., fuzzification, inference, and the de-fuzzification blocks) the set of 49 fuzzy rules are called in the form of a file. After the simulation is run, the performance characteristics are observed on the respective scopes. The response curves of flux, load, torque, terminal voltage, speed, stator currents, slip, id, iq, rotor currents (3 ï„‚ & d-q) v/s time, slip vs. speed, torque vs. slip are observed on the respective scopes & are shown in the Figs. 5.6 to 5.16 respectively.

From the simulation results shown in the Figs. 6.6 to 6.16, it is observed that the stator current does not exhibit any overshoots nor undershoots. The response of the flux, slip, torque, terminal voltage, speed, currents, etc. takes lesser time to settle & reach the desired value compared to the results presented in [Error: Reference source not found].

It was observed in [Error: Reference source not found] using the Mamdani control strategy for the same set speed & the 49 fuzzy rules, the speed reaches its desired set value (becomes stable) at 1.4 seconds, whereas in this chapter using the TS-fuzzy control for the same mathematical model & for the same set speed of 100 rad/sec & for the same 49 rules, the speed reaches its desired set value at 0.7 seconds as shown in the Fig. 6.6.This shows the effectiveness of the developed controller. It is also observed that with the controller, the response characteristics curves take less time to settle & reach the final steady state value compared to that in [Error: Reference source not found]. The motor speed increases like a linear curve up to the set speed of 955 rpm in 0.7 secs.

From the variation of flux with time as shown in the Fig.6.7, it can be observed that when the motor speed is increasing (during the transient period), more stator current is required to develop the requisite flux in the air gap. Hence, the flux also starts increasing during the transient period (0 to 0.7 sec) exponentially. Once, the motor attains the set rated speed, the flux required to develop the torque almost remains constant after â‰¥ 0.7 secs. Once, the saturation of the flux takes place in the air gap, the variation of the load torque and speed will not disturb the flux curve. Hence, the IM will be operating at a constant flux.

Torque characteristics for a set reference speed of 100 rad/sec (955 rpm) are shown in the Fig. 6.8. From this figure, we arrive at a conclusion that when the motor is operating at lower speeds, the slip is more. Hence, the machine requires more torque to attain the set speed. Once the machine reaches the set speed of 955 rpm the average torque of the machine becomes nearly zero, which is justified from the simulation result in Fig. 6.8.

The terminal voltage of the IM is shown in Figs. 6.9 (a) & 6.9(b) respectively. The load is set to 2 N-m throughout the simulation & is kept constant.

The variation of the 3ï„‚ stator currents (is-abc) with time is shown in the Fig. 6.10. It can be clearly observed from this figure, that at lower speeds, the slip is more, the flux required to develop the suitable torque is also more. Also, the torque required to reach the set speed is also more. Hence, the magnitude of the stator currents will also be more during the transient periods (starting periods) of the induction motor. When the speed is reaching the set value from zero, then the 3ï„‚ stator currents decreases exponentially. Once, it attains the set speed at 0.7 secs, it requires a nominal stator current to drive the IM system.

The Fig. 6.11 shows the variation of slip vs. time characteristics for a speed of 100 rad/sec (955 rpm). From this simulation result, we infer that the IM attains the set reference speed of 955 rpm in 0.7 secs using the TS based fuzzy controller. At that instant, the slip being , which can be verified from the result shown. Note that the slip decreases from 1.0 to 0.46 linearly in a time span of just 0.7 secs.

The slip-speed characteristics are shown in the Fig. 6.12. It can be noted that when the speed is varied from 0 to the rated speed, the slip decreases, i.e., the slip is inversely proportional to the speed, which is the property of the IM. When the speed is zero, the slip is 100 %, while the IM is operating at near the rated speed (180 rad/sec ), the slip is very low (0.46).

The plots of the direct axes (id) & quadrature axes currents (iq) versus time is shown in the Figs. 6.13 & 6.14 respectively. From these figures, it can be inferred that the machine reaches the set reference speed of 955 rpm in a time interval of 0.7 secs.

The variation of the 3ï„‚ rotor currents (ir-abc) with time is shown in the Fig. 6.15. It can be inferred that at lower speeds, the slip is more, the flux required to develop the suitable torque is also more. Also, the torque required to reach the set speed is also more. Hence, the magnitude of the rotor currents will also be more during the transient periods (starting periods) of the induction motor. When the speed is reaching the set value from zero, then the 3ï„‚ rotor currents decreases exponentially.

The 3ï„‚ rotor currents (ir-abc) is transformed to direct axes & quadrature axes currents using the d-q transformation techniques and the variation of the transformed currents with time is shown in the Fig. 6.16. Here, only two phases (d & q axes) of the currents can be observed in the characteristic curve. In this case, also, once the motor achieves the set speed at 0.7 secs, it requires a nominal current to drive the IM system.

## 6.6 Justification of robustness issues

Another important significant contribution of this controller is that, the designed controller can also be used for variable speed also. When the system is in operation (when the simulations are going on), due to sudden changes in set speed (say, the set speed immediately changed from 100 to 140 or anything else & then suddenly decreasing the speed back to normal), with the incorporation of the designed controller in loop with the plant, the system comes back to stability within a few milliseconds (ms), which can be observed from the simulation results.

The simulation results due to the parametric variations of speed from 100 to 140 and then back to normal are shown in the Figs. 6.17 to 6.22 respectively. It is clearly observed from these simulation results that with the developed robust controller, the dynamic performance of the system is quite improved, insensitive to parametric variations with the incorporation of the TS based fuzzy coordination scheme. Further, it can be also concluded that even though that some of the motor parameters are non-linear, it looks like linear in nature.

From the simulation result shown in the Fig. 6.17, it can be observed that when the speed is varied from 100 to 140 rad/sec at say t = 1 s, the motor takes very less time to reach the new set speed point (140 rad/sec) to become stable. Again when the IM is running at 140 rad/sec, the speed is suddenly varied from 140 to 100 rad/sec at say t = 1.7 s, the motor takes very less time to reach the new set speed point (100 rad/sec) to become stable as shown in the Fig 6.17 . From this, it can be observed that the speed of the IM is robust (insensitive) to sudden changes in the speed, which is because of the TS based fuzzy controller.

The torque vs. time for variation in speed from 100 to 140 rad/sec & back to 100rad/sec is shown in the Fig. 6.18. It can be seen that when the speed of the IM is increasing from 0 to the set value (100 rad/sec), the torque is required to reach the set speed in high. After the motor reaches the set speed of 100 rad/sec, the average torque required to run the motor at the set speed of 100 rad/sec will be zero between the period from t = 0.7 sec to 1.0 sec. Now, if the speed is suddenly increased from 100 to 140 rad/sec, again the torque requirement is also high between the period from t = 1.0 sec to1.2 sec.

After the motor reaches the new set speed of 140 rad/sec, the average torque required to run the motor at the new set speed of 140 rad/sec will be zero between the period from t = 1.2 sec to 1.7 sec. Now, if the speed is suddenly decreased from 140 to 100 rad/sec, the torque requirement is less between the period from t = 1.7 sec to 2.2 sec. After the motor reaches the original set speed of 100 rad/sec, the average torque required to run the motor at the original set speed of 100 rad/sec will be zero from t = 2.2 sec onwards.

The plot of the 3ï„‚ stator currents (is-abc) with time for the variation in speed from 100 to 140 rad/sec & back to normal is shown in the Fig.6.19. There is a change in the stator current variation during the change in speed from one value to another. Once the stable point is reached, the stator current becomes normal.

One observation that can be made in the flux characteristics during the change in speed is that, during the speed variation, the flux varies slightly which is shown in the Fig. 6.20.

The load torque is set at a constant value of 2 N-m throughout the process of simulation at the time of change in speed, which can be seen in the Fig. 6.21.

Another significant contribution presented in this chapter is the slip characteristic curves for variable speed of the IM. The speed is varied from 50 rads / sec (477 rpm) to near the rated speed of 180 rads / sec (1717 rpm). For the sake of convenience, 4 cases of variation in speed are considered, viz., 50 rad/sec(477 rpm), 100 rad/sec(955 rpm), 140 rad/sec(1335 rpm), 188.5 rad/sec(1717 rpm). The simulation is run for a period of 3 secs & the quantitative results of the slip vs. time for various speeds are shown in the table 6.1 along with the simulation results in Fig. 6.22.

From these results, we infer that the slip is more for low speed operation of the induction motor & it is very less when the IM is operating at near the rated speeds. Also, the slip characteristics looks like linear in nature due to the incorporation of the TS based fuzzy controller, which is the highlight of this simulation result.

## 6.7 Conclusions

A systematic approach of achieving robust speed control of an induction motor drive by means of Takagi-Sugeno based fuzzy control strategy has been investigated in this chapter. Simulink model was developed in Matlab 7 with the TS-based fuzzy controller for the speed control of IM. The control strategy was also developed by writing a set of 49 fuzzy rules according to the TS control strategy's algorithm.

The main advantage of designing the TS based fuzzy coordination scheme to control the speed of the IM was to increase the dynamic performance & provide good stabilization. Simulations were run in Matlab 7 & the results were observed on the corresponding scopes. The characteristic curves of speed, torque, current, flux, slip, load, etc. vs. time were observed. The outputs take less time to stabilize, which can be observed from the simulation results.

Due to the incorporation of the TS based fuzzy coordination system in loop with the plant, it was observed that the motor reaches the set speed very quickly in a lesser time, i.e., only 0.7 secs to reach the set speed (100 rpm). The performance of the developed method in this chapter also demonstrates the effectiveness of the sudden variation of speed (because of parametric variation) from the normal value & its effects on the various parameters (such as slip, current, torque, etc.) to obtain the stability. Simulation results demonstrate the good damping performance of the designed robust controller even in spite of speed fluctuations.

The simulation results show that the TS-fuzzy controller provides faster settling times, has very good dynamic response & good stabilization. The main advantages of the designed TS based fuzzy scheme being, it is computationally efficient, works well with linear techniques, works well with optimization and adaptive techniques & has guaranteed continuity of the output surface. To achieve still better performance of the controller, a new type of controller called as the adaptive neuro fuzzy based controller can be used to control the speed of the IM, which & is depicted in the further chapter.