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In order to emulate a DC motor control, vector control strategy is employed to decouple flux and torque of an induction motor. The great advantage of this technique is that the induction motor can be controlled with the presentation of all of its properties such as high efficiency, robustness, low maintenance cost. The most widely employed controller is the conventional proportional integral (PI) controller. The limitation of PI controller can be overcome by introducing the concept of artificial intelligence. Literature survey indicates that the fixed gain controllers designed at nominal operation may fail to provide best control performance over a wide rage of operating conditions [90-95].
The design of these controllers depends on exact machine model and accurate model parameters. However, the difficulties of obtaining the exact parameters of the Induction motor lead to cumbersome design approach for these controllers. Moreover, the fixed gain PI controller is very sensitive to disturbance. On the other hand, the design of intelligent controllers such as fuzzy logic, neural network, neuro-fuzzy controllers, etc. do not need exact mathematical model of the system. Simplicity and less intensive mathematical design requirements are the main features of intelligent controllers, which are suitable to deal with nonlinearities and uncertainties of electric motors. Therefore, the intelligent controllers demand particular attention for high performance of drives. However, a simple fuzzy logic controller (FLC) has a narrow speed operation and needs much more manual adjusting by trial and error if high performance is needed. On the other hand, it is extremely tough to create a serial of training data for artificial neural network (ANN). Literature survey shows that a new design technique, that is, Adaptive Neuro-Fuzzy Inference System (ANFIS), is used for Fuzzy Logic Controller design. The tuning of fuzzy inference system is carried out by back propagation algorithm based on some collection of input-output data. This chapter focuses on the design of ANFIS based speed controller for vector controlled induction motor drive.
6.2. Back Propagation Algorithm:
In the field of electrical engineering, one of the most exciting and potentially profitable recent developments is the increasing use of artificial intelligence techniques like neural networks in the design of various controllers. Artificial neural networks have been applied to many problems, and have demonstrated their superiority over classical methods when dealing with noisy or incomplete data. Neural networks are well suited to this method, as they have the ability to pre-process input patterns to produce simpler patterns with fewer components. A fascinating feature of the brain is that its physical organization reflects the organization of the external stimuli that are presented to it. In view of this back propagation algorithm has been used to design controller. In this back propagation algorithm the weights from input layer-hidden layer-output layer are updated iteratively during the learning phase. The updation of weights in back-propagation algorithm is done as follows :
The error signal at the output of neuron at iteration is given by (6.1)
The instantaneous value of error for neuron is. This instantaneous value of total error is obtained by summing of all neurons in output layer
where includes all neurons in the output layer. Average squared error is given by
where is total number of patterns in training set. So minimization of is required. So, back propagation algorithm is used to update the weights. Induced local field produced at input of activation function is given by
where is the number of inputs applied to neuron . So the output can be written as
The back propagation algorithm applies a correction to synaptic weights which is proportional to partial derivative, which can be written as
Differentiating the equation (6.2) with respect to
Differentiating equation (6.1) with respect to
Differentiating equation (6.5) we get
Differentiating equation (6.4) with respect to
So using equations (6.7 - 6.10) in equation (6.6) we get
The correction applied to is defined by
where is learning rate parameter.
6.3. Fuzzy Logic Controller:
In the last few years the applications of artificial intelligent techniques have been opening doors to convert human experience into a form understandable by computers. Advanced control based on artificial intelligent techniques is called intelligent control. Fuzzy logic is a technique to apply human-like thinking into a control system. A fuzzy system can be designed to emulate human deductive thinking that is, the process people use to infer conclusions from what they know.
Fuzzy Logic Controller
Fig 6.1 Schematic diagram of the FLC building blocks
Fuzzy Logic Controller (FLC) is a rule-based controller. The structure of the FLC resembles that of a knowledge-based controller except that the FLC utilizes the principles of fuzzy set theory in its data representation and its logic. The basic configuration of FLC is simply represented in four parts, as shown in Fig 6.1. The various blocks of Fig 6.1 can be explained as follows
i. The fuzzifier
The fuzzifier is used to
Measure the values of input variables.
Perform a scale mapping that transforms the range of values of input variables into corresponding universe of discourse.
Perform the function of fuzzification that converts input into suitable linguistic values.
ii. The knowledge Base
It consists of data base and linguistic rule base
The data base provides necessary definitions which are used to define linguistic control rules and fuzzy data manipulation in an FLC.
The rule base characterizes the control goals and control policy of the domain experts by means of set of linguistic control rules.
iii. The Decision Making Logic
It is the kernel of FLC which has the capability of simulating human decision making based on fuzzy concept and of inferring fuzzy control actions employing fuzzy implication and the rules of the inference in fuzzy logic.
iv. The Defuzzification
A scale mapping which converts the corresponding universe of discourse into range of output variables.
Defuzzification, yields a non-fuzzy, control action from an inferred fuzzy control action.
But the main disadvantages of the Fuzzy logic controller is that it has a narrow speed operation and needs much more manual adjusting by trial and error if high performance is needed. So, new technique employing the combined properties of artificial neural networks ad fuzzy logic known as Adaptive Neuro Fuzzy Inference System (ANFIS) has been developed. The ANFIS employs the property of neural networks in order to develop a fuzzy inference system.
6.4. Adaptive Neuro Fuzzy Inference System:
The selection of the control variables (controller input and controller output) depends on the nature of the system to be controlled and the desired output. In this work reference speed ad actual speed have been considered as inputs ad torque has been considered as output. A normalization procedure has been followed in order to normalize the various input ad output values. The normalization formula used in this work is given by
Figure 6.2 shows the network structure of the ANFIS that maps the inputs by the membership functions and their associated parameters, and so through the output membership functions and corresponding associated parameters. These will be the synaptic weights and bias, and are associated to the membership functions that are adjusted during the learning process. The computational work to obtain the parameters and their adjustments is helped by the gradient descendent technique. As shown in Fig. 6.2 the layers are defined as follows :
Layer 1: Every node in this layer contains membership functions
Layer 2: This layer chooses the minimum value of two input weights
Layer 3: Every node of these layers calculates the weight, which is
Layer 4: This layer includes linear functions, which are functions of the
Layer 5: This layer sums all the incoming signals
6.4.1 Design of Adaptive Neuro Fuzzy Inference System:
In order to generate fuzzy system sixty five thousand data have been considered. Out of these sixty five thousand data, fifty thousand has been considered as training set data and remaining data has been considered as testing data. Since the ANFIS involves the combined properties of neural network and fuzzy logic, it provides a method for the fuzzy modeling procedure to learn information about a data set, in order to compute the membership function parameters that allow the associated fuzzy inference system (FIS) to track the give input/output data. In order to develop the FIS structure, a network type structure similar to that of neural network which maps inputs through input membership function and associated parameters and then through output membership functions and associated parameters to outputs can be considered. The parameters associated with the membership functions will change through the learning process. The computation of these parameters is done by a gradient vector, which provides a measure of how well the FIS system is modeling the input/output data for given set of parameters. In this work number of membership functions considered during the development of ANFIS is 7 and the number of epochs considered is 30. So, in this work in order to develop the FIS system reference speed and actual speed have been considered as inputs and torque has been considered as output. Fig 6.3 shows the various inputs and the outputs for the proposed ANFIS controller.
Fig. 6.3 Schematic of the proposed ANFIS controller
Fig 6.4 - Fig. 6.5 show the structure of various membership functions considered in the development of ANFIS controller for both the inputs. It can be seen that the seven membership functions considered in this work are negative large (nl), negative medium (nm), negative small (ns), zero (z), positive small (ps), positive medium (pm) and positive large (pl). Fig. 6.6 shows the various rules developed for the proposed ANFIS controller. It is to be noted that since seven membership functions have been considered for each input, as a result a total of 49 (7x7) rules have evolved. Fig 6.7 shows a 3-dimensional view of the ANFIS controller developed.
The block diagram of ANFIS and proposed HPWM based vector control of induction motor is shown in the Fig 6.8.
6.5 Simulation Results and Conclusions:
To validate the proposed ANFIS based vector controlled induction motor drive, numerical simulation studies have been carried out by using Matlab/Simulink. The simulation parameters and specifications of induction motor used in this thesis are given in Appendix - I. Various conditions such as starting, steady state, step change in load and speed reversal are simulated. The results for ANFIS and CSVPWM based vector controlled induction motor drive are given from Fig 6.9 - Fig 6.13.
The conventional design approach requires a deep understanding of the system, exact mathematical models and precise numerical values. The basic feature of ANFIS concept is that the process can be controlled with slight knowledge of its underlying dynamics. The control strategy learned through experience can be expressed by a set of rules that describe the behavior of controller using linguistic terms. Proper control action can be inferred from this rule base that emulates the role of human operator or a benchmark control action. To validate the proposed ANFIS controller, numerical simulation has been carried out and results are presented. From the results, it can be concluded that the proposed ANFIS controller gives good performance at all operating conditions with reduced complexity in the design procedure.