28-01-2013, 04:09 PM
A Comparative Study of Neural networks and Fuzzy Systems in Modeling of a Nonlinear Dynamic System
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Abstract.
The aim of this paper is to compare the neural networks and fuzzy modeling
approaches on a nonlinear system. We have taken Permanent Magnet Brushless Direct Current
(PMBDC) motor data and have generated models using both approaches. The predictive
performance of both methods was compared on the data set for model configurations. The paper
describes the results of these tests and discusses the effects of changing model parameters on
predictive and practical performance. Modeling sensitivity was used to compare for two methods.
Introduction
Building models of real systems is a central topic
in many disciplines of engineering and science.
Models can be used for simulations, analysis of
the system's behavior and for a better
understanding of the underlying physical
mechanisms in the system. In control
engineering, a model of the plant can be used to
design a feedback controller or to predict the
future plant behavior in order to calculate
optimal control actions [1].
Many of the recent developed computer
control techniques are grouped into a research
area called Intelligent Control, that result from
the integration of Artificial Intelligent techniques
within automatic control systems [2].
There is currently a significant and growing
interest in the application of Artificial
Intelligence (AI) type models to the problems
involved with modeling the dynamics of
complex, nonlinear processes.
Experimental setup of modeling system
MCK243 kit is a complete motion structure, including a power amplifier and a motor,
thus offering the basic platform for motion applications evaluation. The MCK243 kit includes such a power module and a three phase brushless motor. TMS320F243 programs for DC brushless motor speed control. The MC-BUS connectors include the basic I/O signals required in standard motion control applications with DC, AC or step motors.
The BLDC application control scheme is based on the measurement of two phase currents and of the motor position. The speed estimator block is a simple difference block. The measured phase currents, ia and ib, are used to compute the equivalent DC current in the motor, based on the Hall sensors position information. Remark that the Hall sensors give 60 electrical degrees position information. The speed and current controllers are PI discrete controllers. Only one current controller is needed in this case, similar to a DC motor case. The voltage commutator block implements (by software) the computation of the phase voltages references, Vas*, Vbs* and Vcs*, applied to the inverter. Practically, the 6 full compare PWM outputs of the DSP controller are directly driven by the program, based on these reference voltages. In the BLDC case, only four of the inverter transistors are controlled for a given position of the motor. The scheme will commute to a specific command configuration, for each of the 60 degrees position sectors, based on the information read from the Hall sensors.
Modeling of the BLDC motor using ANN
Recently, neural networks have been shown to possess good approximation capability for a wide range of nonlinear functions and have been used in the modeling of nonlinear dynamic systems by many researchers [10-13]. By far the most common type of network used for dynamic modeling work is the backpropagation network, which gets its name from its learning strategy.
The ANN model used is a multilayer perceptron model, in which there is more than one layer between input and output. The backpropagation of the error algorithm used as the training algorithm is used for training of generalized delta rule. The training process of this ANN model is shown Figure 6 [4].
Results and Discussion
The modeling methods were tested using the BLDC data. This data consists of 42 samples of data. Each sample contains Kp, Ki inputs and Mo, Ts outputs. During this work the only the first 30 samples of data were used to train or identify the model, but performance comparison were carried out using all 12 samples. A program written in C++ language was used to generate the neural networks model and Matlab was used to generate the fuzzy model.
Conclusion
The neural networks and fuzzy modeling approaches for BLDC are carried out. The results presented show that both neural networks and fuzzy systems are able to produce accurate dynamic models of process response directly from I/O data (I: Kp - Ki, O: Mo - Ts). Fuzzy model and neural networks model are very similar, but model development is very simple with fuzzy models.
Applications of the two techniques to nonlinear system modeling demonstrate that both techniques are effective in modeling systems with major nonlinearities.