DC motors are often used in industrial processes and consumer products such as steel rolling mills, electric trains, and robotic manipulators where speed control is required. Proportional-Integral-Derivative (PID) controllers have been the conventional technique applied to control the speed of DC motors due to their simple concept, but their performances rely on exact mathematical model of the system to be controlled. This has led to the adoption of artificial intelligence techniques such as Neural Networks and Fuzzy Logic. Neural networks have the capability to learn from data but lack interpretability and the capability to incorporate prior knowledge. Fuzzy logic on the other hand has the capability to incorporate human knowledge but cannot learn beyond the knowledge incorporated by human experts thereby making the tuning of its parameters difficult.
The Adaptive Neuro Fuzzy Inference System (ANFIS) that combines the advantages of both techniques have been recently adopted for the speed control of DC motor. Most of the studies considered the Triangular membership function without a clear justification for the choice. This study filled such gap by considering different membership functions and comparing their performances.
Four ANFIS controllers were modeled using the same training data but different membership functions (triangular, trapezoidal, gaussian, generalized bell). The performances of the resulting controllers were evaluated based on parameters such as rise time, percentage overshoot, and settling time. The results obtained show that the control of speed by ANFIS generally gives fast dynamic response with minimal overshoot and negligible steady-state error.
It can be concluded that the ANFIS controller with Gaussian membership function performs better than others when there are no parameter uncertainties. However, one with Triangular membership function is more robust and its performance is not too affected by the variation of motor parameters. The results of this study will help guide researchers and practitioners on the choice of membership function suitable for speed control of DC motor.
- Background of the Study
DC motors, as components of electromechanical systems take electromotive force as the applied input and convert it into mechanical motion. The application of DC motors spans industrial processes and consumer products due to their simplicity, flexibility, reliability, and favourable cost. Most importantly, the speed of DC motors can be adjusted within wide boundaries thereby providing easy controllability and high performance in applications such as steel rolling mills, electric trains, and robotic manipulators where speed control is required (Mitter et al., 2012; Hameed and Mohamad, 2012; Mahajan and Deshpande, 2013).
Conventional controllers such as Proportional-Integral-Derivative (PID) controllers which are based on the relatively simple concepts of multiplication, integration over time, and rate of change over time have been applied to control the speed of DC motors. The drawbacks of conventional controllers are that they are sensitive to variation in motor parameters and load disturbances (George, 2008).Their performance depends on the accuracy of system models and parameters. Generally, an accurate non-linear model of an actual DC motor is difficult to find, and parameter values obtained from system identification may be approximated values (Tipsuwan and Chow, 1999; Mitter et al., 2012). Additionally, tuning of their parameters to obtain a desired result can sometimes be difficult.
Neural Networks controllers have emerged as a tool for difficult control problems of unknown nonlinear systems. Neural Networks (NN) are used for modeling and control of complex physical systems because of their ability to handle complex input-output mapping without detailed analytical models of the systems. Since Multilayer Neural Networks (MNN) can approximate arbitrary nonlinear mapping through a learning mechanism, they can compensate the nonlinearities. There are several control strategies for neural networks, they include: Feed forward control; Direct inverse control (extracting inverse dynamics); Indirect adaptive control method based on NN identification; Direct adaptive control with guaranteed stability; Feedback linearization; Predictive control (Norgaard et al., 2000; Choi et al., 2001).
Fuzzy logic, another Artificial Intelligence (AI) technique developed by Zadeh (1965) has been extensively used to improve or to replace the conventional PID control technique .Fuzzy logic control (or fuzzy control)provides a means of converting the knowledge of an expert about a process into an automatic control strategy. The methodology of fuzzy control appears to be robust and very useful especially for processes or systems that are difficult to model (Aissaoui and Tahour, 2012).
Neural network controllers and fuzzy logic controllers have performed considerably well in terms of overcoming the shortcomings of conventional PID controllers, however, it should be noted that they both have their various drawbacks. This has led researchers to look for ways of merging them so as to overcome their various individual shortcomings. For instance, neural networks have the capability to learn from data but lack interpretability and the capability to incorporate prior knowledge. Fuzzy logic on the other hand has the capability to incorporate human knowledge but cannot learn beyond the knowledge incorporated by human experts thereby making the tuning of its parameters difficult. Therefore both techniques can be used in a complementary manner to form a hybrid neuro-fuzzy model that will outperform the previous independent models.
1.2 Problem Statement
Several studies have attempted to combine neural networks and fuzzy logic for the speed control of DC motor. The results obtained were generally satisfactory; however the studies lack a comparative analysis on the effect of the choice of membership functions on the performance of the controllers despite the fact that there are various types of membership functions in literature.
1.3 Aim and Objectives of the Study
The aim of this study is to investigate the effect of the choice of membership functions on the performance of neuro-fuzzy controllers for the speed control of DC motor. The objectives are to:
- Model adaptive neuro-fuzzy speed controllers using different membership functions for DC motor.
- Do comparative study of the neuro-fuzzy controllers.
- Evaluate the performance of the Neuro-fuzzy controllers.
1.4 Justification of Study
Majority of the studies that applied Neuro-Fuzzy technique to the speed control of DC motor considered the Triangular membership function without a clear justification for the choice. This study therefore fills that gap by considering different membership functions and comparing their performances. The results of this study will help guide researchers and practitioners on the choice of membership function suitable for speed control of DC motor.
1.5 Scope of Study
In this work, the separately excited DC motor was considered due to its simple model that makes it very easy to simulate. This research focused on the speed control of separately excited DC motor by varying the armature voltage. The armature voltage control was chosen so that the speed of the motor can be varied below its rated speed.