Implementation of Fuzzy Controller to Magnetic Levitation System
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1 IX Control Instrumentation System Conference (CISCON ), November Implementation of Fuzzy Controller to Magnetic Levitation System Amit Kumar Choudhary, S.K. Nagar and J.P. Tiwari Abstract--- Elimination of frictional losses has been receiving large attention to reduce power consumption and the maintenance cost thus increasing the power efficiency. Considering the above facts, Magnetic levitation technology has given the contribution in industry as a part. Now, since Maglev's are highly nonlinear and inherently unstable, the objective is to design a controller that would be an attractive alternative to the existing classical or modern controllers challenging Non-linear control systems without the requirement of any system model or complex mathematical equations governing the transfer function. These requirements raised the design and analysis of Fuzzy Logic Controllers (FLC). Furthermore, the investigation on Proportional Integrated Derivative Controller (PID) is also reported here and its output is compared with that of Fuzzy controller to control the ball levitation in the air. The proposed controllers for MAGLEV system is simulated by using MATLAB/SIMULINK and implemented on a laboratory-scale magnetic levitation system. Index Terms--- Fuzzy Logic Control, Magnetic Levitation, Nonlinear Systems, PID Control, System Model P I. INTRODUCTION RECISED motion control can be understood at its best by, a kind of contact free and wear-free suspension device known as, Magnetic levitation (or maglev) systems, playing an important role among engineers worldwide and applicable to wide applications such as magnetic bearings, high-precision positioning platforms, aerospace shuttles, and fast maglev trains. Problem discussed in the class of magnetic suspension systems is of precisely controlling the magnetic ball s height above the ground by levitating it against the force of gravity using electromagnets. This develops a complex and nonlinear dynamics with open-loop unstable system demanding, an appropriate control strategy to stabilize them. The mathematical model of MAGLEV system depends on various factors. Using this model, it is difficult to design a conventional controller and also results do not yield satisfactory. Several control design strategies have been developed in order to stabilize the ball around a desired operating point. Non-linear and complex systems are proficiently handled by Proportional-Integral-Derivate (PID) controller, but their Amit Kumar Choudhary, Department of Electrical Engineering, Institute of Technology, Banaras Hindu University, Varanasi , India. amitchoudhary005@gmail.com S.K. Nagar, Department of Electrical Engineering, Institute of Technology, Banaras Hindu University, Varanasi , India. J.P. Tiwari, Department of Electrical Engineering, Institute of Technology, Banaras Hindu University, Varanasi , India. modellings are often troublesome and sometimes impossible to attain the satisfaction. Because of the fact that, most of the dynamic processes have nonlinearities, exact mathematical model was not derived and conventional controllers require the system model for the determination of the parameters using control theory, finally developing an algorithm for the controller. Alternatively, Fuzzy Controller came into existence to analyze complex systems whose information can not be interpreted qualitatively, quantitatively or exactly. The proposed logic was characterized by human knowledge and experience, leading to the design of control algorithm. Typically several conventional coding is required to describe systems reducing the design complexity. In recent years, fuzzy logic controllers presented several improvements in numerous applications in comparison to conventional control schemes. This was mainly due to their capacity to handle our inexact knowledge about real world systems. The advantages of fuzzy logic controller over conventional controllers (P, PI, PD, PID or state controller) are in terms of design simplicity and control performance. On the theoretical basis, the lack of rigorous stability and robustness is the greatest drawback of fuzzy control. However, most stable analysis methods for fuzzy controllers are based on approximations, and there is no rigorous way to obtain a measure of robustness. There are many of the tremendous works discussed on Magnetic Levitation Systems. Wang et all discussed classic controller design procedure for a demonstration [1]. In nineties, Bariet et al proposed linear and nonlinear state space controllers for magnetic levitation system showing the position tracking error about ± 0.45 mm [2]. From Cho et al came out the idea of sliding mode control (SMC) to overcome the parameter uncertainties and reject disturbances to achieve robust performance. It was found that the performance of the SMC is better than that of the classical controllers [3]. Wenbai Chen discussed, PID controller can be a robust and reliable system if the parameters can be determined or tuned properly, making the system very stable [4]. The fuzzy set theory was introduced by Zadeh et al [5] became the powerful modeling tool that can work with the unstable system and highly nonlinearities of modern control. It was intelligent and easy to tune by non-expert person is its excellence, as PID controller needs experience person to tune the parameter. Frequency domain H_infinity control have been also applied to MAGLEV systems [6]. Author, Chao-lin Kuo proposed the Novel Fuzzy Sliding- Mode Control (NFSMC) [7]. Among the above studies, Fuzzy Logic Controller proved to have potential to stabilize the ball levitation. This control technique has been studied by various researchers [8, 9, and 10]. This is more
2 IX Control Instrumentation System Conference (CISCON ), November convenient for MAGLEV system and easiest to designing the controller. The Department of Electrical Engineering purchased a laboratory-scale maglev system from Feedback Limited Inc, shown in figure 1. The system includes an analog and digital controller that levitates and stabilizes a set of hollow steel balls about an operating region. However, there is little insight known about the model of the plant, discussed in the next section. Further, the Fuzzy modelling is discussed and its results are obtained and compared with the conventional PID controller output. The results show that this method can greatly improve the control precision and stability of the magnetic levitated system, the performance is better than the optimal PID controller. The design procedure utilizes MATLAB Fuzzy Logic toolbox and is implemented using SIMULINK version 7.5. Figure 1: Magnetic Levitation System II. ANALYTICAL MODEL Mathematical modeling has been the fundamental and must concept in science and technology. In this section, to obtain the plant or system transfer function, System identification is conducted. Figure 2(a, b): Coil Circuit Using Kirchoff s voltage rule around the loop, the electrical equation is: i i h e R i L L0 h0 2 t h t Where: (1) e= coil voltage, i= coil current, R= coil resistance, L=coil inductance, h=ball position ho and Lo are nominal operating constants. On the other hand, the mechanical equation is obtained from the force diagram based on Newton s second law, as shown in figure 2: 2 i F GF EF m g c (2) h Where C= Magnetic constant determined experimentally=1.477x10-4 N.m2/A2 m= mass of steel ball= kg, g= gravitational acceleration= 9.82 m/s 2. Using Taylor series expansion to linearize the non-linear differential equations about the equilibrium point ho=22.5 mm, the plant analytical model is: Gs () s s s (3) It was determined that the coil circuit was driven by an active circuit that indicates the current i is a non-linear function of the coil voltage e. Now once, model obtained and verified, a suitable control law can be implemented to compensate the plant instability and improve performance. Figure 2(a) Analytical and experimental plant models were obtained for comparison and verification. According to T. H. Wong, laboratory-scale maglev systems are represented with electrical and mechanical equations [1]. It is mainly composed of Reference Signal (RS), Power Amplifier (PA), Electromagnet (EM), Platform (PF), and Sensors. The control system includes A/D and D/A converters in addition. Figure 2, shows the RLC coil circuit that displaces the steel ball using electromagnetism. III. CONTROLLER IMPLEMENTATION A control strategy for moving the object to the desired equilibrium location and Levitating it to the position which is a typical situation occurring during the experiments is developed here. The methodology of stabilizing the ball position is based on fuzzy if-then rules defined by an expert to tackle these problems. A fuzzy control system can be considered as a real time expert system, which performs the control tasks in a human-like way.
3 IX Control Instrumentation System Conference (CISCON ), November Fuzzy logic is a technology based on engineering knowledge, experience and observations that are more important than the underlying mathematical model, because linguistic variables are used to define system behavior rapidly. It is a very recent technology relative to conventional controllers, increasing its application areas. Fuzzy PID, fuzzy PI, fuzzy PD and fuzzy mixed controllers are fuzzy controller design approaches, but unlike conventional controllers that focus on system model. Some of the problems, such as stability and performance, are encountered both in fuzzy controllers and conventional controllers. Fuzzy IF-THEN rules are defined with the means of membership functions over a specific universe of discourse. Above a certain number of membership functions the control accuracy is just slightly increased, where as too few membership functions make an accurate control impossible. The membership functions of the fuzzy controller used were determined with trial and error method. As the curve shape of the membership function is sharp, the control sensitivity is high. On the contrary, the curve shape of the membership function is slow, the resultant of the control performances is also gentle, and the systematic ness is good. Therefore, when choosing the fuzzy variable s membership functions, it should be set according to the specific circumstances of specific design, low resolution fuzzy sets should be adopted in the large error region, high resolution fuzzy sets should be adopted in the small error region. The use of triangular membership functions which become narrow around zero results in an accurate control with a small number of membership functions. A. Design Methodology of FLC In the development of the controller for Magnetic Levitation System, first step is to obtain the values through a sensor that can be transformed into the corresponding linguistic variable. The second step performs the fuzzy inference giving the linguistic values of the control variables, preceded by the transformation of these linguistic values to the numerical value of the control variable in order to perform the required task. After executing these steps, the controller is fine tuned in an iterative way. Thus, designing of a FLC consists of four principle components as shown in Fig. 3, namely: 1. Fuzzification: The triangular, trapezoidal and Gaussian membership functions are used for inputs and output 2. Inference mechanism: Mamdani's fuzzy inference method with a max/min rule is used. 3. Rule Base: Various rules are coded on the basis of hit and trial. 4. Defuzzification: The centroid method is used to generate the numerical value of the control voltages from the above fuzzy sets, in the proposed work. Figure 3: Block Diagram of Fuzzy Logic Controller In Maglev Model, the height of the ball obtained is compared to reference height. Choosing the actual height difference h, and the derivative of the difference dh as the inputs and the output assumed to the reference voltage v, for the fuzzy controller. Each variable of the fuzzy controller is represented by using seven membership functions at the inputs and output, as shown in Fig. 4 and 5. Respectively used fuzzy language variables are H, DH, and V, to describe the above parameters. Quantifying the universe of discourse are H= [- 3mm, +3mm], DH= [-3mm/s, +3mm/s] and V= [-1V, +1V]. The full collection of language value is {NB, NM, NS, Z, PS, PM, PB}. Figure 4: Input Membership Functions H and DH
4 IX Control Instrumentation System Conference (CISCON ), November The fuzzy rule base for this fuzzy controller is as shown in table 1. Fig. 6 shows the control surface of the FLC. It can be noted that, FLC has a linear control surface. This is due to the DH H Figure 5: Output Membership Function V Table 1: Rule Base for the Proposed Fuzzy Controller equal widths of membership function for input and output. Finally, this voltage is applied to Maglev Model. NB NM NS Z PS PM PB NB NB NB NB NM NM NS Z NM NB NB NM NM NS Z PS NS NB NM NM NS Z PS PM Z NM NM NS Z PS PM PM PS NM NS Z PS PM PM PB PM NS Z PS PM PM PB PB PB Z PS PM PM PB PB PB nonlinear magnetic levitation system whose design is based on an approximate linear model based on exact feedback linearization is compared in terms of tracking performance with a PID controller and with Fuzzy Logic Controller. The latter nonlinear controller turned out to be more sensitive. Figure 6: Fuzzy Control Surface IV. SIMULATION AND RESULTS Fuzzy controller is developed by the Fuzzy Toolbox incorporated with the MATLAB/SIMULINK software. All simulations are done with the nonlinear model. In this paper, a
5 IX Control Instrumentation System Conference (CISCON ), November Figure 7: Output for PD model with Kp=4 Figure 8: Output for PD model with Kp=50
6 IX Control Instrumentation System Conference (CISCON ), November V. CONCLUSION The output to control the position of a steel ball in a magnetic levitation system using fuzzy logic has been observed and analysed. From the figures, we can conclude that the PID controller gain is proportional with time integral. This means when the K p value is bigger, the output will have smaller value of offset but the more oscillatory the process becomes. From the simulation results of Fuzzy Controller, it can be concluded that they can stabilize the system efficiently Moreover, the performance during the transient period of the fuzzy system is better in the sense that less overshoot was obtained. However completing the rule base becomes much harder than in the case of having only two input signals. Although the laboratory set-up in this paper is built to study magnetic levitation control of a steel ball, this work is directly relevant to industrial applications and is expected that the technique described here would also provide better performance. Future scope, to control the MAGLEV system would be the implementation of PID-Fuzzy controller or Neural Network or Genetic Algorithm controller. Lastly, this simulation was implemented to magnetic levitation system model, in the laboratory. Figure 9: Output for proposed Fuzzy Logic Controller [3] Cho, D.; Kato, Y.; Spilman, D., Sliding-Mode Controller and Classical Controller on Magnetic Levitation System, Control System Magazine, IEEE, Vol.13, pp , [4] Chen Wenbai, Meng Xuan, Li Jinao, PID Controller Design of Maglev Ball System based on Chaos Parameter Optimization, International Conference on Machine Vision and Human- Machine Interface(MVHI), pp , [5] John Yen, Reza Langari, Lotfi A.Zadeh, Industrial Application of Fuzzy Logic and Intelligent Systems, New Jersey: IEEE press.1994 [6] Shen J., Nonlinear h-infinity Ccontrol of Magnetic Levitation System, Asian Journal of Control, [7] Chao-Lin Kuo, Tzuu-Hseng S. Li and Nai Ren Guo, Design of a Novel Fuzzy Sliding-Mode Control for Magnetic Ball Levitation System, Journal of Intelligent and Robotic Systems, Springer, Vol. 42, pp , [8] Stegemann H., Worlitz F., Hampel R., Fuzzy Logic Application for Magnetic Bearings, Proceedings of the East West Fuzzy Colloquim, Zittau, [9] Lo Verso G., Trapanese M., A Fuzzy Control Technique for a Magnetically Levitated System, Proc.Maglev, Bremen, [10] K. Ishaque, Y. Saleem, S.S Abdullah, M. Amjad, M. Rashid, and S. Kazi, Modeling and Control of Magnetic Levitation System via Fuzzy Logic Controller International conference on Modeling, Simulation and Applied Optimization, Kuala Lumpur, Malaysia, April 19-21, REFERENCES [1] Wang, T.H., Design of Magnetic Levitation Control System, An Undergraduate project, IEE Transaction on Education, Vol-28, no.4, pp , [2] Walter Bariet, John Chiasson, Linear and Nonlinear State-space Controllers for Magnetic Levitation, International Journal of System Science, Vol-27, no. 11, pp , 1996.
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