Comparisons of Fuzzy MRAS and PID Controllers for EMS Maglev Train
34 Comparisons of Fuzzy MRAS and PID Controllers for EMS Maglev Train
Mustefa Jibril Eliyas Alemayehu Tadese Abstract
In this paper, a Magnetic Levitation (MAGLEV) train is designed with a first degree of freedom electromagnet-based totally system that permits to levitate vertically up and down. Fuzzy logic, PID and MRAS controllers are used to improve the Magnetic Levitation train passenger comfort and road handling. A matlab Simulink model is used to compare the performance of the three controllers using step input signals. The stability of the Magnetic Levitation train is analyzed using root locus technique. Controller output response for different time period and change of air gap with different time period is analyzed for the three controllers. Finally the comparative simulation and experimental results demonstrate the effectiveness of the presented fuzzy logic controller.
Keywords: -
Magnetic Levitation (MAGLEV) train, Fuzzy logic, PID, MRAS
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May 31 st Magnetic levitation is the process of levitating an item via exploiting magnetic fields. If the magnetic force of enchantment is used, it is recognized as magnetic suspension. If magnetic repulsion is used, its miles referred to as magnetic levitation. Magnetically Levitated (Maglev) trains fluctuate from traditional trains in that they are levitated, guided and propelled alongside a guide manner by means of a converting magnetic field as opposed to through steam, diesel or electric powered engine. The magnetic levitation machine is a difficult nonlinear mechatronic machine in which an electromagnetic pressure is needed to suspend an item in the air and it calls for an excessive-overall performance controller to control the modern via the superconducting magnets. This research is aimed at developing methods of improving efficiency in transportation. Additional applied technologies that may have uses in other applications, from inter-satellite communications, to magnetic field probes. The two main types of maglev Technology are: • Electromagnetic suspension (EMS): Makes use of attractive pressure machine to levitate. Which is a German generation. • Electrodynamic suspension (EDS): uses repulsive force device to levitate. Which is a Japan generation.
The electromagnetic pressure f (i, z), acts on the train, which can be expressed as the subsequent dynamic system in upward course consistent with Newton’s law: (cid:1) (cid:2) (cid:3) (cid:4)((cid:6))(cid:2)(cid:6) (cid:3) = (cid:1)(cid:9) − (cid:11)((cid:12), (cid:4))
Where m is the mass of the automobile and g is the gravitational steady. The electromagnetic force (cid:11)((cid:12), (cid:4)) = − (cid:14) (cid:15) ((cid:16))(cid:3) (cid:17)(cid:18)((cid:19))(cid:17)(cid:19) | (cid:14)(cid:21)(cid:22)(cid:23)(cid:24)(cid:25)(cid:16)(cid:26)(cid:24)(cid:16) (cid:28)(cid:23)(cid:29) (cid:30)(cid:14)(cid:24)(cid:31)(cid:26)(cid:29) (cid:25) (cid:25)(cid:16)(cid:31)! The voltage-current relationship for the coil is given by "((cid:6)) =
The displacement of the train is measured by using the sensor image-detector that is the output and can be formulated as: & = " (cid:19) ((cid:4)) = ’(cid:4)
Where β is the sensor gain The basic transfer function among the coil input voltage V(s) and the sensor output voltage Vz(s) is given as (()) = " (cid:19) ())"()) = − * + ’( , )((cid:1)) (cid:3) − * (cid:19) ) There are two approaches of control system design.
Is a manipulate design approach that begins from interior to outward i.e. First the open loop transfer function is shaped by controlling it poles and zeros, adding right control design to the system, so that stable normal transfer function might be achieved.
Is the reverse of the outward technique i.e. First a preferred closed loop transfer function is designed, and then remedy for required controller. Fig 1. Block Diagram of Closed Loop Maglev Train Control System
The maglev train system model has been represented by a transfer function G(s). (()) = &())-()) = −280() + 29)() + 56)() − 56)
The system has zeros at s = -29 and have poles at s = −56, and s = 56. From this, the system has a pole on the right hand side of the s-plane and this is not stable. Fig 2. Root locus stability of maglev train system
The fuzzy logic control block diagram is shown in Figure 3 below. Fig 3. Block diagram of fuzzy logic Controller The Simulink model of the fuzzy logic controller is shown in Figure 4 below.
36 Fig 4. Simulink model of the fuzzy logic controller
The error and change of error input and the output of the fuzzy logic controller is shown in Figure 5, Figure 6 and Figure 7 respectively. Fig 5. Error input Fig 6. Change in error input Fig 7. Output The rule base of the fuzzy controller is shown in Table 1 below. No Rules 1 If (error is okay) then (output is Zero) (1) 2 If (error is low) then (output is PL) (1) 3 If (error is high) then (output is NL) (1) 4 If (error is okay) and (change of error is positive) then (output is NS) (1)
Normalization can be used to protect against dependence on the signal amplitudes Consider the first-order system ( ) 0.65 uy s s dy ay budt dy y udt ab The desired closed-loop system is
5( ) 2
Ucym s s dym amym bmucdt dym ym ucdt ambm The controller is then ( ) ( ) ( ) u t toUc t soy t
0( )( )( ) s aU toUc soY Y bY to botos aUc s a bsosobbm btoam a bs bto be Y Ym Uc Ucs a bso s ame b bUcto s a bso s amGm s Uc yme b to b bUc Y Yso s a bso s a bso s amGm s Y
With e The MIT rule can be written as d edt
The normalized MIT rule is then T d edt ( )( ( ) ) m m y edtodt ydso Gm s yedt Gm s y The Simulink model of the MRAS controller is shown in the Figure 8 bellow.
38 Fig 8 Simulink model of the Mras controller
The PID (Proportional-Integral-Differential) regulator manipulate depending on the proportional, essential and differential of the deviation General equation of PID: + : (cid:2)(cid:2)(cid:6) 8((cid:6)) Where:
The ZNFD approach may be tough to perform because it is intricate to modify the advantage till the close-loop system oscillates. A little beyond that outcomes causes instability. The reaction of automatic tuning is exceptionally exact whilst in comparison to the reaction of Ziegler Nichols. So, automatic tuning is used in matlab is used to stabilize the system. Based at the parameters discovered from automobile tuning, attempt to error method is used until higher result is achieved. Fig 9 Simulink Diagram of Magnetic Levitation System using PID Controller
The magnetic force versus current graph of the Maglev train system is shown in Figure 10 below.
Fig 10. Magnetic force versus current graph plot
The simulation output for Maglev train system without controller and Step Response of PID Auto-tuning for Maglev System is shown in Figure 11 and Figure 12 respectively.
39 Fig 11 Maglev train system without controller Fig 12 Step Response of PID Auto-tuning for Maglev System
The output response of PID, FUZZY and MRAS Controllers for a step input is shown in Figure 14 below. Fig 14. Output response of PID, FUZZY and MRAS Controllers for a step input. The output response of maglev train system with different time period is shown in Figure 15 below. Fig 15. Output response of maglev train system with different time period
The numerical values of the proposed controllers is shown in Table 2 below. Table 2. Numerical values of the proposed controllers
Controller
Rise time (m sec)
Settling time (sec)
Percent Overshoot (%)
Steady state valuePID
MRAS
FUZZY
40 Table 3 Controller output response for different time period Controller output Time Max Overshoot Rise time (sec) Settling time (sec) Percent Overshoot (%) present 0.0513 0.0523 0.9898 2.6 After 10 years 0.0518 0.0589 1.014 2.73 After 20 years 0.0525 0.0652 1.122 2.78 The Change of air gap with different time period is shown in Table 4 below. Table 4. Change of air gap with different time period Period Air gap (m) Present 0.06 After 10 Years 0.061 After 20 Years 0.062
Magnetic levitation system is inherently unstable system, because of the device nonlinearity. The output of the magnetic levitation device is determined and analyzed. The simulation result showed that the settling time of MRAS controller is smaller than the settling time of PID and Fuzzy Controller. The rising time of MRAS controller is smaller than the rising time of PID and Fuzzy Controller. But the percentage overshoot of PID controller is very good when compared with Fuzzy controller and MRAS controller. And the controller can track the gap change and it could re-arrange itself with the gap change occur by change of time. Finally the simulation result prove the effectiveness of the MRAS controller.
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