im Journal of JET v°iume 12 (2°19) p.p. 41-54 Issue 1, April 2019 Type of article 1.01 Technology www.fe.um.si/en/jet.html PANTOGRAPH DRIVEN WITH A LINEAR INDUCTION MOTOR WITH ADAPTIVE FUZZY CONTROL PANTOGRAF GNAN Z LINEARNIM INDUKCIJSKIM MOTORJEM S PRILAGOJENIMI KRMILNIMI TEHNIKAMI Costica Nituca1, Gabriel Chiriac 1 R Keywords: Linear induction motor, Fuzzy control, Locomotive pantograph, Simulation Abstract This article presents an adaptive fuzzy control for a linear induction motor, which is used to control the vertical movement of a pantograph, which supplies an electric locomotive from a contact line. The system has the goal of eliminating all the discontinuity on the route, the resonance phenomenon, the separation of the pantograph head from the contact wire, and electric arches. The simulations demonstrate functional control of the pantograph driven with a linear induction motor system using fuzzy control techniques. Povzetek V članku je predstavljeno prilagodljivo mehko krmiljenje linearnega indukcijskega motorja, ki se uporablja za krmiljenje navpičnega gibanja odjemnika toka, ki napaja električno lokomotivo iz kontaktne linije. Cilj sistema je odpraviti vse prekinitve na poti, resonančni pojav, ločitev glave odjemnika toka od kontaktnega vodnika in električnih lokov. Simulacije prikazujejo funkcionalno kontrolo odjemnika toka, ki se poganja z linearnim indukcijskim motornim sistemom z uporabo mehkih krmilnih tehnik. R Corresponding author: Ph.D. Gabriel Chiriac, Tel.: +04 0727 645058, Mailing address: Bd. Dimitrie Mangeron, nr. 21- 23, 700050 IASI, Romania, E-mail address: gchiriac@tuiasi.ro 1 Technical University "Gheorghe Asachi" from lasi, Faculty of Electrical Engineering, Bd. Dimitrie Mangeron, nr. 21- 23, 700050 IASI, Romania JET 41 Costica Nituca, Gabriel Chiriac JE TVoi. 12! (2019) Issue 1 1 INTRODUCTION A critical problem of the electric supply of a high-speed locomotive is maintaining the contact force between the pantograph head and the contact line as constant and pursuing the trajectory of the contact point [1, 2]. The dynamic of the pantograph under the influence of the disruptive factors and perturbations is the decisive criteria in the estimation of the energy transfer quality from the contact line to electric vehicles. The contact line (the catenary) and the power supply system of the train (the pantograph) are in a highly dynamic interaction, which is influenced by the speed, the vehicle type, the structure of the catenary and the mechanical tension in the wire, the weather conditions, the structure and the mass of the pantograph and the oscillations and perturbations of the vehicle while moving. The conventional methods to drive the pantograph use systems with compressed air or with springs. The control system can be based on different actuator types (hydraulic, pneumatic, electric), and for different actuator positions (strips suspension, air spring, or frame). The use of the active control strategies for the pantograph [3, 4] may lead to an improvement of contact [5]. New mathematical models for the pantograph-catenary interaction have been developed in [6, 7], as the basis for the control principles. The pantograph-catenary system is also analysed by using the finite element method [8-11], the results being compared with results from the real tests. The damper system of the catenary is analysed by recording the accelerations of the pantograph [12], while in [13] a control is proposed to reduce the oscillations of the pantograph-catenary system. The advanced active control of the pantograph includes the analysis of the vertical body vibration, as in [14]. According to [15], the proposed controller can improve the contact quality, leading to a reduction of the standard deviation of the pantograph-catenary contact force by more than 40% compared to the non-controlled system. The drive and the control of the pantograph head trajectory can be made by using a linear induction motor [16]. The patent [16] relates to a pantograph current collector to be used in locomotives or electric trains, for collecting power from an electric contact line placed along the railway. In addition to the mechanical resort that develops a lifting force and a force for pressing the contact shoe against the contact wire, the pantograph is provided with a supplementary assembly of a linear induction motor providing a supplementary mechanical effort, which is to be added to the mechanical effort achieved by a mechanical resort in order to adapt the resulting effort intended to push the pantograph's shoe. Thus, in parallel with the elastic spring of the pantograph or even independently, a linear induction motor that drives the pantograph head with the aim of pursuing the geometry of the contact line can be used. The linear motor can be controlled with the adaptive fuzzy control technique. Different articles have examined the fuzzy control approach for dynamics of the pantograph-catenary interaction [17, 18] and for the linear induction motors [19-23]. This article presents the fuzzy adaptive control for a pantograph driven by a linear induction motor system used to supply an electric locomotive from a contact line. A mathematical model of the motor and the methodology for the motor control are presented. Simulations are made in Matlab-Simulink software, and data analyses are discussed. 42 JET Pantograph driven with a linearinduction motor with adaptive fuzzycontrol 2 PANTOGRAPH DRIVEN WITH A LINEAR INDUCTION MOTOR -SYSTEM DESCRIPTION The main characteristic of a railway pantograph is to assure good current collecting, without interruptions of the current, regardless of the height of the pantograph and train movement. For this, it is necessary for the pantograph to have a permanent contact, regardless of the movement of the mechanically articulated system, as well as good lateral and transversal stability, to achieve contact pressure, regardless of the height in static and dynamic conditions. The proposed solution is to use a linear induction motor (LIM) to drive the pantograph, a solution that is patented. Using this solution [16], (Figure 1), pantograph detachments will be prevented, and the electric traction equipment will be supplied in good conditions. Figure 1: Phctuorhar drivez by p lizatr ichtctiuc motor The linear induction motor (LIM) is three-phased and composed of a mobile plate armature (1) and two fixed inductors (2) with windings placed in 24 slots. The mobile armature is connected to the railway pantograph (3) and acts over it with force FLIM. The pantograph pushes the contact line (4) with a contact force Fc. The mobile armature has a maximum oscillation motion (5) of 140 mm. The contact is assured by the skates (6). 3 MODEL OF THE SYSTEM 3.1 Model of the linear induction motor (LIM) The dynamic model of the linear induction motor can be described with the following equations [21, 24, 25]: JET 43 Costica Nituca, Gabriel Chiriac JE TVoi. 12! (2019) Issue 1 i qs — f R — L ids — — . a-L a-T . V s r J ( R 1 — a - i +--— qs a-LLT -O —n^.v^ +—1—V ; s r r \ L a-L a-T n L n p m a - L L t --vO + qr a-LLT s r L a-L a-LLT - O + V dr ds a - L n Oqr — —i--O + n — vO, ; T qs t* L qr ' ' ' p t dr'ï n — O dr ——ir, — n —vO--O T ds p t qr T r r F — Kf (Vi —O i. I e f dr qs qr ds (3.1) where: T = Lr/Rr is the time constant for the secondary circuit of the LIM; a — 1 — I L , dispersion coefficient of the LIM; 3n tZL K = —p—m, is constantly used in the formula of the linear induction motor force, FLIM. f 2TL, 3.2 The model of the pantograph - linear induction motor system The mechanical equilibrium equation can be written as [20]: j—< ^ t, dv ds Fe - Fr = M — = -Mv—. dt dt (3.2) The resistant force Fr is the necessary force to lift and to maintain the pantograph at the optimal height to follow the trajectory of the contact line (which is supposed to be sinusoidal) and to assure a constant contact force. Thus, the pantograph will have some vertical oscillations along the contact line and during the vehicle movement. It will be considered as positive (+) for the lift motion and negative (-) for the down motion [26]. To compensate these oscillations movements and to assure a constant contact force, the linear induction motor will operate as an electromagnetic resort [16] having a short oscillating movement and a relatively low speed. The resistant force is given by the equation: F — ±* ^ ± M 0a2 y (3.3) The pantograph-linear induction motor system will be described by the mechanical equilibrium equation, [21, 22]: (3.4) F — Kf (Ojqs —Oqrd)— Mv + Dv + Fr. 44 JET Pantograph driven with a linearinduction motor with adaptive fuzzycontrol 4 CONTROL METHODOLOGY FOR THE LINEAR INDUCTION MOTOR Figure 2 presents the position control system for the linear induction motor [19, 23, 24], with the following parameters: Fe = KfuT Hp (s) = —— =- e Ms + D s + a (4.1) (4.2) where: Hp(s) - transfer function of the motor; uT - control signal; s- Laplace operator; a, b -constants. In Figure 2, the parameter dm is the desired position, and the parameter vm is the desired speed. r ■ dm d Position Vm Speed Controller 7 Í Controller V Ut LIM Servo Drive System Kf b s + a Hp(s) Figure 2: Simplified position control system To obtain the control signal, a fuzzy adaptive regulator is proposed [26]. 4.1 Fuzzy adaptive regulator The design of the fuzzy adaptive regulator is based on the aspects developed into the specific literature [27-31]. Hence, in this article, only the necessary steps to implement the fuzzy adaptive regulator are presented using Matlab-Simulink software. In Figure 3, a schematic for the fuzzy adaptive regulator is presented [27, 28]. LIM Pantograph 0 is solved to obtain a symmetrical matrix P>0. The design parameters Me, Mx and a are described based on practical constraints. Step 2: Initial controller design [28, 29]: uc as a fuzzy system is considered. S c ( x|0 = ( ( -l V^ ^ exp S ( ( -l V2V exp (4.3) —l -l l where erepresents some adjustable parameters y , x, and oi . The command uc is designed according to the relation (4.3) based on M rules characterized by the Gaussian membership functions: ( ( -l V2V exp (4.4) where l = 1,2,...,M and i= 1,2 ...n. Step 3. Design of the adaptive block [27-29]: With the next algorithm, the relation ion is derived: d y duc bl d y S bl (4.5) - - 2| xi - x duc _ y - uc_bi d xi -l M S b (4.6) d "l - 2| x - x'i duc _ y -uc bi da' ' ' l M S b i_1 V ) (4.7) x. - i _1 i_1 U Xj - X i_1 i_1 X. - i_1 i_1 2 46 JET Pantograph driven with a linearinduction motor with adaptive fuzzycontrol where: n exp ( -i \ X: - X 2 ^ (4.8) The above relations are obtained considering the equations in (4.3) and the control ts is given by [13,17]: us (XX) = I*sgn{eTPbc )• \uc\ + -L (fU + |yin)| + \kT e|) (4.9) where: I* = 1 if Ve > V and I* = 0 if Ve < V [15, 16]. The control u (Figure 3) is applied [14, 15]: u = uc (x|8) + us (x), where uc is given by the relation (4.3) and us is given by the relation (4.9). To adjust the vector 8, the next adaptive law is used: if a1. = a, the following equation is used: T re p,. duc da' ■s- T duc if e p —c- < o da' 0 if eTp % > 0 " da' Otherwise, the following equation is used: duc T —c re p —t da' f d if (|| 0 T duc t eel duc „ re pnda-re pn^r— if ( || dg \ ||= MR and eT p 0T < 0 l-l g - Un- dal , (4.10) (4.11) (4.12) b i=i 5 SIMULATIONS AND DATA ANALYSIS For the simulations, a three-phased, bilateral, linear induction motor is used; it has the following parameters: VF = 230V; Ip = 5A; Rs = 5.3Q; Rr = 13.80; Lm = 0.037H; L, = 0.041H; Ls = 0.051H; Kp = 231.15 N/A; h = 23.741 ; b = 0.319; D = 57.1 kg/s; Fa = 150N; M = 12kg; v = 3m/s; t = 0.027. The contact line considered for the simulations has the following parameters: span is 60m, deflection is 0.454m. The main pulsation of the contact line for a locomotive speed of 100km/h is ro = 2.907 1/s. Figure 4 presents the Matlab-Simulink schematic for the fuzzy adaptive regulator. JET 47 Costica Nituca, Gabriel Chiriac JE TVoi. 12! (2019) Issue 1 Supervisor Figure 4: MrSlrU-Simtlink schematic for sha ftzzy rdrpSiva regulator Trttw |J«| Figure 5: Control signal variation Figure 6: Spaad variation of Sha linear induction motor 48 JET Pantograph driven with a linearinduction motor with adaptive fuzzycontrol lime [s] Figure 7: Mubila trmtttra mutiuc (muturpusitiuc) I -Motor pofutioii | OofiHEd ItrtA powlioii / \ \ ............... / i-oís-i-rí-i-li-1,-aÍE- Figure 8: Mutur's muvamact tch cucthct liza pusitiuc Figure 9: Cuctrul sigctl vhrihtiuc witp t stpplamacttry, iccihacttlpurca Figure 10: Spaah vhrihtiuc up tpa licatr ichtctiuc mutur witp stpplamacttry, iccihacttl purca JET 49 Costica Nituca, Gabriel Chiriac JE TVoi. 12! (2019) Issue 1 Tinwfs] Figure 11: Mobile rrmrStra motion (motorposition) in ersa of sha incidental forea " ITfl'l J Figure 12: Motor's movement and eonSreS line position in ersa of sha ineidanSrl forea Figures 5 to 12 present the simulations of the pantograph driven by the linear motor system using a fuzzy adaptive regulator. Figure 5 presents the variation of the control signal, and Figure 6 presents the speed variation of the LIM and, accordingly, the vertical speed variation of the pantograph. The speed of the system has a variation of ±0.314 m/s. Figure 7 presents the movement of the mobile armature (the plate) of the LIM, of the ±0.100 m. These variations are in accordance with the prescribed values of ±0.454 m. Figure 8 presents the movement of the motor (red curve) and the position of the contact line (blue, dash curve) which must be followed by the pantograph. It can be observed that the two curves are very close, with differences of about (±0.1m), which demonstrate good control of the pantograph - linear motor system. To estimate the operability of the system, a simulation for the overload was made, for the situation when the motor has to overcome a supplementary effort. For the simulation, the previous parameters are used, but, currently, a supplementary, incidental force is considered Fip=20N. Figure 9 describes the control signal with supplementary, incidental force F1p at the moment t=4.16s, a force that modifies the shape of the control signal. In Figure 10, the speed of the motor is depicted, with variations of ±0.314m/s in the first part of the simulation. When the supplementary force Fip occurs, the variation speed becomes ±0.378m/s, with an increase of about 16%. In Figure 11, it is observed that the variation of the position of the motor. When the supplementary force occurs, the position is modified from ±0.100m la ±0.117m. 50 JET Pantograph driven with a linearinduction motor with adaptive fuzzycontrol Figure 12 shows the trajectory of the pantograph over the contact line when an incidental force appears. Thus, after the time t=4.163s, an increase also observed for the movement of the pantograph (red curve, ±0.1116m) and for the trajectory of the contact line (blue, dash curve, 0.12m). The difference between the two characteristics is of 0.0084m, which is about 7%; even in this situation, the system operates in the necessary conditions of the deflection of 0.454m. 6 CONCLUSIONS Assuring continuous power collection for railway vehicles is essential for a safe transportation system. Problems regarding power collection are related to the pantograph detachment from the contact line due to the oscillations and parasitic movement of the vehicles and their power-collecting equipment. In this article, a solution to improve the power supply of the electric locomotive by using a linear induction motor to drive the pantograph is presented and analyzed. A mathematical model for the linear induction motor and the motor-pantograph system are developed, considering a fuzzy control technique. Simulations are made for two cases, with and without supplementary incidental force acting over the pantograph. The speed and position of the pantograph are discussed. Furthermore, the trajectory of the pantograph head in concordance with the trajectory of the contact line is also analysed. The simulations demonstrate good control of the pantograph-linear induction motor system using a fuzzy control technique. References [1] S. Walters, A. Rachid, A. Mpanda: Oc Muhallico tch Cuctrul up Pictograph Chtactry Systems, In: PACIFIC 2011, Amiens, France, 2011 [2] C. Nituca, A. Rachid, L. Cantemir, G. 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Hsu: Ractrract-Natrhl-Natwurk-Bhsah Ahhativa-Bhckstaaaico Cuctrul pur Ichtctiuc Sarvumuturs, IEEE Transactions on Industrial Electronics, vol. 52, no. 6, pp. 1677- 1684, December 2005 JET 53 Costica Nituca, Gabriel Chiriac JET Vol. 12 (2019) Issue 1 Nomenclature (Symbols) (Symbol meaning) d0 diameter of the shaft load of the pantograph D viscous friction and iron-loss coefficient Fe electromagnetic force Fr external force disturbance iqs q-axis primary current ids d-axis primary current Kf force constant Lm magnetizing inductance per phase Lr secondary inductance per phase Ls primary inductance per phase M total mass of the moving element M0 total mass of the pantograph related to the skate; np number of pole pairs P0 the static equivalent load of the pantograph; Rs winding resistance per phase Rr secondary resistance per phase referred primary Tr secondary time-constant v mover linear velocity Vds d-axis primary voltage Vqs q-axis primary voltage y amplitude of the catenary a leakage coefficient 0dr d-axis secondary flux 0qr q-axis secondary flux T pole pitch the friction coefficient in bearings m catenary angular frequency 54 JET