Flash Butt Welding of Large Workpieces Based on Model-Free Adaptive Control

Transcription

1 Proceedings of 011 International Conference on System Science and Engineering, Macau, China - June 011 Flash Butt Welding of Large Workpieces Based on Model-Free Adaptive Control Lunhai Yin School of Electrical Engineering, Liaoning University of Technology, Jinzhou, 11001, Liaoning, China ylh @16.com Abstract: The hdraulic system of flash welding machine and loading system has nonlinearity, force coupling arising from mechanical sructure and time-varying parameters and demands huge upset force, respond with high-speed and two loading hydraulic cylinder move and load synchronously while the cylinders sharing the even load. It s difficult to model mathematics accurately. So we designed the control scheme of model-free adaptive and the conroller of model-free adaptive. By simulation, we succeeded in solving the problem that it is difficult to model mathematics accurately. Simulation result show that the error of dynamic pressure synchronization is little and that the error is stable. The control effect of upset force servo is good and the output of upset force servo is stable. The control scheme is feasible. Keywords: Flash butt weldding MFAC Force Servo Simulation Research I. INTRODUCTION Large workpiece jointing adopts flash butt welding technology not adding solder. The character of weld is the same as workpiece material, not influencing jointing workpiece character. And it has the advantage of jointing good quality, fast speed and high efficiency [1]. In the meanwhile, it can enhance large workpiece clamp force and upset force. It usually adopts hydraulic servo system to complete. Therefore it is important to improve the operation performance and accuracy of the electro-hydraulic hybrid system and accuracy of the upset force servo. There are three kinds flash butt welding technics include continuous flash butt welding and preheating flash butt welding and flash-preheating-flash butt welding. For large cross-section workpiece, and head face relatively flat usually adopts preheating flash butt welding. Preheating flash butt welding process consists of preheating stage and flash stage and upset stage. In the upset stage, a high speed and a huge upset force must be provided by the actuator in a very short time, such as welding 70cm the cross axle we will need force reaching to 400kN []. To meet the requirment of the huge upset load at quick pace and ensure the stiffness and stability of the loading system, parallel pairs of hydraulic cylinder is used to drive a mechanical fixture for loading, and configuration is used in the flash welding machine. In order to improve jointing quality, the output force of two upset hydraulic cylinder must laod consistently and reach maximum at the same time in the upset stage. The flash welding machine itself has a certain ability of synchronization performance, at the Dong Guo School of Electrical Engineering, Liaoning University of Technology, Jinzhou, 11001, Liaoning, China guodong@asee.buaa.edu.cn same time system allows some error. Therefore, our approach is only when the two cylinders synchronazition error exceeds a certain limit, the controller will be act based on the deviations between expected value and two cylinders value. The control parameter of conventional controllers does t change in the controlling process and the control parameter affects directly synchronizaton of dual hydranlic cylinders and further affect the welding quality. During the upset loading hydraulic system is nonlinear, in the meanwhile the load stiffness of hudraulic system is time-varing function, therefore the controller based on simplified linear model can not accurately reflect the parameters time variation about controlled objects, the synchronization performance of two cylinders maybe degrade. To sovle the above mentioned problems, the system adopted MFAC which is independent of the control system model and can be self-adaptive by adjustable control law, and meanwhile it can accomplish the synchronous loading control of two cylinders. So that it can improve the quality of flash butt welding. II. THE MAIN PROCESS OF FLASH BUTT WELDING A. Preheating stage When the head face of jointing workpiece is larger and the preheating of two porkpiece reaches an adequate temperature, the quality of flash butt welding will be improved and the impurity (e.g. oxide) at the welding line will be decreased. For example, the adequate preheating temperature of rolled steel is , that is, when it is within austenitic temperature extent, flash and upset will be carried out []. If there s no preheating, it can t be guaranteed whether the oxide impurity and other gasiform impurity between the two head face will be ejeceted by the sparks torrent during the course of flash process. After preheating, on both side of welding line, the temperature of some region in a certain depth will reach the degree of plastic deformation, which is easier to upset. After the welding zone is preheated, in the flash stage, the muzzle velocity that the workpiece delivers will be speeded up and the time that the last rapidity of flash needs will be shortened. The higher preheating temperature is the quicker the muzzle velocity is. For example, the preheating temperature of the steel jointing workpiece reaches , the muzzle velocity of flash is 0.5mm/s, while the muzzle velocity that is not preheated is 0.mm/s. After preheating, the work efficiency and jointing quality will be improved [], which they will adopt the same electrical source. But when heated DC will be modulated into square-wave power, duty factor and duration of heat can be /11/$ IEEE 617

2 adjusted by welding materials and cross section. The temperature of heating can be controlled, if the temperature is low it can t reach our preheating purpose, and on the contrary if the temperature is extremely high it will burn out the head face of workpieces. B. Flash stage The purpose of flash is heating workpiece. Flash evening makes jointing workpiece head face from a symmetrical liquid metal and it can depend on furious flash causing ambience to protect liquid metal, thereby it can avoid being oxidated and contaminated. On the assumption that dynamic fixture s speed is v g and the speed of flash melting is v s. In order to assure the welding quality, flash must be stable and intensity. What stability mean is during the process of flash it can t cause openning circuit and short circuit, namely v g = v s. Intensity means in the unit time there can be enough lintel blow up. The stronger the flash is the better the weld self-protection, its quality of welding line is higher. C. Upset stage When flash finishs we must bring to bear enough upset force immediately, interface gap will be decrease rapidly and stop blowing up, It will enter upset stage immediately. The effect of upset stage is pressurize welding line gap and cleft which left by liquid metal blowing up, in the meanwhile it can squzze out liquid metal and oxide impurrity. It can made undefiled plastic metal impinge on, and joint area can produce plastic deformation. It can enhance recrystallization forming common crystallization grain and win firm joint. The hydraulic loading model is shown in Figure ; the main elements parameters are shown in Table 1 and Table. This system adopts gasbag type accumulators as supplementary energy. III. THE CONTROL SCHEME OF THE FLASH BUTT WELDING During the flash butt welding process, the upset force impacts directly on the effect of flash butt welding quality. The upset force must reach the design values at high speed. Therefore the upset process is the control system that takes output force feedback as a control target. During the upset process the implementation principle is that needing two workpiece approach rapidly, extrude tightly with each other, and must meet a certain value extrusion force ultimately. In the meanwhile, in order to ensure adequate upset force, to ensure uniformity of the upset force and to get a better welding quality, the upset process is accomplished by two hydraulic cylinders simultaneous action, namely, the upset force is the sum of the output force of two cylinders. So the synchronization between two parallel cylinders must be taken into account in the upset hydraulic control system. For the flash butt welding technology, the most important control factor is the size of the applied force, and the load is the servo load provided by the two hydraulic cylinders which is under a mechanical coupling device, therefore, we adopt "parallel structure" synchronous control mode for our plant. "Parallel structure" refers that the set ideal output is tracked by two simultaneous control actuators which can be controlled respectively and driven synchronously.under the premise of compulsory synchronization by the mechanical coupling device, in order to further reduce the damage to the system itself caused by asynchrony from the two cylinders. Displacement synchronization error of the two cylinders is included, only when the error exceeds a certain limit corresponding adjusting will be made to the force servo control law. Flash butt welding process is carried out in motion. Because the force sensor cannot be installed in most of the moving flash butt welding equipment, indirect force feedback methods are applied in practical applications, namely, the pressure of the hydraulic cylinder is used as a force control feedback signal [3,4]. In the upset process if the dynamic pressures of two hydraulic cylinders keep the same, because the pistons areas of the two cylinders are basically consistent, then the output force of the two hydraulic cylinders can be basically synchronous in the fast upset process. Considering the fast force servo requirements in the upset stage, the expected value can be simplified as the step input, and we take response speed, accuracy of pressure difference and output force as the evaluating standard for the system. To sum up, the control scheme principle for the flash butt welding upset stage is shown in Figure 1. In figure 1, subsystem 1 consists of electro-hydraulic servo valve 1 and hydraulic cylinder 1; subsystem consists of electro-hydraulic servo valve and hydraulic cylinder ; the upset output force F needed in the flash butt welding process is sum of F 1 and F, which are generated by the two subsystems. The displacements and pressure values of the two subsystems are detected respectively through the corresponding displacement sensor and pressure sensor. The e 1 and e are the difference between r and the two pressure value respectively, and then both e 1 and e function as the input for MFAC; the third input for the controller is the e p, the feedback cylinders displacement signals difference; the two output signals u 1 and u are the control signals for two servo valves. Fig. 1 The control scheme in the upset stage of flash butt welding When e 1 - e >, MFAC generates force control laws based on the e 1 and e, thus adjusts two cylinder output force F 1 and F. When e 1 -e <, the accuracy requirements of load force is ensured by the synchronous measures of mechanical structure. When hydraulic cylinder output force F 1 and F are regulated, two cylinders position synchronous is corrected 618

3 according to the value of e p. When e p <0.1FS (full stroke of the cylinder), position difference signals are not involved in the force control, and the position synchronization are ensured by the mechanical position synchronization measures in the system; when e p >0.1FS, the values of u 1 or u are adjusted to ensure the mechanical position synchronization and to prevent the damage to the loading device. the hydraulic loading model is shown in Figure ; the main elements parameters are shown in Table 1 and Table. As it is shown in Figure, the Simulink interface module can output the control signals to the two servo valves, which respectively drive the corresponding servo cylinder complete the action and output the upset force. Meanwhile signals of the sensors in the hydraulic model are fed back to the Simulink. The corresponding controller generates the control law according to the control strategy. The control law reacts on the hydraulic loading servo system to make the force servo act. The system consists of three parts, as is shown in the dashed box, from left to right being mechanical load with the coupling force characteristics, hydraulic valve-servo-cylinder system, and hydraulic power source system. Fig. : Hydraulic system model Tab. 1: Table of Elements Parameters Subsystem Subsystem Parameters 1 Servo valve rated flow/(l min -1 ) Servo valve response frequency /Hz Servo valve damping ratio Servo valve dead zone/% Hydraulic cylinder coulomb force/kn Hydraulic cylinder viscous friction coefficient/(n s m -1 ) Hydraulic cylinder piston quality/kg The servo-cylinder butt hydraulic systems share a constant pressure variable pump. Pilot-type electromagnetic relief valve (usually open) plays the role of protecting system and leaking overload. The set pressure of the relief valve is slightly higher than the oil pressure in the system. When the system does not work, the two-bit-two-way valve is powered off and the system leaks charge. The accumulator in the loop plays the role of supplementary oil source and elimination of hydraulic fluctuation. Tab. : Table of others Elements Parameters Title System pressure Variable pump s theoretical flow Rated speed of motor Precharge pressure accumulator initial pressure accumulator capacity Parameters 5MPa 60L/min 1450r/min 18MPa 5MPa 3L The plunger chamber of constant pressure variable pump consists of a plunger and leakage and viscous drag pieces. The plunger is the converter which makes the energy from the mechanical domain to the hydraulic field. The volume of the container depends on the hydraulic plunger displacement and liquid elastic modulus. Meanwhile the inner leakage and the viscous friction of the plunger cavity are taken into account in modeling [4,5]. The system load characteristics include friction, elastic and plastic deformation, and coupling etc., which need to be comprehensively set when modeled. As the servo valve is a typical nonlinear element, it is influenced by oil pressure, load pressure, oil viscosity and elastic modulus etc. IV. MODEL FREE ADAPTIVE CONTROL (MFAC) As mentioned above, the endless rolling process have properties of uncertainty, multi-variable, strong coupling, large degree of complexity, and nonlinearities in the system dynamics. So a practical mathematical model is often unavailable, and this poises a huge obstacle to the design of control system. Recently, some new dynamical linearization model and method are proposed for nonlinear MIMO discrete-time system by Hou [8], which directly based on the so called pseudo Jacobi matrix derived on-line from the input and output information of the system. Hou also gave the relevant modelfree adaptive control (MFAC) algorithms [9-10]. In contrast to other adaptive control scheme, this new adaptive control possesses three main features: 1) the proposed MFAC scheme only use I/O data of controlled system. ) MFAC mechanism does not require any external testing signals and any training process, which are necessary to the nonlinear system adaptive control by using neural networks. 3) the scheme is simple and can be easy used. In this paper, a model-free adaptive controller (MFAC) is adopted to solving the problem of upsetting control. Consider the following MIMO nonlinear discrete-time equation: y( k + 1) = f ( y( k), y(,, y( k ny ), 1 u( k), u(,, u( k nu )) where y ( k ), u( k ) are the output and input at time k, n, y 619

4 m n are the unknown orders of the system, and u f (.) R are unknown nonlinear function. We first make two assumptions with regards to the system. Assumptions 1: The Jacobi matrix of f (., u ( k ),.) with respect to control input u ( k ) is continuous, and the system (1) is generalized Lipschitz with respect to control input output u ( k ), that is meaning for any u ( k ), u ( k ) satisfying 1 f (., u ( k),.) f (., u ( k),.) L u ( k) u ( k) () where L is a finite positive constant. 1 Assumption : The system (1) is Lipschitz-like, that is, for any k satisfying: y( k + 1) y( k) L Δu ( k) (3) where Δ u( k) = u( k) u (, L is a finite positive constant. Lemma1:[9] For the nonlinear system (1), satisfying assumption1-, then there must exist a matrix Φ ( k ), called pseudo Jacobi matrix, when Δu ( k ) 0 we have Δ y( k + 1) = Φ ( k) Δu( k) (4) and Φ ( k) L,where Δ y( k + 1) = y( k + 1) y ( k). [9-10] Fig. 3: The system simulation model Given upset force step signal input as 0MPa. Simulation results are shown in Figure 4 and Figure 5. As we known that the system can be viewed as a -input-3- out control system. So we can adopted the following parameter estimation algorithm (5) and control strategy (6). ˆ( φ k) = ˆ( φ + ηk Δu( [ Δy( k) ˆ( φ Δu( ] μ + Δu(,where ˆ φ ( k) = ˆ(1 φ ) if ˆ φ( k ) ε or Δ u ( ε. (5) Fig. 4: The plot of system s output ρk ˆ( φ k) * u( k) = u( + [ y ( k + 1) y( k)] λ + ˆ( φ k) (6) where η k, ρ k (0,), is step length sequence. μ, λ is weighting factor, ε is a fully small positive number, ˆ(1 φ ) is initial value of ˆ φ ( k ). V. SIMULATION RESEARCH Corresponding to the control block diagram in Figure 1, the system model in section 3 and the design of the controller in section 4, the system comprehensive simulation model in Matlab is shown in Figure 3. Simulation parameters are selected as following: η = 1, ρ = 1, μ = 0., λ = 3.4 u(1,:) = (0.1,0.), u(,:) = (0.05,0.1) y(1,:) = (0,0,0), y(,:) = (0,0,0), y(3,:) = (0,0,0) φ(:, :,) = (0.1,0.1,0.1,;1,0.1,0.5) Fig. 5: The plot of synchronous error VI. CONCLUSION Simulation results show that with MFAC scheme, the maximal dynamic pressure synchronization error is 5 MPa, and the response rising time is less than 1s. The desired pressure input is tracked well in the steady state. By simulation, we succeeded in solving the problem that it is difficult to model mathematics accurately. Simulation result show that the error of dynamic pressure synchronization is little and that the error is stable. The control effect of upset force servo is good and the output of upset force servo is 60

5 stable. Therefore, the MFAC scheme is a feasible control scheme for the flash butt welding of large workpieces system. REFERENCES [1] T. H. Austen, Endless rolling in bar and wire rod mills, IRON And STEEL, Vol.39, pp , October 004. [] K. Wang, Q. Tang, W. Liu, et al. Flash butt welding of large workpieces with industral computer control, J T singhua Univ(Sci & Tech), Vol.4, pp , February 00. [3] N. Lu, X. Sun, Y. Fu, Z. Chen, Method of eliminating synchronism control error in flash butt welding of bill, Journal of Beijing University of Aeronautics and Astronautic, Vol.33, pp , August 007. [4] N. Lu, The research of crucial technology of hydraulic system in steel billet flash butt welding,. Beijing University of Aeronautics and Astronautic, 006 [5] N. Lu, Y. Fu, X.Sun, Digital modeling of double press axialpiston pump and its thermal analysis basing on AMEsim, Journal of Beijing University of Aeronautics and Astronautic, Vol.3 pp ,1086, September 006. [6] Z.Hou, Nonparametric models and its adaptive control, Beijing, Science Press, (In China) [7] K. K. Tak, T H, Huang S.N, Leu F M. Adaptive predictive control of a class of SISO nonlinear systems, Dynamics and control, Vol.11, pp , February 001. [8] R. H. Chi, Z. S. Hou, Dual-stage optimal iterative learning control for nonlinear non-affine discrete-time systems, Acta Automatica Sinica, Vol.33 pp , October 007. [9] Z. Hou, Z. Han, Robust modelless learning adaptive control of nonlinear systems, Control and Decision, Vol.10 pp , March [10] R. Cao, Z. Hou, X. Bai, et al, DC motor speed regulating control system based on the model-free adaptive control method, Electric Drive, Vol.38, pp. 6-30, July