3D Control System of the Electron Beam Spot

3D Control System of the Electron Beam Spot S. E. Oltean 1, M. Abrudean 2 1 Petru Maior University of Târgu Mure, Electrical Engineering Department, soltean@upm.ro 2 The Technical University of Cluj Napoca, Automation Department, Mihai.Abrudean@aut.utcluj.ro Abstract - Electron beams have many special properties which make them particularly well suited for use in materials processing, wherever conventional techniques failed or proved to be inefficient. The entire process has many time varying parameters, but some of the most important for the quality of the material processing are given by the directing parts. The paper presents a 3d control system of the electron beam spot which contains the using and deflecting components. Due the nature of the process we used a PI control for the deflecting system and an adaptive fuzzy control for the using system. I. INTRODUCTION Electron beam material processing is a non-conventional technique used in microelectronics, nuclear technologies, aeronautics. The special electron beams properties like high resolution, long depth of field attainable, high power density energy make them very useful in material processing. Some applications of the electron beam system are melting, welding, evaporation, refining and thermal surface treatment. If we consider just the welding process the desired geometrical parameters are the depth h and width b of the penetration shown in figure 1 [1]. The welding parameters and the heat affected zone (abbrev. HAZ) depend on the electron beam equipment variables such as electron beam current, accelerating voltage, using distance, electron beam speed, deflections in the Ox and Oy directions, electron beam diameter, using coil current and deflection coil current. Also, the quality of processing is influenced by the electrons emission, vacuum in the work chamber or electron beam gun, electromagnetic fields, X radiation, material properties. Figure 1. The weld and HAZ The heat absorption, the penetrations of the electrons in metal, using of beam are rather complicated, making their modeling a difficult task to solve. Also, the examination of the electron guns variable is very difficult due the nature of the process. Thus it is a necessity of a modern control strategies implemented on the digital systems to obtain the technological demands. The using module is one of the final stages that interference in the electron beam motion and because of the complexity of the process we designed in [2,3] a fuzzy adaptive using system which controls the energy density of the electron beam transmitted to the workpiece. The minimum spot diameter on the material surface (obtained with electron beam using) provides the highest depth of penetration. Figure 2 shows the influence of the using system over the size, shape and quality of the weld [4,5]. Figure 2. Beam us influence over the weld Deflecting system or/and mechanical movement with CNC table are used to cover all possible target points positions of the workpiece surface or to follow the seam trajectory. We designed in [2,6] a PI control system for linear deflection of the electron beam. Combining these automatic systems (one using and two deflecting components for the Ox and Oy directions) result a multivariable 3d control of the electron beam spot. The reference signals for the using and deflecting systems are obtained using a 3d decomposition of the seam trajectory detected via a image capturing system. The paper is structured in three parts as follows: - the presentation of the electron beam equipment; - the presentation of the 3d control system of the electron beam spot position; - the presentation of the experimental results for a case study using the electron beam 3d control. In the final section of the paper some conclusions about the electron beam processing control are given. The study of the documentation in this field and the experiments are currently being put into practice by the authors based on the electron beam equipment CTW 5/60 (5kW maximum power at 60kV accelerating voltage) developed by Petru Maior University of Târgu Mure in partnership with Electrical Research Institute ICPE Bucharest [7]. 1-4244-2577-8/08/$20.00 2008 IEEE

II. ELECTRON BEAM EQUIPMENT The most common systems of this type used in manufacturing are high vacuum design. The main parts of the equipment are the triode gun and the vacuum system that provides high vacuum environment, without the beam cannot be generated. The triode gun design consists of the cathode, composed of the filament and the massive cathode, electrode or grid, anode, using and deflection coils. The vacuum system ensures a pressure level of 10-3 10-4 Pa and it is controlled by a multitasking digital system implemented on the microcontroller and on PC. To avoid accidents, any error that may appear in this unit is pointed out and preparing sequences for material processing are halted. The emission of electrons from the incandescently heated termoemission filament, which is saturated during the process by a predetermined amount of electrical current, generates the main beam. A negative high voltage potential is applied to the filament cathode assembly, referred to as the accelerating voltage of 4060kV. Another voltage, lower than the accelerating voltage is applied to the grid cup or bias assembly. In this way the grid cup acts as a valve that controls the volume of electron energy that can flow from the cathode to attracting targets. The first target, situated in the triode gun, is an anode at a positive potential, which forms the beam. Then the used beam of electrons is led using using coil to a secondary target, situated in the workbox, consisting of a metallic workpiece, where the kinetic energy of the electrons is converted into thermal energy and the metal is heated. The metallic workpice offers a conductive path to earth to complete the circuit. This target can be stationary and the electron beam energy deflected using deflection coils or the workpiece can be moved using a CNC table [4,5]. The high power electron beam system with the classic triode gun is shown in the figure 1. In this scheme the high voltage supply, high voltage controller, electron beam current controller and other intermediary or secondary modules are not drawn [7]. The magnetic using coil is located beneath the anode assembly and is circular in design and concentric with electron beam. An electrical current is passed through the coil, which produces magnetic fluxes that provides convergence of electron beam. The deflection coil is created with four wound coils positioned at right angles to the column. Another important part in the experimental equipment is the electrons collector composed of the four electrodes used to capture reflected electrons from target surface (workpiece). These electrons offer utile information about the material processing. III. ELECTRON BEAM 3D CONTROL SYSTEM Electron beam 3D control system contains two types of control: classical PI for the deflecting components and fuzzy adaptive (Fuzzy Model Reference Learning Control FMRLC) for the using component [2]. A. Deflecting System The two deflecting coils, located beneath the using coil, create two magnetic fields; both are perpendicular to the symmetry axis of the electron gun. A constant deflection on the linear axis (Ox or Oy) needs a magnetic field with constant intensity generated by the one deflecting coil (Ox or Oy). The magnetic fields created with both coils determine the position of the al spot on the workpiece plane xoy. To prevent the aberrations of the magnetic lenses and deformations of the spot, the deflection is made on small angles. From this point of view the resulting maximum working area is 5cm 2. The mathematical model of the deflecting systems contains two components: the stationary model and the dynamic model. The deflection of the electron beam on Ox axis x defl for a deflecting current i xdefl and a constant value of the accelerating voltage Uacc is given by (1). Stationary model is in fact a particular solution of the dynamic equations of the electrons when the electric and magnetic fields distributions are known. We neglect the variation of the electron beam velocity crossing through deflecting coils [2,6] x defl e0 2 m e k b a 0 d U defl acc l b n i xdefl (1) Where the distance from the coils to the material surface d defl, the coil length l b, the coil dispersion a, the induction curve k b, the electron charge e 0, the electron mass m e, the absolute permitivity µ 0 and the number of turns n are constants. The dynamic model of the deflecting system on the linear axis Ox is given by (2). L s di xdefl dt R i u (2) s xdefl xdefl Figure 3. Electron beam equipment The inductivity L s and resistance R s characterize the dynamics of the deflecting coil. Due the nature of the deflecting system we designed in [6] a PI controller which gives the desired performances ( =4.3%, st=0). The PI controller has 0.045 seconds integrative and

73.94 proportional constants. This controller was translated in discrete time form using Tustin method and 1 milliseconds sampling time. In the Oy direction the process and controller models have similar forms. B. Focusing System Using the using coil the convergence of electron beam and Oz axis movement are assured at high precision. Finally, the geometry of the welded seam is obtained with desired depth and width and the concentrated high energy determines a very small heat affected zone. Mathematical model of the using system has also two components: the stationary model and the dynamic model [2]. Including the magnetic field distribution and using some optics concepts from the dynamic equations of the electrons that cross through the electromagnetic coil results the stationary model of the using system. This approximate model consists in the nonlinear dependencies between the number of turns n, using current i and using distance z [2,3]. z i 85 m e 0 e 2 0 R U n i 2 This model is influenced by the accelerating voltage and cross-over distance (distance from starting point of the electron beam termoemission and using coil). The cross-over distance value depends on the electrodes potentials, main current and space charge distribution around the massive cathode. Equation (4) represents the dynamic model of the using coil. L s di dt acc (3) R i u (4) s This dynamic model has as input the prescribed using coil voltage u and as output the using current i. The inductivity L s and resistance R s characterize the dynamics of the using coil. Because the relation 3 is an approximation, influenced by the electron beam equipment variables, nonlinearity and disturbances we implemented a fuzzy model reference learning control FMRLC for the using system [2,3]. This fuzzy adaptive system is capable to learn and to adapt to different unknown situations. FMRLC has the same structure as conventional model reference adaptive control MRAC, which is composed of four main parts: the plant, the controller, the reference model and the adjustment mechanism [8,9,10]. The reference model characterizes the desired performance of the system. In this case we use a unitary model because plant output z has to follow the shape of the seam depth (contained in z d ). The adjustment mechanism uses the adaptation error e a to adjust the controllers parameters. The adaptation error e a =z m -z represents the deviation of the plant output from the desired using distance. The using distance will generate the desired depth of penetration of electron beam. The FMRLC structure is shown in figure 4. Figure 4. FMRLC for electron beam using The adaptive controller is fuzzy and to develop the FMRLC a direct fuzzy controller had been designed first. Designing direct fuzzy controller means to choose and to process the inputs and outputs of the controller and to build its four elements [2,3,8]: the rule base, the inference engine, the fuzzification interfaces and the defuzzification interface. We consider as inputs to the fuzzy system: the error e (kt)=z d (kt)-z (kt) and change in error d (kt)=(e (kt)- e (kt-t))/t. The output variable of the fuzzy controller is the command uf oc (kt) applied to the using coil. The universe of discourse of the variables (the domain) was modified using three scaling gains (g e, g d, g u ). Five symmetric membership functions MF for the three fuzzy variables was chosen, 50% overlapping triangular shaped membership functions. The fuzzy controller implements a rule base made of a set of IF-THEN type of rules. These rules were determined heuristically based on the knowledge of the plant [2]. Figure 5. Inputs MF and RB for the fuzzy controller

The inference engine is min-max type, which for the premises, uses maximum for the OR operator and minimum for the AND operator. The conclusion of each rule, introduced by THEN, is also done by minimum. The final conclusion for the active rules is obtained by the maximum of the considered fuzzy sets. To obtain the crisp output, the centre of gravity (COG) defuzzification method is used. This crisp value is the resulting controller output. The learning mechanism contains an additional fuzzy system, called fuzzy inverse model which acts like a second controller. This second controller updates the rule base of the direct fuzzy controller by acting upon the output variable (its membership functions centers). The fuzzy inverse model has a similar structure to that of the controller (the same rule base, membership functions, inference engine, fuzzification and defuzzification interfaces) [8]. The output of the inverse fuzzy model is an adaptation factor p(kt) which is used by the rule base modifier to adjust the centers of the output membership functions of the fuzzy controller. The adaptation is stopped when p(kt) gets very small and the changes made to the rule base are no longer significant [8]. The rule base modifier adjusts the centers of the output membership functions in two stages: the active set of rules for the fuzzy controller at time kt is first determined and than the centers of the output membership functions, which were found in the active set of rules are adjusted. The centers of the output membership functions, which are not found in the active set of rules, will not be updated. This ensures that only those rules that actually contributed to the current output z were modified. These means that only local changes will be made to the controllers rule base. C. 3D Control System Welding is the main application of the electron beam equipment and usually welding after a regular trajectory with electron beam can be done with manual control of the deflecting and using systems or moving the CNC table. If the seam trajectory is more complex in a random manner the welding process must be assisted by digital equipments and the desired seam welding is obtained using 3d control systems. Via capturing and digitizing interface images of 256x256 pixels representing the 5x5cm 2 workpiece surfaces are recorded on personal computer. These images are saved in grayscale bitmap format with 8bits per pixel (Figure 6) [2]. The seam trajectory is determined from the images of the material surface using image processing methods and decomposed on the Ox, Oy and Oz axes for the directing systems. Three dimensional control system of the electron beam spot is shown in figure 7 [2,3]. Figure 7. 3d control system The trajectory (on xoy plane) is followed with deflecting systems and the desired depth of penetration is achieved with using system. IV. RESULTS This section presents the results we obtained using the multivariable control system of the electron beam spot which contains deflections on two axes and using in depth of the material. For Ox deflecting system the reference varies from 0 to 5 centimeters in 2.5 seconds. The reference, the response of the system (Ox component of the welding trajectory) using PI controller, the command voltage of the coil and the control error are shown in figures 8 and 9. Figure 6. Material surface image Figure 8. Reference and deflection on Ox axis

Figure 11. Control error on Oy The deflection on Oy axis y defl follows the reference signal y defld for this component and steady state error shown in figure 11 converges to zero. Figure 12 shows the evolution of the Oz using system reference and the response signal, the command voltage of the using coil, control error and adaptation error. Figure 9. Command voltage and control error on Ox It is obvious that the deflection on Ox axis x defl tracks the reference signal x defld obtained from the seam trajectory and steady state error shown in figure 9 is zero. For Oy deflecting system the reference, the response (Oy component of the welding trajectory) using PI controller, the command voltage of the coil and the control error are shown in figure 10 and 11. Figure 10. Reference, deflection, command voltage on Oy Figure 12. Functional signals on Oz

The using distance z follows very closely the reference signal z d for this component and steady state error shown in figure 12 converges to zero. This demand it is carried out via the fuzzy adaptive control. The learning mechanism uses the learning error e a to modify the fuzzy controller parameters. The start regime used in this case for the using coil current is 0.65 amperes which considers the 0.4 meters distance from the using coil to the material. The response of the three dimensional control system represents the 3d position of the electron beam spot. This 3d response viewed from different points is shown in figure 13 and tracks the seam trajectory shown in figure 6. affected zone (HAZ) of the material are some characteristics that depend on the digital control systems. Focusing distance control and trajectory tracking are the final stages of automation in the electron beam equipment. Following unknown seam trajectories with random shapes on small areas just using the manual command and CNC table may be a difficult task to solve. The plant modeling error, the disturbance influences and nonlinearities are also some unwanted elements in classic system control. So, modern strategies are recommended in these situations. Deflecting components of the electron beam equipment permit al spot control on the material surface without mechanical inertia. The seam trajectory on the material surface is determined by the image capturing system which captures the reflected electrons. Due the nature of the deflecting components the deflections on Ox and Oy axes are obtained with PI control. The major problem is provided by the using component (al spot control in Oz direction) because this part has a big influence over the final weld shape. Overused or underused beams are some effects that must be avoided in this type of welding. Moreover, the using model is nonlinear and depends on other electron beam variables. These phenomenons diminish the suppleness of the weld. The advantage of the fuzzy model reference learning control is given by the learning mechanism which assures that us distance follows the seam depth and in this way high performance and quality of material processing are carried out. Combining the deflections components with the using part a 3d control system of the electron beam spot was presented in this paper. The results of PI and adaptive fuzzy control shown in this paper indicate the possibility to perform a distributed and modern strategy control of the 3d spot position of the electron beam. REFERENCES Figure 13. 3d response V. CONCLUSIONS The electron beam processing system is complex with many variables, which make it very hard to be controlled. The high depth and reduced width of welding penetration, the specific power of the electron beam in al point and the small heat [1] R. Bakish, Introduction to electron beam technology, John Wiley & Sons, Inc., New York, 1985. [2] S.E. Oltean, Aplica ii de conducere inteligent i adaptiv a instala iilor de prelucrare neconven ional cu FE, PhD Technical Report, The Technical Universitz of Cluj Napoca, 2006. [3] S.E. Oltean, H. Grif and A.V. Duka, Fuzzy adaptive control simulation of the electron beam using, 13 th International Symposium on Modelling, Simulation and Systems Identification, Gala i, 2007, pp. 46-51. [4] M. Dul u, Controlul proces rii cu FE, Universitatea Petru Maior Târgu Mure, 2005. [5] S.E. Oltean, Stadiul actual în tehnologii neconven ionale de prelucrare a materialelor, PhD Technical Report, The Technical Universitz of Cluj Napoca, 2005. [6] S.E. Oltean, H. Grif and A.V. Duka, Electron beam using and deflection control systems, Interdisciplinarity in engineering Scientific International Conference, Târgu Mure, 2007, pp. IV-26-1-IV-26-6. [7] ***, Technical documentation. Instala ia de prelucrare cu fascicul de electroni CTW5/60, Universitatea Petru Maior Târgu Mure. [8] K.M. Passino and S. Yurkovich, Fuzzy Control, Addison Wesley Longman Inc., 1998. [9] P. Ioannou, Robust adaptive control, University of Southern California, 2003. [10] K.J. Astrom and B. Wittenmark, Adaptive Control (2 nd edition), Addison Wesley Longman Inc., 1995.