The development of an accurate analysis procedure for many laser applications, including the surface treatment of architectural materials, is extremely complicated due to the multitude of process parameters and materials characteristics involved. A one-dimensional analytical model based on Fourier's law, with quasi-stationary situations in an isotropic and inhomogeneous workpiece with a parabolic meltpool geometry being assumed, was successfully developed. This model, with the inclusion of an empirically determined correction factor, predicted high power diode laser (HPDL) induced melt depths in clay quarry tiles, ceramic tiles and ordinary Portland cement (OPC) that were in close agreement with those obtained experimentally. It was observed, however, that as the incident laser line energy increased (>15 W mm -1 s -1/2 ), the calculated and the experimental melt depths began to diverge at an increasing rate. It is believed that this observed increasing discrepancy can be attributed to the fact the model developed neglects sideways conduction which, although it can be reasonably neglected at low energy densities, becomes significant at higher energy densities since one-dimensional heat transfer no longer holds true.
Laser marking of ceramic materials is a multivariable non-linear process. Real-time control of the process requires the understanding of system dynamics and parameter interaction. In this work, direct inverse control ( DIC ) and non-linear predictive control (NPC ) based on arti cial neural networks were applied. The output variable considered for the laser clay tile-marking process was melt pool temperature. The input quantities investigated were laser power and traverse speed. The results show that the NPC accomplished a better reference tracking than the DIC. It was also found that the beam velocity and laser power could well be used to counteract disturbances.
INTRODUCTIONfor non-linear control design has yet evolved. A range of 'traditional' methods for the analysis and synthesis of nonlinear controllers for speci c classes of non-linear systems Laser marking is one of the most widely used techniques exists; phase plane methods, linearization techniques and in producing permanent features on the surface of matedescribing functions are three examples. rials and components [1, 2]. It is necessary to control However, it is the ability of the neural networks to repthe temperature of the melt pool during laser markresent non-linear mappings, and hence to model noning in order to achieve a good quality of the mark. linear systems (e.g. laser processes), which is the feature to Laser marking, which is mainly a thermal process, was be most readily exploited in the synthesis of non-linear characterized as a non-linear process [3].controllers [4]. This ability of neural networks to model a Much literature is available on system identi cation wide class of systems in many applications can reduce time and control system design, but traditionally most of it spent on development and oVer a better performance than has focused on dealing with models and controllers can be obtained with conventional techniques, such as described by linear diVerential or diVerence equations.autotuned proportional-integral-derivative controllers. However, motivated by the fact that all systems exhibit There has been no prior work reported for the closedsome kind of non-linear behaviour, there has recently loop control of laser marking, although work has been been much focus on diVerent approaches to non-linear reported on the modelling of the process [5, 6 ]. In this system identi cation and control design. The ability of paper, arti cial neural networks are used to model and neural networks to deal with non-linear systems is most control a laser marking process. As a test case, high-power signi cant. Arti cial neural networks represent a discidiode laser ( HPDL) marking clay tiles was considered. pline that originates from a desire to imitate the functions of a biological neural network, namely the brain.The great diversity of non-linear systems is the primary 2 ON-LINE CONTINUOUS SYSTEM reason why no systematic and generally applicable theory IDENTIFICATION WITH NEURAL NETWORKS
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