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Previous discrete event simulation studies have found that information exchange can be beneficial to the various stakeholders in resource sharing networks. However, the fundamental dynamic behavior that produces these benefits has yet to be theoretically characterized and quantified. In this paper, frequency response analysis is used to predict the magnitude of inventory variations that result from different options for information sharing between and within entities in a production network. An example from the steel industry is used to illustrate how control theoretical models can be constructed and used to explain how variations in demand propagate through a production network.

Changeability and flexibility are increasingly important features of production in today’s global environment. The influences of change drivers (e.g. fluctuating demand) lead to pressure for change in production systems, and various types of change can be applied. An approach for determining a cost-efficient plan for types of change by analyzing the demand from a frequency perspective is presented in this paper. The approach iteratively optimizes the allocation of types of change in the frequency domain and evaluates the obtained solution in the time domain. The result is improved decision support and increased transparency for planners in obtaining cost-efficiency and agility.

Changeability is an increasingly important feature in today’s production environment. Influences of external and internal change drivers lead to fluctuating pressure for change in production systems, for which various types of change are available as countermeasures. In this paper, fluctuations are analyzed for their frequency content and linked to types of change, characterized by frequency and amplitude of change that can be implemented. This approach is expected to contribute to improved decision making regarding the implementation of change. Industrial data are used to illustrate the frequency content of fluctuation in demand in production systems and relationships with types of change.

The objective of this work is to develop a method for detecting the creation of discontinuities ( i.e. , voids, volume defects) during friction stir welding. Friction stir welding is inherently cost effective, however, the need for significant weld inspection can make the process cost prohibitive. A new approach to weld inspection is required in which an in-situ characterization of weld quality can be obtained, reducing the need for post-process inspection. To this end, friction stir welds with subsurface voids and without voids were created. The subsurface voids were generated by reducing the friction stir tool rotation frequency and increasing the tool traverse speed to create “colder” welds. Process forces were measured during welding, and the void sizes were measured post-process by computerized tomography ( i.e. , 3D X-ray imaging). Two parameters, based on frequency domain content and time-domain average of the force signals, were found to be correlated with void size. Criteria for subsurface void detection and size prediction were developed and shown to be in good agreement with experimental observations. With the proper choice of data acquisition system and frequency analyzer the occurrence of subsurface voids can be detected in real time.

Friction stir forming (FSF) refers the process variant of friction stir welding (FSW) where a joint is achieved through the creation of mechanical interlocking between two constituents by plasticizing one material through the use of the FSW process and in turn forcing said material to flow into the second material. In order to increase the understanding of material flow within this process, a method of quantifying the plasticity of flowing material during the FSF process is needed. A method is proposed in which a capillary hole is drilled into a backing plate used for FSW, and material is extruded through the capillary during processing. The flow of material is characterized and related back to an effective viscosity using the models that form the basis of a capillary rheometer. Initial testing shows promising agreements with CFD simulations of the FSW process (effective viscosity values within the range of 10 5 to 5×10 6 Pa-s). Furthermore, a promising initial agreement is shown when using effective viscosity values determined from the capillary method in a previously derived model that describes the infiltration for carbon fiber with plasticized aluminum produced by the FSW/FSF process.

Adjusting planned lead times when order due dates are missed is an intuitive reaction, but these adjustments can be counterproductive when inherent order lead time instability endangers achievement of logistic targets. In this paper, dynamic models are used to characterize lead time instability in two approaches to work system lead time adjustment. Minimum damping is calculated as a function of lead time adjustment parameters. Industrial data are used to illustrate how the approach provides guidance in selecting production planning and control parameters, with the goal of ensuring stability as a key dynamic foundation for satisfying work system logistic performance targets.

The objective of this work is to develop a surface prediction model for thermocapillary regime pulsed laser micro polishing (PLμP). Two distinct polishing regimes have been discovered: capillary and thermocapillary. The difference between the two regimes is the melt pool flow mechanisms. A surface prediction model for capillary regime PLμP has been developed with results within 10% of experimental measurements. However, this model's predictions deviate from measured outcomes for longer pulse durations due to the presence of thermocapillary flow, which is not included in the capillary regime model. Previous work has also shown that this thermocapillary flow can be well predicted by multiphysics modeling [5] and that a simpler analytical relation can be derived to predict the extent of thermocapillary flow in the form of a normalized average displacement (NAD) of the liquid metal during laser polishing [5] . The current work incorporates the NAD analytical prediction for thermocapillary flow into the capillary regime surface prediction method to create a model that is valid for both the capillary and thermocapillary polishing regimes. The proposed thermocapillary flow model was tested for area polishing of titanium alloy Ti-6Al-4V and S7 tool steel. Conditions were chosen to include both the capillary and thermocapillary regimes. In all cases, the predicted average surface roughnesses were within 15% of the measured values. The results indicate that the proposed prediction model adequately captures the process physics and can provide a guide for parameter selection and process optimization of PLμP across a wide processing window.

The goal of this work is to develop a method for detecting the creation of discontinuities during friction stir welding. This in situ weld monitoring method could significantly reduce the need for post-process inspection. A process force model and a discontinuity force model were created based on the state-of-the-art understanding of flow around an friction stir welding (FSW) tool. These models are used to predict the FSW forces and size of discontinuities formed in the weld. Friction stir welds with discontinuities and welds without discontinuities were created, and the differences in force dynamics were observed. In this paper, discontinuities were generated by reducing the tool rotation frequency and increasing the tool traverse speed in order to create “cold” welds. Experimental force data for welds with discontinuities and welds without discontinuities compared favorably with the predicted forces. The model currently overpredicts the discontinuity size.

Future cyber-physical production systems will support new business models such as sharing concepts for the joint use of resources by different companies. This paper explores resource sharing in a production network and explains how different sharing mechanisms impact the performance of the stakeholders and the dynamics of the entire network. These analyses are carried out using a simulation model and a control-theoretic model. The results show that the introduced sharing approach controls inventory and resource utilization, but it can cause shifts and fluctuations in performance depending on the information that is exchanged.

Tool steels such as S7 are often used for molds and dies, an application that requires both an extremely smooth surface and tight geometric tolerances. Pulsed laser micro polishing (PLμP) is a process capable of achieving significant surface smoothing quickly and without removing material. This paper presents the effect of melt pool diameter (laser spot diameter) on surface topography during pulsed laser polishing. How the manipulation of melt pool diameter during three-pass laser polishing can reduce surface roughness is also discussed.

It is desirable to maintain consistent dynamic behavior of WIP regulation in work systems with multiple modes of capacity adjustment (floaters, overtime, etc.) and different adjustment periods, delays and limits in the various modes. Coordination of these modes is necessary in order to keep optimal dynamic behavior. In this paper, a control-theoretic model of WIP regulation is presented first that accommodates multiple capacity adjustment modes with different adjustment periods (per shift, per day, per week, etc.) and different delays in implementing adjustments. Then an algorithm is presented for adapting WIP adjustment parameters in the presence of capacity adjustment limits and mode priorities so that a specified dynamic performance goal continues to be met. Results of simulations driven by industrial data are used to illustrate the effect of limits and performance goals on dynamic behavior, and conclusions are drawn regarding the effectiveness of adaptive regulation of WIP by coordinating multiple modes of capacity adjustment.

A control-theoretic, order due date deviation regulation method is presented in this paper for work systems that can dynamically adjust their capacity and order release times. The relationship between due date deviations and work system capacity is shown to be nonlinear and time varying, and a method is presented for characterizing the relationship quantitatively in real time and using this information in an adaptive capacity adjustment control law that maintains favorable dynamic behavior in the presence of the nonlinearities. Control theoretic analyses are included in the paper for designing the dynamic behavior of due date deviations and work system capacity, and results of discrete event simulations driven by industrial data are used to illustrate dynamic behavior. Conclusions are presented regarding the efficacy of combining scheduling and due date deviation regulation and the resulting tradeoffs between due date deviation and capacity.

Reducing lead time variability of production systems has been shown to be advantageous, enabling constant flows and improved on time production. Nevertheless, fluctuating order inflows, disturbances and other factors are known to induce varying workloads, and hence produce fluctuating actual lead times. Adjusting planned lead times as a countermeasure against low due date reliability could lead into the drawbacks of the Lead Time Syndrome. The update frequency of planned lead time adjustments as well as the delay until changes take effect in a production system can significantly influence the occurrence of the Lead Time Syndrome. Nevertheless, taking these effects into account, production control via planned lead time adjustments remains a suitable means for increasing due date reliability. Another production planning and control approach is to avoid fluctuating actual lead times using capacity adjustments, which can be implemented by either lead time regulation or work in process regulation. These strategies have been integrated into a control theoretic simulation model that enables comparisons to be made of resulting performance; thus, preferable strategies can be identified for different settings of inflow fluctuations, update frequencies and delay.

The objective of this work is to establish nominal friction stir [butt] welding process parameters for joining 4.76-mm-thick aluminum alloys 6061-T6 and 7075-T6 and to improve the joint quality via programmed tool offsets. In addition, dynamic tool–workpiece interface temperatures are measured during welding and used to explain the effects of alloy placement and weld tool offset from the joint. Weld tool offsets into the retreating side AA7075 increase the measured tensile strength of the dissimilar joint. The increased joint strength is facilitated by lower average weld temperatures with increasing amount of AA7075 stirred into the nugget.

A real-time wireless temperature measurement system has been developed and successfully implemented for closed-loop control of tool shoulder–workpiece interface temperature. The system employs two thermocouples in through holes and measures the shoulder and pin interface temperatures with an angular resolution as small as 10°. Both temperatures correlate with weld quality (mechanical testing and weld cross sections), e.g., all welds in 4.76-mm-thick 6061-T6 with an average shoulder interface temperature below 520 °C and an average pin interface temperature below 460 °C fail in the weld zone instead of the heat-affected zone, have unacceptable tensile strengths and in some cases voids. Similarly, welds with shoulder temperatures above the solidus temperature result in a degradation of the weld quality. It was found that a shoulder interface temperature of 533 °C results in the highest weld quality; hence, this temperature should be used as the setpoint temperature in the control system with a constant travel speed of 400 mm/min. The temperature measurement strategy was shown to be able to indicate welds with insufficient shoulder–workpiece contact, thus potentially identifying and preventing welds with detrimental weld quality due to lack of penetration. It was shown that backing plates of different thermal diffusivity change the heat flow out of the weld zone, hence weld temperature, and caused a measurable impact on the weld strength. By changing other process parameters, e.g., through a temperature control system, weld quality can be maintained in the presence of such changing thermal boundary conditions.

Thermocapillary flows can be generated in pulsed laser micro polishing by using longer melt durations, significantly reducing surface roughness at the expense of creating residual high spatial frequency process features. However, polishing with short melt durations, with no thermocapillary flows, effectively smoothens high spatial frequency surface features. This paper presents a two-pass polishing process in which the first pass takes advantage of thermocapillary flows in significantly reducing the surface roughness, and the second pass removes the residual process features. Experimental results of polishing micro end milled Ti6Al4V surfaces are presented that indicate 72% improvement in average surface roughness.

A method is presented in this paper for coordinating multiple modes of capacity adjustment in work systems with autonomous WIP regulation with the goal of maintaining desired fundamental dynamic behavior. To prevent overcorrection of capacity, adjustments involving floaters, temporary workers, overtime, etc. need to be coordinated, and it is shown that control-theoretic analysis can be used to develop algorithms for determining combinations of adjustments that result in WIP regulation that is as fast-acting as possible yet non-oscillatory. Results of discrete event simulations in Arena, driven by industrial data, are used to illustrate the dynamic behavior of WIP regulation in an autonomous work system that incorporates such an algorithm and multiple modes of capacity adjustment.

The current methods for welding aluminum alloys to carbon fiber composites rely heavily on the adhesive bond created when a melted polymer solidifies in contact with the aluminum surface. This bond may be improved by achieving mechanical interlocking of the carbon fibers and the aluminum alloy, so that load bearing fibers contribute to the bond strength. Friction Stir Welding (FSW) holds potential as a process to achieve such interlocking by locally heating and plasticizing the metal under significant load to cause infiltration of the metal into the carbon fiber weave. During preliminary investigations, AA6061-T6 was friction stir welded in contact with dry carbon fiber bundles, and the infiltration of aluminum into the fibers was measured. The results were compared to an accepted polymer infiltration model that was adapted for aluminum infiltration, giving promising initial agreement. This suggests that the plasticized aluminum in FSW can be treated as a fluid with an effective viscosity, and that well established polymer infiltration models can form the base of a metal composite FSW model.

The objective of this work is to predict the final roughness of metal surfaces that have undergone pulsed laser micro polishing. The motivation for pulsed laser micro polishing is to reduce the surface roughness of parts whose surface texture can approach the feature size. Being able to predict the magnitude of the polishing and frequency (wavelength) content of the surface will assist in the design of optimal processing parameters with minimal experiments. Laser pulses are used to create shallow melt pools with a controlled size (e.g., depth) and duration in order to allow surface tension forces to “pull down” asperities with small radius of curvature. There is no ablation occurring in the process being modeled. The melt depth and duration are predicted with a transient, two-dimensional axisymmetric heat transfer model with temperature-dependent material properties. The surface of the melt pool is analytically modeled as oscillations of stationary capillary waves with damping resulting from the forces of surface tension and viscosity. Above a critical spatial frequency, f cr , a significant reduction in the amplitude of the spatial Fourier components is expected. The work described in this paper extends the concept of critical frequency to a physics-based prediction methodology for predicting the spatial frequency content and surface roughness after polishing, given the features of the original surface, the material properties, and laser parameters. The proposed prediction methodology was validated using line polishing data for stainless steel 316L and area polishing results for pure nickel, Ti6Al4V, and Al-6061-T6. The predicted average surface roughnesses were within 12% of the values measured on the polished surfaces.

Autonomous production is characterized by local and autonomous decision making of intelligent logistic objects such as work systems that adjust production rates and parts that decide which products they “want” to become and which orders they will fill. It is important to understand and have confidence in dynamic interactions of these objects and their resulting performance. In this paper the dynamic interaction of autonomous products and work systems is investigated using a hybrid simulation model and a control-theoretic model. Results obtained using both models show that these dynamic interactions can be well behaved and predictable. Through linearized models of continuous input flows at nominal rates, tools of control theory are shown to build confidence in complex system dynamic behavior of interacting autonomous logistics objects when decision-making logic is modeled in a way that makes control-theoretic analyses tractable.

One means of adapting to variation in demand is making capacity flexible so that work in progress (WIP) can be regulated; however, this can significantly influence the dynamic behavior of production networks in which there is high local autonomy. Control-theoretic models are a convenient means for investigating and designing the dynamics of such networks, but the fidelity of these models is not well understood. In this paper, results obtained using discrete-event simulations are used to assess the control-theoretic approach, providing evidence that fidelity varies depending upon factors such as WIP level and the magnitude of capacity adjustments.

This paper considers the problem of local capacity H∞ control for a class of production networks of autonomous work systems with time-varying delays in the capacity changes. The system under consideration is modeled in a discrete-time singular form. Attention is focused on the design of a controller gain for the local capacity adjustments which maintains the work-in-progress (WIP) in each work system in the vicinity of planned levels and guarantees the asymptotic stability of the system and reduces the effect of the disturbance input on the controlled output to a prescribed level. In terms of a matrix inequality, a sufficient condition for the solvability of this problem is presented using an appropriate Lyapunov function, which depends on the size of the delay and is solved by existing convex optimization techniques. When this matrix inequality is feasible, the controller gain can be found by using LMI Toolbox Matlab. Finally, numerical results are provided to demonstrate the proposed approach.

In this paper, we consider the capacitated multi-item lot sizing problem with setup times. The problem is to schedule J different items over a horizon of T periods with the objective to minimize the sum of setup cost and inventory holding cost. To achieve feasible high-quality solutions, we propose a new solution approach which hybrids Nested Partitions and Mathematical Programming (HNP-MP). Nested Partitions is a partitioning and sampling based heuristic method with a global perspective on the problem. In the proposed new method the Mathematical Programming method is implemented to calculate the promising index and to provide a good guidance on partitioning in the Nested Partitions framework. A time-oriented decomposition heuristic method, Relax-and-Fix, is also implemented to obtain good promising regions and speed up the computational process. Computational results based on benchmark test problems show that the approach is computationally tractable and is able to obtain good results. The approach outperforms other state-of-the-art approaches found in the literature.

In this paper, dynamic behavior is compared for two methods of local work in progress (WIP) regulation in autonomous work systems in production networks. In one method, work systems do not share information regarding the expected physical flow of orders between them; in the other, order-flow information is shared to compensate for the variable dynamic effects of physical order-flow coupling. In both methods, the work systems adjust production rate with the objective of maintaining a desired amount of local WIP. A linear discrete-time dynamic model of the flow of orders between work systems is used, which promotes identification of fundamental properties such as characteristic times and damping. The results demonstrate the need for order-flow information sharing in establishing desired network dynamic behavior. Examples are used to illustrate behavior in the general case of omnidirectional order flows and the special case of unidirectional order flows.

The objective of this work is to generate irregular, smooth, adaptive laser scan trajectories for pulsed laser polishing. Traditionally pulsed laser polishing, like other surface finishing processes has used zig-zag scan paths. Zig-zag trajectories are simple in nature, are comprised of sharp turns, the dynamics of the positioning system are not considered, and more importantly are not adaptable because the path generation is independent of surface condition. In this paper, the authors present an intelligent scan trajectory generation scheme that can overcome these limitations. These trajectories are based on the artificial potential fields method of path planning that take the surface condition into account. Computer simulations are presented to illustrate the characteristics of the path and guidelines are developed for choosing the trajectory generation parameters. Experiments show that these trajectories result in marginal improvements in the average surface roughness when compared to the traditional zig-zag trajectories, all the while overcoming the limitations. Finally, smooth, irregular scan trajectories are generated for a micro end milled Ti6Al4V surface with a feature that needs no polishing, thus illustrating the versatility of the trajectory generations scheme., by Madhu Vadali, Chao Ma, Xiaochun Li, Frank E. Pfefferkorn and Neil A. Duffie

In this paper, a method is presented for information sharing in production networks with large numbers of autonomous work systems for the purpose of maintaining constant dynamic properties when the structure of physical order flows between the work systems is omni-directional and variable. It is shown that information sharing is necessary if undesirable behaviors such as oscillation or slow response are to be avoided. A method for designing the dynamic properties of such networks is presented along with a method for distributed computation and communication of information needed to locally compensate for the expected order flows from other work systems.

In this paper, a dynamic model is presented for production networks with a potentially large number of autonomous work systems, each having local capacity control. The model allows fundamental dynamic properties to be predicted using control-theoretic methods, together with the response of variables such as work-in-progress and lead-time for the network and its individual work systems. This is illustrated using industrial data. The behavior of one of the work systems in this network is analyzed further, and the results are compared with results obtained using a discrete event simulation model.

A hybrid surface treatment method is presented on S7 tool steel by alloying the surface layer with boron and following with pulsed laser micro polishing (PLuP). The objective of the hybrid approach is twofold: First, surface alloying changes the properties of the surface layer that are relevant to the PLuP process (e.g. liquid metal density, viscosity, and surface tension). This allows more control over the laser polishing phenomena for better smoothing. Second, surface alloying and laser melting/quenching is proposed as a novel method of creating amorphous surface coatings. In this work, boron was introduced into the surface of an S7 tool steel sample using pack cementation. This sample was then ground on a bias to create a flat surface with a gradient in chemical composition and this surface was laser melted. The effect of this variation in alloy chemistry on the surface features created by pulsed laser melting is presented.

1Department of Engineering, Faculty of Engineering and Science, University of Agder, 4898 Grimstad, Norway 2College of Engineering, University of Wisconsin System, Madison, WI, USA 3ArcelorMittal Bremen GmbH, Bremen, Germany 4BIBA-Bremer Institut fur Produktion und Logistik GmbH, Planning and Control of Production Systems (PSPS), University of Bremen, Hochschulring 20, 28359 Bremen, Germany 5University of Picardie Jules Verne, MIS-UPJV, 7 Moulin Neuf, 80000 Amiens, France

In this paper, a dynamic model is developed for multi-workstation production systems in which closed-loop capacity controls for regulating WIP in individual workstations are coupled by adding predictive control, making capacity adjustments a combination of compensation for local disturbances and anticipation of downstream effects of capacity adjustments made upstream in the system. The added coupling at the control level combined with intrinsic coupling at the order-flow level effectively integrates planning and control, but increases system complexity. Control-theoretic methods are used to make dynamic analysis tractable and improve understanding of dynamic behaviour, which is illustrated using data from an industrial production system.

In this paper, a model is described that represents the dynamics of a multi-workstation production system that incorporates closed-loop production planning and control. The model is used to predict the response of the production system to work disturbances and the propagation of disturbances through the system. Capacity control designs are evaluated with respect to their removal of the effects of work disturbances and response to changing capacity demands in upstream workstations. Methods of control engineering are used to make the analysis tractable, as well as improve understanding and control of complex dynamic behavior.

In this paper a discrete dynamic model of a single workstation is used to design and analyse control algorithms for closed-loop PPC that improve performance, especially response to disturbances such as rush orders and periodic fluctuations in capacity, while ensuring that dynamic behavior remains favorable and robust. The presence of delays in adjusting capacity presents challenges in both dynamic analysis and control algorithm design that are addressed in the paper. Methods of control engineering, such as transfer function and frequency response analysis, are used to make analysis of fundamental system properties tractable and to improve control of dynamic behavior.

Distribution of control in heterarchical manufacturing systems creates challenges in making and modelling cooperative decisions, such as when to produce discrete parts on multiple manufacturing machines. Furthermore, the dynamics of decision-making interactions between highly autonomous entities in these systems are poorly understood and can be undependable because of the absence of a master controller or optimizer. To investigate these phenomena, a system for distributed control of the arrival time of discrete parts in multiple-machine, multiple-processing-step manufacturing systems has been developed and is described in this paper. In the system, continuous control laws replace heuristics, and part arrival times are adjusted locally using feedback of expected completion times. The reported results confirm that the dynamics of the distributed systems are favorable, with arrival times converging exponentially to theoretically predictable values regardless of whether or not a set of arrival times exists that, given the machine resources available, results in parts being completed on their due dates. In the paper, closed-form solutions are obtained for nonlinear, discontinuous differential equations that describe system behavior in different dynamic regions and explain arrival time convergence and intrinsic cooperation between discrete parts in their competition for production machinery. Furthermore, the systems are shown to be responsive to real-time disturbances that can be caused by rush orders, machine failures, and changes in part processing times. These results build confidence in design, implementation, and operation of distributed control systems for manufacturing, regardless of whether they are heuristic or control-law based, even though they appear to behave in a chaotic manner due to the interactions of highly autonomous entities.

An analysis of a production planning and control system with closed-loop control of backlog and work-in-progress is presented in this paper, illustrating integration of methods of control engineering with methods of production engineering. The architecture of the system is described and a control-theoretic dynamic model is developed that includes uncertainties in capacity and work input that result from equipment failures, rush orders, etc. Transfer function analysis is used to model dynamic relationships between system inputs and variables including backlog and work-in-progress. The results are used to select control laws for desired system performance and to calculate system response.

The objective of this paper is to define and derive a dimensionless number as a function of material properties and process parameters to quantify the extent (magnitude) of thermocapillary flow in pulsed laser micropolishing (PLμP). Experimental work has shown that thermocapillary flow can tremendously reduce surface roughness (smoothing effect) although it inevitably introduces additional surface features (roughening effect) at the same time. Both the smoothing and roughening effects increase as the extent of thermocapillary flow increases. The extent of thermocapillary flow is the bridge from the available information (i.e., initial surface profile, material properties, and process parameters) to the polished surface profile to be predicted. A dimensionless number, called the normalized average displacement of a liquid particle in a single laser pulse, is proposed and derived via analytical heat transfer and fluid flow equations. The calculated normalized displacement is found to be proportional to the measured slope of the introduced features on Ti6Al4V surface polished with various process parameters, which indicates that the dimensionless number successfully describes the extent of thermocapillary flow. The normalized average displacement will be very useful for prediction of polished surface profile and hence parameter selection and process optimization in the future.

Extensive experimental work has shown that pulsed laser micro polishing (PLμP) is effective for polishing micro metallic parts. However, the process physics have not been fully understood yet, especially with respect to the melt pool flow. A reliable physical model can be of significant assistance in understanding the fluid flow in the melt pool and its effect on PLμP. In this paper, a two-dimensional axisymmetric transient model that couples heat transfer and fluid flow is described that was constructed using the finite element method. The model not only provided the solutions to the temperature and velocity fields but also predicted the surface profile evolution on a free deformable surface. The simulated melt depth and resolidified surface profiles matched those obtained from optical images of PLμPed Ti6Al4V sample cross-sections. The model was also used to study the effect of laser pulse duration on the melt pool flow. The study suggests that longer pulses produce more significant fluid flows. The cut-off pulse duration between capillary and thermocapillary regimes, below which minimal Maragoni flow should be expected, was estimated to be 0.66 μs for Ti6Al4V, which also matched well with the experimental results. It is evident that the coupled model offers reliable predictions and thus can be extended for a more complex parametric study to provide further insights for PLμP.

Heterarchical control architectures with fully distributed control have been developed in order to improve responsiveness and effectiveness of manufacturing shop-floor control systems. The dynamics of these highly distributed systems have been difficult to predict particularly when control is based on heuristics. In this paper a dynamical model is developed for a single machine processing an arbitrary number of parts. The structure of the system, which requires queuing of parts when they arrive at a machine, leads to nonlinearities such as dead-zone and discontinuities. A continuous arrival time controller of the integrating type is used that results in a system that can be modeled using nonlinear differential equations that can be solved using a method due to Filippov (1960, 1988). This enables prediction of trajectories of part arrival times and derivation of closed form expressions for steady-state values. The analytical model for the dynamics is validated and the dynamic response of the system is illustrated using numerical simulation.

Heterarchical manufacturing systems with highly-distributed, real-time control of arrival times of parts exhibit high levels of robustness and adaptability to changes in machine availability, part mix, processing times, and due dates. However, distribution of control and queuing in these systems makes analysis and modeling difficult, particularly when parts proceed through multiple processing steps and these processing steps can be performed by more than one machine. In this paper, a general approach is presented for modeling these systems. Examples of multiple-machine and multiple-processing-step systems are presented, illustrating their behavior and closed-form solutions obtained of discontinuous differential equations that represent their dynamics.