Krist V. Gernaey, Jakob K. Huusom and Rafiqul Gani (Eds.), 12th International Symposium on Process Systems Engineering and 25th European Symposium on Computer Aided Process Engineering. 31 May – 4 June 2015, Copenhagen, Denmark © 2015 Elsevier B.V. All rights reserved.
Optimal Management of Shuttle Robots in a Laboratory Automation System of a Cement Plant Christian Schoppmeyer, a Christian Sonntag, b,c Siddharth Gajjala, d Sebastianb Engell a
Materna GmbH, Voßkuhle 37, 44141 Dortmund Germany Process Dynamics and Operations Group, Department of Biochemical and Chemical Engineering, Technische Universität Dortmund, Emil-Figge-Str. 70, 44227 Dortmund, Germany c euTeXoo GmbH, Behringstraße 65, 44225 Dortmund, Germany d ThyssenKrupp Industrial Solutions AG, Resource Technologies, Cement Services, Graf-Galen-Straße 17, 59269 Beckum, Germany
[email protected];{c.sonntag|s.engell}@bci.tu-dortmund.de b
Abstract To meet the quality requirements in the production of cement, samples are taken in the production process, transported to a central lab and analysed partially automatically. The measurements are used to adjust the parameters of the production process. An optimal management of the laboratory system can lead to significant throughput gains and shorter analysis times. In this contribution, we describe the optimal scheduling of the robots-based laboratory automation system a cement plant. The TA-based approach is embedded into a reactive scheduling approach to handle the different uncertainties in the system, e.g. manually inserted jobs. We show that compared to a priority-based dispatching rule, this approach leads to significant throughput gains while meeting all process-related timing restrictions. Keywords: Process operations, Reactive scheduling, timed automata, laboratory automation.
1. Introduction The increasing demand for high quality cement in construction calls for an efficient integrated quality analysis process in cement production plants. To analyse the quality of the cement, small samples of material are collected online in several stages of the cement production process, and the composition and the properties of the samples are analysed in a central laboratory. Based on these measurements, various control parameters of the production process are adjusted. In advanced cement plants, the sample collection, transportation and analysis is partially automated. In the automated lab, human operators and robots interact in a cooperative setup. In the automated analysis process, the time between the sample collection and the adjustment of the control parameters is strictly restricted but the actual time depends on the load on the lab and on material composition and quality. Additionally, the human workers can insert new samples that have to be analysed at any point in time and are allowed to switch analysers that are required to process the samples to a manual mode thus disconnecting them from the automatic system. The assignment, sequencing, and timing decisions that are required to execute the automated sample handling and analysis process are taken by a scheduling solution, either in the form of a dispatching rule (He
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and Hui (2012)) or by an optimization-based technique, e.g. mathematical programming (Mendez and Cerda (2006)) or TA-based scheduling (Subbiah et al. (2011)). One of the crucial characteristics that make a scheduling problem challenging, especially if strict time limits have to be met, is the presence of uncertainty in the information on the operational level, e.g. varying analysis times, insertion of new samples, decoupling of idle analysers from the automatic system, etc. Such highly dynamic environments demand optimization techniques that can compute new decisions within small amounts of computation time when reacting to unforeseen events. In this contribution, it is shown that a real-time optimization of the sample handling and analysis system can lead to significant efficiency increases in the shuttle-based laboratory automation system that is connected to a cement production plant. The sample scheduling problem is modelled using timed automata (TA). To handle the different kinds of uncertainties in an efficient and robust fashion, the TA-based approach is extended to a reactive scheduling approach that combines the idea of a moving window approach in which schedules are computed one after the other for temporally overlapping windows with an explicit event handling procedure to quickly cope with unforeseen deviations in the schedule execution and the insertion of new jobs. We show that this approach can successfully handle the different uncertain events and can lead to significant throughput gains compared to priority-based dispatching rules while meeting all process-related timing restrictions.
2. The laboratory Automation System The industrial case study considered is the shuttle-based laboratory automation system (LAS) of a cement production plant located in Solnhofen, Germany. The layout of the LAS is shown in Fig. 1. The LAS is equipped with seven collectors which are located in different parts of the continuous cement production plant and collect sample material from the production process. The collectors are connected by a single-capsule pneumatic tube system that transfers the material samples - one at a time - to the laboratory. The laboratory itself consists of a cup filling machine, three storage areas, four analysers and two material crushers which are connected by a single-track shuttle lane and one shuttle robot. All parts of the laboratory, except of the cup filling machine, can also be accessed by human workers. In this case they are decoupled from the automatic system. Furthermore the workers can insert additional samples in the storage areas that must be analysed.
Figure 1: Layout of the laboratory automation system (LAS).
Optimal Management of Shuttle Robots in a Laboratory Automation System of a Cement Plant 3 The cyclic sample analysis process starts with the collection of material in one of the collectors. When the collection of the material is finished, the capsule of the pneumatic tube system is sent to the corresponding collector, filled with the material and sent back to the cup filling machine. Once the material has been poured into up to three different cups, each cup can be picked up by the shuttle robots and has to be transported to different units in the laboratory based on a predefined sample route. The time required by the shuttle robot to transport a cup from one of the unit to another is in the range of a few seconds to tens of seconds and depends on the current position of the shuttle robot, hence it is sequence-dependent. Furthermore, the time required to process the sample in one of analysers depends on the material composition and the quality of the current sample, and may vary. In total, 340 different sample routes exist including the transportation from the seven collectors to the laboratory, the splitting into up to three subsamples. In the current control system, the samples and the shuttle-robot movements are dispatched using a problem-specific algorithm implemented on a programmable logic controller. The complexity of dozens of priority rules makes it challenging to improve the existing algorithm and to implement new features. It can happen that deadlines are missed or that manually inserted samples suffer from starving which means that these samples are not started for a long period of time.
3. Timed Automata-based Scheduling A relatively new method to model and to solve scheduling problems is by means of reachability analysis of timed automata (TA). Timed automata are finite state automata extended by the notion of clocks. They are used to model and to analyse real time systems with discrete dynamics. The timed automata framework offers a transparent graphical problem representation, and models can be built in a modular fashion, making the approach intuitive and comprehensible also for inexperienced users. Due to the modular nature of the framework, changes in the model formulation can easily be implemented. For a detailed introduction to timed automata, see Behrmann et al. (2005). The model of the case study was built in a generic fashion taking advantage of the modular framework of the TA formalism. Following the standard modelling approach for batch scheduling problems, see Panek et al. (2008), for each sample route a separate recipe automaton was created. If the material that was collected is split and poured into more than one cup in the cup filling machine, for each of the subsamples a separate recipe automaton was created. Similarly, for each unit in the laboratory, for each collector, for the pneumatic tube system and for the shuttle robots, separate resource automata were created. The movements of the shuttle robot were modelled according to the modelling procedure for sequence-dependent changeovers (Subbiah et al. (2011)), similar to the shuttle management of a high-rise warehouse in a polymer production plant described in Schoppmeyer et al. (2014a). The large number of 340 different sample and subsample routes made it impossible to create all recipe automata by hand. Therefore the generation of the recipe automata is done online in an automated fashion based on the current state of the system including the current execution state of all samples in the system, the current position of the robot and the current operating mode of the units in the laboratory, i.e. available or decoupled. The automatic procedure developed in Gajjala (2014) works as follows: first, a recipe
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automaton for the sample collection and the transportation using the pneumatic tube is created. In a second step, additional subsample recipe automata are created including the shuttle movements to transport the samples in the laboratory. Once the TA model has been created, the sets of job automata and resource automata are combined on-the-fly by the technique of parallel composition to form a composed global automaton that represents the complete scheduling problem as a directed graph. Every path from the initial node of this graph to a leaf node represents a feasible schedule and the shortest path according to a given cost criterion represents the optimal schedule. To compute the shortest path, the cost-optimal reachability algorithm for TA models is used that was presented in Panek et al. (2008). To enhance the efficiency of the search, different graph search and state space reduction techniques were introduced, see Panek et al. (2008) and Schoppmeyer et al. (2012).
4. Reactive Scheduling Approach As mentioned in the description of the case study above, the material composition and hence the duration of the operations, the insertion times of manually started samples, and the times at which human workers disconnect idle units from the automatic system are not known to the shuttle management system in advance. To tackle the problem of optimizing the sample scheduling problem with online information on the processing duration and insertions and decoupling times, a reactive scheduling approach has been developed. The reactive scheduling approach combines the idea of a moving window approach (Schoppmeyer et al., 2014a) in which schedules are computed one after the other for overlapping windows with an explicit event handling procedure to quickly cope with deviations in the execution of the schedule from the nominal schedule. Fig. 2 shows the structure of the reactive scheduling approach. , The monolithic problem is decomposed into overlapping windows where the decisions in later windows are not taken at the beginning of the scheduling horizon but at later points in time. Hence, it is possible to incorporate new information on the execution status and new job arrivals in the later decisions.
Figure 2: Schematic structure of the reactive scheduling approach.
Optimal Management of Shuttle Robots in a Laboratory Automation System of a Cement Plant 5 The response time tres denotes the time that is required to calculate a new decision. In a dynamic production environment where new decisions have to be taken quickly, the response time should be as short as possible. The actual response time of any algorithm does not only include the calculation time to compute new decisions but also the time required for data handling and communication. Hence not all unexpected events can be handled by a re-computation of the schedule in a new window. The moving window approach is therefore combined with a lightweight explicit event handling procedure based on pre-calculated dependencies between operations. Dependencies are defined following the principles introduced in Schoppmeyer et al. (2014b). Dependencies exist between operations of the same recipe, so-called recipe-based dependencies, requiring to stick to the sequence of the recipe, between operations that are scheduled on the same resource (unit), so-called resource-based dependencies, and between operations that share or require a common utility, so-called utility-based dependencies. Based on these dependencies and using the currently valid schedule, the explicit event handling procedure can quickly – in the range of a few milliseconds - determine upon recording of an unexpected event that occurred at time tu in Fig. 2 which operations can continue, which operations can start as planned and which operation have to be delayed or aborted. Of course, the capabilities of the event handling procedure are limited to redecide on the operations that were planned in the current window. At the same time at which the event handling procedure is started, a new window in the moving window approach is created and a new schedule is computed. In other words, the explicit event handling procedure only has to bridge the response time tres to avoid that the systems stops while waiting for the computation of a new schedule. In principle, the reactive scheduling solution can be used with any scheduling algorithm that solves the static problems within the individual windows. The advantages of selecting the TA-based scheduling approach are that good and feasible schedules are found within seconds, even for larger scale problems, and that the developed automatic model builder can adapt the model easily to the current state of the system, exploiting the modular nature of the TA formalism.
5. Numerical Results To test the performance of the developed approach, a 24 hours scenario that had been recorded in the real plant was simulated. The scenario includes 82 automatically collected samples with strict timing restrictions and 20 additional samples that were inserted at random points in time by human workers – counting the individual subsamples, the total number of orders is 415. Additionally, the scenario includes several delays in the operations that are executed in the analysers caused by the varying material composition and a few disconnections of units by the human workers. In case of any of the uncertain events, the explicit event handling procedure of the reactive scheduling approach is called and a new window is created and scheduled. Table 1 shows the comparison of the results for the 24 hours scenario between the existing dispatching rule and the proposed reactive scheduling approach. It can be seen that the dispatching rule is not able to meet the timing restrictions for all samples while the proposed approach not only meets these constraints but also reduces the average execution time required to process the samples as shown in the last column. For the manually inserted samples, the proposed approach is able to reduce the average execution time by up to 47%.
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Table 1. Comparison of results for the 24 hours scenario. Recipe type
Time limit
Dispatching rule Av. ex. Max. ex. Constr. time time vio. 26.55 46.40 5 28.59 36.46 0 49.37 55.27 0 53.58 61.55 1 124.52 255.01 -
Reactive scheduling approach Av. ex. Max. ex. Constr. time time vio. 25.01 28.33 0 28.56 34.25 0 50.44 51.35 0 49.15 53.55 0 66.11 122.41 -
Perf. difference
Raw meal 30 +7.1% Kiln feed 60 +0.2% Hot meal 60 -2.3% Clinker 60 +8.8% Manually +47.0% inserted Times in minutes, av. – average, ex. – execution, t. – time, max. – maximum, constr. – constraint, vio. – violations, perf. - performance
6. Summary In this paper, a reactive scheduling approach for the sample handling and analysis in the shuttle-based laboratory automation system of a cement production plant was developed. The reactive scheduling approach combines a moving window approach with an explicit event handling procedure to provide an instantaneous reaction to unforeseen events. To solve the scheduling problems in the moving window approach, the TA-based schedule optimization is used, exploiting the advantages of the modular modelling formalism and its performance in calculating good and feasible schedules quickly. The numerical results show that the reactive scheduling approach is able to meet all crucial process-related time restrictions while handling the different uncertain events in a robust fashion. The performance in terms of the throughput of the system is increased by serving all additional samples inserted by the human workers within the required time.
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