Reductions and Abstractions for Optimization of Modular Timed Automata

Time optimization of concurrent sequences of operations is in this paper solved by timed automata. To reduce the complexity of this classical problem, including applications such as planning and scheduling, an abstraction method has recently been proposed based on local optimization (Hagebring and Lennartson, 2019). In a modular subsystem, local paths without any communication with other subsystems are optimized with respect to time, and when subsystems are synchronized more local behavior appears. The proposed method has shown to be successful, drastically reducing computational complexity for important classes of planning problems. The only drawback is that the synchronous composition includes a heuristic non-standard synchronous composition procedure to achieve true con currency. In this paper a simple solution to this problem is presented based on the original synchronous composition of timed automata. In the transformation of the timed automaton to an ordinary automaton, where time weights are generated, it is first observed that the state space often increases dramatically in this transformation. To solve this complexity problem, an efficient reduction is proposed as a complement to local optimization, and both methods are demonstrated to be very efficient when they are applied to realistic benchmark examples. Copyright (C) 2022 The Authors

Modeling and Optimization of Synchronous Behavior for Packaging Machines

This paper proposes a new modeling solution for the synchronous behavior of packaging machines, and a strategy for maximizing the production rate based on a formal model. A common modeling platform is recommended to handle information exchange and to develop a collaborative workflow, in this paper involving mechanical design and software development. The modeling solution for the synchronous behavior is developed in SysML (Systems Modeling Language), being the common platform. Then a formal modeling language called Sequence Planner Language (SPL) is interfaced with SysML, to overcome some limitations of SysML. The synchronous behavior of the packaging machine is also developed in SPL, from which the optimization problem is defined. The result of the optimization shows that it is possible to improve the efficiency of packaging machines with new configurations compared to more conventional design. The proposed strategy is evaluated for a filling machine at Tetra Pak

Energy optimization of trajectories for high level scheduling

Minimization of energy consumption is today an issue of utmost importance in manufacturing industry. A previously presented technique for scheduling of robot cells, which exploits variable execution time for the individual robot operations, has shown promising results in energy minimization. In order to slow down a manipulator's movement the method utilizes a linear time scaling of the time optimal trajectory. This paper attempts to improve the scheduling method by generating energy optimal data using dynamic time scaling. Dynamic programming can be applied to an existing trajectory and generate a new energy optimal trajectory that follows the same path but with another execution time. With the new method, it is possible to solve the optimization problem for a range of execution times in one run. A simple two-joint planar example is presented in which energy optimal dynamic time scaling is compared to linear time scaling. The results show a small decrease in energy usage for minor scaling, but a significant reduction for longer execution times

Concurrent Design and Control of Automated Material Handling Systems

Lean and agile design and control of an automated material handling system are investigated in this paper. The demands for a minimal number of handling resources and their maximal utilization emphasize the importance of a concurrent structure and control design for a handling mechanism in the conceptual phase. To provide this concurrency, a universal model based on mathematical linear constraints is developed to define a set of part movements without concerning a specific handling technology. Furthermore, an objective characterizing optimal part movements, according to the lean and agile paradigms, is formulated in the conceptual design phase. Control measures, which are obtained by solving the mixed integer linear model including the objective and constraints, provide important keys for designers to conceptualize a proper design of an automated material handling system. To show the application of developed approach, a case study is presented and discussed

Scheduling model for systems with complex alternative behaviour

In this paper we propose a flexible model for scheduling problems, which allows the modeling of systems with complex alternative behaviour. This model could for example facilitate the step from process planning model to optimization model. We show how automatic constraint generation can be performed for both Constraint Programming and Mixed Integer Linear Programming (MILP) models. Also, for the MILP case, a new formulation for mutual exclusion of resources is proposed. This new formulation works well for proving optimality in systems with multiple capacity resources. Some benchmarks for such job shop scheduling problems as well as systems with a large number of alternatives are also presented

Numerical sensitivity of Linear Matrix Inequalities for shorter sampling periods

The numerical sensitivity of Linear Matrix Inequalities (LMIs) arising in the H∞ norm computation in discrete time is analyzed. Rapid sampling scenarios are examined comparing both shift and delta operator formulations of the equations. The shift operator formulation is shown in general to be arbitrarily poorly conditioned as the sampling rate increases. The delta operator formulation includes both recentering (to avoid cancellation problems) and rescaling, and avoids these difficulties. However, it is also shown that rescaling of the shift operator formulation gives substantial improvements in numerical conditioning, whilst recentering is of more limited benefit

A Universal Framework for Lean Design and Control of Automated Material Handling Systems

Lean design and control of an automated material handling system is investigated in this study. A universal framework for modeling and analysis of different types of material handling mechanisms is introduced to obtain a minimum number of resources in a system design and fulfill a desired throughput. This framework is developed in a discrete event simulation environment and applied to a case study based on a real pallet system technology. The minimal design of the pallet system is realized by devising the system universal model

An Integrated CP/OR Method for Optimal Control of Modular Hybrid Systems

This paper concerns the optimal control of modular hybrid systems synchronized by shared variables. Instead of synchronizing the discrete dynamics of the system into one global mode before optimization, Constraint Programming (CP) is used to model the discrete dynamics of each modular system separately. Integrated in the CP solver are also classic Operations Research (OR) models in the form of Nonlinear Programs (NLPs) approximating the continuous dynamics of the system. Using CP considerably decreases the number of NLPs which must be solved, compared to that of using a traditional mixed integer nonlinear programming approach

Optimal Performance of Modular and Synchronized Mechatronic Systems

Optimizing the configuration and overall performance of synchronized modular systems is considered in this paper. The synchronized modules can be considered as a hybrid system, including continuous-time dynamics of local moving devices, combined with high-level discrete event sequences. The continuous-time trajectories are approximated by the Gauss pseudospectral method, resulting in a nonlinear programming (NLP) problem. The optimal configuration generates the maximal production rate subject to dynamic constraints. A complete design procedure is presented and applied to a case study of a packaging machine, where an alternative optimal configuration is achieved compared to current industrial practices