State-space Construction of Hybrid Petri Nets with Multiple Stochastic Firings

Hybrid Petri nets have been extended to include general transitions that fire after a randomly distributed amount of time. With a single general one-shot transition the state space and evolution over time can be represented either as a Parametric Location Tree or as a Stochastic Time Diagram . Recent work has shown that both representations can be combined and then allow multiple stochastic firings. This work presents an algorithm for building the Parametric Location Tree with multiple general transition firings and shows how its transient probability distribution can be computed using multi-dimensional integration. We discuss the (dis-)advantages of an interval arithmetic and a geometric approach to compute the areas of integration. Furthermore, we provide details on how to perform a Monte Carlo integration either directly on these intervals or convex polytopes, or after transformation to standard simplices. A case study on a battery-backup system shows the feasibility of the approach and discusses the performance of the different integration approaches.

Manufacturing Technology on a Mechatronics Line Assisted by Autonomous Robotic Systems, Robotic Manipulators and Visual Servoing Systems

This paper proposes the implementation of an assisting technology to a processing/reprocessing mechatronics line (P/RML), comprising the following: two autonomous robotic systems (ARSs), two robotic manipulators (RMs) and three visual servoing systems (VSSs). The P/RML has four line-shaped workstations assisted by two ARSs—wheeled mobile robots (WMRs): one of them equipped with an RM, used for manipulation, and the other one used for transport. Two types of VSSs—eye to hand and eye in hand—are used as actuators for precise positioning of RMs to catch and release the work-piece. The work-piece visits stations successively as it is moved along the line for processing. If the processed piece does not pass the quality test, it is taken from the last stations of the P/RML and it is transported to the first station where it will be considered for reprocessing. The P/RML, assisted by ARSs, RMs and VSSs, was modelled with the synchronized hybrid Petri nets (SHPN). To control the ARSs, we propose the use of trajectory-tracking and sliding-mode control (TTSMC). The precise positioning that allows the picking up and releasing of the work-piece was performed using two types of VSSs. In the case of the first one, termed eye to hand VSS, the cameras have a fixed position, located at the last and the first workstations of the P/RML. For the second one, named eye in hand VSS, the camera is located at the end effector of the RM.

Management of Hybrid Renewable Energy Systems Using Differential Hybrid Petri Nets

Investigations in this paper concern management of Hybrid Renewable Energy systems. To achieve it, a supervisory system based on hybrid systems concept is designed, in order to ensure power flow between energy generators (solar panel and pico-hydroelectric), batteries and load. Differential Hybrid Petri Net is used to model the proposed supervisory and simulations are made in Matlab environment.Results obtained present a good performance criteria Loss of Power Supply Probability, and this show the effectiveness of our approach in the coordination of HREs components during the energy sharing process by reducing load shedding in microgrid system.

A Graphical Approach for Hybrid Simulation of 3D Diffusion Bio-Models via Coloured Hybrid Petri Nets

Three-dimensional modelling of biological systems is imperative to study the behaviour of dynamic systems that require the analysis of how their components interact in space. However, there are only a few formal tools that offer a convenient modelling of such systems. The traditional approach to construct and simulate 3D models is to build a system of partial differential equations (PDEs). Although this approach may be computationally efficient and has been employed by many researchers over the years, it is not always intuitive since it does not provide a visual depiction of the modelled systems. Indeed, a visual modelling can help to conceive a mental image which eventually contributes to the understanding of the problem under study. Coloured Hybrid Petri Nets (HPNC) are a high-level representation of classical Petri nets that offer hybrid as well as spatial modelling of biological systems. In addition to their graphical representations, HPNC models are also scalable. This paper shows how HPNC can be used to construct and simulate systems that require three-dimensional as well as hybrid (stochastic/continuous) modelling. We use calcium diffusion in three dimensions to illustrate our main ideas. More specifically, we show that creating 3D models using HPNC can yield more flexible models as the structure can be easily scaled up and down by just modifying a few parameters. This advantage of convenient model configuration facilitates the design of different experiments without the need to alter the model structure.