Alan A. Desrochers

A hybrid methodology for synthesis of Petri net models for manufacturing systems

Beginning with a bounded (safe), live, or reversible Petri net as a first-level net model for a system, Petri nets are synthesized by first refining operation places through basic design modules in top-down modular ways, then adding nonshared resource places stepwise, and finally adding shared resource places step by step in a bottom-up manner. Refinement theory is extended to include reversibility of Petri nets. Parallel and sequential mutual exclusions are used to model shared resources. Design of the first-level Petri nets is discussed, and two basic kinds of Petri nets, choice-free and choice-synchronization, are given to cope with different types of manufacturing systems. The major advantages of the method are that the modeling details can be introduced in incremental ways such that complexity can be handled, and the important properties of the resulting Petri net are guaranteed so that costly mathematical analysis for boundedness, liveness, and reversibility can be avoided. A manufacturing system consisting of four machines, one assembly cell, two shared robots, and two buffers is used to illustrate the design methodology. >

Performance evaluation of automated manufacturing systems using generalized stochastic Petri nets

Generalized stochastic Petri net (GSPN) modules are used as basic building blocks to model and analyze complex manufacturing systems. This modular approach facilitates model construction and helps manage the complexity of modeling large manufacturing systems. The structural analysis ensures that the model is live and bounded, which guarantees that the equivalent Markov chain (MC) is ergodic. The temporal analysis is used to derive performance measures such as average production rates and average in process inventories. The main advantage of Petri nets (PNs) over MCs is that the number of places and transitions increases only slightly as the manufacturing system complexity increases, whereas the number of states in the MC increases exponentially. In addition, there is no need to enumerate all the possible states manually since they are automatically generated from the GSPN model. As a result, PN models can still be easily obtained for complicated interconnected systems. The straightforward application of this approach is demonstrated and reviewed for several manufacturing case studies. For serial transfer lines it is proven that this modular approach results in live and bounded GSPN models. Comparisons are made with deterministic and reduced state-space models. Examples containing as many as 9614 states are presented. >

Pumped-storage hydro-turbine bidding strategies in a competitive electricity market

This paper develops optimal pump-hydro unit bidding strategies in a competitive electricity market. Starting from a weekly forecasted market clearing price (MCP) curve, an algorithm to maximize the profit of a pump-hydro unit considering reserve bids is developed. A comparison between the optimal bidding strategy and a fixed-schedule weekly generating and pumping strategy is provided.

Real time control of multilevel manufacturing systems using colored Petri nets

A colored Petri net (CPN) model of a cell controller capable of real-time control and monitoring of multiple workstations is described. The need to incorporate the ideas of both computer integrated manufacturing (CIM) and flexible manufacturing systems (FMS) is discussed, and the controller is based on these concepts. The CPN for the cell controller is presented and described. The controller in this case controls two workstations: the Cincinnati Milacron 5VC machining center and a robotic assembly workstation using an Adept robot. An analysis of the net is performed, and relevant portions are presented. A data structure for implementing this type of a CPN is given. The code for the controller is divided into application-dependent and -independent code. An execution algorithm is provided. The conclusions emphasize the advantages of CPNs in modeling and analysis for discrete-event control of manufacturing systems.<<ETX>>

Modeling of nonlinear discrete-time systems from input-output data

Abstract An algorithm is presented that produces a polynomial state affine model for a discrete-time nonlinear system. The method uses only input-output information and is based on a difference equation approximation to the input-output map. From the difference equation, a behaviour matrix is constructed, to be used in the state affine realization algorithm. The difference equation approach requires the estimation of fewer parameters than the usual Volterra series. A state space model is then obtained directly from the difference equation. As a byproduct, a method for calculating the Volterra series directly from the difference equation is obtained. Practical applications to nonlinear systems are included.

Structure of minimum-time control law for robotic manipulators with constrained paths

The authors address the problem of the structure of minimum-time control (MTC) of robotic manipulators along a specified geometric path subject to hard control constraints. By using the extended Pontryagin minimum principle (EPMP) and a set of parameterized robot dynamic equations, it is shown that the structure of the minimum-time control law requires that one and only one control torque is always in saturation on every finite time interval along its time-optimal trajectory, while the rest of the torques are adjusted so that the path constraint on the motion is not violated. This is in contrast to the point-to-point minimum-time control law, which requires that at least one of the control torques is always in saturation. Simulation results are presented to verify the structure of the MTC law.<<ETX>>

A proof of the structure of the minimum-time control law of robotic manipulators using a Hamiltonian formulation

A Hamiltonian canonical formulation that yields a new and straightforward proof of the structure of the minimum-time control (MTC) law for m-link robotic manipulators is used. It is shown that the structure of the MTC law requires that at least one of the actuators always be in saturation. A numerical algorithm is presented. The algorithm converts the original problem, possibly a partially singular one, into a totally nonsingular optimal control problem by introducing a perturbed energy term in the performance index. It is shown that the solution to the perturbed problem converges to that of the MTC problem in the sense of the performance index as the perturbation parameter approaches zero. The control algorithm is used in a simulation to verify the MTC law structure. >

A top-down approach to systematic synthesis of Petri net models for manufacturing systems

The authors propose an approach to systematic synthesis of Petri net models for manufacturing systems. It is based on top-down, modular, and decomposition philosophies which make the stepwise refinement of the Petri-net models possible. Using the proposed method, it is possible to obtain a Petri net model which is guaranteed to have the most important properties in the context of manufacturing: safeness, liveness, and reversibility. A formal problem statement is presented first. Then, the previous research on synthesis approaches is reviewed. Next, several modules are defined which, when combined according to a proposed algorithm, lead to the derived model. It is proven that the algorithm yields the safeness, liveness, and reversibility properties. An example of piston-rod assembly is used to demonstrate the proposed method.<<ETX>>

Multiobjective optimization of a plastic injection molding process

It is well known that the PID regulator has been very successful and widely accepted for controlling industrial systems where one objective function is the performance criterion. The question is whether the same success can be achieved for more than one objective function using the basic PID controller, while preserving its simplicity for use by an operator. Here the authors explore the use of multiobjective optimization for the purpose of extending PID controllers to applications that require the optimization of multiple objectives. An algorithm is implemented that runs in real-time and provides immediate feedback to a process operator about the current operating point. It was applied to the tuning of a PID controller to meet multiple objectives for the plastication phase of an injection molding process. The algorithm was implemented on an injection molding machine and allowed to tune the controller on-line. Simulation and experimental results are presented and compared. >

Modeling and analysis of multi-agent systems using petri nets

The development of theoretical-based methods for the assessment of multi-agent systems properties is of critical importance. This work is a preliminary investigation on methodologies for modeling, analysis and design of multi-agent systems. Multi-agent systems are regarded as discrete-event dynamic systems and Petri nets are used as a modeling tool to assess the structural properties of the multi-agent system. Our methodology consists of defining a simple multi-agent system based on the abstract architecture for intelligent agents. The abstract architecture is modeled as a discrete-event system using Petri nets and structural analysis of the net provides an assessment of the communication and coordination properties of the multi-agent system. Deadlock avoidance in the multi-agent system is considered as an initial key property, and it is evaluated using liveness and boundedness properties of the Petri net model.