Deadlock prevention technique using additional transitions for Petri nets

ABSTRACT

Siphon control has been utilized as a general methodology for systems of simple sequential process with resource (S³PR) deadlock systems. Although siphon control imposes additional control places on S³PR systems, it cannot guarantee that the maximum permissiveness is achieved. To solve the problem of deadlock prevention for S³PR, a new policy to design a deadlock-free supervisor with the maximally permissive system is proposed using additional transitions. Additionally, this approach can solve the problem of deadlock prevention for systems of sequential systems with shared resources (S4PR) system models.     

Minimal strict siphons extraction for S3PMR

Abstract

A siphon is an important structure object for deadlock control. Insufficiently marked siphons lead to deadlocks. Deadlock occurs due to inappropriate resource sharing. Hence most of the research focuses on the minimal siphon extraction problem covering a set of places representing resources, which, for general Petri Nets is known to be an NP‐Complete problem. Control places and arcs are often added to the original net to prevent a siphon from becoming insufficiently marked. The number of siphons grows rapidly with the size of the net leading to very complicated control nets. Efficient enumeration of problematic siphons is an urgent research topic. Earlier, we proposed fast algorithms to find all such siphons for both S³PR and S²CPR (System of Synchronized Choice Processes with Resources). However, it was assumed that siphons occur between adjacent processes. This paper removes this assumption and develops an algorithm for S³PMR which is more powerful than S³PR by allowing a state to use more than one resource and than S²CPR by allowing more than one state to use the same resources. Comparisons with previously published work have been made.     

A deadlock prevention policy for a class of Petri net models of flexible manufacturing systems

This paper focuses on the problem of deadlocks in automated flexible manufacturing systems (FMS). Based on Petri nets, a deadlock prevention policy is proposed for a special class of Petri nets, S³PR. We embed the deadlock avoidance policy (DAP) of conjunctive/disjunctive resources upstream neighbourhood (C/D RUN) into the deadlock prevention policy (DPP), and allocate the underlying (sequential) resources reasonably to guarantee the absence of deadlock states and processes. First, siphons in a net model are distinguished by elementary and dependent ones. From the set of elementary siphons, a set of linear inequality constraints expressed by the state vector can be formalised. After being modified by the proposed policy, a set of generalised mutual exclusion constraints (GMEC) expressed by the marking vector can be found. Then monitors based on the GMEC are added to the plant model such that the elementary siphons in the S³PR net are all invariant-controlled and no emptiable siphon is generated due to the addition of the monitors. This novel deadlock prevention policy can usually lead to a more permissive supervisor by adding a smaller number of monitors and arcs than the existing methods for the design of liveness-enforcing Petri net supervisors. Two manufacturing examples are utilised to illustrate the proposed method and compared with the existing ones.     

Comment on ‘Technical Note – Reaching more states for control of FMS’

Uzam and Zhou (Uzam, M. and Zhou, M., 2006. An improved iterative synthesis method for liveness enforcing supervisors of flexible manufacturing systems. International Journal of Production Research, 44 (10), 1987–2030) were able to obtain a near optimal controlled model for the net S³PR with 21,562 good states. Chao's deadlock recovery scheme (Chao, D.Y., 2010. Technical Note – Reaching more states for control of FMS. International Journal of Production Research, 48 (4), 1217–1220) improves by reaching more states (21,585). However, this paper identifies a problem and proposes a solution.     

Maximally permissive deadlock prevention via an invariant controlled method

Recently, researchers have proposed a novel and computationally efficient method to design optimal control places and an iteration approach that computes the reachability graph once to obtain a maximally permissive, if any, liveness-enforcing supervisor of flexible manufacturing systems (FMS). The approach solves the set of integer linear inequalities to compute control places. If, given a Petri net model, no solution exists, the optimal control place does not exist for the Petri net model. We discover that a solution always exists for systems of simple sequential processes with resources (S³PR), but not for the case of FMS modelled by generalised Petri nets (GPN). We propose a theory to prove that there are no good states that will be forbidden by the control policy for S³PR, in which live and dead states cannot have the same weighted sum of tokens in the complimentary set of a siphon. For a system of simple sequential processes with general resource requirements (S³PGR²) modelled by GPN, we find the reason why the integer linear programming (ILP) may not have solutions, which is consistent with the fact that optimal supervisor synthesis for GPN remains unknown. We show that live and dead states may have the same weighted sum of tokens in the complimentary set of a siphon in a GPN. These theoretical results are verified by case studies.     

Regular trends in complexation of <Superscript>188</Superscript>Re with human blood albumin microspheres

A study of regular trends in the complexation of ¹⁸⁸Re with denatured albumin in microspheres (AMSs) prepared by dispersing a solution of human blood albumin in olive oil with continuous stirring and heating to 130°C showed that the reaction course largely depends on the concentration of the reducing agent (Sn²⁺) and on the temperature. With an increase in the Sn²⁺ concentration and temperature, the rate of the complex formation and the level of ¹⁸⁸Re binding with AMSs regularly increase. The ¹⁸⁸Re-AMS stability in vitro is essentially independent of the reaction mixture acidity in the pH range 3–7, whereas the stability of the labeled AMSs in vivo is influenced by pH more appreciably. Tests on laboratory animals showed that the most stable preparation was obtained at pH 5.     

An efficient real-time deadlock-free control algorithm for automated manufacturing systems

In recent years, deadlock issue has received considerable attention in the real-time control realm of automated manufacturing system (AMS). In this paper, we propose a simple and easily adaptable deadlock avoidance algorithm using a graph theoretic approach. Unlike Petri-net based methods which are complex and static from the viewpoint that once they are constructed and implemented, it is not easy to modify them as the system configuration is changed, and operate them coupled with other shop-floor control modules such as a dispatching controller, our algorithm can be used cooperatively with a dispatching controller and expanded with little modification. The core of the algorithm consists of two modules: resource allocation policy and a cycle detection method. In particular, the resource allocation policy is of importance in our algorithm because even though the cycle detection method is employed, deadlock may occur under wrong resource allocation policies. Throughout this paper, we propose a quasi two-step resourceallocation policy with which our deadlock avoidance algorithm can detect and avoid deadlock just one step before deadlock.     

Scheduling of deadlock and failure-prone automated manufacturing systems via hybrid heuristic search

This work focuses on the scheduling problem of deadlock and failure-prone automated manufacturing systems, and presents a new scheduling method by combining a robust supervisory control policy and hybrid heuristic search. It aims to minimise makespan, i.e. the completion time of the last part. Based on the extended reach ability graph of the system, it establishes a new heuristic function and two dispatching rules to guide the search process for a schedule. By embedding a robust supervisory control policy into the search process, it develops a polynomial robust dynamic window search algorithm. Failure and repair events of unreliable resources may occur during the execution of a schedule obtained by the proposed algorithm and may make the schedule infeasible. To reduce the influence caused by them and ensure all parts to be finished, this work proposes two event-driven strategies. The first one suspends the execution of the parts requiring failed resources and those to be started until all failed resources are repaired and permits only those parts that have already been processed on working machines to be completed. The second one invokes the proposed algorithm to obtain a new schedule at the vertex generated after a resource failure or repair event and executes the new schedule. Both strategies are effective while the latter performs better at the expense of more computation.     

Robust H 8 output feedback control for general nonlinear systems with structured uncertainty

Abstract

In this paper, the robust H ⁸ output feedback control problem for general nonlinear systems with L ₂‐norm‐bounded structured uncertainties is considered. Sufficient conditions for the solvability of robust performance synthesis problems are represented in terms of two Hamilton‐Jacobi inequalities with n independent variables. Based on these conditions, a state space characterization of a robust H ⁸ output feedback controller solving the considered problem is proposed. An example is provided for illustration.     

An algorithm to find the minimal initial markings of resource places ensuring liveness of finite-capacity S3PR

Deadlock prevention can be achieved by configuring proper initial markings to obtain a live Petri net model. For a class of Petri nets called finite-capacity Systems of Simple Sequential Processes with Resources (S³PR), an algorithm is proposed to find the minimal initial markings of resource places ensuring its liveness. First, conditions on initial markings of resource places are computed under which the strict minimal siphons (SMS) can never be emptied. Then, the minimal initial markings of resource places are computed to ensure liveness of the net. By the proposed algorithm, a live net can be obtained without changing the structure of the original model. The main practical implication of our work is that it can lower the facility cost. A simple example is used to illustrate the application of the algorithm.     

LQR/RPS design of robust controllers for a one‐link robot

Abstract

In this paper, a design method for robust controllers for a one‐link robot is developed. Based on a linearized model of this nonlinear robot system, the linear quadratic regulator (LQR) design method is incorporated with a reduced parameter sensitivity (RPS) technique to design a robust proportional‐plus‐integral (PI) controller to achieve better performance in position control. This robust controller can tolerate real parameter variations resulting from the mechanical loads of applications. A direction method is further developed and used to evaluate the stability robustness of this controlled system. Combining the direction method with the LQR/RPS method, a robust PI controller can be generated to avoid improper over‐design. Both computer simulation and experimental results demonstrate the feasibility and effectiveness of the proposed approach.     

Control of deadlock and blocking for production systems with unreliable workstations

Over the past decade, the development of supervisory controllers for automated manufacturing systems has been an active area of research with particular attention focusing on deadlock avoidance. Most work to date assumes that system workstations do not fail. This paper considers deadlock and blocking problems in systems with one unreliable workstation, the objective being to develop supervisory control policies that allocate workstation buffer space so that failure of the workstation server does not propagate through blocking to effectively stall other portions of the system. In short, when a workstation fails, the system should automatically continue producing all part types not requiring that workstation. To accomplish this, the supervisory controller must simultaneously avoid deadlock and buffer allocation states that are not feasible initial states for the 'reduced' system resulting from workstation failure. When the workstation fails, the controller must then simultaneously avoid both deadlock and buffer allocation states that are not feasible initial states for the original system so that transition to normal operation is smooth when the failed workstation is restored. This paper shows this class of problems through several examples, identifies properties that controllers must satisfy to deal effectively with these problems and develops a polynomial control policy that satisfies these properties.     

Adaptive backstepping motion control of induction motor drives

Abstract

In this paper, an adaptive backstepping controller is proposed for position tracking of a mechanical system driven by an induction motor. The mechanical system is a single link fixed on the shaft of the induction motor such as a single‐link robot. The backstepping methodology provides a simpler design procedure for an adaptive control scheme and provides a method to define the sliding surface if the robust slidingmode control is applied. Thus, the backstepping control can be easily extended to work as an adaptive sliding‐mode controller. The presented position control system is shown to be stable and robust to parameter variations and external disturbances. The effectiveness of the proposed controllers is demonstrated in experiments.     

Fuzzy adaptive preventive maintenance in a manufacturing control system: a step towards self-maintenance

In this paper, a framework of integrating preventive maintenance (PM) and manufacturing control system is proposed. Fuzzy-logic control is used to enable an intelligent approach of integrating PM and a manufacturing control system. This will contribute to the novel development of an integrated and intelligent framework in those two fields that are sometimes difficult to achieve. This idea is based on combining work on an intelligent real-time controller for a failure-prone manufacturing system using a fuzzy-logic approach (Yuniarto, M.N. and Labib, A.W., Optimal control system of an unreliable machine using fuzzy logic control: from design to implementation. Int. J. Prod. Res. (in press a); Yuniarto, M.N. and Labib, A.W., Intelligent real time control of disturbances in manufacturing systems. Integr. Manuf. Syst.: Int. J. Manuf. Technol. Manage. (in press b) and the work on PM proposed by Labib et al. (Labib, A.W., Williams, G.B. and O’Connor, R.F., An intelligent maintenance model (system): an application of analytic hierarchy process and a fuzzy logic rule-based controller. J. Oper. Res. Soc., 1998, 49, 745–757)). The aim of the research is to control a failure-prone manufacturing system and at the same time propose which PM method is applicable to a specific failure-prone manufacturing system. The mean time to repair and mean time between failures of the system are used as integrator agents, by using them to couple the two areas to be integrated (i.e. a maintenance system and manufacturing system).     

Formulation study of a patch containing propranolol by design of experiments

Objective: To evaluate the feasibility of a transdermal patch containing propranolol (PR).

Method: Skin penetration enhancers (SPEs) able to improve the skin permeability of PR were selected and a quality by design approach was applied to the development of the patch by a 2⁴ full factorial design. The permeation profile of PR from the formulations was assessed in in vitro permeation studies performed by using Franz diffusion cells and human epidermis as membrane. Finally, skin irritation was evaluated by the Draize test.

Results: N-methyl pyrrolidone (NMP) resulted as the best SPE: in addition, the critical factors influencing the PR diffusion through the human epidermis when loaded in the patch resulted in the matrix thickness (X₁, p?=?0.0957) and PR content (X₃, p?=?0.0004) which improved the flux; conversely, NMP lacked its enhancement effect when loaded in the patch and the increase in its concentration (X₄, p?=?0.006) affected the drug permeation through human epidermis. The flux of optimal formulation was 12.7?μg/cm²/h. On the basis of the steady-state concentration and clearance of PR, the estimated patch surface was 100–120 cm², since the activity of PR is related to its Senantiomer and no in vivo bioconversion occurs.

Conclusion: A patch containing (S)-PR was prepared and the (S)-PR flux (13.3?μg/cm²/h) permitted to confirm the suitability of a transdermal administration of PR. In particular, the use of a 50?μm thick methacrylic matrix containing 8% (S)-PR and 15% NMP can allow to develop a patch non-irritating to the skin, in order to ensure a constant permeation flux of PR over 48?h.     

Real-time deadlock-free scheduling for semiconductor track systems based on colored timed Petri nets

This paper addresses the problem of real-time deadlock-free scheduling for a semiconductor track system. The system is required to process wafers continuously, cassette by cassette. The process is not necessarily a repeated one. In addition, the system is deadlock-prone and its modules are failure-prone. Thus, real-time scheduling approaches are required to achieve high-performance. The problem can be solved in a hierarchical way. A deadlock avoidance policy is developed for the system as a lower-layer controller. With the support of the deadlock avoidance policy, heuristic rules are proposed to schedule the system in real-time. An effective modeling tool, colored–timed resource-oriented Petri net, is presented. It is shown that with this model we can schedule a system to achieve satisfactory results in real-time. This method is tolerant to module failures.     

Robust controllers design and efficiency analysis for a brushless servo system

Abstract

This paper investigates the design of robust controllers for a class of ac servo drives, the brushless servo motor drive, and presents the efficiency and power factor analysis of the drive system. Robust PI, H ², and H ⁸ control techniques are applied to the design of servo controllers. A fully digital control system is constructed to experimentally verify the controller performance. The steady‐state characteristics of the servo drive are derived and are measured on‐line by a microcomputer‐based efficiency measurement system. The theoretical development is validated by the experimental work.     

Reaching more states for control of FMS

Uzam and Zhou (Uzam, M. and Zhou, M., 2006. An improved iterative synthesis approach for liveness enforcing supervisors of flexible manufacturing systems. International Journal of Production Research, 44 (10), 1987–2030) synthesised a near optimal controlled model for a well-known S³PR with 21,562 good states, 19 states short of the optimal one (21,581). It is non-trivial and interesting to synthesise an optimal controlled model as we will present it in this paper.     

Robust mixed H 2/H ∞ controller for uncertain neutral state‐input delayed systems via LMI optimization approach

Abstract

In this paper, the problem of designing a robust mixed H ₂/H _∞ controller for a class of uncertain neutral state‐input delays system is considered. Based on Lyapunov‐Krasovskii functional theory, a delay‐dependent criterion is derived for the existence of a desired mixed H ₂/H _∞ controller, which can be easily constructed by certain feasible linear matrix inequalities (LMIs). Furthermore, a convex optimization problem is formulated to solve for a robust mixed H ₂/H _∞ controller which achieves the minimization of an upper bound of the closed‐loop H ₂ perforance measure.