Supervisory Control And Performance Analysis Of Stochastic Petri Nets

A flexible manufacturing system(FMS)is defined as a computer control system composed of computer numerical control machine tools and a material transfer system.The resource competition in the system may lead to deadlocks and bring huge economic losses and security problems in some cases.In this work,stochastic Petri nets are used as the main mathematical tool to model FMSs,design the supervisors and analyze the system performance.Its research results are summarized as follows:1.For a stochastic Petri net model,an algorithm of a supervisor with control priority values is first proposed.By combining the optimal deadlock prevention strategy based on the theory of regions with the steady-state marking probability of each deadlock marking and the isomorphic Markov chain of the system,an algorithm for solving the supervisor with control priority values is constructed.Based on the traditional supervisor,the supervisory control strategy defines a control priority value for each control place,and designs an algorithm to solve the control priority value.2.A strategy based on fast transitions is used to control the firing of transitions,so as to prevent deadlocks.Inspired by the properties of immediate transitions and timed transitions of generalized stochastic Petri nets,this thesis defines two different types of transitions: fast transitions and ordinary transitions.By setting the transition types of all enabled transitions under a certain marking,the firing of some transitions can be prevented and the purpose of preventing deadlock markings is achieved.3.A stochastic Petri net is used to model an FMS,and analyze its performance,including token probability density function,dwell time in each marking M,probability of being in a subset of markings,mean number of tokens in a place,utilization rate of a transition and throughput.For a stochastic Petri net system with unreliable resources,a recovery subnet is added to the holder of unreliable resources to simulate resource failure and repair.The probability of failure is defined by adding immediate transitions to the recovery subnet.We calculate the throughput of the system with failure probability and observe the impact on the system throughput by changing the failure probabilities,transition firing rates and supervisory control strategies separately.4.Considering some practical problems and demands found after investigating the actual production line of a factory,we design a mathematical programming problem for different preferences of decision makers is designed.Under the premise of introducing various actual conditions(including the demand ratio of each production line,the functional relationship between failure probability and maintenance cost,transition firing rate,etc.),using the throughput algorithm,combined with mathematical programming,the parameters of the system can be determined according to the different preferences of decision-makers.