R. Judd

Ohio University · Department of Electrical Engineering and Computer Science

Calculating the performance measures of a manufacturing system is of fundamental importance in many industrial engineering problems, particularly scheduling. Graph theory and max-plus algebra provide mathematical tools that aid in the analysis of these systems. The max-plus algebra representation of a system is represented by the system matrix A. I...

A common way to represent a deterministic job shop is by a graph, where the nodes represent the operations and edges represent the sequence of the operations along with the schedule. Makespan is the popular measurement used to measure the efficiency of a manufacturing system. Previous research has shown that a very computational efficient mechanism...

The goal of this research is to accelerate improvement heuristics which use a graph to model the system and calculates the makespan, i.e., longest path in the graph, during each iteration. These heuristics iteratively perturb the graph and recalculate the makespan in each iteration until a satisfactory schedule is determined. We propose Improved St...

This paper proposes an algorithm called the Maximum Length Recalculation Algorithm (MLRA) to update the length of the longest path to affected nodes in a perturbed Directed Acyclic Graphs (DAG) where multiple edges are simultaneously deleted and added. MLRA can find all these lengths through a single pass. It is mathematically proved that MLRA is c...

Manufacturing scheduling improvement heuristics iterate over trial schedules to determine a satisfactory schedule. During each iteration, a performance measure (e.g. makespan) is calculated. The paper presents an efficient algorithm, Structural Perturbation Algorithm (SPA), that accelerates the calculation of the makespan. This means all scheduling...

In this paper, max-plus algebraic techniques are used to develop an efficient method to calculate the makespan of a perturbed job-shop manufacturing system. The methodology assumes that the perturbations in schedule are confined to a particular sub-system which is termed the variant V and the rest of the system is called the invariant I. The paper...

This paper presents an improvement of the work presented at the ISERC 2012 & 2013. It focuses on reducing the complexity of calculation of makespan for a perturbed job shop with recirculation of jobs. Recirculation is defined to be when the time that jobs enter a machine is dependent on the time when jobs leave the same machine. The work presented...

The paper extends work presented a year ago at the 2012 ISERC [2]. It focuses on reducing the complexity of calculating the makespan of a perturbed job shop. This paper allows the recirculation of jobs. Recirculation is defined to be when the time that jobs enter a machine is dependent on when jobs leave the same machine. As in the previous work, t...

In this paper, a novel pictorial methodology to calculate the makespan of a perturbed job shop manufacturing system is developed. The work is based on work that was developed in last year ISERC [2]. This new methodology is called the CSBAD (Compressed Serial Block Addition Diagram). The methodology assumes that the perturbations in schedule are con...

The chapter presents a novel building block approach to developing models of manufacturing systems. The approach is based on max-plus algebra. Within this algebra, manufacturing schedules are modeled as a set of coupled linear equations. These equations are solved to find performance metrics such as the make span. The chapter develops a generic mod...

Scheduling is a decision-making process that concerns the allocation of limited resources to a set of tasks with the view of optimising one or more objectives. In this work, we are concerned with the cyclic permutation flow-shop problem where a set of parts is repeatedly produced (cyclic) and the sequence of parts on all the machines remains the sa...

The problem of computing an eigenvector of an inverse Monge matrix in max–plus algebra is addressed. For a general matrix, the problem can be solved in at most O(n3) time. This note presents an O(n2) algorithm for computing one max–plus algebraic eigenvector of an inverse Monge matrix A. It is assumed that A is irreducible.

This work investigates properties of signal flow graphs (SFGs) over max-plus algebra, which are referred to as synchronous SFGs. New topological methods for evaluating gains of synchronous matrix SFGs are described. These methods are based on the existing theory for matrix SFGs over regular algebra. SFGs are useful in studying complex engineering s...

The cost of manufacturing a part is an important consideration as it is being designed. However, early in the design process, not all of the design details of a part are decided, so the cost must be estimated from a limited amount of data. Raw material typically represents a significant portion of the part’s final cost, especially when parts are fo...

This paper describes a method for quickly estimating a part volume based on attributes of the geometric features found on a given part. The method is based on defining feature attributes, then applying rules to connect feature volumes. The attributes describe the types and dimensions of features and the relative location of each feature in the part...

A novel approach to modeling of manufacturing systems is proposed. The model is based on block diagrams. The block can be a single machine, a single part or a factory. The interconnection of blocks in the block diagram correspond to routing of parts and resources through the manufacturing subsystems. The model is hierarchial - a network of blocks c...

A novel approach to modeling of manufacturing systems is proposed. The model is based on block diagrams. The block can be a single machine, a single part or a factory. The interconnection of blocks in the block diagram correspond to routing of parts and resources through the manufacturing subsystems. The model is hierarchial – a network of blocks c...

With the advancements in information technology and the growing importance of concurrent design and development in both manufacturing and service industries, it becomes necessary for more and more diverse applications to interact with one another and function in a cohesive manner in order to satisfy the ever-changing customer requirements. Increase...

The paper describes a novel approach to model any deterministic manufacturing system. A function block diagram type of model is proposed. A block can be a single machine or a factory. The model is expressed as a system of linear event timing equations using max-plus algebra. One of the advantages of block diagram representation is the simplicity of...

Modern flexible manufacturing systems (FMS) are highly automated and flexible in which raw parts of various types are processed concurrently. Deadlock issue arises easily in these systems due to shared equipment usage and high production flexibility. It was indicated in Wysk et al . (Wysk, R., Yang, N. and Joshi, S., Detection of deadlocks in flexi...

Learning is a decrease in the time to perform an operation due to repetition and is an important consideration when forecasting process times or product costs. This paper presents a new method for calculating the learning rate for a family of parts using a matrix-based approach to organize historical data on production times. By calculating a singl...

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Due to existence of concurrent part flows and resource sharing in modern automated flexible manufacturing systems (FMS), deadlock is a common problem and its occurrence causes loss of productivity. When a manufacturing system is modeled by a digraph, existence of circuits in such a graph is a necessary condition for deadlock. Our previous work furt...

In this paper we consider cyclic flow-shop system, which dynamics can be described by the max-plus vector equation of the form s(k + 1) = D ⊗ s(k), where D is the Dynam-ics matrix of the system calculated from processing times of operations. The method for finding D in O(nm 2) time is presented. We prove that D fulfills the inverse Monge property,...

The ability to estimate the manufacturing cost of a product proves to be critical through all phases of the development cycle. When developing an estimate, the two components of the process, the equations which estimate the cost and the data supplied to those equations may both contribute error to the estimate. The error associated with input data...

Scheduling is a decision-making process that concerns the allocation of limited resources to a set of tasks with the view of optimizing one or more objectives. In this work, we are concerned with the cyclic permutation flow-shop problem where a set of parts is repeatedly produced (cyclic) and the sequence of parts on all the machines remains the sa...

Cost estimation is an important consideration in product design because decisions made during preliminary design should consider the impact of the decision on the cost to manufacture the product. There are two main approaches to providing a manufacturing cost estimate: bottoms-up and parametric. The bottoms-up method allows greater accuracy in the...

In manufacturing and other processes, repetition causes learning to occur, which decreases the time to perform the operation as it is repeated. Previously, the learning rate for a family of similar parts was calculated as a weighted average of the learning rates that had been calculated separately for each part. This paper describes a method using...

Dynamic real-time systems require adaptive resource management to accommodate varying processing needs. This paper addresses the problem of resource management on a single resource for soft real-time systems (no hard deadline requirements) consisting of tasks that have discrete quality of service (QoS) settings that correspond to varying resource r...

Modern flexible manufacturing systems (FMS) are highly automated and flexible in which raw parts of various types are processed concurrently. Deadlock issue arises easily in these systems due to shared equipment usage and high production flexibility. This paper presents a deadlock avoidance algorithm for FMS with free choices in part routing by cal...

The ability to estimate the manufacturing cost of a product proves to be critical through all phases of the development cycle. In order to arrive at a better estimate, there is not only the need for relevant and up-to-date data from both engineering and business processes, but also the ability to consider the cost history of the organization. This...

As typical discrete event systems, flexible manufacturing systems have been extensively studied in such aspects as modeling, control and performance analysis. One important topic in the study of such systems is the deadlock detection, prevention and avoidance. In the past decade, two major modeling formalisms, i.e., Petri nets and digraphs, have be...

Cost prediction is an important activity in all phases of product development. However, accurate estimation of the actual manufacturing cost in early phases of product design is challenging due to the limited data available in the early design stages. This paper describes a new tool for cost estimation using a hybrid approach that supports several...

Accurate prediction of manufacturing costs is required in very early stages of the product design and development. Usually these costs are estimated using a parametric approach, in which several simplifications are utilized, resulting in less accurate cost estimation. This paper presents a novel approach in which a hierarchical library is used in c...

Circuits and knots in the diagraph model of a manufacturing system are the rudimentary causes of deadlocks - a type of deadlock that is difficult to detect. A new deadlock avoidance algorithm that dynamically evaluates the order of circuits is presented. The algorithm is highly permissive since the order evaluation captures more parts flow dynamics...

The estimation of the manufacturing cost of a part in all phases of the design stage is crucial to concurrent engineering. To better estimate the cost for a product, data must be available from both engineering systems and business systems. This paper presents a cost estimation system being developed to support design time cost estimation using the...

A deadlock avoidance method for flexible manufacturing systems with both free choices and multiple resource requests allowed in part routing is presented. Based on a digraph model of the system, the method classifies whether moving a part to its next step is safe, unsafe, or undetermined. An undetermined part movement is further analyzed using a ve...

ISO 10303 is the set of standards that define the Product Data Exchange using STEP or PDES. Part 11 of the standard is the EXPRESS modelling language, an objectoriented modelling language upon which the application protocols for data exchange are based. To display and analyse EXPRESS schema, ISO10303 contains a graphical depiction of a subset of EX...

A deadlock avoidance algorithm for flexible manufacturing systems containing both multiple capacity resources and mixed choices in part routing is presented. The method determines whether moving a part to its next step is safe, unsafe, or undetermined. That classification is linear in complexity. Undetermined part movements are further analyzed usi...

A new deadlock avoidance algorithm for flexible manufacturing systems that contain both multiple capacity resources and free choice in part routing is presented. The method determines whether moving a part to its next step is safe, unsafe, or undetermined. This classification is linear in complexity. Part movements that are classified as undetermin...

The estimation of a part’s manufacturing cost in all phases of the design stage is crucial to concurrent engineering. To better estimate the cost for a product, data must be available from both engineering systems and business systems. This paper presents a cost estimation system being developed to support design time cost estimation using FIPER; t...

A method that classifies part movements to avoid deadlock in manufacturing systems which contain single capacity resources is presented. The proposed method determines whether a particular part movement is safe, unsafe, or undetermined. This classification is linear in complexity. Part movements that are classified as undetermined are analyzed usin...

EQL, an acronym for EXPRESS Query Language, is an SQL-like query language that is used to perform ad hoc queries on data in PART 21 files. PART 21 is the clear text encoding of data in the object-oriented EXPRESS modeling format and is the format for the STEP standards like AP203. Traditional uses for STEP files have been for transferring data betw...

A method to detect deadlock in manufacturing systems that contain single capacity resources is presented. The proposed stack-based algorithm is polynomial in complexity, and is very simple to implement for any flexible manufacturing system in this class. This algorithm determines whether a system is in deadlock by trying to calculate a sequence of...

Manufacturing systems design includes the determination of the, manufacturing operations, operation sequence, spatial layout, and part routings required to make a part. Currently, manufacturing systems design is done by a team of experts. Such an approach is prone to errors. Also, unfortunately, during this process there is usually no documentation...

This paper presents an architecture and a schema for the integration of heterogeneous manufacturing databases. Termed the Unified Data Meta Model (UDMM), this structure is based on common relational data modeling methods and was developed to support the integration of CAD, CAPP, NC tool path verification and MRP systems. The model was developed bas...

Scheduling resources to avoid deadlock in a manufacturing system has been studied extensively over the past decade. Previous work developed sufficient conditions to avoid deadlocked states. What distinguishes the different approaches is the number of nondeadlocked states that are allowed by the application of the method. This is an important consid...

This paper considers the integration of commercial off-the-shelf manufacturing engineering tools to produce a manufacturing engineering toolkit. These issues are considered by describing the work taking place in an on-going project to develop such a toolkit. In particular, the approach being taken toward integration of the tools is described, conce...

Manufacturing system design is a complex process involving the integration of multiple systems designed by several designers each optimizing sub-systems. The life cycle of manufacturing systems design is also problematic because the size of the manufacturing system makes it incomprehensible by a single person, interdisciplinary in approach, asynchr...

A method to avoid deadlock for a large class of manufacturing systems is presented. It is shown that deadlock can be avoided if the system satisfies a set of simple linear constraints. Several examples of the approach are presented and results compared to other deadlock avoidance schemes. The examples demonstrate that significantly higher utilizati...

Current manufacturing system design methodologies produce multiple models of the eventual manufacturing system. These models reflect either the designers view of some subsystem, like materials handling, some level of abstraction, or some developmental stage in the design of the system. These models serve to break the complex system design into smal...

A model for a class of manufacturing systems using Petri nets is presented. An algorithm that eliminates deadlock markings is developed. The net resulting from the application of the algorithm maximizes the number of markings and, therefore, is an optimal solution to the deadlock avoidance problem. The paper presents several examples of the approac...

Significant work in robot calibration has been done over the past several years. The calibration process assumes a kinematic model and performs a series of experiments to determine the parameters of the model. Current research focuses on the development of models and the measurement techniques to best estimate the parameters. This paper takes a dif...

The paper discusses an extension to conventional Perturbation Analysis techniques for discrete event systems that combines simulation with existing perturbation analysis techniques. This allows system designers to analyze the performance of systems with structural changes as well as parameter perturbations. A wide range of research into perturbatio...

A system which repeatedly tracks a specified trajectory is considered. The error between a specified trajectory and the actual trajectory of system from the previous trial is used by an iterative learning control law in order to reduce this error on the current trial. Sufficient conditions which were developed by the authors for iterative learning...

The paper discusses how the Combined Simulation and Perturbation Analysis (CSPA) algorithm can be applied to object oriented models. Object CSPA implements perturbation analysis (PA) techniques in an object oriented class hierarchy to generate system performance information. Recall that PA techniques use behavior generated from a previous system (t...

L. Hideg et al. (1990) described an equivalent time domain condition for learning control stability and compared it to the well known frequency domain condition (J. Craig, 1988). Here the authors expand the class of learning controls systems and plants whose stability can be studied with the time domain formulation. The stability condition consider...

A coefficient test for determining the stability of a class of iterative learning control systems is presented. The test is similar to the Routh test used to study the stability of dynamic systems. The test provides both necessary and sufficient conditions for iterative learning system stability and is useful in the design of iterative learning con...

The stability of learning systems for linear time invariant discrete time plants is studied. A standard Lyapunov function for sufficiency in the time domain is proposed. An equivalent condition in the Z domain is also presented to show necessity.

The paper developes the Combined Simulation and Perturbation Analysis (CSPA) algorithm. CSPA integrates perturbation analysis (PA) techniques and simulation to generate performance information about a new system (the perturbed system) usig information about a preceding system (the nominal system). This will aid system designers in analyzing and com...

A coefficient test for the stability of discrete time learning systems is developed. The test is based on the Jury criteria. Necessary and sufficient conditions result from the test. Several examples are provided

An improved method for designing manufacturing systems is presented. Primary features of the improved method include frequent design iterations by executing the specification early in the life cycle, flexibility to accommodate changing requirements, coordination of engineering disciplines in evolving integrated solutions, and reuseability of common...

The paper describes a design procedure and a design tool that supplements the XSpec methodology. The procedure is explained in detail. The procedure was applied to an actual automotive system. A complete description of this experience is given

An improved method for designing manufacturing systems is presented. Primary features of the improved method include frequent design iterations by executing the specification early in the life cycle, flexibility to accomodate changing requirements, coordination of engineering disciplines in evolving integrated solutions, and reuseability of commonl...

A method to calibrate industrial robots is presented. Models are developed to correct problems with robot accuracy resulting from errors in the link and joint parameters, imperfections in the main spur and encoder pinion gears, and structural deformations. Additionally, a method that places a single transformation, which is a simple cyclic function...

The error between the desired and actual output of a single input, multiple output plant is used by a learning law to modify the input in order to reduce the output error. Lyapunov stability analysis is used to determine criteria for the learning law coefficients. The plant is assumed to be stable, linear and time invariant. Formulations include re...

A new method for the digital control of a nonlinear, continuous time system is presented. The digital controller is called a discrete time quantized data (DTQD) controller. The DTQD controller uses a table look-up algorithm to determine the desired control effort. In order to minimize the number of table entries, a hystersis scaling process is prop...

Learning systems are evolving into a significant method to allow physical systems to track a desired trajectory. Frequency domain analysis has contributed to a better understanding of the behavior of learning systems. This paper proposes a method which uses the errors from both the previous trial and the second trial back. This law yields better co...

The construction of a digital model of a continuous-time system is considered. A method for determining the quantization levels such that the digital model will accurately predict the state of a continuous-time system after one transition is presented. This digital model will be used to design a digital controller for the continuous-time system. Th...

In 1986 and 1987, four patients with tibial malunion involving both angular and torsional misalignment underwent surgical correction by a single-cut technique based on a mathematical model of long bone deformity. The technique involved a single surgical cut, followed by rotation of the two fragments along the osteotomy plane. The orientation of the...

Frequency domain arguments on a general learning law are presented to verify claims of convergence which relax earlier requirements on the learning law transfer function. Known convergence properties are used to develop a pole-placement interpretation for an example for which simulations using a proportional-derivative learning law form are carried...

In a recent paper, a new method for the digital control of a continuous-time system based on a table look-up technique was presented. This digital controller is called a discrete-time quantized data (DTQD) controller. In order to minimize the number of table entries, a grid embedding process is proposed. This control technique proved successful whe...

The method described in this paper promotes accurate tracking of a given path by a robotic manipulator. The manipulator's velocity along the path is slowed as manipulator singularities or path corners are encountered. This adjustment is necessary to keep the manipulator tracking close to the path to satisfy error criteria. A numerical example is pr...

A new technique for the digital control of continuous time systems is presented. This technique is based on a table look-up algorithm. To minimize the number of entries in the table, a grid embedding process is proposed. Using this process, an accurate, fast, and low-cost controller can be constructed using a table of a few thousand entries. The pa...

This paper presents a method to calibrate industriaI robots. Models developed in the paper correct problems with robot accuracy resulting from errors in the Iink and joint parameter, imperfections in the main spur and encoder pinion gears, and structuraI deformations. Additionaliy, a method that places a singIe transformation which is a simple cycl...

The paper proposes a new robot control system which simultaneously tracks position and force commands along a constrained surface. The model of the constraints is incorporated into the control algorithm. This leads to a more robust controller than those developed previously. The paper presents a general model for constrained surfaces and the archit...

A new approach to feedback control based on a table look-up technique is developed. A grid embedding technique is used which maintains high accuracy with minimal table size. This report describes the use of the new control scheme as a regulator. A cricuit which implements the control scheme is developed. This circuit is simpler, cheaper, faster, an...

This paper presents the kinematic and dynamic analysis of an n-link manipulator with flexible members. The deformation of a link from its rigid body position is modeled by a homogeneous transformation. The dynamic equations are obtained using an Euler-Lagrange formulation. These equations are compared to those describing a rigid link mechanism.

The paper addresses state estimation in a dynamic system with quantized data. It is assumed that all quantized states are accessible. The formulation of the state estimation problem is based on a geometric interpretation of the mapping of the quantized state. Two important theorems regarding estimation and prediction are presented.

A new approach to digital control is developed. A model for discrete time quantized data systems is formulated. An optimal control problem is then posed and solved within this structure. The control law is stored in a PROM which is addressed using feedback information. Static accuracy can be achieved without the attendant problem of large memory st...