Konstantin K. Starkov

Performance analysis for tandem manufacturing lines under variable structure production control method

In this paper we introduce novel results for the performance of the surplus-based decentralised production control method. The main objective of this production method is to guarantee that the cumulative number of produced products follows the cumulative production demand on the output of any given network. As a starting point of our research a general idea of this method is presented for the case of one manufacturing machine. Then our analysis is extended to a line of N machines. The proposed methodology is reformulated in terms of variable structure control. The production flow process is described by means of difference equations and, in order to analyse the performance, the Lyapunov theory approach is exploited. The results obtained for the production error bounds for each machine in the line and for the buffer content bounds for each intermediate buffer are discussed. Performance and robustness issues of closed-loop flow line models are illustrated by numerical simulations. It is shown that the method can be implemented in enterprise planning tools.

Performance analysis of re-entrant manufacturing networks under surplus-based production control

Motivated by the problem of planning and scheduling in large semiconductor manufacturing facilities we study the performance of re-entrant production networks. In such networks, each product has to go multiple times through the entire manufacturing line before it is ready. Each machine in a re-entrant network can receive products from different routings, but the products from only one of the routings can be served at a time. This complicated network structure makes it difficult, and at the same time important, to estimate in advance the performance of such a network under a demand-driven control policy. In this paper we present results on the influence of perturbations, buffer inventory levels and the number of manufacturing stages on the production tracking error of each machine in the re-entrant network operated under a surplus-based production control policy. The results are provided in the form of so-called ‘worst case scenario’ bounds on the steady-state production demand tracking accuracy of each stage as well as bounds on the content of each intermediate inventory level. By means of simulation examples we show that the results obtained have an important meaning and can be used as a practical reference tool.

Design and implementation of a water-based emulator of manufacturing processes

In this paper we present a prototype developed for education and research purposes. The prototype is a liquid based emulator of manufacturing network processes. In its core, the liquid-base emulator consists of several electrical pumps and liquid reservoirs. The electrical pumps emulate a manufacturing machine behavior while the liquid reservoirs serve as the intermediate product storages also called buffers. In the platform pumps and tanks can be interconnected in a flexible manner. In that way the prototype permits an easy and intuitive way of studying manufacturing control techniques and performance for several network topologies. This paper contains a detail system description and its application. Several network configurations and experimentations are presented and discussed.

Frequency and time-domain analysis on performance of a production line operated by observer-based distributed control

This article deals with the problem of controlling a tandem line of manufacturing machines such that an unknown production demand is tracked with a desired accuracy. To study this problem, a manufacturing machine is approximated by an integrator which is subject to input saturation as a result of the finite capacity of the machine. To solve the problem in the case of unknown demand rate, a combination of feedforward–feedback controller with a reduced-order observer is proposed. The decentralised feedback control strategy for a line of machines is proposed and studied both in continuous time-domain and in frequency-domain representation. The presented illustrating example for a line of four machines underlines the efficiency of the proposed frequency-domain-based performance analysis tool.

Distributed Control of Manufacturing Networks: Analysis of Performance

The aim of this chapter is to introduce the reader to one of the important applications of distributed control that is manufacturing networks. In this chapter, we present selected results of our study focused on performance analysis of manufacturing machines and tandem lines operated under distributed surplus-based control. The distributed nature of the controller ensures that the control action for each machine in the network depends merely on the state of its neighboring machines. This fact significantly simplifies implementation of the control algorithm. By rigorous mathematical analysis in combination with classical control theory, we are able to show the optimality of surplus-based control for a single manufacturing machine and evaluate the demand tracking accuracy of a manufacturing line with bounded intermediate buffers. Particular attention is given to the flow models that describe the dynamical behavior of a manufacturing machine and a line. The analytical results of this chapter are supported by a simulation example.

Manufacturing lines under surplus-based control: multiple products and bounded buffers

Challenged by the scheduling complexity for production flow processes in industrial facilities, we study the performance of multi-product producing lines. We analyse the performance of multi-product lines that consist a number of machines and bounded buffers with preselected base stock levels. It is assumed that each manufacturing machine in the line is capable of working with several product types, but only operate on one product at a time. The network is operated under a surplus-based production control policy in the presence of perturbations and production demand fluctuations. We derive bounds on the demand tracking accuracy for each product type, regardless its flow direction in the multi-product line. In addition, for a multi-product line with unidirectional product flow, we obtain a quantitative relation between demand tracking accuracy, its inventory levels, numbers of product types, buffer capacity limits and perturbations. The accuracy of the obtained demand tracking bounds is illustrated by numerical simulations. By means of simulation experiments, we show that the obtained results have a valuable meaning and can be used as a reference tool in practice.

Nonlinear Problems in Control of Manufacturing Systems

Abstract Nowadays, production control problems has been widely studied and a lot of valuable approaches have been implemented. This paper addresses the problem of tracking the uncertain demand in case of uncertain production speeds. The uncertainties are described by deterministic inequalities and the performance is analyzed in from of the worst-case scenario. First, simple mathematical models are introduced and the control problem is formulated. In continuous-time, the cumulative output of a manufacturing machine is the integral of the production speed over time. At the same time, the production speed is bounded from below and above, and hence the manufacturing process can be modeled as an integrator with saturated input. Since the cumulative demand (which is the reference signal to track) is a growing function of time, it is natural to consider control policies that involve integration of the mismatch between the current output and current demand. In the simplest consideration it results in models similar to a double integrator closed by saturated linear feedback with an extra input that models disturbances of a different nature. This model is analyzed and particular attention is devoted to the integrator windup phenomenon: lack of global stability of the system solutions that correspond to the same input signal. As a systematic design procedure to prevent the windup phenomenon we present observer based techniques with full and reduced-order observers. The next part of the paper deals with a similar control problem in discrete-time under the surplus-based policy: each machine in the production network tracks the demand trying to keep the downstream buffer at some specified safe level. The performance of manufacturing networks with different topologies is analyzed via the second Lyapunov method, while the disturbances are modeled by deterministic inequalities. The nature of the approach leads to performance analysis in the form of a worst case scenario and allows to find a trade-off between the inventory for each machine in the system and the demand tracking accuracy. The final part of the paper illustrates how to make the theoretical findings operational with the experimental setup called Liquitrol. The experimental setup consists of a number of water tanks and pumps that can be interconnected via flexible piping. Due to its flexibility and mobility, the setup allows not only to verify theoretical results via experiments, but it also can be used in an educational process to illustrate different phenomena in tandem and re-entrant manufacturing networks.

Variable structure control of a line of manufacturing machines

Abstract In this paper a control method is introduced for a line of manufacturing machines based on the variable structure control. First the flow model of one manufacturing machine with variable structure control is presented where the uniform ultimate boundedness of the tracking error trajectories is proven. Then, the flow model of a manufacturing line with variable structure control is presented where the necessary conditions are derived in order to guaranty the uniform ultimate boundedness of the tracking error trajectories of each machine. Performance and robustness issues of the closed-loop flow models are illustrated in numerical simulations.