Synthesis of control policies for cascaded production-inventory systems

n this paper the Brunovsky canonical form is used to synthesize piecewise-constant control policies for a class of production-inventory systems which consist of a set of production-inventory sub-systems connected in cascade. It is shown that each production-inventory sub-system can be controlled in isolation but that control policies based on this approach lead to undesirable transient behaviour. The alternative approach whereby the control policies are formulated for the composite system leads to improved transient behaviour.     

Control policies for production-inventory systems with bounded input

In this paper nearly time-optimal control policies are derived for a class of linear time-invariant models of production-inventory systems which comprise a cascade of basic production-inventory subsystems with bounded input. The sub-optimal control policies are obtained by constructing the sampled-data model of the production-inventory system where the sampling period is chosen to give the maximum control input for the given shipping rate. The theory is illustrated by the presentation of the results of simulation studies which show the transient behaviour of two production-inventory subsystems in cascade.     

Singular perturbation methods in the synthesis of control policies for multi-stage production-inventory systems

In this paper, singular perturbation methods are used to synthesize control policies for a class of multi-stage production-inventory systems. It is shown that when the production-inventory sub-systems are connected in cascade, the control of each sub-system in isolation leads to undesirable transient behaviour. However, the control of the composite system is shown to yield improved transient behaviour. Furthermore, it is also shown that trade-off between rapid adjustments in production rate and large inventory-level deviation can be achieved by selecting an appropriate value for the feedback gain parameter.     

DYNAMICS AND CONTROL OF INTEGRATED PRODUCTION-INVENTORY-SHIPPING SYSTEMS

Abstract

In this paper, multivariable system theory is used to synthesize piecewise-constant control policies for production-inventory systems which incorporate unfilled-order backlogs. The state variables of the systems are the actual production rate, the inventory level discrepancy, and the unfilled-order backlog respectively. The control inputs are the desired production rate and the desired shipping rate, and the disturbance input is the demand for finished parts. It is shown that the original multi-input system can be decoupled into a set of single-input sub-systems in the modal domain by using a suitably chosen generalised modal matrix. The required policies for the original system are then readily obtained by considering each of the decoupled sub-systems separately. The behaviour of the controlled production-inventory system is illustrated by the presentation of the results of computer simulation studies showing typical transient and steady state response characteristics.     

容许输入下的无纹波跟踪问题

研究最少拍和最少拍无纹波控制系统的一般情况,研究的基本目标是要求输入信号在某些特定类型中变化时,系统的响应无纹波并在调节时间之后无稳态误差,而且暂态过程的调节时间应尽可能的短.为改善系统的鲁棒性,还要求考虑设计非最少拍系统,这时系统的调节时间会有所延长.另外,为进一步改善系统对多种输入的灵活性,还要考虑引入惯性因子.这是对有限调节时间和系统超调的折衷,此时系统已不再是有限拍无差系统.在探讨了某些基本代数概念之后,着重论述系统在容许输入下的无纹波跟踪问题,同时使用MATLAB进行计算机辅助设计并给出仿真结果.     

Design of production-inventory control systems incorporating fast-sampling control policies with implementation lead time

In this paper, singular perturbation methods are used to synthesize fast-sampling error-actuated control policies for two production-inventory system models in which there is a finite time delay of several sampling periods between the formulation and the implementation of the control policies. In the first model it is assumed that the demand for the product cannot be influenced by the management of the production-inventory system, and in the second model it is assumed that the demand for the product can be influenced by advertising and that the desired instantaneous demand rate is specified by management. In both cases, it is shown that the system will exhibit good transient and steady-state behaviour when controlled by such control policies. Furthermore, it is also shown that non-interacting control can be achieved when effective expenditure on advertising is introduced in order to influence the demand for the product, and that the provision of this extra flexibility thus leads to improved transient behaviour.     

Output-maximal control policies for cascaded production-inventory systems with control and state constraints

Optimal control policies are derived for cascaded production-inventory systems. As objectives, output maximization and the minimum time to produce a fixed output are considered. An example consisting of three subsystems is detailed to illustrate the proposed theory.     

Modal control of production-inventory systems using piecewise-constant control policies

In this paper a discrete-time model of a production-inventory system is considered, and model control theory is used to synthesize piecewiso-constant control policies which result in both good transient and good steady-state behaviour of the system. The theory is illustrated by the presentation of typical response characteristics of a production-inventory system subject to a deadbeat control policy of this class.     

Multi-item-multi-plant inventory control of production systems with shortages/backorders

A multi-item model of a production-inventory system incorporating deterioration, shortages and capacity/budget constraints is considered. An optimal control policy for the model is developed using linear quadratic (LQ) theory for the case of deterministic demands. The problem of controlling large-scale production-inventory facilities is also considered, and the interaction prediction method is used to develop optimal policies. Results of simulations show that using the developed policy, any desired inventory levels can be maintained while minimizing costs and satisfying demand without violating capacity constraints.     

一类不确定非线性系统的停息时间可调的有限时间镇定

研究了一类带有零动态不确定非线性系统有限时间镇定问题, 给出了具有更强实用性的停息时间可调的有限时间稳定控制设计方法. 基于有限时间稳定的Lyapunov理论和反推技术, 给出了停息时间可调有限时间稳定控制器的设计步骤. 所设计的状态反馈控制器使得闭环系统全局有限时间稳定, 且停息时间可调整, 特别是当系统初始值已知时, 停息时间可以任意调节. 仿真例子验证了本文的主要结论.     

Buyer–vendor coordination for fixed lifetime product with quantity discount under finite production rate

Buyer–vendor coordination has been widely addressed; however, the fixed lifetime of the product is seldom considered. In this paper, we study the coordination of an integrated production-inventory system with quantity discount for a fixed lifetime product under finite production rate and deterministic demand. We first derive the buyer’s ordering policy and the vendor’s production batch size in decentralised and centralised systems. We then compare the two systems and show the non-coordination of the ordering policies and the production batch sizes. To improve the supply chain efficiency, we propose quantity discount contract and prove that the contract can coordinate the buyer–vendor supply chain. Finally, we present analytically tractable solutions and give a numerical example to illustrate the benefits of the proposed quantity discount strategy.     

Analysis of a production-inventory control system for a diffusion department

The dynamic behaviour of an actual production-inventory control system, designed for a diffusion department, is analysed by means of classical control theory. The actual control rule acts on the basis of norms for the production progress derived from the application of the line-of-balance technique to the production-inventory system. Attention is paid to the steady-state behaviour, the impulse response and the variance amplification of the controlled system. The cause of the poor dynamic performance observed after implementation of the system in practice is releaved. Especially the variance amplification can be decreased without a general loss of performance with respect to other criteria. An alternative control rule is derived from the application of design notions from classical control theory to the production-inventory problem. The new control rule shows an improved performance in some respects over the actual control rule. The case presented shows that some serious errors in production-inventory control design can be avoided through analysis by means of classical control theory.     

Bang-bang control strategy using a tabular adaptive model

An adaptive-predictive model for nonlinear, finite settling-time processes has been described by Roy et al., This paper utilizes this model for the trajectory following control of both finite and infinite settling-time nonlinear systems with switched two-level input.     

Optimum control of distributed parameter systems with time delays

This paper discusses the optimum control of distributed parameter systems with time delays which are governed by a set of partial differential-difference equations. The technique of dynamic programming is used to derive the functional equations associated with optimization. Specific results are derived for linear systems with quadratic performance index. Also, an explicit condition for the complete null controllability of linear systems is given. The paper concludes with a discussion on the approximate solutions for the minimum energy control of a simple linear parabolic system with a time delay.     

Optimal control of production-inventory systems

Optimal policies for the pontrol of a class of production-inventory systems are derived. Typical response characteristics are presented which illustrate the effects of using different weighting parameter values in the performance cost functional.     

Optimal linear control of linear production-inventory systems

Modern control theoretical principles are used to derive necessary conditions for the optimal linear control of a general linear production-inventory system with non-linear costs per period. The main assumptions are stationary normal distribution of all random"variables and optimization of the average expected costs per period.     

Model-induced term-weighting schemes for text classification

Access control policies are specified within systems to ensure confidentiality of their information. Available knowledge about policies is usually incomplete and uncertain. An essential goal in reasoning is to reach conclusions which can be justified. However, since justification does not necessarily guarantee truth, the best we can do is to derive “plausible/ tentative” conclusions from partial and conflicting information. Policies are typically expressed as rules that could be complex and include timing constraints. Complex sets of access policies can contain conflicts e.g., a rule allows access while another rule prevents it. In this paper, we aim at providing a formalism for specifying authorization policies of a dynamic system. We present a temporal defeasible logic (TDL) which allows us to specify temporal policies and to handle conflicts. It can be shown that the proposed model is a generalization of the role-based access control model.     

A technique for choosing zero locations for minimal overshoot

An approach is presented to the specification of optimal overshoot controllers when the controller order is fixed and the closed-loop system poles are at a fixed location. The essential effect of the technique is to pick the best possible locations of the free zeros of the system in terms of minimizing the overshoot. The solution is obtained by solving an affine minimax optimization problem. An example illustrates how this technique can be used as a design aid when it is necessary to trade off conflicting design requirements, such as overshoot and settling-time specifications. It is shown that the method is not restricted to the deadbeat case, but can also be used for any prescribed set of closed-loop poles     

Scheduling one-part-type serial manufacturing system under periodic demand: a solvable case

The paper studies one-part type, multiple-stage production system with periodic demands. A buffer of infinite capacity is placed after each machine. Inventory flow through buffers is controlled by machine production rates. The objective is to find a cyclic production rate, which minimizes all inventory-related expenses over an infinite planning horizon. With the aid of the maximum principle, optimal production policies are derived and the continuous-time scheduling problem is reduced to a discrete timing problem. As a result, a polynomial-time algorithm is suggested to calculate the optimal production rate. A numerical example is used to illustrate the algorithm.Scope and purposeNumerical and heuristic approaches have been suggested for production control of automated-serial-manufacturing systems. These approaches try to derive production control policies that would minimize overall costs related to inventory, backlog, and production. The quality of these approaches is often difficult to assess, and they can be time-consuming to implement. Therefore, increasing attention has been directed to optimal control policies of production systems that can be derived precisely and quickly. This paper addresses a special case of the production system manufacturing a single product type to meet a periodic demand. Given a certain assumption on cost relationship, we derive a fast and simple scheduling algorithm that calculates the optimal policy.     

Projection based MIMO control performance monitoring: I—covariance monitoring in state space

In this paper we propose a new control performance monitoring method based on subspace projections. We begin with a state space model of a generally non-square process and derive the minimum variance control (MVC) law and minimum achievable variance in a state feedback form. We derive a multivariate time delay (MTD) matrix for use with our extended state space formulation, which implicitly is equivalent to the interactor matrix. We show how the minimum variance output space can be considered an optimal subspace of the general closed-loop output space and propose a simple control performance calculation which uses orthogonal projection of filtered output data onto past closed-loop data. Finally, we propose a control performance monitoring technique based on the output covariance and diagnose the cause of suboptimal control performance using generalized eigenvector analysis. The proposed methods are demonstrated on a few simulated examples and an industrial wood waste burning power boiler.