Process Control Problems Research Articles

Poisson progressive mean control chart

AbstractIn real life applications, many process‐monitoring problems in statistical process control are based on attribute data resulting from quality characteristics that cannot be measured on numerical or quantitative scales. For the monitoring of such data, a new attribute control chart has been proposed in this study, namely, the Poisson progressive Mean (PPM) control chart. The performance of the PPM chart is compared with the existing charts used for the monitoring of Poisson processes such as the Shewhart c‐chart, Poisson Exponentially Weighted Moving Average chart, Poisson double Exponentially Weighted Moving Average chart and the Poisson Cumulative Sum charts. The average run length comparison indicated the superior performance of the PPM chart in terms of shift detection ability. This study will help quality practitioners to choose an efficient attribute control chart.

Maintenance process control: cellular automata approach

In this work we consider an industrial maintenance process control problem using cellular automata approach. The problem consists on finding an optimal control for the assignment and the displacement of agents in a spatial area to maintain the equipments in good working state. The approach by cellul

A direct approach to linear-quadratic stochastic control

A direct approach is used to solve some linear-quadratic stochastic control problems for Brownian motion and other noise processes. This direct method does not require solving Hamilton-Jacobi-Bellman partial differential equations or backward stochastic differential equations with a stochastic maximum principle or the use of a dynamic programming principle. The appropriate Riccati equation is obtained as part of the optimization problem. The noise processes can be fairly general including the family of fractional Brownian motions.

A Variational Formula for Risk-Sensitive Reward

We derive a variational formula for the optimal growth rate of reward in the infinite horizon risk-sensitive control problem for discrete time Markov decision processes with compact metric state and action spaces, extending a formula of Donsker and Varadhan for the Perron--Frobenius eigenvalue of a positive operator. This leads to a concave maximization formulation of the problem of determining this optimal growth rate.

A Distribution-Free Multivariate Control Chart

Monitoring multivariate quality variables or data streams remains an important and challenging problem in statistical process control (SPC). Although the multivariate SPC has been extensively studied in the literature, designing distribution-free control schemes are still challenging and yet to be addressed well. This article develops a new nonparametric methodology for monitoring location parameters when only a small reference dataset is available. The key idea is to construct a series of conditionally distribution-free test statistics in the sense that their distributions are free of the underlying distribution given the empirical distribution functions. The conditional probability that the charting statistic exceeds the control limit at present given that there is no alarm before the current time point can be guaranteed to attain a specified false alarm rate. The success of the proposed method lies in the use of data-dependent control limits, which are determined based on the observations online rather than decided before monitoring. Our theoretical and numerical studies show that the proposed control chart is able to deliver satisfactory in-control run-length performance for any distributions with any dimension. It is also very efficient in detecting multivariate process shifts when the process distribution is heavy-tailed or skewed. Supplementary materials for this article are available online.

Some control problems for non-homogeneous birth-death processes

We consider non-homogeneous Markov birth-death processes in a case of the constant ratio c of death and birth intensities. We solve three control problems by choosing the parameter c for such processes. We solve the problem of minimizing the probability of moving out of range as t→∞. We use the golden section search to find the existing minima, which depend on a threshold value and an integral birth intensity value. We solve the control problem by choosing the parameter c using the stabilization function. The existence of a minimum is proved and the minimum is found; also, important selected cases are considered. The parameter identification problem for an exponential stabilization function is also solved. We solve the problem of minimizing the mean of an extinction time with a small probability of exceeding the threshold. The convergence conditions for the mean are found, the conditions of the threshold exceeding probability are simplified, the problem is solved under an assumption of a constant birth intensity.

Problems of process control for shifting gears on tractors without torque interruption

The article considers the problem of optimizing the process control for shifting gears on tractors without torque interruption. The opinion on the dynamics of process control for shifting gears is explained, it takes into account the occurrence of torque deficit in the shafts, when changing gear, and increasing of friction losses in spinning clutch. The formulas for calculating the dynamic parameters used in the mathematical model of the dynamics of the tractor when shifting gears without torque interruption are shown. With the help of the mathematical model developed in Scientific and Research Tractor Institute (NATI) for debugging the system of electro-hydraulic control of gear shifting process for CHN-6 tractor were calculated several variants of gear shifting. Particular attention is given to occurrence, development and completion of the power circulation process in the circuit of switched clutches, because the lack of circulation of power the majority of authors call the basis of optimal switching. The results of the calculations in terms of the circulation of power, failure to slipping of switching off the clutch and interlocking of switched on clutch are shown. Calculation results suggest that when the clutch of lowest gear is closed the torque growth in spinning clutch of switched on top gear causes an increase in friction losses of disks, which leads to a decrease in engine shaft speed and reduction of the tractor speed. The magnitude and duration of fall of the engine speed and the speed of the tractor are low, but due to a decrease in the speed of the tractor the moments of forces inertia are large enough and need to be taken into account in the calculations. In all experiments, where power circulation was present, it started earlier than top gear clutch created torque, which corresponds to the resistance movement. In all experiments, where power circulation was present, it ended as a result of reducing the pressure in the clutch booster of lower gear after its failure to spinning in the power circulation mode. The circulating power after the failure to spinning and clutch switching off is redirected to output shaft accelerating the tractor and accelerating the synchronization and interlocking of switched on clutch.

A self-tuning control method for Wiener nonlinear systems and its application to process control problems

Many chemical processes can be modeled as Wiener models, which consist of a linear dynamic subsystem followed by a static nonlinear block. In this paper, an effective discrete-time adaptive control method is proposed for Wiener nonlinear systems with uncertainties. The parameterization model is derived based on the inverse of the nonlinear function block. The adaptive control method is motivated by self-tuning control and is derived from a modified Clarke criterion function, which considers both tracking properties and control efforts. The uncertain parameters are updated by a recursive least squares algorithm and the control law exhibits an explicit form. The closed-loop system stability properties are discussed. To demonstrate the effectiveness of the obtained results, two groups of simulation examples including an application to composition control in a continuously stirred tank reactor (CSTR) system are studied.

Process control using finite Markov chains with iterative clustering

Abstract Finite state Markov Decision Processes (MDP) for process control are considered. MDP provide robust tools to perform optimization in closed-loop, and their finite state description enables an easy implementation of Bayesian state estimation. An approach to tackle the curse of dimensionality problem, yet retaining the benefits of the finite state MDP in control and estimator design, is proposed. The suggested approach uses iterative re-discretization based on clustering of closed-loop data. An efficient modification of the k-means clustering technique is proposed. The performance of the approach is demonstrated using a challenging benchmark from chemical engineering, the van der Vusse continuous stirred tank reactor control problem. It is shown that the requirements of the benchmark are met, and that the suggested iterated clustering significantly improves the performance. It is concluded that the finite state MDP approach is a viable alternative for small-to-medium scale problems of practical process control and state estimation.

On the policy improvement algorithm in continuous time

We develop a general approach to the Policy Improvement Algorithm (PIA) for stochastic control problems for continuous-time processes. The main results assume only that the controls lie in a compact metric space and give general sufficient conditions for the PIA to be well-defined and converge in continuous time (i.e. without time discretization). the PIA in continuous time is applicable in the context of weak stochastic control. We give simple explicit examples of control problems demonstrating the need for the weak formulation as well as diffusion-based classes of problems where the PIA in continuous time is applicable.

Predictive iterative learning control with experimental validation

This paper develops an iterative learning control law that exploits recent results in the area of predictive repetitive control where a priori information about the characteristics of the reference signal is embedded in the control law using the internal model principle. The control law is based on receding horizon control and Laguerre functions can be used to parameterize the future control trajectory if required. Error convergence of the resulting controlled system is analyzed. To evaluate the performance of the design, including comparative aspects, simulation results from a chemical process control problem and supporting experimental results from application to a robot with two inputs and two outputs are given.

Monitoring and control system for RepRap 3D-printer with FDM printing technology

The problems of 3D-printing process monitoring, verification and control and the way how to achieve the best results of quality for 3D-printed models by improving the design and software for RepRap 3d-printers with FDM printing technology are considered.

Robustness and performance parameterization of smooth second order sliding mode control

Novel robustness and performance parameters are established for Smooth Super Twisting Algorithm (SSTA). The stability of SSTA is well established for arbitrary gains using homogeneity approach. The design and tuning of the controller parameters is a major issue and no analytic design method is available so far. A novel Lyapunov function is proposed and by the virtue of stability analysis, the stability bounds for a certain class of uncertainties are determined. In addition, the issue of finite time convergence is also explored, resulting in determination of the settling time as a function of the controller parameters. The proposed settling time formulation suggests a methodical approach to SSTA design in contrast to the available rules of thumb. Unlike the literature available for Higher Order Sliding Mode (HOSM) controllers, the proposed design framework is validated against a challenging problem of the Underground Coal Gasification (UCG) process control. Like the other process control problems the chosen problem is nonlinear and contains significant uncertainties.

A Change-Point Approach for Phase-I Analysis in Multivariate Profile Monitoring and Diagnosis

Process monitoring and fault diagnosis using profile data remains an important and challenging problem in statistical process control (SPC). Although the analysis of profile data has been extensively studied in the SPC literature, the challenges associated with monitoring and diagnosis of multichannel (multiple) nonlinear profiles are yet to be addressed. Motivated by an application in multioperation forging processes, we propose a new modeling, monitoring, and diagnosis framework for phase-I analysis of multichannel profiles. The proposed framework is developed under the assumption that different profile channels have similar structure so that we can gain strength by borrowing information from all channels. The multidimensional functional principal component analysis is incorporated into change-point models to construct monitoring statistics. Simulation results show that the proposed approach has good performance in identifying change-points in various situations compared with some existing methods. The codes for implementing the proposed procedure are available in the supplementary material.

A feedback control framework for safe and economically‐optimal operation of nonlinear processes

Maintaining safe operation of chemical processes and meeting environmental constraints are issues of paramount importance in the area of process systems and control engineering, and are ideally achieved while maximizing economic profit. It has long been argued that process safety is fundamentally a process control problem, yet few research efforts have been directed toward integrating the rather disparate domains of process safety and process control. Economic model predictive control (EMPC) has attracted significant attention recently due to its ability to optimize process operation accounting directly for process economics considerations. However, there is very limited work on the problem of integrating safety considerations in EMPC to ensure simultaneous safe operation and maximization of process profit. Motivated by the above considerations, this work develops three EMPC schemes that adjust in real‐time the size of the safety sets in which the process state should reside to ensure safe process operation and feedback control of the process state while optimizing economics via time‐varying process operation. Recursive feasibility and closed‐loop stability are established for a sufficiently small EMPC sampling period. The proposed schemes, which effectively integrate feedback control, process economics, and safety considerations, are demonstrated with a chemical process example. © 2016 American Institute of Chemical Engineers AIChE J, 62: 2391–2409, 2016

Control of wood thermal treatment and its effects on decay resistance: a review

AbstractKey messageAn efficient use of thermal treatment of wood requires a depth understanding of the chemical modifications induced. This is a prerequisite to avoid problems of process control, and to provide high quality treated wood with accurately assessed properties to the market. Properties and structural anatomy of thermally modified woods are slightly different than un-processed woods from a same wood species. So it is necessary to create or adapt new analytical methods to control their quality.ContextHeat treatment as a wood modification process is based on chemical degradation of wood polymer by heat transfer. It improves mainly the resistance of wood to decay and provides dimensional stability. These improvements, which come at the expense of a weakening of mechanical properties, have been extensively studied. Since a decade, researches focused mainly on the understanding of wood thermal degradation, on modelling, on quality prediction and quality control.AimsWe aimed at reviewing the recent advances about (i) the analytical methods used to control thermal treatment; (ii) the effects on wood decay resistance and (iii) the advantages and drawbacks of a potential industrial use of wood heating.MethodsWe carried out a literature review of the main industrial methods used to evaluate the conferred wood properties, by thermal treatment. We used papers and reports published between 1970 and 2015, identified in the web of science data base..ResultsApproximately 100 papers mostly published after 2000 were retrieved. They concentrated on: (i) wood mass loss due to thermal degradation determination, (ii) spectroscopic analyses of wood properties, (iii) colour measurements, (iv) chemical composition, (v) non-destructive mechanical assessments and (vi) use of industrial data.ConclusionsOne of most interesting property of heat-treated wood remains its decay resistance. Durability test with modified wood in laboratory are expensive and time-consuming. This review displays data from different analytical methods, such as spectroscopy, thermogravimetry, chemical analyses or mechanical tests that have the potential to be valuable indicators to assess the durability of heat treated wood at industrial scale. However, each method has its limits and drawbacks, such as the required investment for the equipment, reliability and accuracy of the results and ease of use at industrial scale.

Regular finite fuel stochastic control problems with exit time

We consider a class of exit time stochastic control problems for diffusion processes with discounted criterion, where the controller can utilize a given amount of resource, called “fuel”. In contrast to the vast majority of existing literature, concerning the “finite fuel” problems, it is assumed that the intensity of fuel consumption is bounded. We characterize the value function of the optimization problem as the unique continuous viscosity solution of the Dirichlet boundary value problem for the correspondent Hamilton–Jacobi–Bellman (HJB) equation. Our assumptions concern the HJB equations, related to the problems with infinite fuel and without fuel. Also, we present computer experiments for the problems of optimal correction and optimal tracking of a simple stochastic system with the stable or unstable equilibrium point.

Dynamics of nonlinear chemical process with multiplicative stochastic noise

Motivated by problems in process design, monitoring and control, the effect of multiplicative stochastic uncertainty injection on the behavior of nonlinear dynamical system is studied with Fokker Planck theory for two rather simple case examples selected to draw rigorous results with analytic formulae. The effect of noise multiplicativeness on the shape of the stationary state PDF and of the transient one along deterministic, probability diffusion, and escape time scales is characterized. The findings are corroborated and illustrated with numerical simulations. The results provide insight to assist the improvement of numerical Monte Carlo and polynomial chaos methods for stochastic multi-state multi-noise dynamical chemical processes underline by complex nonlinear behavior.

Optimal Strategies for the Multi-Task Inventory Control Model

We consider the control problem for Markov processes with discrete time. The multi-task model of inventory control for decreasing functions of general costs is analyzed and the existence conditions for the optimal strategy are found. The existence of optimal (s, S)-strategy in inventory control is proved.

A Modular Dynamic Simulation Model for Comminution Circuits

Abstract: Properly controlling comminution circuits is generally acknowledged to be highly profitable for any mining site’s bottom line. On the other hand, the process control problem of comminution circuits is challenging due to circulating loads and non-linear transport/transformation rates. As the performance and robustness of the control system highly rely on a good understanding of the process dynamics, characterizing the deterministic behavior requires a certain level of operation disruption (bump tests). For a grinding circuit, it implies affecting the throughput and product size distributions. The management team can be reluctant to risk obvious consequences on downstream processing stages i.e. inadequate mineral liberation, reduction of product quality, and perhaps even recovery losses. Process simulation becomes in this case an attractive tool to design, assess, and pre-commission advanced control strategies. This paper presents a phenomenological dynamic simulator for comminution circuits developed in Matlab/Simulink®. The block model programming allows changing plant layout or control loops easily, and is flexible for future extensions or model upgrades as any block can be simply added to the library or replaced with its updated version. The flexibility of the modular approach allows testing any control system, from basic PID loops to advanced control schemes. A simulation case study shows how the simulation model can capture the behavior of an actual circuit once properly calibrated.