Process Control Problems Research Articles

A dynamic model of fluidized-bed flotation

Abstract The concept of fluidized-bed flotation (FBF) (e.g. HydroFloatTM) was recently introduced to improve the recovery of coarse particles (425 to 1180 µm). In spite of encouraging results from the first industrial applications dating back more than a decade, FBF still remains an emerging technology in the global mining industry. This paper presents a dynamic model of a FBF cell based on first principles describing volume conservation balances and macro hydrodynamic conditions. It was specifically developed to address process design, monitoring, and control problems. The model relies on the drift-flux theory to predict the flow of three populations (free particles, attached particles and bubbles) throughout the proposed vertical mixer-in-series framework. A calibration of empirical parameters on literature data demonstrates the ability to reproduce the effect of operating parameters (airflow rate, fluidization water flow rate and bed height) on steady-state recovery as long as the equipment operates at low turbulence.

$$L^p$$ L p solution of backward stochastic differential equations driven by a marked point process

We obtain existence and uniqueness in $$L^p$$ , $$p>1$$ of the solutions of a backward stochastic differential equation (BSDE for short) driven by a marked point process, on a bounded interval. We show that the solution of the BSDE can be approximated by a finite system of deterministic differential equations. As application, we address an optimal control problem for point processes of general non-Markovian type and show that BSDEs can be used to prove existence of an optimal control and to represent the value function.

Phase-II monitoring in multichannel profile observations

Process monitoring and fault diagnosis using profile data remains an important problem in statistical process control (SPC). It is particularly challenging with multichannel profiles. This article proposes a novel scheme for Phase-II monitoring of multichannel profiles. The proposed method integrates the exponentially weighted moving average (EWMA) scheme with multichannel functional principal component analysis (MFPCA) to obtain the charting statistics. Their control limits can be effectively computed by the Markov chain method. Moreover, we provide a natural diagnostic procedure to locate the possible change point once the chart is out-of-control. Our proposed method is demonstrated to be effective and efficient through simulation results and an industrial case study from a multioperation forging process.

Event-triggered boundary feedback control for networked reaction-subdiffusion processes with input uncertainties

This paper is concerned with the event-triggered boundary feedback control problems for networked reaction-subdiffusion processes governed by time fractional reaction-diffusion systems with unknown time-varying input uncertainties over sensor/actuator networks. The event-triggered boundary state feedback controller is first designed and implemented via backstepping technique. Moreover, we realize that the availability of full-state measurements in many practical applications may be impossible due to the difficulties in measuring. To solve this limitation, we design an extended Luenberger observer that embeds within the networked sensor to estimate the whole states of the systems under consideration. Based on this, the boundary output feedback event-triggered implementation of the studied system in the context of sensor/actuator networks is then proposed. It is shown that both two kinds of event-triggered strategies could significantly asymptotically stabilize the estimation with the Zeno phenomenon being excluded. Two numerical illustrations are finally included.

Optimal stochastic sequential control with fractional rewards

In this paper we discuss the optimal stopping problem for multiparameter stochastic processes with the index set Nd, and in general, the optimal sequential control problem for stochastic processes with the index set consisting of increasing paths. We give the formulation of new control problems which combine the discrete time optimal sequential control problem with the criterion of a fractional reward. Using the standard mathematical argument in the theory of mathematical programming, we prove the existence of optimal stopping points and optimal controls for these problems under the certain assumption on the regularity of the stochastic processes. Further we discuss ε – optimal controls, finite time controls, and Markov case, respectively.

Iterative learning fault-tolerant control for networked batch processes with event-triggered transmission strategy and data dropouts

ABSTRACTThis paper studies the iterative learning fault-tolerant control (ILFTC) problem for networked batch processes with event-triggered transmission strategy and data dropouts. During the transmission of input signal, the event-triggered mechanism is adopted to reduce the number of updated data items. The data dropouts are assumed to obey the Bernoulli random binary distribution. The objective of this paper is to design a state feedback controller such that the system is fault-tolerant and satisfies the robust performance requirement. By combining 2D stochastic system theory and linear matrix inequality (LMI) technique, some sufficient conditions are given to ensure the existence of the designed controller. Finally, an example of nozzle pressure control is utilized to verify the availability of the proposed method.

Phase I outlier detection in profiles with binary data based on penalized likelihood

AbstractProfile monitoring has been proven to be important among statistical process control problems. In some specific applications, the response variable of a profile can be categorical data, and numerous methods have been proposed for monitoring this type of profiles. Nevertheless, outlier detection for profiles with categorical data still attracted insufficient attention in the literature. To this end, this paper focuses on binary profiles and develops two schemes for outlier detection, from the viewpoint of penalized likelihood, based on the group LASSO method and directional information, respectively, in which the profiles of interest are treated as an integrated high‐dimensional vector. Simulation study shows that the proposed group‐type scheme usually performs better than the existing chart in terms of detecting outliers correctly and alleviating the masking effect. Finally, a real example is used for illustrating the implementation of the proposed scheme.

Nonparametric control schemes for profiles with attribute data

Abstract Attribute data are very common in the real production and service processes. Therefore, many kinds of control charts for attribute data have been studied in the literature. On the other hand, profile monitoring has been a popular statistical process control (SPC) problem recently. Moreover, in some cases, the response variables of profiles are attribute data, such as binary or Poisson data. Thus, the research on SPC for profiles with attribute data is very important, which motivates us to undertake this current research and try to develop a unified framework for monitoring such kind of profiles. In this paper, the unified framework of control schemes based on the nonparametric regression is proposed, including the generalized likelihood ratio chart, the T 2 chart and the exponential weighted moving average chart. These schemes could tackle linear or nonlinear profiles with a wide class of response variables belonging to the exponential family of distributions. The performance of the proposed control charts is studied under the binomial and Poisson profiles by numerical simulations. Furthermore, two examples are used for illustrating the implementation of the proposed control charts.

Optimal Management of Oil Field Development in the Buckley–Leverett Model

We consider the problem of two-phase filtering (oil and water) in a horizontal layer of an oil deposit. We propose an asymptotic method for calculating both the filtering process and related optimal control problems, namely the problems of choosing optimal control actions to achieve maximum oil production at a given level of water resource consumption or a minimum water flow rate that provides the level of oil production required by the plan.

Necessary conditions of first-order for an optimal boundary control problem for viscous damage processes in 2D

Controlling the growth of material damage is an important engineering task with plenty of real world applications. In this paper we approach this topic from the mathematical point of view by investigating an optimal boundary control problem for a damage phase-field model for viscoelastic media. We consider non-homogeneous Neumann data for the displacement field which describe external boundary forces and act as control variables. The underlying hyberbolic-parabolic PDE system for the state variables exhibit highly nonlinear terms which emerge in context with damage processes. The cost functional is of tracking type, and constraints for the control variable are prescribed. Based on recent results from [M.H. Farshbaf−Shaker and C. Heinemann, Math. Models Methods Appl. Sci. 25 (2015) 2749–2793], where global-in-time well-posedness of strong solutions to the lower level problem and existence of optimal controls of the upper level problem have been established, we show in this contribution differentiability of the control-to-state mapping, well-posedness of the linearization and existence of solutions of the adjoint state system. Due to the highly nonlinear nature of the state system which has by our knowledge not been considered for optimal control problems in the literature, we present a very weak formulation and estimation techniques of the associated adjoint system. For mathematical reasons the analysis is restricted here to the two-dimensional case. We conclude our results with first-order necessary optimality conditions in terms of a variational inequality together with PDEs for the state and adjoint state system.

Optimal control of piecewise deterministic Markov processes: a BSDE representation of the value function

We consider an infinite-horizon discounted optimal control problem for piecewise deterministic Markov processes, where a piecewise open-loop control acts continuously on the jump dynamics and on the deterministic flow. For this class of control problems, the value function can in general be characterized as the unique viscosity solution to the corresponding Hamilton−Jacobi−Bellman equation. We prove that the value function can be represented by means of a backward stochastic differential equation (BSDE) on infinite horizon, driven by a random measure and with a sign constraint on its martingale part, for which we give existence and uniqueness results. This probabilistic representation is known as nonlinear Feynman−Kac formula. Finally we show that the constrained BSDE is related to an auxiliary dominated control problem, whose value function coincides with the value function of the original non-dominated control problem.

Optimization for the Starting Process of Turbofan Engine Under High-Altitude Environment

The control of the starting process for turbofan engine is a difficult task, especially under high-altitude and low-temperature environment, where its characteristics are more complex and strongly nonlinear. In this paper, the working characteristics of the starting process were analyzed and the corresponding mathematical model was established first. In the starting process control problem, since the fuel supply act as the main control parameter, the model of the fuel regulator system was also built. Then, according to the control requirements and combined with models, an optimization expression for minimization of starting time with working and physical constraints was given. The genetic algorithm was utilized to solve the constrained optimization problem and the performance was compared with the classical one that is acquired from actual flight test data. Without exceeding the temperature bound, the starting time can be shortened by about 30%. Moreover, during the unloading process, the starting time in the plateau state and the highest exhaust temperature are reduced by 18.2% ~ 29.3% and 4.7% ~ 8.6%, respectively.

Metallurgical Aspects of Inclusion Assessment in Al–6%Si Casting Alloy Using the LiMCA Technique

In the production of high-quality aluminum castings, melt cleanliness is important in regard to the performance and quality of the cast part and is determined, among other factors, by the inclusions present in the molten metal. Besides causing problems in process and quality control, other harmful consequences include reduced mechanical properties, poor machinability and increased porosity. Thus, control of melt cleanliness requires monitoring and minimizing the presence of impurities and inclusions. The liquid metal cleanliness analyzer (LiMCA) technique was used in the present study to investigate its capability for measuring inclusions such as Al2O3, Al4C3, MgO, CaO, TiB2 and TiAl3 typically found in aluminum alloys, where these inclusions were added to Al–6%Si alloy melts using powder, master alloy, pure metal and metal matrix composite sources. Melts containing the different inclusion types were prepared, and the melt cleanliness was quantified using the LiMCA technique. Samplings for microstructural examination were also taken simultaneously. Evidence of the agglomeration of a vast amount of TiB2 inclusions as captured by the LiMCA probe tube shows that LiMCA is the only technique that is able to capture such agglomerates in-line, without any problem, as other techniques such as the PoDFA and Prefil cannot measure such TiB2 agglomerates without their filter systems getting clogged and interrupting the measurements. This is a significant finding and demonstrates a very important aspect of the LiMCA technique, particularly in view of the fact that Al–Ti–B master alloys are regularly employed for grain refining aluminum casting alloys.

Practical algorithm for stochastic optimal control problem about microbial fermentation in batch culture

How to add glycerol to maximize production of 1,3-propanediol (1,3-PD) is a critical problem in process control of microbial fermentation. Most of the existing works are focusing on modelling this process through deterministic-based differential equations. However, this process is not deterministic, but intrinsically stochastic considering nature of interference. Thus, it is of importance to consider stochastic microorganism. In this paper, we will modelling this process through stochastic differential equations and maximizing production of 1,3-PD is formulated as an optimal control problem subject to continuous state constraints and stochastic disturbances. A modified particle swarm algorithm through integrating the hybrid Monte Carlo sampling and path integral is proposed to solve this problem. The constraint transcription, local smoothing and time-scaling transformation are introduced to handle the continuous state constraints. Numerical results show that, by employing the obtained optimal control governed by stochastic dynamical system, 1,3-PD concentration at the terminal time can be increased compared with the previous results.

Optimal false alarm controlled support vector data description for multivariate process monitoring

One-class classification plays a key role in the detection of outliers and abnormalities. Recently, several attempts have been made to extend the application of one-class classification techniques to statistical process control problems, where many of these one-class classification-based approaches have used a support vector data description algorithm. The monitoring statistics for a support vector data description-based control chart are sufficiently defined. However, the control limits are not obvious because the procedure used to derive the control limit does not include a method for controlling the false alarm rate (i.e., Type I error rate), which clearly limits its use in process monitoring. In this study, we propose a new multivariate control chart based on a technique for optimal false alarm-controlled support vector data description, which minimizes the radius of a spherically shaped boundary so that it includes the normal data that are equal to an assigned constant value. By modifying this constant value, users can precisely control the proportion of abnormal data determined by the spherically shaped boundary, which equals the expected Type I error rate. We demonstrated the usefulness of the proposed charts in experiments with simulated data and real process data based on a thin film transistor–liquid crystal display.

Robust Iterative Learning Fault-Tolerant Control for Multiphase Batch Processes with Uncertainties

In this paper, the iterative learning fault-tolerant control problem for multiphase batch processes with uncertainty and actuator faults is studied. First, making full use of the characteristics of the two-time dimension (2D) feature and repetitiveness in batch processes and introducing the state error and output error between the adjacent batches, the established model is transformed into an equivalent 2D-Roesser switched system with different dimensions. Under the framework of the 2D system theory and by means of the average dwell time method, sufficient conditions ensuring the system to be 2D robustly stable along the time and batch directions and the minimum running time lower bound in each phase are given. Simultaneously, the designed updating law is derived. In order to examine the control performance of the proposed method, the traditional reliable control method is also investigated in this paper. The batch process is regarded as a continuous system, in which only the fault-tolerant control along ...

Shall I Sell or Shall I Wait? Optimal Liquidation Under Partial Information with Price Impact

We study the optimal liquidation problem in a market model where the bid price follows a geometric pure jump process whose local characteristics are driven by an unobservable finite-state Markov chain and by the liquidation rate. This model is consistent with stylized facts of high frequency data such as the discrete nature of tick data and the clustering in the order flow. We include both temporary and permanent effects into our analysis. We use stochastic filtering to reduce the optimal liquidation problem to an equivalent optimization problem under complete information. This leads to a stochastic control problem for piecewise deterministic Markov processes (PDMPs). We carry out a detailed mathematical analysis of this problem. In particular, we derive the optimality equation for the value function, we characterize the value function as continuous viscosity solution of the associated dynamic programming equation, and we prove a novel comparison result. The paper concludes with numerical results illustrating the impact of partial information and price impact on the value function and on the optimal liquidation rate.

石油・化学プロセスにおけるPID制御の新しい展開 : 「評価」と「設計」を統合するアプローチ( 化学産業におけるプロセス制御の現状と課題)

石油・化学プロセスにおけるPID制御の新しい展開 : 「評価」と「設計」を統合するアプローチ( 化学産業におけるプロセス制御の現状と課題)

化学プロセス制御の「いま」をお伝えします( 化学産業におけるプロセス制御の現状と課題)

化学プロセス制御の「いま」をお伝えします( 化学産業におけるプロセス制御の現状と課題)

化学プロセス制御技術者の実践と挑戦 : 何をしてきたのか,何をすべきか( 化学産業におけるプロセス制御の現状と課題)

化学プロセス制御技術者の実践と挑戦 : 何をしてきたのか,何をすべきか( 化学産業におけるプロセス制御の現状と課題)