Error‐triggered on‐line model identification for model‐based feedback control

In industry, it may be difficult in many applications to obtain a first‐principles model of the process, in which case a linear empirical model constructed using process data may be used in the design of a feedback controller. However, linear empirical models may not capture the nonlinear dynamics over a wide region of state‐space and may also perform poorly when significant plant variations and disturbances occur. In the present work, an error‐triggered on‐line model identification approach is introduced for closed‐loop systems under model‐based feedback control strategies. The linear models are re‐identified on‐line when significant prediction errors occur. A moving horizon error detector is used to quantify the model accuracy and to trigger the model re‐identification on‐line when necessary. The proposed approach is demonstrated through two chemical process examples using a model‐based feedback control strategy termed Lyapunov‐based economic model predictive control (LEMPC). The chemical process examples illustrate that the proposed error‐triggered on‐line model identification strategy can be used to obtain more accurate state predictions to improve process economics while maintaining closed‐loop stability of the process under LEMPC. © 2016 American Institute of Chemical Engineers AIChE J, 63: 949–966, 2017     

Enhanced Performance Assessment of Subspace Model‐Based Predictive Controller with Parameters Tuning

This study focuses on performance assessment of model predictive control. An MPC‐achievable benchmark for the unconstrained case is proposed based on closed‐loop subspace identification. Two performance measures can be constructed to evaluate the potential benefit to update the new identified model. Potential benefit by tuning the parameter can be found from trade‐off curves. Effect of constraints imposed on process variables can be evaluated by the installed controller benchmark. The MPC‐achievable benchmark for the constrained case can be estimated via closed‐loop simulation provided that constraints are known. Simulation of an industrial example was done using the proposed method.     

Closed‐loop Fault Detection Using the Local Approach

Fault detection and isolation (FDI) has become a crucial issue for industrial process monitoring in order to increase availability, reliability and production safety. Model‐based FDI methods rely on a mathematical model and input‐output data of a process to perform detection. The local approach is a new model‐based FDI method that aims to detect slight changes of a system's parametric properties. Closed‐loop detection is an important issue for the local approach since all control systems work under closed‐loop conditions. A new algorithm was proposed to revise the original detection algorithm in order to make it work for closed‐loop data. Simulation results show that the proposed method can detect the changes of parameters of a system that can affect closed‐loop performance.     

Relay feedback‐based time domain modelling of off‐diagonal elements of linear 2‐by‐2 MIMO systems

A novel approach to model the off‐diagonal closed‐loop transfer function of 2‐by‐2 multi input multi output (MIMO) system in time domain using ideal as well as biased relay feedback tests are presented. Analytical expressions are derived, for transfer function models of 2‐by‐2 MIMO system having individual transfer function elements of first‐order plus dead time (FOPDT) nature, using ideal and biased relay feedback tests in time domain and have been validated on 2‐by‐2 multivariable distillation column examples from the literature as well as on coupled tanks liquid level experimental set‐up. The results show that the derived expression matches with the original undesired relay response even without approximation of time delay in the denominator of closed‐loop transfer function of 2‐by‐2 MIMO system. These analytical expressions are useful to identify unknown system parameters. © 2012 Canadian Society for Chemical Engineering     

On Measuring Closed‐Loop Non‐Linearity: A Topological Approach

The focal point of this paper is to develop a measure of closed‐loop non‐linearity. In this work, the Vinnicombe metric and the Quasi‐Linear Parameter Varying representation of a non‐linear system are exploited for this purpose. It is expected that the proposed measure can serve as a decision making tool for control engineers when considering whether a linear or a non‐linear control strategy should be employed to close the loop for a non‐linear system operating in a prescribed range.     

Hydrodynamics and Mass Transfer in Gas‐Liquid‐Solid Circulating Fluidized Beds

Although extensive work has been performed on the hydrodynamics and gas‐liquid mass transfer in conventional three‐phase fluidized beds, relevant documented reports on gas‐liquid‐solid circulating fluidized beds (GLSCFBs) are scarce. In this work, the radial distribution of gas and solid holdups were investigated at two axial positions in a GLSCFB. The results show that gas bubbles and solid particles distribute uniformly in the axial direction but non‐uniformly in the radial direction. The radial non‐uniformity demonstrates a strong factor on the gas‐liquid mass transfer coefficients. A local mass transfer model is proposed to describe the gas‐liquid mass transfer at various radial positions. The local mass transfer coefficients appear to be symmetric about the central line of the riser with a lower value in the wall region. The effects of gas flow rates, particle circulating rates and liquid velocities on gas‐liquid mass transfer have also been investigated.     

Economic model predictive control of nonlinear time‐delay systems: Closed‐loop stability and delay compensation

Closed‐loop stability of nonlinear time‐delay systems under Lyapunov‐based economic model predictive control (LEMPC) is considered. LEMPC is initially formulated with an ordinary differential equation model and is designed on the basis of an explicit stabilizing control law. To address closed‐loop stability under LEMPC, first, we consider the stability properties of the sampled‐data system resulting from the nonlinear continuous‐time delay system with state and input delay under a sample‐and‐hold implementation of the explicit controller. The steady‐state of this sampled‐data closed‐loop system is shown to be practically stable. Second, conditions such that closed‐loop stability, in the sense of boundedness of the closed‐loop state, under LEMPC are derived. A chemical process example is used to demonstrate that indeed closed‐loop stability is maintained under LEMPC for sufficiently small time‐delays. To cope with performance degradation owing to the effect of input delay, a predictor feedback LEMPC methodology is also proposed. The predictor feedback LEMPC design employs a predictor to compute a prediction of the state after the input delay period and an LEMPC scheme that is formulated with a differential difference equation (DDE) model, which describes the time‐delay system, initialized with the predicted state. The predictor feedback LEMPC is also applied to the chemical process example and yields improved closed‐loop stability and economic performance properties. © 2015 American Institute of Chemical Engineers AIChE J, 61: 4152–4165, 2015     

Adaptive Internal Model Control of a High‐Purity Heat‐Integrated Air Separation Column

An internal model control scheme based on a second‐order internal model (SI‐IMC) is proposed for the heat‐integrated air separation column (HIASC). An adaptive internal model control (ASI‐IMC) scheme is further presented to make the model more accurate. The IMC scheme based on the first‐order model (F‐IMC) and the multi‐loop PID (M‐PID) scheme are also explored as the comparison basis of ASI‐IMC and SI‐IMC schemes. Comparative researches among these four control schemes are carried out in detail. The results indicate that ASI‐IMC presents the best performances among the four control schemes in both servo control and regulatory control, which proves the improvement of ASI‐IMC over the SI‐IMC and the superiority of ASI‐IMC for the high‐purity HIASC.     

Dynamic real‐time optimization with closed‐loop prediction

Process plants are operating in an increasingly global and dynamic environment, motivating the development of dynamic real‐time optimization (DRTO) systems to account for transient behavior in the determination of economically optimal operating policies. This article considers optimization of closed‐loop response dynamics at the DRTO level in a two‐layer architecture, with constrained model predictive control (MPC) applied at the regulatory control level. A simultaneous solution approach is applied to the multilevel DRTO optimization problem, in which the convex MPC optimization subproblems are replaced by their necessary and sufficient Karush–Kuhn–Tucker optimality conditions, resulting in a single‐level mathematical program with complementarity constraints. The performance of the closed‐loop DRTO strategy is compared to that of the open‐loop prediction counterpart through a multi‐part case study that considers linear dynamic systems with different characteristics. The performance of the proposed strategy is further demonstrated through application to a nonlinear polymerization reactor grade transition problem. © 2017 American Institute of Chemical Engineers AIChE J, 63: 3896–3911, 2017     

Non‐Linear Predictive Control of a Three‐Phase Catalytic Reactor

In this work, the predictive control of a three‐phase catalytic reactor is considered. A predictive control algorithm, which has a non‐linear internal model represented by functional link networks, is proposed. This network structure has been shown to have a good non‐linear approximation capability, with the advantage that the estimation of its weight is a linear optimization problem. The results show the potential of the proposed procedure when it is applied to the 2‐methyl‐cyclohexanol production process, which is a non‐linear, distributed parameter and time‐varying process, typical of many important industrial systems.     

3‐D full‐loop simulation of an industrial‐scale circulating fluidized‐bed boiler

Three‐dimensional (3‐D) simulations using an Eulerian multiphase model were employed to explore flow behaviors in a full‐loop industrial‐scale CFB boiler with and without fluidized‐bed heat exchanger (FBHE), where three solids phases were employed to roughly represent the polydisperse behavior of particles. First, a simulation of the boiler without FBHE is implemented to evaluate drag models, in terms of pressure profiles, mixing behaviors, radial velocity profiles, etc. Compared to the conventional model, the simulation using the energy‐minimization multiscale (EMMS) model successfully predicts the pressure profile of the furnace. Then, such method is used to simulate the boiler with FBHE. The simulation shows that solid inventory in the furnace is underpredicted and reduced with an increase of the valve opening, probably due to the underevaluated drag for FBHE flows. It is suggested to improve EMMS model which is now based on a single set of operating parameters to match with the full‐loop system. © 2012 American Institute of Chemical Engineers AIChE J, 59: 1108–1117, 2013     

Data‐based linear Gaussian state‐space model for dynamic process monitoring

This article develops a data‐based linear Gaussian state‐space model for monitoring of dynamic processes under noisy environment. The Kalman filter is introduced for construction of the linear Gaussian state‐space model, and an iterative expectation‐maximization algorithm is used for model parameters learning. With the incorporation of the dynamic data information, a new fault detection and identification approach is proposed. The feasibility and effectiveness of the two monitoring statistics in the new method are theoretically evaluated and further confirmed through two case studies. Furthermore, detailed fault smearing effect analysis of the proposed method is provided and compared with other identification methods. Based on the simulation results of two case studies, the superiority of the proposed method is explored. © 2012 American Institute of Chemical Engineers AIChE J, 2012     

Characterization of Air‐Water Two‐Phase Vertical Flow by Using Electrical Resistance Imaging

The characterization of air‐water two‐phase vertical flow in a 12 m flow loop with 1.5 m of vertical section is studied by using electrical resistance tomography (ERT). By applying a fast data collection to a dual‐plane ERT sensor and an iterative image reconstruction algorithm, relevant information is gathered for implementation of flow characteristics, particularly for flow regime recognition. A cross‐correlation method is also used to interpret the velocity distribution of the gas phase on the cross section. The paper demonstrates that ERT can now be deployed routinely for velocity measurements and this capability will increase as faster measurement systems evolve.     

Unique block molecules based on glycerol skeleton as C‐3 building blocks for liquid crystals formation by self‐assembly and their future potential for the “nano‐chemistry”

Studies on design of liquid crystalline block molecules with non‐conventional mesophase morphoplogies have been proposed by Tschierske and co‐workers. These block molecules have a rigid core, a lateral substituent, and an alkyl chain segmenting blocks from each other. Related to this, diglyceryl alkyl ethers found by us have glycerol as a rigid core, a lateral substituent, and an alkyl chain similar to the Tschierske design. These two cases are compared with each other with regard to the relationship between the molecular structure and the liquid crystalline morphologies and other properties. Recently, new soft materials suitable for liquid crystals exhibiting self‐assembly of phase‐segregated structures have been designed. Typical examples of such “block” molecules containing glycerol having a C‐3 building block include: (i) undecyl‐glycerylether‐ modified siloxane derivatives with a siloxane segment as the rigid core and alkyl chains with 2, 3‐dihydroxypropoxy group as a hydrophilic group at a lateral or terminal position of the siloxane segment; (ii) novel hyper branched dendrimers forming the basis of polyglycerol nanocapsules with a core‐shell molecular architecture; (iii) carbon nanotubes based on cyclodextrins (CDs); (iv) polymerizable amphiphilic diacetylene‐containing phospholipids suitable for construction of functional nanocomposites. This is done by self‐assembly and polymerization of diacetylene creating a “block molecular structure” with a polyacetylene chain as a rigid core segment, the lipid headgroups as the hydrophilic segment, and terminal flexible alkyl chains. On the basis of these results, future potential of block molecules as a soft building material for liquid crystalline structures was discussed.     

Time‐varying multi‐regime models fitting by genetic algorithms

Many time series exhibit both nonlinearity and non‐stationarity. Though both features have been often taken into account separately, few attempts have been proposed for modelling them simultaneously. We consider threshold models, and present a general model allowing for different regimes both in time and in levels, where regime transitions may happen according to self‐exciting, or smoothly varying or piecewise linear threshold modelling. Since fitting such a model involves the choice of a large number of structural parameters, we propose a procedure based on genetic algorithms, evaluating models by means of a generalized identification criterion. The performance of the proposed procedure is illustrated with a simulation study and applications to some real data.     

3‐D Simulations of an Internal Airlift Loop Reactor using a Steady Two‐Fluid Model

Three‐dimensional (3‐D) simulations of an internal airlift loop reactor in a cylindrical reference frame are presented, which are based on a two‐fluid model with a revised k‐? turbulence model for two‐phase bubbly flow. A steady state formulation is used with the purpose of time saving for cases with superficial gas velocity values as high as 0.12 m/s. Special 3‐D treatment of the boundary conditions at the axis is undertaken to allow asymmetric gas‐liquid flow. The simulation results are compared to the experimental data on average gas holdup, average liquid velocity in the riser and the downcomer, and good agreement is observed. The turbulent dispersion in the present two‐fluid model has a strong effect on the gas holdup distribution and wall‐peaking behavior is predicted. The CFD code developed has the potential to be applied as a tool for scaling up loop reactors.     

Moving horizon closed‐loop production scheduling using dynamic process models

The economic circumstances that define the operation of chemical processes (e.g., product demand, feedstock and energy prices) are increasingly variable. To maximize profit, changes in production rate and product grade must be scheduled with increased frequency. To do so, process dynamics must be considered in production scheduling calculations, and schedules should be recomputed when updated economic information becomes available. In this article, this need is addressed by introducing a novel moving horizon closed‐loop scheduling approach. Process dynamics are represented explicitly in the scheduling calculation via low‐order models of the closed‐loop dynamics of scheduling‐relevant variables, and a feedback connection is built based on these variables using an observer structure to update model states. The feedback rescheduling mechanism consists of, (a) periodic schedule updates that reflect updated price and demand forecasts, and, (b) event‐driven updates that account for process and market disturbances. The theoretical developments are demonstrated on the model of an industrial‐scale air separation unit. © 2016 American Institute of Chemical Engineers AIChE J, 63: 639–651, 2017     

Multi‐period planning,design, and strategic models for long‐term,quality‐sensitive shale gas development

In this work we address the long‐term, quality‐sensitive shale gas development problem. This problem involves planning, design, and strategic decisions such as where, when, and how many shale gas wells to drill, where to lay out gathering pipelines, as well as which delivery agreements to arrange. Our objective is to use computational models to identify the most profitable shale gas development strategies. For this purpose we propose a large‐scale, nonconvex, mixed‐integer nonlinear programming model. We rely on generalized disjunctive programming to systematically derive the building blocks of this model. Based on a tailor‐designed solution strategy we identify near‐global solutions to the resulting large‐scale problems. Finally, we apply the proposed modeling framework to two case studies based on real data to quantify the value of optimization models for shale gas development. Our results suggest that the proposed models can increase upstream operators’ profitability by several million U.S. dollars. © 2016 American Institute of Chemical Engineers AIChE J, 62: 2296–2323, 2016     

Delay‐range‐dependent guaranteed cost control for batch processes with state delay

A guaranteed cost control scheme is proposed for batch processes described by a two‐dimensional (2‐D) system with uncertainties and interval time‐varying delay. First, a 2‐D controller, which includes a robust feedback control to ensure performances over time and an iterative learning control to improve the tracking performance from cycle to cycle, is formulated. The guaranteed cost law concept of the proposed 2‐D controller is then introduced. Subsequently, by introducing the Lyapunov–Krasovskii function and adding a differential inequality to the Lyapunov function for the 2‐D system, sufficient conditions for the existence of the robust guaranteed cost controller are derived in terms of matrix inequalities. A design procedure for the controller is also presented. Furthermore, a convex optimization problem with linear matrix inequality (LMI) constraints is formulated to design the optimal guaranteed cost controller that minimizes the upper bound of the closed‐loop system cost. The proposed control law can stabilize the closed‐loop system as well as guarantee H_∞ performance level and a cost function with upper bounds for all admissible uncertainties. The results can be easily extended to the constant delay case. Finally, an illustrative example is given to demonstrate the effectiveness and advantages of the proposed 2‐D design approach. © 2013 American Institute of Chemical Engineers AIChE J, 59: 2033–2045, 2013     

An Approach to Simple Reaction Control for Auto‐thermal Fuel‐reforming Systems

A simple approach to reaction control for auto‐thermal fuel‐reforming systems was proposed and examined. The amount of air supplied to the fuel‐reforming system was chosen as the variable in the feedback (closed‐loop) control operation, and simply by varying the amount of air supplied, it was attempted to control and stabilize the temperature of the auto‐thermal reforming reaction. The amounts of other fuels and water were chosen from pre‐determined values by open‐loop operation. Since the feedback operation was limited to the air‐supply mechanism, it was expected that both the hardware structure of the system and its software configurations could be significantly simplified. The applicability of this simple feedback control operation was confirmed experimentally by using a methanol reformer of the direct‐injection type.