Simulation‐Based Design of Dual‐Mode Controller for Non‐Linear Processes

This paper presents a simulation‐based approach for designing a non‐linear override control scheme to improve the performance of a local linear controller. The higher‐level non‐linear controller monitors the dynamic state of the system and calculates an override control action whenever the system is predicted to move outside an acceptable operating regime under the local controller. The design of the non‐linear override controller is based on a cost‐to‐go function, which is constructed by using simulation or operation data. The cost‐to‐go function delineates the admissible region of state space within which the local controller is effective, thereby yielding a switching rule.     

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     

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.     

Design and fabrication of non‐noble metal catalyst‐based air‐cathodes for metal‐air battery

In this paper, cost‐effective non‐noble metal catalyst‐based air‐cathodes are designed, developed, and fabricated for a metal‐air battery, particularly in a non‐toxic neutral solution environment (sodium chloride). The air‐cathode and its fabrication method comprise two gas diffusion layers (GDLs) bonded on to each side of the current collector (nickel mesh) by a rolling method, and a catalyst layer bonded on one GDL by a spraying method. The GDL paste consists of carbon powder and hydrophobic chemicals, and the catalyst layer contains non‐noble metal catalyst, carbon powder, and hydrophilic chemicals. Several characterization techniques such as DTA/TG thermal analysis, electrochemical impedance spectroscopy, linear sweep voltammetry, and their associated theories are used to understand the properties and performance of the developed air‐cathodes. The advantages of the current method of forming the air‐cathode can decrease the internal electronic resistance and gas flow restriction of the system, and therefore increase air permeability as well as water transportation to the reaction sites. By using such an integrated structure of an air diffusion cathode, the cost‐effectiveness in terms of materials and manufacturing compared to the commercial air‐cathode, and the overall fabrication procedure is achieved, and the method can be easily transferred into a continuous industrial manufacturing process.     

Characteristics‐Based Model Predictive Control of a Catalytic Flow Reversal Reactor

This paper describes the formulation and tuning of a model‐based controller for a catalytic flow reversal reactor (CFRR). A plug flow non‐linear pseudo‐homogeneous mathematical representation of the process is used to model the mass and energy transport phenomena for the model‐based controller. A combination of the method of characteristics and model predictive control (MPC) technology is used to formulate the controller (Shang et al., Ind. Eng. Chem. Res. 43 (9) 2140–2149 (2004)). Mass extraction from the midsection of the reactor is used as the manipulated variable. Numerical simulations are used to show the performance of the formulated controller. The performance of the controller is evaluated on a simulated catalytic flow reversal reactor unit for combustion of lean methane streams for reduction of greenhouse gases emissions.     

Guaranteed cost distributed fuzzy observer‐based control for a class of nonlinear spatially distributed processes

The guaranteed cost distributed fuzzy (GCDF) observer‐based control design is proposed for a class of nonlinear spatially distributed processes described by first‐order hyperbolic partial differential equations (PDEs). Initially, a T–S fuzzy hyperbolic PDE model is proposed to accurately represent the nonlinear PDE system. Then, based on the fuzzy PDE model, the GCDF observer‐based control design is developed in terms of a set of space‐dependent linear matrix inequalities. In the proposed control scheme, a distributed fuzzy observer is used to estimate the state of the PDE system. The designed fuzzy controller can not only ensure the exponential stability of the closed‐loop PDE system but also provide an upper bound of quadratic cost function. Moreover, a suboptimal fuzzy control design is addressed in the sense of minimizing an upper bound of the cost function. The finite difference method in space and the existing linear matrix inequality optimization techniques are used to approximately solve the suboptimal control design problem. Finally, the proposed design method is applied to the control of a nonisothermal plug‐flow reactor. © 2013 American Institute of Chemical Engineers AIChE J, 59: 2366–2378, 2013     

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     

Shell and tube heat exchanger design using mixed‐integer linear programming

The design of heat exchangers, especially shell and tube heat exchangers was originally proposed as a trial and error procedure where guesses of the heat transfer coefficient were made and then verified after the design was finished. This traditional approach is highly dependent of the experience of a skilled engineer and it usually results in oversizing. Later, optimization techniques were proposed for the automatic generation of the best design alternative. Among these methods, there are heuristic and stochastic approaches as well as mathematical programming. In all cases, the models are mixed integer non‐linear and non‐convex. In the case of mathematical programming solution procedures, all the solution approaches were likely to be trapped in a local optimum solution, unless global optimization is used. In addition, it is very well‐known that local solvers need good initial values or sometimes they do not even find a feasible solution. In this article, we propose to use a robust mixed integer global optimization procedure to obtain the optimal design. Our model is linear thanks to the use of standardized and discrete geometric values of the heat exchanger main mechanical components and a reformulation of integer nonlinear expressions without losing any rigor. © 2016 American Institute of Chemical Engineers AIChE J, 63: 1907–1922, 2017     

Integrating data‐based modeling and nonlinear control tools for batch process control

A data‐based multimodel approach is developed in this work for modeling batch systems in which multiple local linear models are identified using latent variable regression and combined using an appropriate weighting function that arises from fuzzy c‐means clustering. The resulting model is used to generate empirical reverse‐time reachability regions (RTRRs) (defined as the set of states from where the data‐based model can be driven inside a desired end‐point neighborhood of the system), which are subsequently incorporated in a predictive control design. Simulation results of a fed‐batch reactor system under proportional‐integral (PI) control and the proposed RTRR‐based design demonstrate the superior performance of the RTRR‐based design in both a fault‐free and faulty environment. The data‐based modeling methodology is then applied on a nylon‐6,6 batch polymerization process to design a trajectory tracking predictive controller. Closed‐loop simulation results illustrate the superior tracking performance of the proposed predictive controller over PI control. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

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.     

Optimal energy consumption in refrigeration systems ‐ modelling and non‐convex optimisation

Supermarket refrigeration consumes substantial amounts of energy. However, due to the thermal capacity of the refrigerated goods, parts of the cooling capacity delivered can be shifted in time without deteriorating the food quality. In this study, we develop a realistic model for the energy consumption in super market refrigeration systems. This model is used in a Nonlinear Model Predictive Controller (NMPC) to minimise the energy used by operation of a supermarket refrigeration system. The model is non‐convex and we develop a computational efficient algorithm tailored to this problem that is somewhat more efficient than general purpose optimisation algorithms for NMPC and still near to optimal. Since the non‐convex cost function has multiple extrema, standard methods for optimisation cannot be directly applied. A qualitative analysis of the system's constraints is presented and a unique minimum within the feasible region is identified. Following that finding we propose a tailored minimisation procedure that utilises the nature of the feasible region such that the minimisation can be separated into two linear programs; one for each of the control variables. These subproblems are simple to solve but some iterations might have to be performed in order to comply with the maximum capacity constraint. Finally, a nonlinear solver is used for a small example without separating the optimisation problem, and the results are compared to the outcome of our proposed minimisation procedure for the same conceptual example. The tailored approach is somewhat faster than the general optimisation method and the solutions obtained are almost identical. © 2012 Canadian Society for Chemical Engineering     

State‐Space Digital PI Controller Design for Linear Stochastic Multivariable Systems with Input Delay

In this paper, a centralized digital PI control scheme is proposed for linear stochastic multivariable systems with input delay. The discrete linear quadratic regulator (LQR) approach with pole placement is used to achieve satisfactory set‐point tracking with guaranteed closed‐loop stability. In addition, the innovation form of Kalman gain is employed for state estimation with no prior knowledge of noise properties. Compared with existing designs, the proposed scheme provides an optimal closed‐loop design via the digitally implementable PI controller for linear stochastic multivariable systems with input delay. Its effectiveness will be demonstrated by the simulation study on examples from both industrial process control and aircraft control.     

Numerical Simulation of Open‐Circuit Continuous Mills Using a Non‐Linear Population Balance Framework: Incorporation of Non‐First‐Order Effects

Population balance modeling has been used as a tool for simulating, optimizing, and designing various particulate processes, including milling. A fundamental tenet of the traditional models for milling processes is the first‐order breakage kinetics. Ample data obtained from batch milling studies show that this assumption is not necessarily valid for certain milling systems. In the present theoretical investigation, an attempt has been made to incorporate these experimentally observed non‐first‐order effects into continuous mill models within the context of a novel non‐linear population balance framework. In view of two idealized flow regimes, i.e., perfect mixing and plug‐flow, continuous mills operating in the open‐circuit mode are numerically simulated. The simulations indicate that not only does the product size distribution depend on the degree of mixedness in a continuous mill, but also on the non‐first‐order effects arising from multi‐particle interactions.     

Optimization‐Based Nonlinear Centralized Controller Tuning of Liquid‐Liquid Extraction Processes

Abstract

The control problem of an agitated contactor is considered in this work. A Scheibel extraction column is modeled using the non‐equilibrium backflow mixing cell model. Model dynamic analysis shows that this process is highly nonlinear, thus the control problem solution of such a system needs to tackle the process nonlinearity efficiently. The control problem of this process is solved by developing a multivariable nonlinear control system implemented in MATLAB?. In this control methodology, a new controller tuning method is adopted, in which the time‐domain control parameter‐tuning problem is solved as a constrained optimization problem. A MIMO (multi‐input multi‐output) PI controller structure is used in this strategy. The centralized controller uses a 2×2 transfer function and accounts for loops interaction. The controller parameters are tuned using an optimization‐based algorithm with constraints imposed on the process variables reference trajectories. Incremental tuning procedure is performed until the extractor output variables transient response satisfies a preset uncertainty which bounds around the reference trajectory. A decentralized model‐based IMC (internal model control) control strategy is compared with the newly developed centralized MIMO PI control one. Stability and robustness tests are applied to the two algorithms. The performance of the MIMO PI controller is found to be superior to that of the conventional IMC controller in terms of stability, robustness, loops interaction handling, and step‐change tracking characteristics.     

Non‐Linear Model Predictive Control: A Personal Retrospective

An overview of non‐linear model predictive control (NMPC) is presented, with an extreme bias towards the author's experiences and published results. Challenges include multiple solutions (from non‐convex optimization problems), and divergence of the model and plant outputs when the constant additive output disturbance (the approach of dynamic matrix control, DMC) is used. Experiences with the use of fundamental models, multiple linear models (MMPC), and neural networks are reviewed. Ongoing work in unmeasured disturbance estimation, prediction and rejection is also discussed.     

Economic model predictive control with time‐varying objective function for nonlinear process systems

Economic model predictive control (EMPC) is a control scheme that combines real‐time dynamic economic process optimization with the feedback properties of model predictive control (MPC) by replacing the quadratic cost function with a general economic cost function. Almost all the recent work on EMPC involves cost functions that are time invariant (do not explicitly account for time‐varying process economics). In the present work, we focus on the development of a Lyapunov‐based EMPC (LEMPC) scheme that is formulated with an explicitly time‐varying economic cost function. First, the formulation of the proposed two‐mode LEMPC is given. Second, closed‐loop stability is proven through a theoretical treatment. Last, we demonstrate through extensive closed‐loop simulations of a chemical process that the proposed LEMPC can achieve stability with time‐varying economic cost as well as improve economic performance of the process over a conventional MPC scheme. © 2013 American Institute of Chemical Engineers AIChE J 60: 507–519, 2014     

Generation of discrete first‐ and second‐order sensitivities for single shooting

In this work, an approach to the forward generation of discrete first‐ and second‐order sensitivities is proposed. For this purpose, an algorithm has been developed, which can basically be applied to general implicit differential‐algebraic equation (DAE) systems. Moreover, the approach has been tailored to both the generation of directional derivatives and sensitivities with respect to discontinuous control trajectories. The implementation of the method is discussed here for the orthogonal collocation method based on Legendre–Gauss–Radau points and considering the linear implicit DAE type, which arises in problems related to chemical engineering. Lastly, the approach has been applied to three case studies of different complexities. The corresponding performance for the generation of Jacobian and Hessian information is discussed in detail. © 2012 American Institute of Chemical Engineers AIChE J, 58: 3110–3122, 2012     

Transition from Batch to Continuous Operation in Bio‐Reactors: A Model Predictive Control Approach and Application

This work considers the problem of determining the transition of ethanol‐producing bio‐reactors from batch to continuous operation and subsequent control subject to constraints and performance considerations. To this end, a Lyapunov‐based non‐linear model predictive controller is utilized that stabilizes the bio‐reactor under continuous mode of operation. The key idea in the predictive controller is the formulation of appropriate stability constraints that allow an explicit characterization of the set of initial conditions from where feasibility of the optimization problem and hence closed‐loop stability is guaranteed. Additional constraints are incorporated in the predictive control design to expand on the set of initial conditions that can be stabilized by control designs that only require the value of the Lyapunov function to decay. Then, the explicit characterization of the set of stabilizable initial conditions is used in determining the appropriate time for which the reactor must be run in batch mode. Specifically, the predictive control approach is utilized in determining the appropriate batch length that achieves stabilizable values of the state variables at the end of the batch. Application of the proposed method to the ethanol production process using Zymomonas mobilis as the ethanol producing micro‐organism demonstrates the effectiveness of the proposed model predictive control strategy in stabilizing the bio‐reactor.     

Conceptual design of ammonia‐based energy storage system: System design and time‐invariant performance

Chemicals‐based energy storage is promising for integrating intermittent renewables on the utility scale. High round‐trip efficiency, low cost, and considerable flexibility are desirable. To this end, an ammonia‐based energy storage system is proposed. It utilizes a pressurized reversible solid‐oxide fuel cell for power conversion, coupled with external ammonia synthesis and decomposition processes and a steam power cycle. A coupled refrigeration cycle is utilized to recycle nitrogen completely. Pure oxygen, produced as a side‐product in electrochemical water splitting, is used to drive the fuel cell. A first‐principle process model extended by detailed cost calculation is used for process optimization. In this work, the performance of a 100 MW system under time‐invariant operation is studied. The system can achieve a round‐trip efficiency as high as 72%. The lowest levelized cost of delivered energy is obtained at 0.24 $/kWh, which is comparable to that of pumped hydro and compressed air energy storage systems. © 2016 American Institute of Chemical Engineers AIChE J, 63: 1620–1637, 2017