Output feedback robust model predictive control with unmeasurable model parameters and bounded disturbance☆

The output feedback model predictive control (MPC), for a linear parameter varying (LPV) process system including unmeasurable model parameters and disturbance (all lying in known polytopes), is considered. Some previously developed tools, including the norm-bounding technique for relaxing the disturbance-related constraint handling, the dynamic output feedback law, the notion of quadratic boundedness for specifying the closed-loop stability, and the el ipsoidal state estimation error bound for guaranteeing the recursive feasibility, are merged in the control design. Some previous approaches are shown to be the special cases. An example of continuous stirred tank reactor (CSTR) is given to show the effectiveness of the proposed approaches.     

A multiple state stochastic model for deep-bed filtration

A one-parameter stochastic model has been developed for the prediction of dynamic pressure drop in a deep-bed filter. The model is based on a finite-state and discrete-time Markov chain method whereby the pressure drop in a deep-bed filter can be estimated at discrete time intervals. The proposed model is simpler than the stochastic birth and death models available in literature. The bed is assumed to pass through different states of porosity during the filtration and it is spatially lumped in each state. For pressure drop calculation, the Carman-Kozeny equation is used in conjunction with the Payatakes-Tien-Turian model. Model equations are simple and can be easily solved on a personal computer. The theoretical results agree well with the plant data as well as with the available experimental data.     

Bounded robust control of constrained multivariable nonlinear processes

This work focuses on control of multi-input multi-output (MIMO) nonlinear processes with uncertain dynamics and actuator constraints. A Lyapunov-based nonlinear controller design approach that accounts explicitly and simultaneously for process nonlinearities, plant-model mismatch, and input constraints, is proposed. Under the assumption that all process states are accessible for measurement, the approach leads to the explicit synthesis of bounded robust multivariable nonlinear state feedback controllers with well-characterized stability and performance properties. The controllers enforce stability and robust asymptotic reference-input tracking in the constrained uncertain closed-loop system and provide, at the same time, an explicit characterization of the region of guaranteed closed-loop stability. When full state measurements are not available, a combination of the state feedback controllers with high-gain state observes and appropriate saturation filters, is employed to synthesize bounded robust multivariable output feedback controllers that require only measurements of the outputs for practical implementation. The resulting output feedback design is shown to inherit the same closed-loop stability and performance properties of the state feedback controllers and, in addition, recover the closed-loop stability region obtained under state feedback, provided that the observer gain is sufficiently large. The developed state and output feedback controllers are applied successfully to non-isothermal chemical reactor examples with uncertainty, input constraints, and incomplete state measurements. Finally, we conclude the paper with a discussion that attempts to put in perspective the proposed Lyapunov-based control approach with respect to the nonlinear model predictive control (MPC) approach and discuss the implications of our results for the practical implementation of MPC, in control of uncertain nonlinear processes with input constraints.     

A model predictive control strategy for supply chain optimization

This paper describes a model predictive control strategy to find the optimal decision variables to maximize profit in supply chains with multiproduct, multiechelon distribution networks with multiproduct batch plants. The key features of this paper are: (1) a discrete time MILP dynamic model that considers the flow of material and information within the system; (2) a general dynamic optimization framework that simultaneously considers all the elements of the supply chain and their interactions; and (3), a rolling horizon approach to update the decision variables whenever changes affecting the supply chain arise. The paper compares the behavior of a supply chain under centralized and decentralized management approaches, and shows that the former yields better results, with profit increases of up to 15% as shown in an example problem.     

A simple adaptive control strategy for temperature trajectory tracking in batch processes

In this paper, a simple adaptive control strategy is suggested for temperature tracking control of batch processes. A nonlinear controller, which is in structure very simple and consists of a single parameter, is proposed. To enable this controller to control a batch process adaptively, a simple parameter tuning algorithm is derived based on the Lyapunov stability theorem. The proposed adaptive control scheme is directly operational, which does not depend on process model and the only a priori process information required is the system response direction. To demonstrate the effectiveness and applicability of the proposed scheme, illustrative examples are provided. Extensive simulation results reveal that the proposed adaptive control strategy appears to be a simple and effective approach to batch process control, which provides robust control despite the wide range of operating conditions and nonlinear dynamics of the system.     

鲁棒模型预测控制系统的评估基准

在控制系统的性能评估中,基准的设计是个重要问题。将基本设计极限理论推广到模型预测控制系统(MPC),建立性能评估基准。直接考虑多输入多输出系统的频域扰动,建立输出反馈鲁棒模型预测控制器。此控制器仅仅依赖于过程参数,也是令闭环系统达到控制性能极限的基准控制器。建立了用于评估的性能指标,提出基于此基准的性能评估程序,用以评价其他模型预测控制系统的性能。数学算例证实了这一评估程序的有效性。     

A feedback glucose control strategy for type II diabetes mellitus based on fuzzy logic

Most patients with severe Type II diabetes mellitus, characterised by both insulin resistance and β‐cell failure, eventually require insulin therapy. According to the nonlinear dynamics of homeostasis of blood glucose, proportional‐integral (PI) controller, modified by penalising the feedback error using a fuzzy inference system has been developed to maintain normoglycaemia in a simulated patient using a closed‐loop insulin infusion pump. The simulation employs a compartment model proposed by Vahidi et al. [Vahidi et al., Biochem. Eng. J. 2011, 55(1), 7–16]. The results demonstrate that the fuzzy‐based PI controller is superior to a conventional PI controller for the regulation of blood glucose by insulin infusion for Type II diabetic patients. © 2012 Canadian Society for Chemical Engineering     

Computer-aided analysis and design of robust multivariable control systems for chemical processes

A conceptual framework to design robust process control systems is develope d and its realization through an interactive computer-aided design software is presented. The overall design methodology is based on a unified treatment of recent theoretical results in modern control and new computational techniques in symbolic logic manipulation, singular value decomposition and optimization. Several physical examples are given to demonstrate the application of the design approach and the utility of its computer software.     

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     

延迟焦化加热炉的自适应状态反馈预测控制和专家控制

An adaptive state feedback predictive control （SFPC） scheme and an expert control scheme are presented and applied to the temperature control of a 1200 kt·a^-1 delayed coking furnace, which is the key equipment for the delayed coking process. Adaptive SFPC is used to improve the performance of temperature control in normal operation. A simplified nonlinear model on the basis of first principles of the furnace is developed to obtain a state space model by linearization. Taking advantage of the nonlinear model, an online model adapting method is presented to accommodate the dynamic change of process characteristics because of tube coking and load changes. To compensate the large inverse response of outlet temperature resulting from the sudden increase of injected steam of a particular velocity to tubes, a monitoring method and an expert control scheme based on heat balance calculation are proposed. Industrial implementation shows the effectiveness and feasibility of the proposed control strategy.     

A simple model for non-linear stress relaxation

A simple model for the prediction of non-linear stress relaxation following the cessation of steady shear flow is proposed. The model allows the calculation of the shear and first normal stress difference components of the stress. The mathematical flexibility of the model is reduced to a minimum with the result that no adjustable parameters are employed and only linear dynamic deformation data are required to calculate the non-linear behaviour. Verification of the model was carried out with data available for two viscoelastic fluids and good agreement between the predictions and the experimental results was obtained for the range of shear rates examined (0.167 ? γ ? 16.7 sec^?1).     

Improving scenario decomposition algorithms for robust nonlinear model predictive control

This paper deals with the efficient computation of solutions of robust nonlinear model predictive control problems that are formulated using multi-stage stochastic programming via the generation of a scenario tree. Such a formulation makes it possible to consider explicitly the concept of recourse, which is inherent to any receding horizon approach, but it results in large-scale optimization problems. One possibility to solve these problems in an efficient manner is to decompose the large-scale optimization problem into several subproblems that are iteratively modified and repeatedly solved until a solution to the original problem is achieved. In this paper we review the most common methods used for such decomposition and apply them to solve robust nonlinear model predictive control problems in a distributed fashion. We also propose a novel method to reduce the number of iterations of the coordination algorithm needed for the decomposition methods to converge. The performance of the different approaches is evaluated in extensive simulation studies of two nonlinear case studies.     

A multiple model approach to nonlinear internal model control design

A nonlinear internal model control (NIMC) design using multiple model is proposed. In this design approach, the process model is described via validity functions as the weighted sum of a set of local models. Subsequently, an approximate inverse of the process model is constructed in order to design NIMC controller. It is shown that the validity functions can be treated as time-varying uncertainties in the resultant NIMC structure, and a structured singular value test for mixed time-varying and time-invariant perturbations is used to assess the performance limitation of the proposed NIMC design. Simulation results of a continuous stirred tank reactor illustrate that the proposed NIMC design method is superior to the conventional IMC design.     

Explicit model predictive control through robust optimization

A strategy that calculates an explicit state feedback policy to regulate constrained uncertain discrete-time uncertain linear systems is presented. We consider uncertain processes, affected by box-bounded multiplicative uncertainty as well as bounded additive uncertainty with linear state and inputs constraints. The proposed method includes (i) the calculation of a terminal set constraint and (ii) the robust reformulation of state constraints in the prediction horizon. These features allow the derivation of the desired policy by solving a single multiparametric quadratic programming problem that guarantees feasible operation in the presence of uncertainty. Additionally, we employ variable and constraint elimination approaches to enhance the computational performance of the strategy. We demonstrate the steps and benefits of these developments with a numerical example and a chemical engineering case study.     

A non-linear viscoelastic material constitutive model for polyurea

A non-linear viscoelastic constitutive model for polyurea by assuming a separable time and strain dependent material behaviour was proposed in this study. The strain dependent function was described by a nine-parameter Mooney–Rivlin model whereas the time function was assumed to follow a Prony series. A method based on the finite time-increment formulation was used to calculate the material parameters using a simple fitting routine. The effectiveness and accuracy of the model was validated using existing compression and tension data from the literature. The proposed model was found to be very efficient in capturing the behaviour of polyurea under both compressive and tensile loadings for a wide range of strain rates.     

基于状态观测器的电镀液温度状态反馈控制系统

针对电镀液温度控制系统,引入状态反馈控制.相对于传统的反馈控制,本方法可以获得更优异的性能.另外,考虑到镀液温度控制具有纯迟延的特点,提出了一种消去纯迟延的方法.仿真验证结果显示,控制效果良好.     

Iterative learning model predictive control for constrained multivariable control of batch processes

In this paper, we propose a model predictive control (MPC) technique combined with iterative learning control (ILC), called the iterative learning model predictive control (ILMPC), for constrained multivariable control of batch processes. Although the general ILC makes the outputs converge to reference trajectories under model uncertainty, it uses open-loop control within a batch; thus, it cannot reject real-time disturbances. The MPC algorithm shows identical performance for all batches, and it highly depends on model quality because it does not use previous batch information. We integrate the advantages of the two algorithms. The proposed ILMPC formulation is based on general MPC and incorporates an iterative learning function into MPC. Thus, it is easy to handle various issues for which the general MPC is suitable, such as constraints, time-varying systems, disturbances, and stochastic characteristics. Simulation examples are provided to show the effectiveness of the proposed ILMPC.