Design of multi-parametric NCO tracking controllers for linear dynamic systems

A methodology for combining multi-parametric programming and NCO tracking is presented in the case of linear dynamic systems. The resulting parametric controllers consist of (potentially nonlinear) feedback laws for tracking optimality conditions by exploiting the underlying optimal control switching structure. Compared to the classical multi-parametric MPC controller, this approach leads to a reduction in the number of critical regions. It calls for the solution of more difficult parametric optimization problems with linear differential equations embedded, whose critical regions are potentially nonconvex. Examples of constrained linear quadratic optimal control problems with parametric uncertainty are presented to illustrate the approach.     

基于ARX-PLS解耦框架下的多回路约束迭代模型预测控制方法(英文)

A multi-loop constrained model predictive control scheme based on autoregressive exogenous-partial least squares （ARX-PLS） framework is proposed to tackle the high dimension, coupled and constraints problems in industry processes due to safety limitation, environmental regulations, consumer specifications and physical restric-tion. ARX-PLS decoupling character enables to turn the multivariable model predictive control （MPC） controller design in original space into the multi-loop single input single output （SISO） MPC controllers design in latent space. An idea of iterative method is applied to decouple the constraints latent variables in PLS framework and recursive least square is introduced to identify ARX-PLS model. This algorithm is applied to a non-square simulation system and a stirred reactor for ethylene polymerizations comparing with adaptive internal model control （IMC） method based on ARX-PLS framework. Its application has shown that this method outperforms adaptive IMC method based on ARX-PLS framework to some extent.     

Lyapunov‐based MPC with robust moving horizon estimation and its triggered implementation

In this work, we consider moving horizon state estimation (MHE)‐based model predictive control (MPC) of nonlinear systems. Specifically, we consider the Lyapunov‐based MPC (LMPC) developed in (Mhaskar et al., IEEE Trans Autom Control. 2005;50:1670–1680; Syst Control Lett. 2006;55:650–659) and the robust MHE (RMHE) developed in (Liu J, Chem Eng Sci. 2013;93:376–386). First, we focus on the case that the RMHE and the LMPC are evaluated every sampling time. An estimate of the stability region of the output control system is first established; and then sufficient conditions under which the closed‐loop system is guaranteed to be stable are derived. Subsequently, we propose a triggered implementation strategy for the RMHE‐based LMPC to reduce its computational load. The triggering condition is designed based on measurements of the output and its time derivatives. To ensure the closed‐loop stability, the formulations of the RMHE and the LMPC are also modified accordingly to account for the potential open‐loop operation. A chemical process is used to illustrate the proposed approaches. © 2013 American Institute of Chemical Engineers AIChE J, 59: 4273–4286, 2013     

A dynamic programming based approach for explicit model predictive control of hybrid systems

This work presents an algorithm for explicit model predictive control of hybrid systems based on recent developments in constrained dynamic programming and multi-parametric programming. By using the proposed approach, suitable for problems with linear cost function, the original model predictive control formulation is disassembled into a set of smaller problems, which can be efficiently solved using multi-parametric mixed-integer programming algorithms. It is also shown how the methodology is applied in the context of explicit robust model predictive control of hybrid systems, where model uncertainty is taken into account. The proposed developments are demonstrated through a numerical example where the methodology is applied to the optimal control of a piece-wise affine system with linear cost function.     

Model predictive control of condensate recycle process in a cogeneration power station: Controller design and numerical application

A model predictive control (MPC) system has been developed for application to the condensate recycle process of a 300 MW cogeneration power station of the East-West Power Plant, Gyeonggido, Korea. Unlike other industrial processes where MPC has been predominantly applied, the operation mode of the cogeneration power station changes continuously with weather and seasonal conditions. Such characteristic makes it difficult to find the process model for controller design through identification. To overcome the difficulty, process models for MPC design were derived for each operation mode from the material balance applied to the pipeline network around the concerned process. The MPC algorithm has been developed so that the controller tuning is easy with one tuning knob for each output and the constrained optimization is solved by an interior-point method. For verification of the MPC system before process implementation, a process simulator was also developed. Performance of the MPC was investigated first with a process simulator against various disturbance scenarios.     

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.     

气垫式流浆箱控制方案仿真研究

针对造纸过程中气垫式流浆箱的控制问题,提出了模型预测控制（MPC）方案。首先描述了气垫式流浆箱控制系统模型,然后分析PID和MPC控制原理和具体实施方案,最后基于MATLAB平台,利用图形用户界面（GUI）设计技术,开发出了气垫式流浆箱控制系统计算机仿真软件。通过该仿真软件,分别对气垫式流浆箱中PID和MPC控制方案进行仿真比较。结果表明,对于气垫式流浆箱这类双输入双输出的控制系统,MPC具有更好的解耦性、稳定性和鲁棒性,其控制效果比较理想。     

新一代的自适应模型预测控制器

提出了新一代的自适应模型预测控制器,自适应MPC控制器由MPC控制模块、在线辨识模块、性能监控模块3个模块组成,相互协调配和来实现自适应MPC控制。除了控制器功能设计以外,其余过程均可自动进行。对于新建MPC应用,首先进行多变量测试与辨识,在模型符合控制要求时,自动进入控制器投运。通过控制器性能监视发现模型不满足控制要求精度时,触发一次多变量模型测试与辨识过程,替换原有模型进行控制,保证控制器性能始终处于最佳状态。自适应MPC控制器在PTA装置上的应用表明了算法的有效性。     

Integration of Design and Control: A Robust Control Approach Using MPC

This paper presents a new method to integrate process control with process design. The process design is based on steady‐state costs, .i.e., capital and operating costs. Control is incorporated into the design in terms of a variability cost. This term is calculated based on the non‐linear process model, represented here as a nominal linear model supplemented with model parameter uncertainty. Robust control tools are then used within the approach to assess closed‐loop robust stability and to calculate closed‐loop variability. The integrated method results in a non‐linear constrained optimization problem with an objective function that consists of the sum of the steady costs and the variability cost. Optimization using the traditional sequential approach and the new integrated method was applied to design a multi‐component distillation column using a Model Predictive Control (MPC) algorithm. The optimization results show that the integrated method can lead to significant cost savings when compared to the traditional sequential approach. In addition, an RGA analysis was performed to study the effects of process interactions on the optimization results.     

Off-line model reduction for on-line linear MPC of nonlinear large-scale distributed systems

Model predictive control (MPC) is an efficient method for the controller design of a large number of processes. However, linear MPC is often inappropriate for controlling nonlinear large-scale systems, while non-linear MPC can be computationally costly. The resulting optimization-based procedure can lead to local minima due to the, non-convexities that non-linear systems can exhibit. To overcome the excessive computational cost of MPC application for large-scale nonlinear systems, model reduction methodology in conjunction with efficient system linearizations have been exploited to enable the efficient application of linear MPC for nonlinear distributed parameter systems (DPS). An off-line model reduction technique, the proper orthogonal decomposition (POD) method, combined with a finite element Galerkin projection is first used to extract accurate non-linear low-order models from the large-scale ones. Trajectory Piecewise-Linear (TPWL) methodologies are subsequently developed to construct a piecewise linear representation of the reduced nonlinear model, both in a static and in a dynamic fashion. Linear MPC, based on quadratic programming, can then be efficiently performed on the resulting low-order, piece-wise affine system. Our combined methodology is readily applicable in combination with advanced MPC methodologies such as multi-parametric MPC (MP-MPC) (Pistikopoulos, 2009). The stabilisation of the oscillatory behaviour of a tubular reactor with recycle is used as an illustrative example to demonstrate our methodology.     

Robust decision making for hybrid process supply chain systems via model predictive control

Model predictive control (MPC) is a promising solution for the effective control of process supply chains. This paper presents an optimization-based decision support tool for supply chain management, by means of a robust MPC strategy. The proposed formulation: (i) captures uncertainty in model parameters and demand by stochastic programming, (ii) accommodates hybrid process systems with decisions governed by logical conditions/rulesets, and (iii) addresses multiple supply chain performance metrics including customer service and economics, within an integrated optimization framework. Two mechanisms for uncertainty propagation are presented – an open-loop approach, and an approximate closed-loop strategy. The performance of the robust MPC framework is analyzed through its application to two process supply chain case studies. The proposed approach is shown to provide a substantial reduction in the occurrence of back orders when compared to a nominal MPC implementation.     

Modelling and explicit model predictive control for PEM fuel cell systems

We present an analytical dynamic model and a general framework for the optima control design of a PEM fuel cell system. The mathematical model consists of a detailed model for the PEM fuel cell stack and simplified models for the compressor, humidifier and cooling system. The framework features (i) a detailed dynamic process model, (ii) a reduced order approximating model obtained by performing dynamic simulations of the system and (iii) the design of an explicit/multi-parametric model predictive controller. The derived explicit/multi-parametric controller is tested and validated off-line on several operating conditions.     

Robust supply chain performance via Model Predictive Control

This paper presents a novel robust Model Predictive Control (MPC) method for real-time supply chain optimization under uncertainties. This method optimizes the closed-loop economic performance of supply chain systems and addresses different sources of uncertainties located external to and within the feedback loop. The future system behavior is predicted by a closed-loop model, which includes both the open-loop system model and a controller model described by an optimization problem. The robust MPC formulation involves the solution of a constrained, bi-level stochastic optimization problem, which is transformed into a tractable problem involving a limited number of deterministic conic optimization problems solved reliably using an interior point method. The robust controller is applied to a real industrial multi-echelon supply chain optimization problem, and its performance is shown to reduce stock-outs without excessive inventories.     

From multi-parametric programming theory to MPC-on-a-chip multi-scale systems applications

An overview of multi-parametric programming and control is presented with emphasis on historical milestones, novel developments in the theory of multi-parametric programming and explicit MPC as well as their application to the design of advanced controller for complex multi-scale systems.     

Optimization-based strategies for the operation of low-density polyethylene tubular reactors: nonlinear model predictive control

In this work, we present a general nonlinear model predictive control (NMPC) framework for low-density polyethylene (LDPE) tubular reactors. The framework is based on a first-principles dynamic model able to capture complex phenomena arising in these units. We first demonstrate the potential of using NMPC to simultaneously regulate and optimize the process economics in the presence of persistent disturbances such as fouling. We then couple the NMPC controller with a compatible moving horizon estimator (MHE) to provide output feedback. Finally, we discuss computational limitations arising in this framework and make use of recently proposed advanced-step MHE and NMPC strategies to provide nearly instantaneous feedback.     

Design and Analysis of Integrated Predictive Iterative Learning Control for Batch Process Based on Two-dimensional System Theory

Based on the two-dimensional (2D) systemtheory, an integrated predictive iterative learning control (2D-IPILC) strategy for batch processes is presented. First, the output response and the error transition model predictions along the batch index can be calculated analytically due to the 2D Roesser model of the batch process. Then, an integrated framework of combining iterative learning control (ILC) andmodel predictive control(MPC) is formed reasonably. The output of feedforward ILC is estimated on the basis of the predefined process 2D model. By minimizing a quadratic objective function, the feedback MPC is introduced to obtain better control performance for tracking problem of batch processes. Simulations on a typical batch reactor demonstrate that the satisfactory tracking performance as well as faster convergence speed can be achieved than traditional proportion type (Ptype) ILC despite the model error and disturbances.     

基于模型预测控制及智能寻优的水泥粉磨优化控制

本文提出一种基于运行状态软测量和成本软约束的多变量模型预测控制(MPC)。MPC控制与传统的专家经验控制和模糊控制相比,通过模型对系统工艺参数的预测,不断地学习更新模型,更符合水泥粉磨大时延、多工况的特性。应用中通过对水泥粉磨装置的阶跃响应实验,建立多变量预测控制模型,解决水泥粉磨系统生产过程的不确定性。在此基础上,通过增量学习和机器学习找到最优运行参数,使水泥粉磨的MPC控制一直保持在最优工况。     

An Off-Line Formulation of Tube-Based Robust MPC Using Polyhedral Invariant Sets

In this paper, an off-line formulation of tube-based robust model predictive control (MPC) using polyhedral invariant sets is proposed. A novel feature is the fact that no optimal control problem needs to be solved at each sampling time. Moreover, the proposed tube-based robust MPC algorithm can deal with the linear time-varying (LTV) system with bounded disturbance. The simulation results show that the state at each time step is restricted to lie within a tube whose center is the state of the nominal LTV system that converges to the origin. Finally, the state is kept within a tube whose center is at the origin, so robust stability is guaranteed. Satisfaction of the state and control constraints is guaranteed by employing tighter constraint sets for the nominal LTV system.     

Robust model predictive control and fault handling of batch processes

This work considers the control of batch processes subject to input constraints and model uncertainty with the objective of achieving a desired product quality. First, a computationally efficient nonlinear robust Model Predictive Control (MPC) is designed. The robust MPC scheme uses robust reverse‐time reachability regions (RTRRs), which we define as the set of process states that can be driven to a desired neighborhood of the target end‐point subject to input constraints and model uncertainty. A multilevel optimization‐based algorithm to generate robust RTRRs for specified uncertainty bounds is presented. We then consider the problem of uncertain batch processes subject to finite duration faults in the control actuators. Using the robust RTRR‐based MPC as the main tool, a robust safe‐steering framework is developed to address the problem of how to operate the functioning inputs during the fault repair period to ensure that the desired end‐point neighborhood can be reached upon recovery of the full control effort. The applicability of the proposed robust RTRR‐based controller and safe‐steering framework subject to limited availability of measurements and sensor noise are illustrated using a fed‐batch reactor system. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

Active design of dynamic GP models for model predictive control using expected improvement

Modelling is a basic and key requirement for model-based controlling, monitoring, or other process strategies. In non-linear model predictive control (NMPC), although data-driven models can be more easily established than first-principle ones, representative data may not be adequately included in advance to train a complete model, which is an attractive research topic. An actively improved Gaussian process (GP) model building strategy is developed, especially for incomplete models based on the idea of Bayesian optimization. The GP model can be used online as the internal model of model predictive control (MPC) directly. The model-building objective is based on the expected improvement strategy, which can exploit information gained from the currently gathered data as well as explore uncharted regions. The proposed method is a real-time design of experiments based on variance information of GP for efficient model building with insufficient initial training data for NMPC. Multi-step ahead prediction model is considered to give full play to predicting features of NPMC. Besides, a novel disturbance rejection strategy is also proposed based on GP outputs. Two simulation results, including comparisons with some traditional algorithms, are presented to demonstrate the effectiveness of the proposed method.