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.     

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。     

Adversarially robust Bayesian optimization for efficient auto-tuning of generic control structures under uncertainty

The performance of optimization- and learning-based controllers critically depends on the selection of several tuning parameters that can affect the closed-loop control performance and constraint satisfaction in highly nonlinear and nonconvex ways. Due to the black-box nature of the relationship between tuning parameters and general closed-loop performance measures, there has been a significant interest in automatic calibration (i.e., auto-tuning) of complex control structures using derivative-free optimization methods, including Bayesian optimization (BO) that can handle expensive unknown cost functions. Nevertheless, an open challenge when applying BO to auto-tuning is how to effectively deal with uncertainties in the closed-loop system that cannot be attributed to a lumped, small-scale noise term. This article addresses this challenge by developing an adversarially robust BO (ARBO) method that is particularly suited to auto-tuning problems with significant time-invariant uncertainties in an expensive system model used for closed-loop simulations. ARBO relies on a Gaussian process model that jointly describes the effect of the tuning parameters and uncertainties on the closed-loop performance. From this joint Gaussian process model, ARBO uses an alternating confidence-bound procedure to simultaneously select the next candidate tuning and uncertainty realizations, implying only one expensive closed-loop simulation is needed at each iteration. The advantages of ARBO are demonstrated on two case studies, including an illustrative problem and auto-tuning of a nonlinear model predictive controller using a benchmark bioreactor problem.     

An LMI Method to Robust Iterative Learning Fault-tolerant Guaranteed Cost Control for Batch Processes

Based on an equivalent two-dimensional Fornasini-Marchsini model for a batch process in industry, a closed-loop robust iterative learning fault-tolerant guaranteed cost control scheme is proposed for batch processes with actuator failures. This paper introduces relevant concepts of the fault-tolerant guaranteed cost control and formulates the robust iterative learning reliable guaranteed cost controller （ILRGCC）. A significant advantage is that the proposed ILRGCC design method can be used for on-line optimization against batch-to-batch process uncertainties to realize robust tracking of set-point trajectory in time and batch-to-batch sequences. For the convenience of implementation, only measured output errors of current and previous cycles are used to design a synthetic controller for iterative learning control, consisting of dynamic output feedback plus feed-forward control. The proposed controller can not only guarantee the closed-loop convergency along time and cycle sequences but also satisfy the H∞ performance level and a cost function with upper bounds for all admissible uncertainties and any actuator failures. Sufficient conditions for the controller solution are derived in terms of linear matrix inequalities （LMIs）, and design procedures, which formulate a convex optimization problem with LMI constraints, are presented. An example of injection molding is given to illustrate the effectiveness and advantages of the ILRGCC design approach.     

基于改进DOB的矿物研磨过程最优运行先进反馈控制(英文)

Advanced feedback control for optimal operation of mineral grinding process is usually based on the model predictive control (MPC) dynamic optimization. Since the MPC does not handle disturbances directly by controller design, it cannot achieve satisfactory effects in controlling complex grinding processes in the presence of strong disturbances and large uncertainties. In this paper, an improved disturbance observer (DOB) based MPC advanced feedback control is proposed to control the multivariable grinding operation. The improved DOB is based on the optimal achievable H 2 performance and can deal with disturbance observation for the nonminimum-phase delay systems. In this DOB-MPC advanced feedback control, the higher-level optimizer computes the optimal operation points by maximize the profit function and passes them to the MPC level. The MPC acts as a presetting controller and is employed to generate proper pre-setpoint for the lower-level basic feedback control system. The DOB acts as a compensator and improves the operation performance by dynamically compensating the setpoints for the basic control system according to the observed various disturbances and plant uncertainties. Several simulations are performed to demonstrate the proposed control method for grinding process operation.     

一种新颖的鲁棒PID控制器设计方法

提出一种新颖的鲁棒PID控制器设计方法,基于最小最大原理寻找一组合理的PID控制器参数,使得闭环系统在一定模型变化范围内仍具有满意的控制品质,降低对模型不确定的敏感程度,提高系统的鲁棒性。鉴于直接求解min-max问题的困难,首先推导出不确定性最坏情况下性能指标的上界,然后将min-max问题转化为最坏性能指标上界的min问题,计算量小且求解容易。同时,证明了该算法的鲁棒稳定性。CSTR仿真例子表明了算法的有效性。     

基于模型预测残差闭环潜能指标的MPC控制器实时性能监控

由于模型预测控制器对模型失配等不确定因素具有较强的鲁棒性,因此现有的多步预测误差方法不能及时显著地检测到由模型失配导致的MPC控制器性能潜能的变化。针对上述问题,提出一种改进的多步预测误差方法和实时性能监控策略。考虑到MPC控制器的模型预测残差能有效反映模型失配等信息,利用预测残差对现有多步预测误差方法进行改进,改进的方法能够更好地检测由模型失配引起的MPC控制器性能潜能的改变。在连续搅拌槽加热器(continuous stirred tank heater,CSTH)系统上的仿真实验验证了该方法的可行性与有效性。     

一种扰动自适应的鲁棒预测控制算法

针对实际生产中扰动的时变性,提出了一种扰动自适应的鲁棒预测控制（RAMPC）算法以提高扰动抑制性能。采用时间序列（ARMA）模型在线辨识系统的不可测扰动,通过基于多次迭代思想的递推辨识算法（multi-iteration pseudo-linear regression,MIPLR）来保证在线辨识的质量和收敛速度。考虑到数据与辨识模型的不确定性,改用min-max形式描述MPC算法的控制作用优化命题,并将在线辨识过程中的误差数据引入min-max命题,使在线辨识与控制作用鲁棒优化求解紧密结合起来,提高算法鲁棒性。进一步将此min-max问题转换为一个等效的非线性min问题,并采用多步线性化方法实现快速求解,解决了传统min-max方法在线计算负荷高的问题。仿真结果表明了该算法的有效性。     

基于微粒群优化的鲁棒PID控制器参数整定方法研究

针对复杂工业过程中存在的一类模型不确定问题,提出一种新的鲁棒PID控制器参数整定方法.通过将鲁棒PID控制器的参数整定问题转化成一个max-min优化问题,利用微粒群优化(PSO)的协作算法对之进行求解,能获得某种鲁棒性能指标最优的PID控制器.对连续搅拌反应釜系统的实例仿真结果表明:与其它典型鲁棒PID控制器设计方法相比,本方法得到的PID控制器具有更强的鲁棒性和抗干扰能力,当过程操作范围发生大的变化时,利用本方法设计的鲁棒PID控制器能获得满意的结果.     

Integration of control theory and scheduling methods for supply chain management

In this paper, we propose to use distributed model predictive control for supply chain optimization. In particular, we focus on inventory management in supply chains. We use cooperative model predictive control, in which each agent makes their local decisions by optimizing the overall supply chain objective. Motivated by recent results in Stewart, Wright, and Rawlings (2011), we develop a new cooperative MPC algorithm that is applicable to any stabilizable system, and in particular to supply chain models. We illustrate cooperative MPC for a two node supply chain example and compare its performance and properties with other classical distributed operating policies.     

Performance assessment of cascade controllers for nitrate control in a wastewater treatment process

A cascade control strategy is proposed to the benchmark simulation model 1 (BSM1) to enhance the treatment performance of nitrogen removal in a biological wastewater treatment plant. The proposed control approach consists of two control loops, a primary outer loop and a secondary inner loop. The method has two controllers of which the primary loop has a model predictive control (MPC) controller and the secondary loop has a proportional-integralderivative (PID) controller, which is a cascade MPC-PID controller. The primary MPC controller is to control the nitrate concentration in the effluent, and the secondary PID controller is to control the nitrate concentration in the final anoxic compartment. The proposed method controls the nitrate concentrations in the effluent as well as in the final anoxic reactor simultaneously to strictly satisfy the quality of the effluent as well as to remove the effects of disturbances more quickly by manipulating the external carbon dosage rate. Because the control performance assessment (CPA) technique has the features of determining the capability of the current controller and locating the best achievable performance, the other novelty of this paper is to suggest a relative closed-loop potential index (RCPI) which updates the CPA technology into a closed-loop cascade controller. The proposed method is compared with a cascade PID-PID control strategy and the original PID controller in BSM1 and an improved performance of the suggested cascade MPC-PID controller is obtained by using the CPA approach.     

Disturbance rejection of dead-time processes using disturbance observer and model predictive control

This article mainly focuses on disturbance rejection of dead-time processes by integrating a modified disturbance observer (MDOB) with a model predictive controller (MPC). The effect caused by model mismatches is regarded as a part of the lumped disturbances. This means that the disturbances considered here include not only external disturbances, but also internal disturbances caused by model mismatches. Control structure of the proposed method includes two parts which can be designed separately. The MPC which acts as a prefilter, is employed to generate appropriate control actions such that a desired setpoint tracking response is achieved. The MDOB is employed to estimate the disturbances of the closed-loop system, and the estimation is used for feedforward compensation design to reject disturbances. Rigorous analysis of setpoint tracking and disturbance rejection properties of the closed-loop system are given in the presence of both model mismatches and external disturbances. The proposed scheme is applied to control the temperature of a simplified jacketed stirred tank heater (JSTH). Simulation results demonstrate that the proposed method possesses a better disturbance rejection performance than those of the MDOB-PI, MPC and PI methods in controlling such dead-time processes.     

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     

循环流化床燃烧系统无终端约束字典序经济预测控制

针对循环流化床锅炉(CFBB)燃烧系统非线性、约束、多变量耦合等过程特性和多目标燃烧优化要求,提出一种无终端约束字典序经济模型预测控制策略。基于字典序多目标优化思想,将CFBB稳定燃烧工况作为最重要控制目标,将燃烧系统经济性能作为次重要目标,构建分层滚动时域优化控制问题。设计关于稳定燃烧性能指标的终端域条件,建立无显式终端约束的稳定字典序经济模型预测控制策略。这不仅降低了多目标燃烧控制器的在线计算量,同时并行实现CFBB燃烧系统的稳定控制和经济性能优化。最后通过仿真对比验证本文提出方法的有效性。     

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.     

Soft-constrained model predictive control based on data-driven distributionally robust optimization

This article proposes a novel distributionally robust optimization (DRO)-based soft-constrained model predictive control (MPC) framework to explicitly hedge against unknown external input terms in a linear state-space system. Without a priori knowledge of the exact uncertainty distribution, this framework works with a lifted ambiguity set constructed using machine learning to incorporate the first-order moment information. By adopting a linear performance measure and considering input and state constraints robustly with respect to a lifted support set, the DRO-based MPC is reformulated as a robust optimization problem. The constraints are softened to ensure recursive feasibility. Theoretical results on optimality, feasibility, and stability are further discussed. Performance and computational efficiency of the proposed method are illustrated through motion control and building energy control systems, showing 18.3% less cost and 78.8% less constraint violations, respectively, while requiring one third of the CPU time compared to multi-stage scenario based stochastic MPC.     

一类带有混合噪声的非线性随机时滞系统鲁棒L_1控制

针对一类带有混合噪声的非线性连续不确定随机时滞系统,研究了鲁棒L_1控制器的设计问题。通过构造时滞依赖的Lyapunov函数,利用积分不等式方法,建立系统在均方意义下渐近有界的充分条件,并在此基础上设计控制器,使闭环系统均方渐近有界且输出峰值小于给定的L_1性能指标γ。基于LMI技术,将鲁棒L_1控制问题转化为凸优化问题,并通过一组线性矩阵不等式予以解决。最后,通过数值仿真验证了所设计控制器的有效性。     

Robustness analysis and synthesis of a multi-PID controller based on an uncertain multimodel representation

This paper presents an effective method for robustness analysis and synthesis of a multi-PID controller for non-linear systems where desirable robustness and performance properties must be maintained across a large range of operating conditions. The robustness analysis problem is solved using an uncertain multimodel of the original non-linear system. The model of uncertainties used is an interval matrix modeled by a stochastic matrix which gives poor conservatism in the analysis of stability robustness. Moreover, the robust stability margin is interpreted as a smallest interval matrix that causes instability. This stability margin is evaluated using a random search algorithm. Simulation studies are used to demonstrate the effectiveness of the proposed method.