多故障并发不确定系统的鲁棒完整性容错控制

针对传统容错控制方法难以保证非线性系统在执行器和传感器多故障并发情形下的稳定性问题,研究了一类时滞不确定模糊系统的鲁棒完整性容错控制方法。建立了基于T-S模糊逻辑的不确定非线性模型,定义执行器和传感器故障阵的标准归一化形式,在利用Newton-Leibniz公式变换系统结构的基础上,根据线性矩阵不等式技术给出了鲁棒容错控制器存在的时滞相关性充分条件,以保证整个闭环系统在执行器和(或)传感器发生故障时的稳定性,同时满足给定的广义鲁棒性能约束,联合抑制扰动、初始状态和时滞状态对系统性能的影响。最后仿真结果验证了方法的必要性和可行性。     

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.     

Robust PID controller design for nonlinear processes using JITL technique

A robust PID controller design methodology for nonlinear processes is proposed based on the just-in-time learning (JITL) technique. To do so, a composite model consisting of a nominal ARX model and the JITL, where the former is used to capture linear process dynamics and the latter to approximate the inevitable modeling error caused by the process nonlinearity, is employed to model the process dynamics in the operating space of interest. The state space realizations of this composite model and PID controller are then reformulated as an uncertain closed-loop system, by which the corresponding robust stability condition is developed. Literature examples are employed to illustrate the proposed methodology and a comparison with the previous result is made.     

Machine learning-based distributed model predictive control of nonlinear processes

This work explores the design of distributed model predictive control (DMPC) systems for nonlinear processes using machine learning models to predict nonlinear dynamic behavior. Specifically, sequential and iterative DMPC systems are designed and analyzed with respect to closed-loop stability and performance properties. Extensive open-loop data within a desired operating region are used to develop long short-term memory (LSTM) recurrent neural network models with a sufficiently small modeling error from the actual nonlinear process model. Subsequently, these LSTM models are utilized in Lyapunov-based DMPC to achieve efficient real-time computation time while ensuring closed-loop state boundedness and convergence to the origin. Using a nonlinear chemical process network example, the simulation results demonstrate the improved computational efficiency when the process is operated under sequential and iterative DMPCs while the closed-loop performance is very close to the one of a centralized MPC system.     

Statistical machine-learning–based predictive control of uncertain nonlinear processes

In this study, we present machine-learning–based predictive control schemes for nonlinear processes subject to disturbances, and establish closed-loop system stability properties using statistical machine learning theory. Specifically, we derive a generalization error bound via Rademacher complexity method for the recurrent neural networks (RNN) that are developed to capture the dynamics of the nominal system. Then, the RNN models are incorporated in Lyapunov-based model predictive controllers, under which we study closed-loop stability properties for the nonlinear systems subject to two types of disturbances: bounded disturbances and stochastic disturbances with unbounded variation. A chemical reactor example is used to demonstrate the implementation and evaluate the performance of the proposed approach.     

Online machine learning modeling and predictive control of nonlinear systems with scheduled mode transitions

This work develops a model predictive control (MPC) scheme using online learning of recurrent neural network (RNN) models for nonlinear systems switched between multiple operating regions following a prescribed switching schedule. Specifically, an RNN model is initially developed offline to model process dynamics using the historical operational data collected in a small region around a certain steady-state. After the system is switched to another operating region under a Lyapunov-based MPC with suitable constraints to ensure satisfaction of the prescribed switching schedule policy, RNN models are updated using real-time process data to improve closed-loop performance. A generalization error bound is derived for the updated RNN models using the notion of regret, and closed-loop stability results are established for the switched nonlinear system under RNN-based MPC. Finally, a chemical process example with the operation schedule that requires switching between two steady-states is used to demonstrate the effectiveness of the proposed RNN-MPC scheme.     

A self-tuning control method for Wiener nonlinear systems and its application to process control problems

Many chemical processes can be modeled as Wiener models, which consist of a linear dynamic subsystem follow-ed by a static nonlinear block. In this paper, an effective discrete-time adaptive control method is proposed for Wiener nonlinear systems with uncertainties. The parameterization model is derived based on the inverse of the nonlinear function block. The adaptive control method is motivated by self-tuning control and is derived from a modified Clarke criterion function, which considers both tracking properties and control efforts. The un-certain parameters are updated by a recursive least squares algorithm and the control law exhibits an explicit form. The closed-loop system stability properties are discussed. To demonstrate the effectiveness of the obtained results, two groups of simulation examples including an application to composition control in a continuously stirred tank reactor (CSTR) system are studied.     

Machine-learning-based construction of barrier functions and models for safe model predictive control

In this paper, we propose a control Lyapunov-barrier function-based model predictive control method utilizing a feed-forward neural network specified control barrier function (CBF) and a recurrent neural network (RNN) predictive model to stabilize nonlinear processes with input constraints, and to guarantee that safety requirements are met for all times. The nonlinear system is first modeled using RNN techniques, and a CBF is characterized by constructing a feed-forward neural network (FNN) model with unique structures and properties. The FNN model for the CBF is trained based on data samples collected from safe and unsafe operating regions, and the resulting FNN model is verified to demonstrate that the safety properties of the CBF are satisfied. Given sufficiently small bounded modeling errors for both the FNN and the RNN models, the proposed control system is able to guarantee closed-loop stability while preventing the closed-loop states from entering unsafe regions in state-space under sample-and-hold control action implementation. We provide the theoretical analysis for bounded unsafe sets in state-space, and demonstrate the effectiveness of the proposed control strategy using a nonlinear chemical process example with a bounded unsafe region.     

基于ANFIS与多模型的一类非线性系统的自适应控制方法

针对一类不确定的离散时间零动态不稳定非线性系统,提出了一种基于自适应神经模糊推理系统(ANFIS)与多模型的非线性自适应控制方法。该方法由线性鲁棒自适应控制器,基于ANFIS的非线性自适应控制器以及切换机制组成。线性控制器用来保证闭环系统输入输出信号有界,非线性控制器用来改善系统性能。切换机制通过对上述两种控制器的切换,保证闭环系统输入输出有界的同时,改善系统性能。在采用ANFIS作为系统未建模动态补偿器时,首先用一个连续、单调、可逆的一一映射把可能无界的未建模动态的定义域转化成一个有界闭集,保证了ANFIS的万能逼近特性成立的前提条件。而且,ANFIS能减小BP神经网络收敛速度慢和容易陷入局部极小的问题,改善了控制效果。建立了保证系统稳定性的引理,并给出了闭环系统的稳定性和收敛性分析。通过仿真比较,说明了所提方法的有效性。     

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.     

反渗透和压力延迟渗透耦合脱盐系统的能效优化研究

针对开环和闭环两类结构的反渗透-压力延迟渗透耦合脱盐系统进行了模型构建与系统优化分析。首先，以标准化比能耗为目标函数，构建了开环结构和闭环结构耦合系统的非线性约束优化模型。在优化模型中，引入包括半透膜性能、操作状态及设计变量的无量纲参数组，建立反渗透和压力延迟渗透单元过程的特征方程以简化模型。同时，为了保证比较的公平性，开环结构的总体能耗中额外包含了预处理和后处理能耗。通过求解上述优化模型，系统地比较和分析了无量纲半透膜总面积和水回收率同时变化导致的最优标准化比能耗、膜面积分配和操作压力的变化规律。结果表明，在水回收率处于正常水平(≤ 0.55)且系统总面积充足(≥0.9)时，闭环结构在节能及减少预处理费用方面比开环结构具有更明显优势。     

A unified framework for detection, isolation and compensation of actuator faults in uncertain particulate processes

This paper presents a methodology for the robust detection, isolation and compensation of control actuator faults in particulate processes described by population balance models with control constraints and time-varying uncertain variables. The main idea is to shape the fault-free closed-loop process response via robust feedback control in a way that enables the derivation of performance-based fault detection and isolation (FDI) rules that are less sensitive to the uncertainty. Initially, an approximate finite-dimensional system that captures the dominant process dynamics is derived and decomposed into interconnected subsystems with each subsystem directly influenced by a single manipulated input. The decomposition is facilitated by the specific structure of the process input operator. A robustly stabilizing bounded feedback controller is then designed for each subsystem to enforce an arbitrary degree of asymptotic attenuation of the effect of the uncertainty in the absence of faults. The synthesis leads to (1) an explicit characterization of the fault-free behavior of each subsystem in terms of a time-varying bound on an appropriate Lyapunov function and (2) an explicit characterization of the robust stability region in terms of the control constraints and the size of the uncertainty. Using the fault-free Lyapunov dissipation bounds as thresholds for FDI in each subsystem, the detection and isolation of faults in a given actuator is accomplished by monitoring the evolution of the system within the stability region and declaring a fault if the threshold is breached. The thresholds are linked to the achievable degree of asymptotic uncertainty attenuation and can therefore be properly tuned by proper tuning of the controllers, thus making the FDI criteria less sensitive to the uncertainty. The robust FDI scheme is integrated with a robust stability-based controller reconfiguration strategy that preserves closed-loop stability following FDI. Finally, the implementation of the fault-tolerant control architecture on the particulate process is discussed and the proposed methodology is applied to the problem of robust fault-tolerant control of a continuous crystallizer with a fines trap.     

Use of bifurcation analysis for development of nonlinear models for control applications

Nonlinear system identification poses challenging questions because a closed general theory is not available for this field. Particularly, nonlinear models based on neural networks (NN) may present incompatible general dynamic process behavior, leading to improper closed-loop responses, even when they allow for satisfactory one step ahead prediction of process dynamics, as required by traditional validation methods. It is shown here that performing detailed bifurcation and stability analysis may be very helpful for the adequate development and implementation of nonlinear models and model based controllers. The study of many parameters that are defined a priori during the training of the NN shows that the spurious dynamic behavior is related mostly to the use of incomplete data sets during the learning process. This is an indication that, for each kind of process, the number, range and distribution of the data points in the operation region of interest are of paramount importance for proper training of the nonlinear model. Strategies to improve the quality of the training procedure are provided and analyzed both theoretically and experimentally, using the solution polymerization of styrene in a tubular reactor as a case study.     

Closed-loop step response identification of integrating and unstable processes

Motivated by the fact that integrating and unstable processes are usually operated in a closed-loop manner for safety and economic reasons, this paper proposes a systematic closed-loop identification method based on step response test to facilitate closed-loop system operation and on-line optimization. To avoid jeopardizing the closed-loop system stability of such a process, guidelines are given for proper implementation of a closed-loop step test for model identification. By introducing a damping factor to the closed-loop step response for realization of the Laplace transform in frequency domain, a frequency response estimation algorithm is developed in terms of the closed-loop control structure used for identification. Accordingly, three model identification algorithms are derived analytically in frequency domain to obtain the widely used low-order process models of first-order-plus-dead-time (FOPDT) and second-order-plus-dead-time (SOPDT). To enhance fitting accuracy for a higher order process, in particular for a specified frequency range interested to control design and on-line tuning, a weighted least-squares fitting algorithm is also given based on the estimated process frequency response points. Illustrative examples from the recent literature are used to demonstrate the effectiveness and merits of the proposed identification algorithms.     

Machine learning-based predictive control of nonlinear processes. Part I: Theory

This article focuses on the design of model predictive control (MPC) systems for nonlinear processes that utilize an ensemble of recurrent neural network (RNN) models to predict nonlinear dynamics. Specifically, RNN models are initially developed based on a data set generated from extensive open-loop simulations within a desired process operation region to capture process dynamics with a sufficiently small modeling error between the RNN model and the actual nonlinear process model. Subsequently, Lyapunov-based MPC (LMPC) that utilizes RNN models as the prediction model is developed to achieve closed-loop state boundedness and convergence to the origin. Additionally, machine learning ensemble regression modeling tools are employed in the formulation of LMPC to improve prediction accuracy of RNN models and overall closed-loop performance while parallel computing is utilized to reduce computation time. Computational implementation of the method and application to a chemical reactor example is discussed in the second article of this series.     

On identification of well‐conditioned nonlinear systems: Application to economic model predictive control of nonlinear processes

The focus of this work is on economic model predictive control (EMPC) that utilizes well‐conditioned polynomial nonlinear state‐space (PNLSS) models for processes with nonlinear dynamics. Specifically, the article initially addresses the development of a nonlinear system identification technique for a broad class of nonlinear processes which leads to the construction of PNLSS dynamic models which are well‐conditioned over a broad region of process operation in the sense that they can be correctly integrated in real‐time using explicit numerical integration methods via time steps that are significantly larger than the ones required by nonlinear state‐space models identified via existing techniques. Working within the framework of PNLSS models, additional constraints are imposed in the identification procedure to ensure well‐conditioning of the identified nonlinear dynamic models. This development is key because it enables the design of Lyapunov‐based EMPC (LEMPC) systems for nonlinear processes using the well‐conditioned nonlinear models that can be readily implemented in real‐time as the computational burden required to compute the control actions within the process sampling period is reduced. A stability analysis for this LEMPC design is provided that guarantees closed‐loop stability of a process under certain conditions when an LEMPC based on a nonlinear empirical model is used. Finally, a classical chemical reactor example demonstrates both the system identification and LEMPC design techniques, and the significant advantages in terms of computation time reduction in LEMPC calculations when using the nonlinear empirical model. © 2015 American Institute of Chemical Engineers AIChE J, 61: 3353–3373, 2015     

基于神经网络和多模型的非线性自适应PID控制及应用

针对一类未知的单输入单输出离散非线性系统,提出了基于神经网络和多模型的非线性自适应PID控制方法。该方法由线性自适应PID控制器、神经网络非线性自适应PID控制器以及切换机构组成。采用线性自适应PID控制器可保证闭环系统所有信号有界;采用神经网络非线性自适应PID控制器可改善系统性能;通过引入合理的切换机制,能够在保证闭环系统稳定的同时,提高系统性能。理论分析表明,该方法能够保证闭环系统所有信号有界,如果适当地选择神经网络的结构和参数,系统的跟踪误差将收敛于任意给定的紧集。将所提出的方法应用于连续搅拌反应釜,仿真结果验证了所提出方法的有效性。由于该方法基于增量式数字PID控制器,在工业过程中有着广阔的应用前景。     

Model based robust control approach for batch crystallization product design

The paper presents a novel control approach for crystallization processes, which can be used for designing the shape of the crystal size distribution to robustly achieve desired product properties. The approach is based on a robust optimal control scheme, which takes parametric uncertainties into account to provide decreased batch-to-batch variability of the shape of the crystal size distribution. Both open-loop and closed-loop robust control schemes are evaluated. The open-loop approach is based on a robust end-point nonlinear model predictive control (NMPC) scheme which is implemented in a hierarchical structure. On the lower level a supersaturation control approach is used that drives the system in the phase diagram according to a concentration versus temperature trajectory. On the higher level a robust model-based optimization algorithm adapts the setpoint of the supersaturation controller to counteract the effects of changing operating conditions. The process is modelled using the population balance equation (PBE), which is solved using a novel efficient approach that combines the quadrature method of moment (QMOM) and method of characteristics (MOC). The proposed robust model based control approach is corroborated for the case of various desired shapes of the target distribution.