一类不确定多时滞系统的鲁棒容错控制研究

讨论一类线性不确定多时滞系统的鲁棒容错控制问题.基于Lyapunov稳定性理论和线性矩阵不等式方法（LMI）,针对一类参数有界不确定多时滞系统,给出了状态反馈鲁棒容错控制器设计方法,并且利用该方法得到的闭环控制系统,不仅在执行器失效情况下具有渐进稳定性,对参数不确定也具有良好的鲁棒性.最后,应用设计实例及仿真结果验证该设计方法的可靠性和有效性.     

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     

基于T-S模糊模型的间歇过程的迭代学习容错控制

间歇过程不仅具有强非线性,同时还会受到诸如执行器等故障影响,研究非线性间歇过程在具有故障的情况下依然稳定运行至关重要。针对执行器增益故障及系统所具有的强非线性,提出一种新的基于间歇过程的T-S模糊模型的复合迭代学习容错控制方法。首先根据间歇过程的非线性模型,利用扇区非线性方法建立其T-S模糊故障模型,再利用间歇过程的二维特性与重复特性,在2D系统理论框架内,设计2D复合ILC容错控制器,进而构建此T-S模糊模型的等价二维Rosser模型,接着利用Lyapunov方法给出系统稳定充分条件并求解控制器增益。针对强非线性的连续搅拌釜进行仿真,结果表明所提出方法具有可行性与有效性。     

Fault-tolerant control of fluid dynamic systems via coordinated feedback and switching

This work addresses the problem of designing a fault-tolerant control system for fluid dynamic systems modeled by highly-dissipative partial differential equations (PDEs) with constrained control actuators. The proposed approach is predicated upon the idea of coordinating feedback controller synthesis and switching between multiple, spatially-distributed control actuator configurations. Using appropriate finite-dimensional approximations of the PDE system, a stabilizing feedback controller is designed for a given actuator configuration, and an explicit characterization of the constrained stability region is obtained. Switching laws are then derived, on the basis of these stability regions, to orchestrate the switching between the control actuator configurations, in a way that guarantees constraint satisfaction and preserves closed-loop stability of the infinite-dimensional system in the event of actuator failures. The results are demonstrated through an application of the proposed methodology to the suppression of wave formation in falling liquid films via the stabilization of the zero solution of the one-dimensional Kuramoto–Sivashinsky equation (KSE), with periodic boundary conditions, subject to actuator constraints and failures.     

基于广义预测控制的间歇生产迭代优化控制

针对间歇生产,提出了一种基于广义预测控制的批次迭代优化控制策略--BGPC,在间歇过程中引入批次间优化的思想,将迭代学习控制ILC和广义预测控制GPC相结合,在GPC实时结构参数辨识的基础上利用前面批次的模型预测误差修正当前批次的模型预测值.该算法能够有效地克服模型失配、扰动和系统参数变化等情况.文章最后以一个数值例子和间歇反应器为对象进行仿真试验,验证了该算法是有效的.     

Improved infinite horizon LQ tracking control for injection molding process against partial actuator failures

Focusing on injection molding processes with partial actuator failures, a new design of infinite horizon linear quadratic control is introduced. A new state space process model is first derived through input–output process data. Furthermore, an improved infinite horizon linear quadratic control scheme, whereby the process state variables and tracking error can both be regulated separately, is proposed to show enhanced control performance against partial actuator failures and unknown disturbances. Under the circumstances of actuator faults, the closed-loop system is indeed a process with uncertain parameters. Hence, a sufficient condition is proposed to guarantee robust stability is presented using Lyapunov theory. The proposed concepts are illustrated in an injection velocity control case study to show the effectiveness.     

Iterative learning controller synthesis using FIR models for batch processes

Adaptive iterative learning control based on the measured input-output data is proposed to solve the traditional iterative learning control problem in the batch process. It produces a control law with self-tuning capability by combining a batch-to-batch model estimation procedure with the control design technique. To build the unknown batch operation system, the finite impulse response (FIR) model with the lifted system is constructed for easy construction of a recursive least squares algorithm. It can identify the pattern of the current operation batch. The proposed model reference control method is applied to feedback control of the lifted system. It finds an appropriate control input so that the desired performance of the batch output can track the prescribed finite-time trajectory by iterative trials. Furthermore, on-line tracking control is developed to explore the possible adjustments of the future input trajectories within a batch. This can remove the disturbances in the current batch rather than the next batch trial and keep the product specifications consistent at the end of each batch. To validate the theoretical findings of the proposed strategies, two simulation problems are investigated.     

Iterative learning control for the systematic design of supersaturation controlled batch cooling crystallisation processes

The paper presents an approach to improve the product quality from batch-to-batch by exploiting the repetitive nature of batch processes to update the operating trajectories using process knowledge obtained from previous runs. The data based methodology is focused on using the linear time varying (LTV) perturbation model in an iterative learning control (ILC) framework to provide a convergent batch-to-batch improvement of the process performance indicator. The major contribution of this work is the development of a novel hierarchical ILC (HILC) scheme for systematic design of the supersaturation controller (SSC) of seeded batch cooling crystallizers. The HILC is used to determine the required supersaturation setpoint for the SSC and the corresponding temperature trajectory required to produce crystals with desired end-point property. The performance and robustness of these approaches are evaluated through simulation case studies. These results demonstrate the potential of the ILC approaches for controlling batch processes without rigorous process models.     

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.     

ENHANCED IMC-PID CONTROLLER DESIGN WITH LEAD-LAG FILTER FOR UNSTABLE AND INTEGRATING PROCESSES WITH TIME DELAY

In this article, a design method for a PID controller is proposed based on IMC principles for control of open loop integrating and unstable first-order processes with time delay. The design is based on H₂ optimal closed-loop transfer function for set point changes and step input disturbances. The method has one tuning parameter, and systematic guidelines are provided for the selection of this tuning parameter based on peak value of the sensitivity function. The performance of the designed controller is verified on various integrating and unstable processes, and it is observed that nominal and robust control performance is achieved with the proposed design method. Improved closed-loop performance was obtained when compared to other methods recently reported in the literature. Further, the proposed method provides good closed-loop performance even when there are large uncertainties in the process parameters.     

Safe-parking of nonlinear process systems: Handling uncertainty and unavailability of measurements

This work considers the problem of handling actuator faults in nonlinear process systems subject to input constraints, uncertainty and availability of limited measurements. A framework is developed to handle faults that preclude the possibility of continued operating at the nominal equilibrium point using the existing robust or reconfiguration-based fault-tolerant control approaches. The key consideration is to operate the plant using the depleted control action at an appropriate ‘safe-park’ point to prevent onset of hazardous situations as well as enable smooth resumption of nominal operation upon fault-repair. First, we consider the presence of constraints and uncertainty and develop a robust Lyapunov-based model predictive controller that enhances the set of initial conditions from which closed-loop stability is achieved. The stability region characterization provided by the robust predictive controller is subsequently utilized in a safe-parking algorithm that appropriately selects ‘safe-park’ points from the safe-park candidates (equilibrium points subject to failed actuators) to preserve closed-loop stability upon fault-repair. Specifically, a candidate parking point is termed a safe-park point if (1) the process state at the time of failure resides in the stability region of the safe-park candidate (subject to depleted control action and uncertainty) and (2) the safe-park candidate resides within the stability region of the nominal control configuration. Then we consider the problem of availability of limited measurements. An output feedback Lyapunov-based model predictive controller, utilizing an appropriately designed state observer (to estimate the unmeasured states), is formulated and its stability region explicitly characterized. An algorithm is then presented that accounts for the estimation errors in the implementation of the safe-parking framework. The proposed framework is illustrated using a chemical reactor example and demonstrated on a styrene polymerization process.     

执行器饱和受限约束下锅炉燃烧系统的鲁棒预测控制

针对执行器饱和受限锅炉燃烧系统,提出一种鲁棒预测控制方法。首先,建立燃烧过程的线性参数变化系统模型,将执行器饱和受限转变成凸包形式描述;进而,设计执行器饱和受限的鲁棒预测控制器;最后,以某电站300MW机组锅炉控制为实例,对所提出的方法进行验证。结果表明:该方法可以在满足执行器饱和受限约束的同时获得满意的性能。     

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.     

High-order iterative learning model predictive control for batch chemical processes

In order to address two-dimensional (2D) control issue for a class of batch chemical processes, we propose a novel high-order iterative learning model predictive control (HILMPC) method in this paper. A set of local state-space models are first constructed to represent the batch chemical processes by adopting the just-in-time learning (JITL) technique. Meanwhile, a pre-clustered strategy is used to lessen the computational burden of the modelling process and improve the modelling efficiency. Then, a two-stage 2D controller is designed to achieve integrated control by combining high-order iterative learning control (HILC) on the batch domain with model predictive control (MPC) on the time domain. The resulting HILMPC controller can not only guarantee the convergence of the system on the batch domain, but also guarantee the closed-loop stability of the system on the time domain. The convergence of the HILMPC method is ensured by rigorous analysis. Two examples are presented in the end to demonstrate that the developed method provides better control performance than its previous counterpart.     

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.     

Optimization of nonlinear process based on sequential extreme learning machine

In this paper, a new approach to the optimal control with constraints is proposed to achieve a desired end product quality for nonlinear processes based on new kernel extreme learning machine (KELM). The contributions of the paper are as follows: (1) In existing ILC algorithm, the model was built only between manipulated input variables U and output variables Y without considering the state variables. However, the states variables X_state are important in the industrial processes, which are usually constrained. In this paper, the variables are divided into state variables X_state, manipulated input variables U and output Y in the process of modeling. Then ΔU can be obtained by batch-to-batch iterative learning control separately. Kernel algorithm is added to ELM. (2) Constraints of state variables X_state and the input variables U are considered in the current version. PSO is used to solve the optimization problem. (3) Kernel trick is introduced to improve accuracy of ELM modeling. New KELM algorithm is proposed in the current version. The input trajectory for the next batch is accommodated by searching for the optimal value through the error feedback at a minimum cost. The particle swarm optimization algorithm is used to search for the optimal value based on the iterative learning control (ILC). The proposed approach has been shown to be effective and feasible by applying bulk polymerization of the styrene batch process and fused magnesium furnace.     

Iterative learning reliable control of batch processes with sensor faults

An iterative learning reliable control (ILRC) scheme is developed in this paper for batch processes with unknown disturbances and sensor faults. The batch process is transformed into and treated as a two-dimensional Fornasini-Marchesini (2D-FM) model. Under the proposed control law, the closed-loop system with unknown disturbances and sensor faults not only converges along both the time and the cycle directions, but also satisfies certain H_∞ performance. For performance comparison, a traditional reliable control (TRC) law based on dynamic output feedback is also developed by considering the batch process in each cycle as a continuous process. Conditions for the existence of ILRC scheme are given as biaffine and linear matrix inequalities. Algorithms are given to solve these matrix inequalities and to optimize performance indices. Applications to injection packing pressure control show that the proposed scheme can achieve the design objectives well, with performance improvement along both time and cycle directions, and also has good robustness to uncertain initialization and measurement disturbances.     

Predictive control of particle size distribution in particulate processes

In this work, we focus on the development and application of predictive-based strategies for control of particle size distribution (PSD) in continuous and batch particulate processes described by population balance models (PBMs). The control algorithms are designed on the basis of reduced-order models, utilize measurements of principle moments of the PSD, and are tailored to address different control objectives for the continuous and batch processes. For continuous particulate processes, we develop a hybrid predictive control strategy to stabilize a continuous crystallizer at an open-loop unstable steady-state. The hybrid predictive control strategy employs logic-based switching between model predictive control (MPC) and a fall-back bounded controller with a well-defined stability region. The strategy is shown to provide a safety net for the implementation of MPC algorithms with guaranteed stability closed-loop region. For batch particulate processes, the control objective is to achieve a final PSD with desired characteristics subject to both manipulated input and product quality constraints. An optimization-based predictive control strategy that incorporates these constraints explicitly in the controller design is formulated and applied to a seeded batch crystallizer. The strategy is shown to be able to reduce the total volume of the fines by 13.4% compared to a linear cooling strategy, and is shown to be robust with respect to modeling errors.     

自适应鲁棒迭代学习控制在陶瓷机械手中的应用

针对一类不确定非线性系统,结合自适应鲁棒控制和迭代学习控制方法,提出了自适应鲁棒迭代学习混合控制策略。学习控制策略用于处理周期性不确定,自适应鲁棒控制策略用于处理具有未知上界的非周期性不确定。所提出的控制方案保证跟踪误差在有限的迭代步骤内收敛到任意指定的误差区域。最后将此控制策略应用于陶瓷机械手的控制,仿真结果表明此方法的有效性。