基于广义最小变差基准的多变量控制性能评估方法

This paper is concerned with the control performance assessment based on the multivariable generalized minimum variance benchmark. An explicit expression for the feedback controller-invariant (the generalized minimum variance) term of the multi-variable control system is obtained, which is used as a standard benchmark for the assessment of the control performance for multi input multi output (MIMO) process. The proposed approach is based on the multivariable minimum variance benchmark. In com-parison with the minimum variance benchmark, the developed method is more reasonable and practical for the control performance assessment of multivariable systems. The approach is illustrated by a simulation example and an industrial application.     

Optimal discrete stochastic control theory for process application

The design of discrete feedback controllers which minimize some linear function of the variances of the output deviations from target subject to possible constraints on the variances of the inputs, for linear systems subject to stochastic disturbances, is treated from two points of view: (1) using transfer function models to characterizing the process dynamics and autoregres-sive-moving-average models to characterize the stochastic disturbances, and then solving the optimal control problem using an approach due to Box and Jenkins and a discrete version of the Wiener-Newton theory; and (2) using state variable models to characterize both the dynamic and stochastic parts of the system, and then solving the optimal control problem using the results of dynamic programming and Kalman filtering. Practical considerations such as model forms, their identification and estimation, and the development of variance relationships that are necessary for the application of these two approaches in the process industries are discussed. The relationship between and a comparison of these two approaches is made.     

DBFact: A better approach to calculate the minimum variance control law for nonminimum phase MIMO systems

This paper presents the diagonal with Blaschke products factorization (DBFact) approach to factor out multivariable time delay and nonminimum phase zeros from multi-input multi-output (MIMO) systems. Based on that, a new output-order independent minimum variance (MV) control law for MIMO systems is proposed. The DBFact method is a two-step factorization procedure, relying on the diagonal and Blaschke factorization methods. This method has the advantage of being a direct and non-iterative procedure. This new factorization approach allows the calculation of an MV control law considering the multivariable time delay as a limiting-performance factor and the nonminimum phase zeros and their corresponding directions. Based on the proposed MV control law, a performance benchmark is introduced, which can be calculated by the DBFact filters and routine operating data. The DBFact methodology was applied to two control structures of the linear plant model of Linde's heat integrated air separation, in which the MV control law output-order dependency property and the suitability of the performance benchmark were evaluated. Some results were compared with those obtained by admitting the generalized interactor matrix instead of the DBFact filters. The results show the capability of the DBFact methodology to factor the nonminimum phase terms to provide a reliable MIMO controller performance benchmark and illustrate the importance of considering the nonminimum phase zeros and their actual directionality in the MV control law.     

ROBUST NONLINEAR PREDICTIVE CONTROL USING A DISTURBANCE ESTIMATOR

A robust nonlinear predictive control strategy using a disturbance estimator is presented. The disturbance estimator is comprised of two parts: one is the disturbance model parameter adaptation and the other is future disturbance prediction. A linear discrete model is proposed as a disturbance model which is formulated by using process inputs and available process measurements. The recursive least square (RLS) method with exponential forgetting is used to determine the uncertain disturbance model parameters and for the future disturbance prediction, future disturbances projected by the future process inputs are used. Two illustrative examples: a jacketed CSTR as a SISO system: an adiabatic CSTR as a MIMO system, and experimental results of the distillation column control are presented. The results indicate that a substantial improvement in nonlinear predictive control performance is possible using the disturbance estimator.     

一类多变量系统的自抗扰非线性动态解耦控制

针对一类多变量系统控制中的耦合问题,提出了一种基于自抗扰技术的非线性动态解耦控制(ADRC)方法。该方法不依赖于系统的精确数学模型,分别在控制器耦合矩阵部分已知和未知的情形下,在局部静态解耦的基础上,将各子系统的模型摄动、外扰和包括输入变量相互作用在内的动态耦合视为各通道上的扰动总和,通过引入虚拟控制和状态量,设计扩张状态观测器(ESO)估计总扰动并进行反馈补偿,进而再对各解耦子对象分别设计非线性单输入单输出ADRC以保证闭环系统稳定。最后以蒸馏塔模型的过程控制仿真验证了该方法具有良好的动态解耦效果,对模型不确定性和外部扰动具有较好的鲁棒性和适应能力。     

Estimating performance enhancement with alternate control strategies for multiloop control systems

A filter based methodology, studied earlier for SISO systems, is extended to MIMO systems. The presented approach facilitates the calculation of best achievable performance for proportional-integral (PI) controller and the optimal multiloop (ML) PI settings for stochastic disturbance rejection in ML control systems. The filter based approach is further extended to answer some of the key questions for ML control systems such as: (a) performance enhancement possible with the alternate pairing scheme, (b) benefits that will accrue through the employment of decouplers and (c) the performance achievable with the use of multivariable controller (as opposed to an ML controller). Further, the trade-off curve between output variance and control effort is generated for the various control configurations within PI controller domain.     

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.     

Development of a heuristic methodology for precise sensor network design

This paper develops a heuristic methodology for designing precise sensor/measurement networks for linear material flow circuits based on the general principle of variance reduction through data reconciliation. Firstly, the paper develops a new ‘flowsheet-independent’ formula for estimating the adjusted variance of process streams on linear material flow circuits. Here, the weighted least squares problem is symbolically optimised to obtain a generalized ‘flowsheet-independent’ formula, which depends only on the measured variances of process streams. Secondly, this formula is used to develop a set of generic design principles/heuristics for maximising the variance reduction of process streams. These design principles/heuristics can be used for making a priori design decisions in selecting optimal flowsheets and/or measurement schemes for reducing the variance of process streams on linear material flow circuits. A precise knowledge of material flow rates is critical to areas such as process accounting and quality control which is important to, for example, large process industries such as the petrochemical and mining industries. Process streams are divided into two categories: (i) terminal and (ii) interacting (interconnecting) streams. The design principles/heuristics illustrate the importance of precise measurement of interacting streams and the benefits of highly interconnected flowsheets and/or measurement schemes in maximising variance reduction. The generalized formula and the design principles/heuristics are tested numerically using an industrial case study.     

Validation of continuous-time models with delay

This article is a continuation of an earlier work by Huang [2000. Multivariate model validation in the presence of timevariant disturbance dynamics. Chemical Engineering Science 55, 4583-4595] for validation of discrete time models. We present validation method for continuous-time transfer models with time delay. The proposed procedure is based on the local approach for change detection of model parameters. Both single input single output (SISO) and multiple input multiple output (MIMO) models are considered. The special feature of the proposed algorithm is its ability to detect and isolate changes in the time delay as well as in other parameters. The performance of the proposed method is demonstrated using Monte-Carlo simulations and by application to experimental data from a laboratory scale process.     

Attainment of PI Achievable Performance for Linear SISO Processes with Deadtime by Iterative Tuning

This work presents a practical scheme to attain PI achievable performance (the performance achievable with a proportional integral (PI) controller) for linear SISO processes with dead time driven by stochastic disturbances. It uses a combination of a quantitative measure called Control Loop Performance Index (CLPI) and signature plots of the closed loop disturbance impulse response (IR) to arrive at PI achievable performance in an iterative manner. The proposed methodology requires only routine operating data and knowledge of the process delay, and its efficacy is illustrated through several case studies.     

基于渐近理论的两阶段过程辨识方法

提出了一种基于渐近理论的两阶段过程辨识方法：先用高阶模型得到无偏估计和频域方差;然后通过OE模型与MDL定阶法进行降阶处理。它将多变量模型结构辨识转换为易于实现的单变量问题,同时通过模型频域方差进行模型验证,解决了传统多变量辨识方法的阶次估计及模型验证难的问题。采用多通道测试信号,测试时间短,对装置生产影响小。应用实例表明了算法的有效性。     

THE REPRESENTATION AND APPROXIMATION OF THE DYNAMICS OF A CLASS OF HIGH ORDER DISTRIBUTED PARAMETER PROCESSES

The dynamic behavior of process models consisting of higher order sets of linear coupled hyperbolic partial differential equations is considered. The formalism of the Riemann representation of the solution to second order hyperbolic equations is extended to problems of any order. The general time domain solution can then be written in terms of integrals of disturbance functions weighted with generalized Riemann matrices. If the solution for the Riemann matrix is approximated, a common approximation method serves to obtain the complete solution for all state variables subject to all disturbances. The approach is demonstrated on two examples, a double pipe heat exchanger and a nonisothermal packed bed reactor.     

THE REPRESENTATION AND APPROXIMATION OF THE DYNAMICS OF A CLASS OF HIGH ORDER DISTRIBUTED PARAMETER PROCESSES

The dynamic behavior of process models consisting of higher order sets of linear coupled hyperbolic partial differential equations is considered. The formalism of the Riemann representation of the solution to second order hyperbolic equations is extended to problems of any order. The general time domain solution can then be written in terms of integrals of disturbance functions weighted with generalized Riemann matrices. If the solution for the Riemann matrix is approximated, a common approximation method serves to obtain the complete solution for all state variables subject to all disturbances. The approach is demonstrated on two examples, a double pipe heat exchanger and a nonisothermal packed bed reactor.     

受扰MIMO系统的前馈-PID最优扰动抑制控制

通过对基于时域状态空间描述的MIMO系统最优扰动抑制控制算法和基于输出反馈的频域PID控制算法的对比分析,设计出系统的最优PID动态补偿网络,实现最优扰动抑制控制.仿真结果表明,该方法对于外部持续扰动具有较强的鲁棒性.     

Generic model controller tuning for chemical processes with input saturation

Control in the face of process input constraints is very common and of great practical importance in the processing industries. Generic Model Control (GMC) is a model‐based control framework for both linear and nonlinear systems. In this paper, a constrained GMC controller tuning approach using a nonlinear least squares technique is proposed. This tuning approach is simple to apply. For a SISO GMC control system with input saturation, the tracking performance is significantly improved by adding a simple heuristic switching strategy. The effectiveness of the proposed controller tuning approach is demonstrated using dynamic simulations and MIMO real‐time experiments.     

受扰双线性系统的近似最优扰动抑制方法

研究具有外界持续扰动作用下双线性系统的最优控制问题.关于二次型性能指标给出了一种设计最优扰动抑制控制律的逐次逼近方法.利用该算法可将在扰动作用下双线性系统的最优控制问题转化为求解一组线性非齐次两点边值序列问题.通过迭代序列得到的最优扰动抑制控制律由解析的线性前馈-反馈项和序列极限形式的非线性补偿项组成.通过截取非线性补偿序列的有限项,可以得到近似最优扰动抑制控制律.仿真结果表明,该方法抑制外部持续扰动的鲁棒性优于经典反馈最优控制.     

MP criterion based multiloop PID controllers tuning for desired closed loop responses

A tuning method of multiloop PID controllers is developed based on the generalized IMC PID tuning rule by Lee et al. (1998a). To extend the SISO PID tuning method to MIMO systems, a new tuning criterion is proposed. The criterion is based on the closed loop frequency response method to meet desired performance and robustness as close as possible. Examples for 2x2, 3x3 and 4x4 systems are used to illustrate the proposed method. The results show that the proposed method is superior to conventional methods such as the BLT tuning method.     

基于变结构扩张状态观测器的状态PI控制器

传统的状态PI控制器只适用于单输入单输出（SISO）线性系统。针对这一不足,将“变结构扩张状态控制器”技术应用到状态PI控制器中,使改进后的控制器适用于非线性系统控制。同时发挥了变结构控制理论的优势,既保留了原控制器的优点又减少了可调参数。仿真结果验证了新状态PI控制器具有良好的稳定性和鲁棒性。     

GRAPHICS-BASED CONTROL DESIGNS FOR NONMINIMUM-PHASE NONLINEAR SYSTEMS SUBJECT TO INPUT AND OUTPUT CONSTRAINTS

This article deals with the output regulation of nonminimum-phase systems subject to input and output constraints. Through the off-line static data reconciliation algorithm for a class of stable nonlinear bioreactors, the static feedforward control can ensure constant disturbance attenuation in spite of input multiplicities and actuators constraints. Under the pseudo-steady-state error diagnoses and a graphics-based mechanism for disturbance estimation, the proposed error feedback control scheme will induce the piecewise output regulation. Based on the “intelligent” algorithm for tuning improvement, the closed-loop simulation shows that the piecewise control strategy turns out to be robust against the unknown disturbances.     

GRAPHICS-BASED CONTROL DESIGNS FOR NONMINIMUM-PHASE NONLINEAR SYSTEMS SUBJECT TO INPUT AND OUTPUT CONSTRAINTS

This article deals with the output regulation of nonminimum-phase systems subject to input and output constraints. Through the off-line static data reconciliation algorithm for a class of stable nonlinear bioreactors, the static feedforward control can ensure constant disturbance attenuation in spite of input multiplicities and actuators constraints. Under the pseudo-steady-state error diagnoses and a graphics-based mechanism for disturbance estimation, the proposed error feedback control scheme will induce the piecewise output regulation. Based on the “intelligent” algorithm for tuning improvement, the closed-loop simulation shows that the piecewise control strategy turns out to be robust against the unknown disturbances.