基于内模控制的Smith反向解耦控制器设计

针对多变量时滞系统提出了一种基于内模控制(Internal Model Control,IMC)的Smith动态解耦控制器设计方法。其中,Smith补偿器被应用在该控制结构中,包含带有时滞项和不带时滞项的补偿结构,以解决不能完全补偿的问题,通过反向解耦设计实现多变量时滞系统动态解耦。多变量系统被解耦成一系列互相独立的单回路对象,通过内模控制原理对Smith控制器进行参数整定,并分析了系统的鲁棒性。仿真实例表明了该方法的有效性,能够较好地克服系统参数扰动导致的干扰,并具有较好的动态性能。     

IMC controller design for multivariable systems

A systematic internal model control (IMC) controller design methodology has been developed for various types of multivariable processes. When we try to apply IMC to various systems several implementation problems are encountered. In this paper, we resolve these problems and suggest a systematic IMC controller design methodology. IMC shows very good performance and is easy to tune for open-loop stable systems. For unstable systems we apply IMC after stabilizing the systems using the pole placement technique. A combination of quadratic programming and IMC can handle constraints on manipulated and controlled variables.     

Design of a multivariable internal model controller based on singular value decomposition

In this article, a novel internal model control (IMC) approach based on singular value decomposition (SVD) is proposed for the control of multiple‐input–multiple‐output (MIMO) systems with multiple time delays. This approach achieves decoupling using a compensation term and improves the robustness using SVD in the inverse of the steady‐state gain matrix of process. Meanwhile, a novel filter is designed for decoupling and fast response speed of multivariable systems with multiple delays. The design of the controller can be extended to non‐square systems where there are more inputs than outputs. Examples are included to illustrate the effectiveness of the method. © 2012 Canadian Society for Chemical Engineering     

多变量多时滞非方系统的解耦内模控制

多变量复杂控制系统不仅具有多耦合和多时滞性,还具有结构上的复杂性,即输入输出不等,传递函数为奇异矩阵。传统的多变量内模控制是基于对非奇异对象求逆来进行的,因此很难解决这类问题。针对该情况引入矩阵论中的广义逆概念,通过求对象的广义逆矩阵来设计解耦内模控制器,打破了内模控制只能对方系统进行控制的局限性,并利用泰勒近似很好地解决了多滞后的问题,最后通过设计特殊形式的滤波器,不仅能够消除由纯滞后近似引入的不稳定极点,保证系统的稳定性,且能够保证系统的正则性。仿真结果表明,该方法不仅跟踪迅速,且继承了内模控制的无余差和强鲁棒性,动态解耦效果良好,仅对时滞变化较为敏感。由于系统基于内模控制设计,故模型匹配度越高,系统响应越好。     

Partial decoupling of non-minimum phase processes with bounds on the remaining coupling

Partial (triangular) decoupling of MIMO systems has been considered in the literature as a way of relaxing the design limitations introduced by diagonal decoupling in non-minimum phase processes. The former strategy allows decoupling a variable of interest without affecting it with non-minimum phase dynamics. However, when right-half plane (RHP) zeros are mainly aligned with this variable, pushing the effect of the RHP zeros to other outputs comes at the cost of great interactions in those variables. This article presents a method to delimit these interactions without degrading significantly the decoupled variable response. To this end, the algorithm shapes the reference signal by means of an auxiliary sliding mode loop.     

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.     

The 2-port control system

The 2-port control structure is introduced to develop a complete framework for the analysis and design of robust predictive controllers. It is particularly suited for the optimum resolution of controller design trade-offs, such as performance to set-point tracking vs. disturbance rejection, and performance at various frequencies. Furthermore, the 2-port control structure allows the transparent design of effective controllers for processes with non-minimum phase characteristics, or inherently unstable open-loop dynamics. Finally, it offers, the necessary and sufficient conditions for the design of effective adaptive control strategies. Various illustrations are also provided to demonstrate the relationship of the 2-port control structure to other design frameworks, such as internal model control (IMC), and conventional feedback with analytic predictors.     

Advantage of Low‐Cost Predictive Control: Study Case on a Train of Distillation Columns

The process of enriching the ¹³C isotope, performed in trains of cryogenic distillation columns, exhibits large settling times, nonlinearities, large dead‐times, and are difficult to model precisely. Such equipment has been developed in Romania, with concentration increasing up to 70 %. A control analysis for a single unit has already been done including a decentralized multivariable PI controller and two decoupling control algorithms based on the internal model control (IMC) approach. Here, a multivariable predictive controller, the extended prediction self‐adaptive controller is proposed. The simulation results, considering significant modeling errors, demonstrate that this represents a more suitable choice than the previously designed strategies. Comparisons are included to support this idea.     

ADAPTIVE INTERNAL MODEL CONTROL OF HAMMERSTEIN-NONLINEAR SYSTEMS

Adaptive internal model control is analyzed for a single-input-single-output nonlinear system represented by the Hammerstein model wherein the nonlinearity is an odd order polynomial. The recursive least-squares method of Chang and Luus (1971) is used for parameter estimation. To obtain a stable approximation to the inverse of the process model for use as the controller, Vogel-Edgar's method (1980) for linear system is employed. Simulation results have shown that the adaptive internal model control (IMC) performs well even with non-minimum phase Hammerstein systems in the presence of unmeasured load changes and dead-time variations. The performance of nonlinear IMC is found to be superior to that of linear IMC.     

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.     

A feedback control scheme for SISO systems with time delays and constrained inputs

A feedback control scheme for SISO systems with time delays and constrained inputs is proposed. The controller is designed through the internal model control (IMC) technique and the Smith predictor structure is used for dead time compensation. Through computer simulation, the performance of the proposed scheme has been compared with the classic feedback scheme designed via the IMC procedure. The results show that the proposed scheme performs better due to the preservation of the predictive property.     

RECURRENT NEURAL NETWORKS IN DECOUPLING CONTROL OF MULTIVARIABLE NONLINEAR SYSTEMS

In this work we focus on the synergy between modeling with RNNs, and nonlinear controller design for decoupling control. The thesis of the paper is that recurrent neural networks (RNNs) can be conveniently used in an integrated black-box modeling and controller design methodology for decoupling control of multivariable nonlinear systems. A simulation example on a multivariable continuous-stirred-tank-reactor (CSTR) is provided to elucidate related issues. The effects of modeling uncertainty and state reconstruction on decoupling performance are specifically discussed.     

Low-gain internal model control PID controller design based on second-order filter

A design method is proposed for low-gain internal model control (IMC) proportional-integral-derivative (PID) controllers based on the second-order filter. The PID parameters are obtained by approximating the feedback form of the IMC controller with a Maclaurin series, in which the second-order filter is applied using the IMC approach to achieve a low-gain PID controller that is suitable for model mismatch problems. Analytical PID tuning rules based on the second-order filter are derived for several common-use process models. The second-order filter is designed from the desired time domain performances of maximum overshoot and settling time. Furthermore, the robustness of the IMC PID controller based on the second-order filter is analyzed, and results show that its robustness performance is better than the first-order filter under certain conditions. Finally, three categories of models divided by the ration of time constant and time delay are presented in the comparative numerical simulations to validate the effectiveness and generality of the proposed PID controller design method.     

SOPDT模型不确定性界及其在内模控制器设计中的应用

引　言内模控制 (ＩＭＣ)是一种在化工过程中有广泛应用前景的鲁棒控制 ,由于这一先进控制能保证系统的鲁棒稳定性和鲁棒性能 ,从而在过程控制界引起了极大的兴趣[1～ 8] .鲁棒控制器设计的必要条件之一 ,是首先要有实际过程的不确定信息 ,即模型 (或过程 )的不确定性界[7] .对于在过程控制中经常采用的一阶加纯滞后过程 (ＦＯＰＤＴ) ,其模型不确定性界的计算方法已有报道[5～ 7,9] .然而 ,过程控制中常常会遇到二阶加纯滞后过程 (ＳＯＰＤＴ) ,有时更高阶的过程采用ＦＯＰＤＴ模型来近似往往不能保证闭环系统的性能 ,需要采用ＳＯＰＤＴ模…     

ROBUST DECOUPLING CONTROL BASED ON EXTERNAL LOOPS

Decoupling control can substantially simplify the design of multivariable control systems. However, decouplers are usually sensitive to modeling errors, especially for the systems with relative gains being far away from unity. Hence, decoupling control is limited in practical application. In the present study, robust control of a decoupling system with external loops is developed. Design of the control system consists of two steps. The first step is to design the decoupler and the controller based on the nominal plant. The second step is to design the filters in the external loops by using a robust stability criterion. The robust control is implemented without changing the original design of the decoupler and the controller. The control system with external loops for decoupling control significantly improves the control performance. The proposed robust control enhances the applicability of decoupling control.     

化工双输入输出时滞过程解耦PID控制器解析设计

基于常规单位反馈控制结构,针对具有时滞特性的化工双输入输出过程提出一种解耦PID控制器的解析设计新方法.该解耦PID控制器的突出优点是控制器设计过程简单直观;控制器可以实现标称系统输出间的显著解耦;系统输出分别使用相应控制器对角元素中的调节参数进行单参数整定.同时,对于实际生产过程中常见的被控过程乘性不确定性,分析了系统保持鲁棒稳定的充要条件.仿真实例验证了该方法优于其它方法.     

PID Controller Design Based on the Time Domain Information of Robust IMC Controller Using Maximum Sensitivity

The IMC (Internal Model Control) controller based on robust tuning can improve the robustness and dynamic performance of the system. In this paper, the robustness degree of the control system is investigated based on Maximum Sensitivity (Ms) in depth. And the analytical relationship is obtained between the robustness specification and controller parameters, which gives a clear design criterion to robust IMC controller. Moreover, a novel and simple IMC-PID (Proportional-Integral-Derivative) tuning method is proposed by converting the IMC controller to PID form in terms of the time domain rather than the frequency domain adopted in some conventional IMC-based methods. Hence, the presented IMC-PID gives a good performance with a specific robustness degree. The new IMC-PID method is compared with other classical IMC-PID rules, showing the flexibility and feasibility for a wide range of plants.     

A unified approach to the design of advanced proportional-integral-derivative controllers for time-delay processes

A unified approach for the design of proportional-integral-derivative (PID) controllers cascaded with first-order lead-lag filters is proposed for various time-delay processes. The proposed controller’s tuning rules are directly derived using the Padé approximation on the basis of internal model control (IMC) for enhanced stability against disturbances. A two-degrees-of-freedom (2DOF) control scheme is employed to cope with both regulatory and servo problems. Simulation is conducted for a broad range of stable, integrating, and unstable processes with time delays. Each simulated controller is tuned to have the same degree of robustness in terms of maximum sensitivity (Ms). The results demonstrate that the proposed controller provides superior disturbance rejection and set-point tracking when compared with recently published PID-type controllers. Controllers’ robustness is investigated through the simultaneous introduction of perturbation uncertainties to all process parameters to obtain worst-case process-model mismatch. The process-model mismatch simulation results demonstrate that the proposed method consistently affords superior robustness.     

Optimization‐Based Nonlinear Centralized Controller Tuning of Liquid‐Liquid Extraction Processes

Abstract

The control problem of an agitated contactor is considered in this work. A Scheibel extraction column is modeled using the non‐equilibrium backflow mixing cell model. Model dynamic analysis shows that this process is highly nonlinear, thus the control problem solution of such a system needs to tackle the process nonlinearity efficiently. The control problem of this process is solved by developing a multivariable nonlinear control system implemented in MATLAB?. In this control methodology, a new controller tuning method is adopted, in which the time‐domain control parameter‐tuning problem is solved as a constrained optimization problem. A MIMO (multi‐input multi‐output) PI controller structure is used in this strategy. The centralized controller uses a 2×2 transfer function and accounts for loops interaction. The controller parameters are tuned using an optimization‐based algorithm with constraints imposed on the process variables reference trajectories. Incremental tuning procedure is performed until the extractor output variables transient response satisfies a preset uncertainty which bounds around the reference trajectory. A decentralized model‐based IMC (internal model control) control strategy is compared with the newly developed centralized MIMO PI control one. Stability and robustness tests are applied to the two algorithms. The performance of the MIMO PI controller is found to be superior to that of the conventional IMC controller in terms of stability, robustness, loops interaction handling, and step‐change tracking characteristics.     

Multivariable Nonlinear Proportional-Integral-Derivative Decoupling Control Based on Recurrent Neural Networks

A nonlinear proportional-integral-derivative (PID) controller is constructed based on recurrent neural networks. In the control process of nonlinear multivariable systems, several nonlinear PID controllers have been adopted in parallel. Under the decoupling cost function, a decoupling control strategy is proposed. Then the stability condition of the controller is presented based on the Lyapunov theory. Simulation examples are given to show effectiveness of the proposed decoupling control.