Performance assessment of MIMO systems based on I/O delay information

The minimum variance (MV) control is one of the most popular benchmarks in control performance assessment. For a SISO process, the minimum variance can easily be estimated given the information of the process time delay. However, it is more difficult to obtain the MV benchmark for a multivariable system since the solution relies on the process interactor matrix. The computation of the interactor matrix requires knowledge of Markov parameter matrices of the plant, which is tantamount to complete knowledge of the process model. This requirement is usually unrealistic, since the model is either not available or not accurate enough for a meaningful calculation. However, the time delays between the inputs and outputs are relatively easy to obtain and can be used to construct an I/O delay matrix. This paper shows how to estimate upper and lower bounds of the MIMO MV performance from routine operating data with the I/O delay matrix known. In order to estimate the upper bound, the introduction of additional time delays into the controller is normally needed. However, should this be considered restrictive, then another upper bound which has recently been proposed can be used instead. On the other hand, the lower bound can readily be estimated from routine data. The results are illustrated by a simulation example.     

Projection based MIMO control performance monitoring: I—covariance monitoring in state space

In this paper we propose a new control performance monitoring method based on subspace projections. We begin with a state space model of a generally non-square process and derive the minimum variance control (MVC) law and minimum achievable variance in a state feedback form. We derive a multivariate time delay (MTD) matrix for use with our extended state space formulation, which implicitly is equivalent to the interactor matrix. We show how the minimum variance output space can be considered an optimal subspace of the general closed-loop output space and propose a simple control performance calculation which uses orthogonal projection of filtered output data onto past closed-loop data. Finally, we propose a control performance monitoring technique based on the output covariance and diagnose the cause of suboptimal control performance using generalized eigenvector analysis. The proposed methods are demonstrated on a few simulated examples and an industrial wood waste burning power boiler.     

Alternative solutions to multi-variate control performance assessment problems

Performance assessment of multi-variate control with minimum variance control as the benchmark requires an interactor matrix to filter the closed-loop output. This is to transfer the coordinate of the original variables into a new one in order to identify the control invariant disturbance dynamics from the first few terms of the closed-loop output Markov parameters. There has been a great deal of interest to simplify this approach, in particular, to find methods that do not need the interactor matrix. With this motivation, this paper explores alternative solutions to multi-variate control performance assessment problems. In particular, we will consider two practical scenarios: (1) known time delays between each pair of inputs and outputs, (2) no a priori knowledge about the process model or time delays at all. Solutions to these two scenarios are proposed. Two data-driven algorithms based on subspace approach are derived for the calculation of performance measures. Several examples illustrate the feasibility of the proposed approaches.     

MIMO control performance monitoring using left/right diagonal interactors

Although the minimum variance control (MVC) benchmark is popular for control performance monitoring, the requirement of a general interactor for multivariable processes is equivalent to knowing the Markov parameters, which is inconvenient in practice. To reduce the model requirement of a general interactor, a right diagonal interactor matrix is first used for a class of MIMO processes. Then a solution to the MIMO MVC benchmark is developed using the right diagonal interactor. Next, both the left and right diagonal interactors are integrated to characterize the complex time-delay structure of an extended class of multivariate processes. The factorization of the combined left/right diagonal interactors and the corresponding MVC benchmark estimation are also presented. The advantages of the new approach lie in the reduced a priori process knowledge and the simplified numerical procedures. A number of simulated examples are provided to illustrate the validity and effectiveness of the proposed performance monitoring approach.     

一种基于初始闭环系统的性能评估方法

基于初始闭环系统的输出方差和最小方差指标, 提出了一种新的性能评估方法. 在过程时滞变化的情况下, 基于最小方差指标的评估可能会得到错误的结论, 而新的方法可以避免这一缺点. 扩展的性能指标以控制器投运后的初始状态作为零基准, 能够更准确地反映操作工系统性能的变化, 能够很好地替代最小方差指标. 利用交互矩阵可将扩展指标推广到多变量系统的评估中, 本文将这一算法应用于精馏塔过程的评估. 精馏塔过程的仿真示例验证了方法的有效性, 表明过程时滞变化时用扩展指标来进行评估更能反映系统性能的变化.     

Minimum variance control and performance assessment of time-variant processes

This paper is concerned with (1) an explicit solution of a minimum variance control law for linear time-variant (LTV) processes in the transfer function form, and (2) performance assessment of LTV processes using minimum variance control as the benchmark. It is shown that there exists a time-variant, absolute lower bound of process variance that is achievable under LTV minimum variance control and can be estimated from routine operating data. This lower bound can subsequently be used to assess the benefit of implementing LTV control such as adaptive control. The proposed methods are illustrated through simulated examples and an industrial case study.     

Monitoring control performance via structured closed-loop response subject to output variance/covariance upper bound

Owing to the process time delays, the closed-loop response can be divided into feedback control invariant part and feedback controller dependent part. If the latter part is replaced by a user specified response trajectory, we refer to the resultant closed-loop response as structured closed-loop response. The user specified structured closed-loop response has been used as an achievable control against which one can assess performance of control loops. In the control performance monitoring literature, the user specified response is often given as a first-order transfer function with some specified performance requirement, such as time constant. In this paper, we solve this problem from a systematic approach, i.e., in viewpoint of a variance/covariance upper bound on the outputs. With available closed-loop routine operating output data and process time delay/interactor matrix, the desired structured closed-loop response can be obtained directly via estimated closed-loop time series model. A significant feature is that the output variance/covariance upper bound constraint can be explicitly specified according to the product specifications and is always satisfied when the problem is feasible. This desired structured closed-loop response can thus be served as a benchmark against which the existing controller performance can be compared. We also show that two approaches, linearizing change of variables and Frank and Wolfe algorithm, are suitable for solving this problem, which result in a full order and a reduced order structured closed-loop response, respectively. Both approaches are illustrated by two case studies.     

控制性能评价中单位关联矩阵的求解

多回路控制性能评价中单位关联矩阵的求解很重要,会影响到时延项的确定与控制性能指标的计算,因此探讨关联矩阵的计算问题是个有意义的话题。关联矩阵求解一般需要知道一些过程模型的信息,这个条件对于实际应用比较苛刻。为避开先验知识的约束,提出了基于闭环数据的单位关联矩阵求解方法。通过对辨识所得各类传函模型的预处理,能从多项式矩阵中直接求解出对角单位关联矩阵或迭代求解出非对角单位关联矩阵。应用结果证明了该方法的有效性。     

基于历史性能基准的模型预测控制性能监控

针对实际工业过程中希望只利用过程的日常运行数据对控制系统进行监控的情况,提出了1种用历史性能基准对预测控制系统进行性能评估、监控以及分析的方法.利用运行状态良好的1段历史数据计算出历史性能基准,并将历史性能基准与实际性能的比值用于控制器性能的实时监控.根据历史性能指标的残差监控检测出性能变化时,进一步通过历史数据协方差监控及广义特征值分析,区分出性能显著变差或变好的方向和子空间.为现场工程师提供性能变化的一些原因,用于系统维护.最后通过Shell重油分馏塔仿真证明该方法可以获得很好的评估与监控结果.     

Performance assessment and robustness analysis using an ARMarkov approach

Application of the ARMarkov model-based formulation offers significant advantages for assessment/monitoring and robustness analysis of process systems. The ARMarkov method does not require a priori specification of the system time delay/interactor matrix, needs only an approximate estimate of model order and can be done using open or closed-loop process data. By appropriate use of standard, linear model estimation techniques, it directly produces statistically consistent estimates of the first few, user-specified number of Markov parameters even in the presence of colored noise. It is shown in this paper that the Markov parameters and the ARMarkov model can be used to calculate the interactor matrix and several process performance metrics including sensitivity/complementary-sensitivity functions and time-domain criteria such as speed of response, minimum variance values etc. In addition it is shown that model-based predictive control (MPC) systems formulated using ARMarkov models have a special state space structure that leads to less conservative robustness bounds for specific types of uncertainties (such as gain mismatch, uncertainty in the fast or slow dynamics, etc.) than applying the Small Gain Theorem directly to the conventional state space model structure.     

The unitary interactor matrix and its estimation using closed-loop data

This paper is concerned with the factorization and estimation of the unitary interactor matrix or the time-delay matrix of multivariable systems. The important properties of the unitary interactor matrix for minimum variance control are discussed. An algorithm for factorization of the unitary interactor matrix from the Markov parameters is introduced. A method for direct estimation of the interactor matrix from closed-loop data is proposed. The proposed algorithm is evaluated by application to a simulated example, pilot-scale experiment and actual industrial data.     

基于用户自定义指标的多变量控制系统性能评估技术

大量的计算以及对一般关联矩阵先验知识的需求导致用户自定义指标在实际工业应用中存在诸多不便,鉴于此,为了减少对过程模型信息的需求,避免估计一般关联矩阵,研究了如何简化用户自定义指标的计算,并提出了两种改进的用户自定义指标的计算方法.该方法仅需过程常规数据和对过程输入/输出时延或关联矩阵阶次的估计便可完成指标的计算.最后通过仿真验证了两种方法的优越性和有效性.     

Adaptive control of a class of multivariable nonlinear systems andconvergence analysis

Adaptive control is discussed of a class of multivariable nonlinear systems which can be characterized by a stochastic multivariable Hammerstein model whose linear part possesses an arbitrary interactor matrix. A simple suboptimal control law is derived which provides an efficient way to control a multivariable Hammerstein model whose linear part is not necessarily minimum phase. A direct adaption scheme is presented to implement the control law, and the global convergence of the algorithm is established     

Direct adaptive decoupling control for general stochastic multivariable systems

This paper presents a novel adaptive decoupling controller for general stochastic multivariable systems with arbitrary time delay structure. The decoupling controller is constructed using a diagonal dynamic precompensator to diagonalize the system interactor matrix and then combining the feedforward control strategy and the generalized minimum variance approach. It cannot only control unstable and'or non-minimum phase processes but also decouple the closed-loop systems both dynamically and in the static state. It is adaptively implemented in direct form. The global convergence properties and parameter estimate consistency for this adaptive decoupling algorithm are also discussed. It is shown that this adaptive controller not only has globally convergent properties but also generates strongly consistent parameter estimates. The results of simulations and an application are proposed to demonstrate the effectiveness of the algorithm.     

前馈反馈线性时变多变量控制系统性能评价

本文研究一类具有可确定“时滞”的线性时变多变量(linear time-varying multiinput-multioutput, LTV MIMO)控制系统的性能评价方法。定义了该类系统中相当于单回路“过程滞后”的矩阵因子——关联矩阵，并利用该关联矩阵和正常乘法提出一套建立线性时变多变量控制回路前馈反馈最小方差(minimum variance, MV)基准的系统化算法和过程．需要考虑到LTV系统特有的计算特性，利用实际最小方差输出而不是关联滤波最小方差输出获得MV基准。理论和仿真研究表明，所提方法能准确和有效地评价线性时变多变量过程．     

一类确定性多变量非线性系统的自适应控制

本文研究了可用确定性多变量Hammerstein模型描述的一类多变量非线性系统的自适 应控制,基于对一步最优控制律所产生的闭环系统的稳定性条件的分析,提出了一种适用于线 性部分为具有任意关联矩阵的非最小相位系统的简单次优控制律及相应的直接自适应控制算 法,并证明了算法的全局收敛性.     

The role of the interactor matrix in multivariable stochastic adaptive control

This paper is concerned with the extension of the well-known minimum variance control strategy to the multi-input-multi-output case. It is shown that this extension is straightforward when the system interactor matrix is diagonal but presents some unexpected difficulties in the general case. We develop a suitable stochastic controller for the general case as a logical extension of the single input algorithm. We also explore the properties of the algorithm in detail. We also address the question of adaptive control of multivariable stochastic systems and investigate one possible strategy for overcoming the requirement of knowing the system interactor matrix a priori.     

综合的多变量控制系统性能分析方法及应用实例

提出了综合的多变量控制系统性能分析方法．其中，将多变量最小方差控制的性能评价准则用于确定整个过程控制系统运行的好坏；利用归一化多变量脉冲响应曲线图来获得过程动态性能的信息；并用自相关函数图和互相关函数图分析系统是否存在振荡，从而从多个角度对控制系统的性能给出充分的评价．文中给出了这一综合性的性能评价方法在精馏塔控制中的应用．     

Performance assessment of control loops with time-variant disturbance dynamics

If a process is subject to time varying disturbance dynamics (or time varying disturbance models), the time invariant minimum variance control for one type of disturbance dynamics is no longer minimum variance control for another type of disturbance. An explicit solution to a time-invariant optimal control that can optimize overall performance of time-variant processes is derived in this paper and is used as a benchmark to assess control performance of time variant process under time invariant control. This work is a continuation of the work by Huang [Can. J. Chem. Eng. 77(5) (1999) 1044]. It is shown that this performance benchmark can be found from routine operating data through time series analysis and optimization technique. The developed performance assessment technique is illustrated by a simulated example and applied to an industrial process.