基于多模型混合最小方差控制的时变扰动控制系统性能评估

在实际工业过程中,控制系统经常会受到时变扰动的影响,致使针对单一扰动模型设计的最小方差控制准则不再适用于评估时变扰动控制系统的性能. 当多个扰动信号同时出现时,采用常规多模型切换方法会发生间歇切换进而产生较大的暂态误差,不能准确评估系统当前性能. 针对上述问题,本文提出了一种基于多模型混合最小方差控制准则的性能评估方法. 首先根据每个扰动模型分别制定最小方差控制器,组成多模型最小方差控制器,然后在每个时间点混合多模型最小方差控制器,并将在其作用下的输出方差作为最终的性能评估基准,该方法既 充分考虑到每个扰动的特性,又避免了常规多模型切换方法因间歇切换而产生的暂态误差对评估结果准确性带来的影响,实现了准确、可靠地评估时变扰动控制系统的性能. 通过仿真,验证了基于多模型混合最小方差控制准则的性能评估方法的有效性.     

Performance monitoring of SISO control loops subject to LTV disturbance dynamics: An improved LTI benchmark

This paper is concerned with performance assessment of univariate control loops subject to time varying disturbance dynamics. The problem is motivated by the observation that most industrial controllers are linear time invariant (LTI) but the process, particularly the disturbance dynamics, is time varying. The time varying behavior of disturbance dynamics is modelled by piecewise constant parameters of linear disturbance models, namely linear time varying (LTV) dynamics. Thus, during a period of process operation, the process may be affected by several disturbances in terms of different disturbance dynamics or models. This problem has been previously solved by minimizing the variance of a most representative disturbance while satisfying a structured regulatory performance requirement for one of other disturbances, typically the transient but most significant disturbance. This leaves performance in regulating the remaining disturbances unspecified. In this paper, we formulate the problem as minimization of the sum of the weighted variances of all but one major disturbance that is considered under the structured regulatory performance requirement. Furthermore, the problem is solved from the following two perspectives: (1) Models of LTV disturbances are given, the limit of the achievable structured closed-loop performance of any LTI controller for the LTV disturbances is calculated, and the optimal LTI control law is derived if the process model is also known; (2) no complete models about the process or the disturbances are available except for the time delay of the process, an algorithm is developed to assess the performance of the existing LTI controller in the presence of LTV disturbances. Simulation and industrial examples are used to illustrate the proposed algorithms.     

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.     

Alternative model structure with simplistic noise model to identify linear time invariant systems subjected to non-stationary disturbances

Non-stationary disturbances are of common occurrence in chemical process industry. These cannot be modeled using constant parameterized models and hence pose a difficult problem in the identification of true process and disturbance dynamics. A simple system identification technique to identify the linear processes affected by non-stationary disturbances is proposed in this work. This uses a time varying bias term, a representative of the additive non-stationary external disturbance entering the process, in addition to the output predictions in an ARMAX or OE model framework. Decoupled loss function and covariance update with different forgetting factors for linear time invariant input–output dynamics part and time varying part (bias term) of the model ensures the unbiased estimation of true process dynamics along with disturbance dynamics. Practical issues such as time delay estimation, model order selection are discussed. Extensions for time varying processes and MIMO processes are also proposed. Validation is performed using various simulation studies.     

Performance monitoring of model-predictive controllers via model residual assessment

Model quality is a main factor that affects the control performance of model-based controllers. In this paper, a new closed-loop model assessment approach is proposed to assess model deficiency from routine closed-loop data. The proposed model quality index is a minimum variance benchmark for the model residuals obtainable from closed-loop data. From the feedback invariant principle the disturbance innovations are shown to be unaffected by the feedback controller. Then it is shown that the disturbance innovations can be estimated from closed loop data by an orthogonal projection of the current output onto the space spanned by past outputs, inputs or setpoints. With the estimated disturbance innovations as the benchmark, a model quality index is developed by using the ratio of a quadratic form of model residuals and that of the estimated disturbance innovations. The effectiveness of the proposed methods is demonstrated by simulations.     

Practical solutions to multivariate feedback control performance assessment problem: reduced a priori knowledge of interactor matrices

The research on control loop performance monitoring and diagnostics has been and remains to be one of the most active research areas in process control community. Despite of numerous developments, it remains as a considerably challenging problem to obtain a minimum variance control benchmark from routine operating data for multivariable process since the solution relies on the interactor matrix (or inverse time delay matrix). Knowing the interactor matrix is tantamount to knowing a complete knowledge of process models that are either not available or not accurate enough for a meaningful calculation of the benchmark. However, the order of an interactor matrix (OIM) for a multivariable process, a scalar measure of multivariate time delay, is a relatively simple parameter to know or estimate a priori. This paper investigates the possibility to estimate a suboptimal multivariate control benchmark from routine operating data if the OIM is available. The relation between this suboptimal benchmark and the true multivariate minimum variance control benchmark is investigated. Analytical expressions for the lower and upper bounds of the true multivariate minimum variance are derived. Although not minimum variance control, this benchmark answers important practical questions like “at least how much potential of the improvement does the control have by tuning or redesigning?”. It is further shown that the proposed suboptimal benchmark is achievable by a practical control provided that the system of interest is minimum phase. Simulation examples illustrate the feasibility of the proposed approach.     

基于输出方差限制的广义多变量控制系统性能评价

研究具有线性时变扰动的多变量控制系统性能评价的方法.通过将时变扰动分为三类定常扰动, 进而构造一个加权的性能指标,权值矩阵与不同扰动类型和优先级相对应.在指定合理的输出方差后, 运用对角关联矩阵方法明确计算出广义多变量系统闭环输出方差的上下限值.经过ITAE (Integral of time-weighted absolute value of the error) 寻优得到最 小输出方差下的控制器参数,并给出可实现的最优控制器模型.仿真实例证明了该方法计算的简便性和有效性.     

四水箱控制系统的性能评价

针对基于最小方差的性能评价准则由于只考虑时滞引起的性能限制,不适合对PID控制回路进行性能评价的问题,本文采用PID能实现最小方差控制准则,对四水箱控制系统进行性能分析,得到的性能指标比传统最小方差准则明显提高,控制器参数大大改善了过程的输出方差。实验表明,PID能实现最小方差准则能够为PID控制器的性能评价提供一个合理的评价基准,更说明其对特定类型控制器性能评价所具有的实际意义。     

Performance assessment of single-loop industrial controllers

The most common metric for controller performance assessment is a comparison of the process output variance to that which would have been obtained if some optimal controller had been applied to the process over the same time frame. Usually this optimal controller is a minimum variance controller, as a metric based on this controller requires a minimum of process knowledge and no plant tests. While minimum variance controllers by definition contain an accurate disturbance model, industrial controllers contain a simple fixed disturbance model, which may or may not be an accurate representation of the actual disturbance. Shown in this paper is the effect that this simple disturbance model has on performance indices, and methodologies for controller performance assessment that accounts for this simple model. In addition, a performance metric for non-deadtime-compensated (i.e., PID) controllers is shown.     

Adaptive generalized minimum variance congestion controller for dynamic TCP/AQM networks

Generic generalized minimum variance-based (GMV) controllers have been adopted as efficient control mechanisms especially in presence of measurement noise. However, such controllers exhibit degraded performance with change in process dynamics. To overcome this problem, a novel congestion controller based on active queue management (AQM) strategy for dynamically varying TCP/AQM networks known as adaptive generalized minimum variance (AGMV) is proposed. AGMV is the combination of the real-time parameter estimation and GMV. The performance of the proposed scheme is evaluated and compared with its adaptive minimum variance (AMV) counterpart under two distinct scenarios: TCP network with unknown parameters and TCP network with time varying parameters. Simulation results indicate that, in either case, AGMV is able to keep the queue length around the desired point. In addition, the superior performance of the proposed controller has been shown with regard to the PI controller, which is well-known in the AQM domain.     

Control performance assessment for multivariable systems based on a modified relative variance technique

In this paper, a new technique is presented which enables the relative performance of both single and multiple loop control systems to be determined. The technique is based on the relative variance index technique which has been proposed recently for monitoring single loop control systems. This technique provides a control loop performance metric that considers the performance of the control system relative to both minimum variance and open-loop control. A major limitation with this technique is that it requires a highly restrictive assumption to be made regarding the structure of the disturbance to the process and the extension of the technique to multiple loop systems is not straight forward. The technique proposed in this paper does not require any assumptions to be made regarding the structure of the disturbance and can be extended to multiple loop situations with relative ease. The ability of the proposed technique to assess the performance of controllers applied to two simulated systems and also an industrial process is examined and it is shown that the proposed approach is superior to alternative techniques. A further benefit of the proposed technique is that it is able to provide an estimate of the potential improvement to the performance of the control loop that is achievable if the control system is retuned or redesigned.     

基于多模型混合的广义最小方差控制性能评估

针对实际工业过程中控制系统经常会受到时变扰动的影响,致使针对单一扰动模型设计的性能评估方法不再适用于时变扰动控制系统的问题,提出了基于多模型混合的广义最小方差控制性能评估方法．该方法综合考虑被控对象输出方差与控制器输出方差的两个指标,同时提出了一种“判断—加权”的控制器设计策略．首先,在任一时间段选取使广义输出方差最小的控制器,并判断其与上一时间段采用的控制器是否一致;然后,在此基础上采用多模型混合思想进行控制器设计,并将其作用下的广义输出方差作为性能评估的基准．通过乙烯裂解炉仿真,验证了本文所述方法在时变系统性能评估中的有效性．     

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.     

Optimal robust disturbance attenuation for continuous time‐varying systems

In this paper we consider the Optimal robust disturbance attenuation problem (ORDAP) for continuous time‐varying systems subject to time‐varying unstructured uncertainty. We show that for causal (possibly time‐varying) continuous systems, ORDAP is equivalent to finding the smallest fixed point of a ‘two‐disc’ type optimization problem under time‐varying feedback control laws. Duality is applied in the context of nest algebra of causal stable systems, to prove existence of optimal continuous time‐varying controllers. We also show that for time‐invariant nominal plants, time‐varying control laws offer no improvement over time‐invariant feedback control laws. Copyright © 2003 John Wiley & Sons, Ltd.     

Minimum‐variance control of astronomical adaptive optic systems with actuator dynamics under synchronous and asynchronous sampling

Adaptive optic (AO) systems are now routinely used in ground‐based telescopes to counter the effects of atmospheric turbulence. A deformable mirror (DM) generates a correction wavefront, which is subtracted from the turbulent wavefront using measurements of the residual phase provided by a wavefront sensor (WFS). Minimizing the variance of the residual phase defines a sampled data control problem combining a continuous time minimum‐variance (MV) performance criterion with a discrete‐time controller. For a fairly general class of linear time‐invariant DM and turbulence WFS models, this control problem can be transformed into an equivalent discrete‐time LQ optimization problem involving a set of (discrete‐time) control‐sufficient statistics of the incoming continuous‐time turbulence. This paper shows how to constructively solve this MV problem in the presence of DM's dynamics, starting from continuous‐time models of DM and turbulence. This result is extended to the case of asynchronous DM/WFS sampling. An illustrative application to optimal control of tip‐tilt turbulent modes for the European extremely large telescope in the presence of first‐order DM's dynamics is presented. Copyright © 2010 John Wiley & Sons, Ltd.     

基于LS-SVM的一类非线性系统的性能估计

控制系统性能估计的研究多数针对线性系统,但是非线性系统本质上更加复杂,用传统的方法进行估计存在局限性.对于一类可由非线性部分叠加线性干扰表示的非线性系统,首先分析了其反馈不变量的存在性,指出此类系统性能估计的关键在于构造超前预测模型.接着用最小二乘支持向量机辨识非线性模型,把最小方差性能估计问题转换成模型参数辨识问题,...     

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.     

Cyclic moving average control approach to cylinder pressure and its experimental validation

Cyclic variability is a factor adversely affecting engine performance. In this paper a cyclic moving average regulation approach to cylinder pressure at top dead center （TDC） is proposed, where the ignition time is adopted as the control input. The dynamics from ignition time to the moving average index is described by ARMA model. With this model, a one-step ahead prediction-based minimum variance controller （MVC） is developed for regulation. The performance of the proposed controller is illustrated by experiments with a commercial car engine and experimental results show that the controller has a reliable effect on index regulation when the engine works under different fuel injection strategies, load changing and throttle opening disturbance.     

Detection of model-plant mismatch in closed-loop control system

The performance of model-based control systems depends a lot on the process model quality, hence the process model-plant mismatch is an important factor degrading the control performance. In this paper, a new methodology based on a process model evaluation index is proposed for detecting process model mismatch in closed-loop control systems. The proposed index is the ratio between the variance of the disturbance innovation and that of the model quality variable. The disturbance innovations are estimated from the routine operation data by an orthogonal projection method. The model quality variable can be obtained using the closed-loop data and the disturbance model estimated by adaptive Least absolute shrinkage and selection operator (Lasso) method. When the order of the disturbance model is less than 2 or the process time delay is large enough, no external perturbations are required. Besides, the proposed index is independent of the controller tuning and insensitive to the changes in disturbance model, which indicates that the proposed method can isolate the process model-plant mismatch from other factors affecting the overall control performance. Three systems with proportional integral (PI) controller, linear quadratic (LQ) controller and unconstrained model predictive control (MPC) respectively are presented as examples to verify the effectiveness of the proposed technique. Besides, Tennessee Eastman process shows the proposed method is able to detect process model mismatch of nonlinear systems.     

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.