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.     

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．     

Restricted Structure Control Loop Performance Assessment For Pid Controllers And State‐Space Systems

A novel H₂ optimal control performance assessment and benchmarking problem is considered for discrete‐time state‐space multivariable systems, where the structure of the controller is assumed to be fixed apriori. The controller structure may be specified to be of PID, reduced order, or lead/lag forms. The theoretical problem considered is to represent the state‐space model in discrete polynomial matrix form and to then obtain the causal, stabilising, controller, of a prespecified form, that minimises an H₂ criterion. This then provides the performance measure against which other controllers can be judged. The underlying practical problem of importance is to obtain a simple method of performance assessment and benchmarking low order controllers. The main theoretical step is to derive a simpler cost‐minimization problem whose solution can provide both the full order and restricted structure (PID) optimal benchmark cost values. This problem involves the introduction of spectral factor and diophantine equations and is solved via a Wiener type of cost‐function expansion and simplification. The numerical solution of this problem is straightforward and involves approximating the simplified integral criterion by a fixed number of frequency points. The main benchmarking theorem applies to multivariable systems that may be unstable, non‐minimum phase and non‐square.     

Implicit and explicit LQG self-tuning controllers

The design of optimal controllers for use in self-tuning systems is considered. Linear Quadratic Gaussian (LQG) controllers are widely used elsewhere but have not until recently been applied in self-tuning systems, except in minimum output variance forms. The LQG controllers offer a guarantee of stability (when the plant parameters are known) which is particularly useful for nonminimum phase systems. The explicit LQG self-tuning controllers introduced in the following are relatively simple to implement. The first version of an implicit LQG self-tuning controller is also introduced. The magnitude of the transport delay terms need not be known a priori and integral action may be introduced easily. If required the desired closed-loop poles of the system can be prespecified.     

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 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.     

For model-based control design, closed-loop identification gives better performance

We compare open loop versus closed loop identification when the identified model is used for control design, and when the system itself belongs to the model class, so that only variance errors are relevant. Our measure of controller performance (which is used as our design criterion for identification) is the variance of the error between the output of the ideal closed loop system (with the ideal controller) and that of the actual closed loop system (with the controller computed from the identified model). Under those conditions, we show that, when the controller is a smooth function of the input-output dynamics and the disturbance spectrum, the best controller performance is achieved by performing the identification in closed loop with an operating controller that we characterize. For minimum variance and model reference control design criteria, we show that this ‘optimal operating controller for identification’ is the ideal controller. This then leads to a suboptimal but feasible iterative scheme.     

风扰影响下的无人机非线性广义最小方差跟踪控制

本文以鱼鹰型固定翼无人机为研究对象,基于非线性广义最小方差(nonlinear generalized minimum variance,NGMV)最优控制理论,研究了受到非线性阵风干扰影响下的无人机跟踪控制问题.首先对鱼鹰型无人机动力学模型解耦,在解耦后的横向和纵向模型上分别实现跟踪控制;然后针对阵风非线性模型的特定形式,根据NGMV理论设计了增维的非线性广义最小方差控制器,使得模型充分考虑了阵风干扰的特性.所设计的NGMV最优控制器的主要优势在于它能处理带有干扰和时滞环节的非线性系统.多组阵风扰动的仿真试验结果表明,非线性广义最小方差最优控制器具有跟踪性和收敛性.     

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.     

Multivariable disturbance modelling for web processes

This paper considers suitable disturbance models for use in the design of control systems for web forming processes. It suggests a practical disturbance representation and, using spectral factorization, presents a multivariable aggregated model of the disturbance. The paper compares generalized minimum variance (GMV) controllers designed using uncorrelated and correlated disturbance models and demonstrates the improvement in performance of a multivariable GMV controller which is designed to accommodate the cross direction correlation in the disturbance compared to the GMV controller that is commonly used in practice, which is based on a model that ignores the effects of correlated disturbances.     

Sub-optimal PID controller settings for FOPDT systems with long dead time

We propose a method for setting up PI and PID controllers based on stable FOPDT process model, where dead-time dynamics is manipulated without approximation. The main idea used is a partial compensation of the system dynamics, which makes possible obtaining simple tuning rules. Remaining unknown controller parameters are determined on the basis of the modulus optimum and the minimum ISE criterions. Besides the performance indices, quality of the settings is also evaluated by the stability margin. Although optimal values of the parameters are valid for the reference tracking problem, a compensation of the disturbance lag that preserves the stability margin is proposed for the disturbance rejection problem.     

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.     

Tuning rules for optimal PID and fractional-order PID controllers

In this paper we present a set of tuning rules for standard (integer-order) PID and fractional-order PID controllers. Based on a first-order-plus-dead-time model of the process, the tuning rules have been devised in order to minimise the integrated absolute error with a constraint on the maximum sensitivity. The achieved performance indexes can also be used for the assessment of the controller performance. Both set-point following and load disturbance rejection tasks are considered. By comparing the results obtained for the two kinds of controllers, it is shown that the use of fractional-order integral action is not advantageous, while the use of a fractional-order derivative action provides a performance improvement.     

Identification for control: Optimal input intended to identify a minimum variance controller

It is well known that the quality of the parameters identified during an identification experiment depends on the applied excitation signal. Prediction error identification using full order parametric models delivers an ellipsoidal region in which the true parameters lie with some prescribed probability level. This ellipsoidal region is determined by the covariance matrix of the parameters. Input design strategies aim at the minimization of some measure of this covariance matrix. We show that it is possible to optimize the input in an identification experiment with respect to a performance cost function of a closed-loop system involving explicitly the dependence of the designed controller on the identified model. In the present contribution we focus on finding the optimal input for the estimation of the parameters of a minimum variance controller, without the intermediate step of first minimizing some measure of the model parameter accuracy. We do this in conjunction with using covariance formulas which are not asymptotic in the model order, which is rather new in the domain of optimal input design. The identification procedure is performed in closed-loop. Besides optimizing the input power spectrum for the identification experiment, we also address the question of optimality of the controller. It is a wide belief that the minimum variance controller should be the optimal choice, since we perform an experiment for designing a minimum variance controller. However, we show that this may not always be the case, but rather depends on the model structure.     

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.     

统计过程监测与反馈控制的整合: 状态空间下的一般方法

将状态空间模型引入统计过程监测,选取状态变量为统计过程控制(SPC)统计量,以解决自相关过程的统计监测问题.在分析常用的最小均方误差(MMSE)和PID控制器的基础上,提出了工业过程控制(EPC)反馈控制器的一般设计方法和基本设计原则.作为演绎示例,给出了两组新型反馈控制器,并与MMSE和PID的反馈调整进行比较,当过程均值发生阶跃扰动时,可进一步提高统计监测效果.     

基于线性二次型高斯基准的多变量预测控制技术经济性能评估

由于受控过程参数的漂移及缺乏维护,令采用的控制器性能逐渐降低,需要做经济性能评估,以确保其最佳运行状态.因为目前最小方差评估算法没有考虑控制器的约束条件,对此我们采用线性二次型高斯(linearquadratic Gaussian,LQG)基准的模型预测控制(model predictive control,MPC)双层优化控制结构,将控制和输出的加权值引入上层经济性能指标,通过求解LQG问题获取控制与输出方差关系的离散点集,进一步拟合Pareto最优曲面方程,建立优化命题并求解最优经济指标及设定值.对延迟焦化加热炉的多变量MPC控制进行了性能评估及分析,证明该方法可以改进控制器设计,提高经济效益.     

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.     

Constrained minimum variance control using hybrid genetic algorithm – An industrial experience

This paper develops a method for minimum variance control of proportional–integral (PI) controllers in the presence of input stochastic noise, the abatement of which is an important issue in many control systems. The underlying objective is to mitigate the effect of input noise in the process output, subject to process inequality constraints. For this purpose, a hybrid genetic algorithm is used. It combines the genetic operations of selection, crossover, and mutation with Newton search. The developed method is applied in an industrial setting to find the optimal controller parameters of different control loops at Falconbridge Smelter in Sudbury, Canada. The optimal parameters significantly improve the performance of the PI controllers.     

工业过程运行的解耦内模控制方法

工业过程运行控制的目的是实现反映过程整体运行性能的工艺指标. 将常规解耦内模控制(Internal model control, IMC)进行推广, 提出了优化过程运行的解耦IMC方法. 通过对广义解耦内模控制器的设计获得了具有高维解耦能力、鲁棒稳定性和抗干扰能力强的回路设定模型. 该模型能够响应系统的各种不确定性和干扰, 对回路设定值进行调整, 通过控制回路的输出跟踪调整后的设定值, 从而实现期望的工艺指标. 磨矿回路运行的解耦IMC设计实例及仿真验证了所提方法的有效性.