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 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.     

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．     

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．     

基于MMTMV方法的多变量时变扰动系统性能评估

工业控制系统性能评估关系到工业生产安全与企业绩效. 工业过程扰动频繁且存在时变特性,多变量时变扰动系统缺少统一有效的性能评估方法. 本文提出了基于多模型混合时变最小方差(Multi-model mixing time-variant minimum variance, MMTMV)的多变量系统性能评估方法. 首先,根据扰动作用起止时间设定混合权重,基于多模型混合的思想利用混合权重与每一时变扰动特性设计多变量MMTMV控制器. 然后,利用多变量MMTMV控制器得出各被控变量输出方差,将多变量MMTMV控制器下被控变量的平均方差作为性能评估的基准. 最后,本文通过在裂解过程和精馏过程中的控制性能评估应用,验证了多变量MMTMV评估方法的有效性.     

Robust Performance Analysis for Structured Linear Time-Varying Perturbations With Bounded Rates-of-Variation

The robust performance analysis problem is considered for linear time-invariant (LTI) systems subject to block-diagonal structured and bounded linear time-varying (LTV) perturbations with specified maximal rates-of-variation. Analysis methods are developed in terms of semidefinite programming for the computation of upper and lower bounds for the optimum robust performance level. The upper bound computation is based on an integral quadratic constraint (IQC) test developed using a generalized version of the so-called swapping lemma. The lower bound computation method employs an extended version of the power distribution theorem together with a generalized version of the Kalman-Yakubovich-Popov (KYP) lemma and serves as a means to assess the conservatism of the computed upper bounds in the case of dynamic LTV perturbations. As corollaries of the underlying result for lower bound computation, it is shown for general block-diagonal uncertainty structures that thefrequency-dependent/constant D-scaling tests are exact for robust performance analysis against arbitrarily slow/fast dynamic LTV perturbations, respectively     

Performance assessment for iterative learning control of batch units

A new method is developed to estimate the minimum variance bounds and the achievable variance bounds for the assessment of the batch control system when the iterative learning control is applied. Unlike continuous processes, the performance assessment of batch processes requires particular attention to both disturbance changes and setpoint changes. Because of the intrinsically dynamic operations and the non-linear behavior of batch processes, the conventional approach of controller assessment cannot be directly applied. In this paper, a linear time-variant system for batch processes is used to derive the performance bounds from the routine operating batch data. The bounds at each time point computed from the deterministic setpoint and the stochastic disturbance for the controlled output variance can help create simple monitoring charts. They are used to track the progress easily in each batch run, to monitor the occurrence of the observable upsets, and to accordingly improve the current performance. The applications are discussed through simulation cases to demonstrate the advantages of the proposed strategies.     

A general theory of linear time-invariant adaptive feedforward systems with harmonic regressors

Establishes necessary and sufficient conditions for an adaptive system with a harmonic regressor (i.e., a regressor comprised exclusively of sinusoidal signals) to admit an exact linear time-invariant (LTI) representation. These conditions are important because a large number of adaptive systems used in practice have sinusoidal regressors, and the stability and performance of such systems having LTI representations can be completely analyzed by well-known methods. The theory is extended to applications where the LTI conditions do not hold, in which case the harmonic adaptive system can be written as the parallel connection of a purely LTI subsystem and a linear time-varying (LTV) subsystem. An explicit upper bound is established on the induced two-norm of the LTV block, which allows systematic treatment using emerging robust control methods applicable to LTI systems with norm-bounded LTV perturbations.     

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.     

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.     

基于极点与输出方差约束相容性分析的状态反馈

研究一类线性随机系统的满意状态反馈,期望闭环系统同时满足给定的圆形极点与输出方差约束,先分析这两类约束指标的相容性,利用线性矩阵不等式（LMI）方法,给出与极点指标相容的输出方差上界（或下界）指标的较好取值范围,然后,对具有相容极点与输出方差指标的控制问题,给出设计理论,特别对输出方差指标是区间的情形提出一种控制设计方法,算例对所得结果及所提设计方法作了说明。     

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,...     

On the adaptive control of a class of systems with random parameters and disturbances

The adaptive control of discrete time parameter linear stochastic systems with random parameters is investigated. It is shown that systems whose (unknown) autoregressive parameters undergo bounded martingale difference disturbances may be stabilized by the application of the so-called Modified Least Squares adaptive control algorithm. Asymptotically, the sample mean square performance criterion is equal to the one step ahead minimum variance control loss (which equals the prediction error variance when the system parameters are known) plus a term which is bounded by a quantity proportional to the square of the bound on the parameter disturbance. This latter term may be interpreted as the increase in the prediction error variance due to the random parameter variation.     

Robust self-tuning control based on discrete-time sliding mode for auto-regressive mathematical model in the presence of unmodelled dynamics

In this paper, we propose a new robust self-tuning control, called the generalized minimum variance αl-equivalent selftuning control (GMVSTC-αl) for the linear timevarying (LTV) systems, which can be described by the discrete-time auto-regressive exogenous (ARX) mathematical model in the presence of unmodelled dynamics. The estimation of the parameters contained in this mathematical model is made on the basis of the proposed modified recursive least squares (m-RLS) parametric estimation algorithm with dead zone and forgetting factor. The stability analysis of the proposed parametric estimation algorithm m-RLS is treated on the basis of a Lyapunov function. A numerical simulation example is used to prove the performances and the effectiveness of the explicit scheme of the proposed robust self-tuning control GMVSTC-αl.     

Persistency of excitation and performance of deterministic learning

Recently, a deterministic learning theory was proposed for locally-accurate identification of nonlinear systems. In this paper, we investigate the performance of deterministic learning, including the learning speed and learning accuracy. By analyzing the convergence properties of a class of linear time-varying (LTV) systems, explicit relations between the persistency of excitation (PE) condition (especially the level of excitation) and the convergence properties of the LTV systems are derived. It is shown that the learning speed increases with the level of excitation and decreases with the upper bound of PE. An optimal learning speed is shown to exist. The learning accuracy also increases with the level of excitation, in particular, when the level of excitation is large enough, locally-accurate learning can be achieved to the desired accuracy, whereas low level of PE may result in the deterioration of the learning performance. This paper reveals that the performance analysis of deterministic learning can be established on the basis of classical results on stability and convergence of adaptive control. Simulation studies are included to illustrate the results.     

An electrical model with equivalent elements in a time-variant environment for an ionic-polymer-metal-composite system

Ionic polymer metal composite (IPMC) is a kind of ionic electroactive polymer (EAP) smart material that can exhibit conspicuous deflection with low external voltages (~ 5 V). It can be cut in various sizes and shapes, and used and applied in robots and artificial muscles with the capability in aquatic operation. An IPMC strip can be modeled as a cantilever beam with a loading distribution on the surface. Nevertheless, the loading distribution is non-uniform due to the imperfect surface conductivity that causes four different imaginary loading distributions employed in our structural model. The difference can be up to 5 times (3:8 mm to 19 mm). In this paper, a novel linear time-variant (LTV) model is introduced and applied to model an IPMC system. This modeling method is different from previous linear time-invariant (LTI) models because the internal environment of IPMC may be unsteady due to mobile cations with water molecules. In addition, the influence of surface conductivity is simulated and proven based on this model. Finally, by applying this novel modeling method, hysteresis that exists in IPMC and affects the relationship between the output deflection and the corresponding input voltage, such as 0:1-, 0:2-, and 0:3-rad/s sinusoidal waves, has been shown and simulated.     

ROBUST LTV FEEDBACK SYNTHESIS FOR SISO NON-LINEAR PLANTS

Given a feedback system with uncertain nonlinear plant, it is required that the plant's output, to a set of command inputs, will satisfy certain specifications, i.e., will be bounded between a maximum response β(t) and a minimum response α(t). A rigorous synthesis technique to solve this problem using an LTV controller is developed. A design example is included, and it is shown that the LTV design has much lower bandwidth as compared to LTI designs. All design steps utilize the well-established QFT technique for LTI SISO uncertain systems. The methodology also suits rejection of disturbances at the plant's input or output, and for output specifications for nonzero initial conditions. © 1997 by John Wiley & Sons, Ltd.     

Finite-time control with H-infinity constraints of linear time-invariant and time-varying systems

This paper presents finite-time control methods with H-infinity constraints for linear time-invariant (LTI) and time-varying (LTV) systems. The basic idea of the proposed approaches is to construct controllers for the LTI and LTV in such a way that a constant quadratic Lyapunov function and a time-varying quadratic Lyapunov function can be used to establish the finite-time stability and the H-infinity performance of the resulting closed-loop systems. It is shown that the control laws can be obtained by solving a set of linear matrix inequalities (LMIs) and Differential Riccati Inequalities (DRIs) that are numerically feasible with commercially available software. Finally, the results are illustrated by application to the design of guidance law for a class of terminal guidance system.     

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.