传递函数阵递阶随机梯度辨识方法的收敛性分析

阐述了递阶辨识原理,提出了传递函数阵模型参数的递阶随机梯度（HSG）辨识方法,在递阶辨识中,系统参数被分解为参数向量和参数矩阵,前者是由系统的特征多项式的系数构成的,后者是由传递函数矩阵分子多项式的系数构成的,借助于鞅超收敛定理的收敛性分析表明,HSG算法的参数估计误差一致有界;当持续激励条件成立时,参数估计误差一致收敛于零,递阶辨识方法具有计算量小和容易实现等特点。     

Multi-output process identification

In model based control of multivariate processes, it has been common practice to identify a multi-input single-output (MISO) model for each output separately and then combine the individual models into a final MIMO model. If models for all outputs are independently parameterized then this approach is optimal. However, if there are common or correlated parameters among models for different output variables and/or correlated noise, then performing identification on all outputs simultaneously can lead to better and more robust models. In this paper, theoretical justifications for using multi-output identification for a multivariate process are presented and the potential benefits from using them are investigated via simulations on two process examples: a quality control example and an extractive distillation column. The identification of both the parsimonious transfer function models using multivariate prediction error methods, and of non-parsimonious finite impulse response (FIR) models using multivariate statistical regression methods such as partial least squares (PLS2), canonical correlation regression (CCR) and reduced rank regression (RRR) are considered. The multi-output identification results are compared to traditional single-output identification from several points of view: best predictions, closeness of the model to the true process, the precision of the identified models in frequency domain, stability robustness of the resulting model based control system, and multivariate control performance. The multi-output identification methods are shown to be superior to the single-output methods on the basis of almost all the criteria. Improvements in the prediction of individual outputs and in the closeness of the model to the true process are only marginal. The major benefits are in the stability and performance robustness of controllers based on the identified models. In this sense the multi-output identification methods are more ‘control relevant’.     

MODEL‐REFERENCE OUTPUT‐FEEDBACK SLIDING MODE CONTROLLER FOR A CLASS OF MULTIVARIABLE NONLINEAR SYSTEMS

This paper proposes an output‐feedback sliding mode control design for a class of uncertain multivariable plants with nonlinear disturbances. The approach used here is based on the control parameterization employed in model‐reference adaptive control. The disturbances are allowed to be unmatched and to depend not only on the plant output but also on its unmeas‐urable state. A less restrictive condition on the uncertainty of the high frequency gain matrix is also obtained.     

Consistency of the extended gradient identification algorithm for multi-input multi-output systems with moving average noises

The consistency of identification algorithms for systems with colored noises is a main topic in system identification. This paper focuses on the extended stochastic gradient (ESG) identification algorithm for the multivariable linear systems with moving average noises. By integrating the noise regression terms and the noise model parameters into the information matrix and the parameter vector, and based on the gradient search principle, the ESG algorithm is presented. The unknown noise terms in the information matrix are replaced with their estimates. The convergence analysis shows that the parameter estimation error converges to zero under a persistent excitation condition. Two simulation examples are given to illustrate the effectiveness of the algorithm.     

Characteristic locus method robustness improvement through optimal static normalizing pre‐compensation

Controlled systems designed by using the characteristic locus method can be very sensitive to small perturbations in the plant input and output at the frequencies where the plant transfer matrix is far from normal. In order to improve the closed‐loop system robustness, previous work proposes the design of a dynamic normalizing pre‐compensator followed by the design of a commutative controller for the pre‐compensated plant. The restriction on its structure and the need for approximation by a stable rational transfer matrix were among the limitations of the dynamic pre‐compensator. This paper shows that it suffices to design a static pre‐compensator that makes the pre‐compensated plant as closely as possible to a normal matrix in a frequency band containing the crossover frequency. The pre‐compensator is found by solving an optimization problem, whose solution is obtained directly by computing either a singular value decomposition of a real matrix or the spectral decomposition of a symmetric matrix, depending on whether normalization is to be achieved in one or more frequencies. Numerical examples illustrate the theoretical results of the paper. Copyright © 2009 John Wiley & Sons, Ltd.     

LPV decoupling for control of multivariable systems

This article investigates methods for decoupling multivariable linear parameter varying (LPV) systems and proposes a new interaction measure for decoupled proportional-integral (PI) feedback control design in LPV systems. The proposed approach seeks to benefit the multivariable control of multi-input multi-output (MIMO) systems with variable operating conditions, variable parameters or nonlinear behaviour. This method can improve the tracking performance and reduce the operating conditions variability of such systems with significant coupling in the system dynamics. We design MIMO decoupling feedback LPV controllers to address loop interaction effects. The proposed method uses a parameter-dependent static inversion or SVD decomposition of the system to minimise the effects of the off-diagonal terms in the MIMO system transfer function matrix. A new parameter-dependent interaction measure is introduced based on the SVD decomposition and static inversion which is subsequently utilised for tuning multi-loop PI controller gains. Numerical examples are presented to illustrate the validity of the proposed LPV decoupling methods, as well as the use of the proposed interaction measures for a decoupled multi-loop PI control design.     

Output regulation and internal models—A frequency domain approach

The algebraic regulator problem is formulated and solved in a transfer matrix setting. It is shown that, provided the closed loop system disregarding disturbances is stable, a necessary and sufficient condition for output regulation to take place is that the open loop path consisting of the plant and compensator in cascade, contains a suitably defined internal model of the environment. The disturbance model is more general than the ones used before. The results also generalize earlier results on internal models since they are necessary and sufficient under weaker assumptions. The internal model property is used to construct a compensator which achieves output regulation and internal stability. It is shown that any such compensator can be obtained in two steps: (a) create an internal model of the environment in the forward path and (b) stabilize the system. Our concept of internal model generalize earlier definitions and, unlike most earlier results, is valid even if structural stability (robustness) is not imposed.     

矩阵分解的多变量模型参考自适应控制

研究了基于高频增益矩阵分解的多变量模型参考自适应控制 .为此首先基于矩阵分解构造出新的参数化方程 ,选取必然等价自适应控制律 .然后 ,引入规范化信号和类Lyapunov函数 ,获得了规范化自适应律 .并进一步给出了虚拟规范化信号的有用性质 .最后 ,严格地给出了闭环系统的稳定性和收敛性分析     

实现系统解耦的预补偿阵设计新方法

本文提出一种实现多变量系统解耦的预补偿器常数阵的设计方法,即从传递函数阵G(s) 导出一个复常阵C,通过C求得预补偿阵Kp.文中还论述了这种方法的原理，同时给出了应 用实例,结果令人满意.     

Chattering-free fuzzy variable structure control for multivariable nonlinear systems

In this paper, a fuzzy logic controller (FLC) based variable structure control (VSC) with guaranteed stability for multivariable systems is presented. It is aimed at obtaining an improved performance of nonlinear multivariable systems. The main contribution of this work is firstly developing a generic matrix formulation of the FLC-VSC algorithm for nonlinear multivariable systems, with a special attention to non-zero final state. Secondly, ensuring the global stability of the controlled system. The multivariable nonlinear system is represented by T-S fuzzy model. The identification of the T-S model parameters has been improved using the well known weighting parameters approach to optimize local and global approximation and modeling capability of T-S fuzzy model. The main problem encountered is that T-S identification method cannot be applied when the membership functions (MFs) are overlapped by pairs. This in turn restricts the application of the T-S method because this type of membership function has been widely used in control applications. In order to overcome the chattering problem a switching function is added as an additional fuzzy variable and will be introduced in the premise part of the fuzzy rules together with the state variables. A two-link robot system and a mixing thermal system are chosen to evaluate the robustness, effectiveness, accuracy and remarkable performance of proposed FLC-VSC method.     

A neurofuzzy scheme to on-line identification in an adaptive–predictive control

A neurofuzzy scheme has been designed to carry out on-line identification, with the aim of being used in an adaptive–predictive dynamic matrix control (DMC) of unconstrained nonlinear systems represented by a transfer function with varying parameters. This scheme supplies to the DMC controller the linear model and the nonlinear output predictions at each sample instant, and is composed of two blocks. The first one makes use of a fuzzy partition of the external variable universe of discourse, which smoothly commutes between several linear models. In the second block, a recurrent linear neuron with interpretable weights performs the identification of the models by means of supervised learning. The resulting identifier has several main advantages: interpretability, learning speed, and robustness against catastrophic forgetting. The proposed controller has been tested both on simulation and on a real laboratory plant, showing a good performance.     

Diagonal dominance for multivariable nyquist array methods using function minimization

A new method of achieving diagonal dominance for Nyquist array design methods is presented. The technique utilizes a conjugate direction function minimization algorithm to obtain dominance over a specified frequency range by minimizing the ratio of the moduli of the off-diagonal terms to the moduli of the diagonal terms of the appropriate open loop transfer matrix. The new dominance algorithm is easily implemented in either a batch or interactive computer mode and will yield dominant compensators when alternative methods fail. Several concepts new to the Nyquist array methods are also presented. The proposed method is applied to the control system design for a sixteenth order state model of the Pratt-Whitney F-100 turbofan engine with three inputs.     

Stable LPV realisation of the Smith predictor

The paper is concerned with the control of a linear plant with an output delay. As is known, when the plant parameters do not vary in time, the transfer function approach can be used to find a high-performing controller with the Smith-predictor structure. Such an approach in the domain of the Laplace transform is not directly applicable in the time-variant case. Nevertheless, it is shown that the transfer function of the Smith controller valid for constant values of the parameters can be realised in such a way that closed-loop stability, as well as point-wise optimal performance, is ensured also when the parameters vary with time. The suggested technique is applied to the control of a heat exchanger whose varying parameters include a measurement delay.     

全局收敛的鲁棒极点配置自校正控制算法

提出了一种可消除确定性扰动影响的鲁棒极点配置自适应控制器的设计方法.这种方法可以直接获得控制器参数,无需求解Diophantine方程,也不需要辨识多余的辅助参数和进行参数分离,而且根据内模原理可以消除未知确定性扰动的影响,实现对参考输入的稳态无误差跟踪.给出了所提算法的全局收敛性证明,并通过仿真实验验证了算法的有效性.     

Design of pole-placement compensators for multivariable systems

The paper describes a two-stage method for the design of dynamic compensators for pole placement in linear multivariable systems. In the first stage, a number of poles are assigned by means of constant output feedback. In the second stage, the assigned poles are preserved and a number of additional poles are placed using dynamic output feedback. The pole placement is achieved using a compensator of lower order than required by the existing methods, since now the compensator has non-unity rank transfer function matrix. In particular, for a compensator of given order, a larger number of poles can be placed using this method compared to the existing methods.     

随机状态空间系统的梯度优化辨识

提出了随机状态空间系统参数的梯度优化辨识方法。通过极小化输出预报误差而获得系统的参数估计。提出了动态选择雅可比矩阵奇异值比率确定参数搜索方向的方法,用以解决因雅可比矩阵的线性相关性引起的算法失效问题。给出了融合参数局部逼近性能信息的辨识算法,并得到了算法收敛速度的解析表达式。数值仿真实验的结果说明了所提出方法的有效性。     

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.     

Brazilian Society of Simulation

Estimation of the parameters of a reducible (inflated common denominator) model for the transfer function matrix of MIMO systems is well known. However, the reduction of the model to the minimal form by pole-zero cancellation is possible only in the noise-free case. This paper presents an algorithm for the estimation of the minimal continuous-time transfer function matrix model. Monte Carlo simulation results are presented for discrete-time and continuous-time models. Least-squares and generalized least-squares methods have been used in both cases. An asymptotic analysis of convergence has also been provided for these models in the noise-free case. The computation times and space complexities of different variants of the algorithm are compared. The results show that in noisy situations, obtaining a discrete-time model by discretizing an estimated continuous-time model may be a viable proposition     

Genetic Tuning of PID Controllers Using a Neural Network Model: A Seesaw Example

When genetic algorithms (GAs) are applied for PID parameter tuning, since the PID parameters are adjusted almost randomly, it is possible that the plant will be damaged due to abrupt changes in PID parameters. To solve this problem, a neural network will be used to model the plant and the genetic tuning procedure will be performed on the neural network instead of the plant. After determining the PID parameters in this off-line manner, these gains are then applied to the plant for on-line control. Moreover, considering that the neural network model may not be accurate enough, a method is also proposed for on-line fine-tuning of PID parameters. To show the validity of the proposed method, a seesaw system that has one input and two outputs will be used for experimental evaluation