On-line time- and frequency-domain identification of unstable processes

An on-line scheme for identifying stable or unstable linear time-invariant processes subject to a class of deterministic and/or stochastic disturbances is proposed. The disturbances are restricted to be the outputs of some unknown linear time-invariant system. The identification scheme consists of: (a) a probing signal input which is a sum of sinusoids (or an exponentially increasing sum of sinusoids when the process is unstable or the disturbances are unbounded), (6) linear time-varying filters which have the properties of asymptotic stability, asymptotic signal tracking and asymptotic noise annihilation, and (c) a parameter update algorithm which uses the filtered input-output data. The frequency response of the process (at the probing signal frequencies) is also estimated. The proposed scheme is verified by simulation.     

Parameter learning for the nonlinear system described by Hammerstein model with output disturbance

A novel parameter learning scheme using multi-signal processing is developed that aims at estimating parameters of the Hammerstein nonlinear model with output disturbance in this paper. The Hammerstein nonlinear model consists of a static nonlinear block and a dynamic linear block, and the multi-signals are devised to estimate separately the nonlinear block parameters and the linear block parameters; the parameter estimation procedure is greatly simplified. Firstly, in view of the input–output data of separable signals, the linear block parameters are computed through correlation analysis method, thereby the influence of output noise is effectively handled. In addition, model error probability density function technology is employed to estimate the nonlinear block parameters with the help of measurable input–output data of random signals, which not only controls the space state distribution of model error but also makes error distribution tends to normal distribution. The simulation results demonstrate that the developed approach obtains high learning accuracy and small modeling error, which verifies the effectiveness of the developed approach.     

Identification Scheme for Fractional Hammerstein Models With the Delayed Haar Wavelet

The parameter identification of a nonlinear Hammerstein-type process is likely to be complex and challenging due to the existence of significant nonlinearity at the input side. In this paper, a new parameter identification strategy for a block-oriented Hammerstein process is proposed using the Haar wavelet operational matrix(HWOM). To determine all the parameters in the Hammerstein model, a special input excitation is utilized to separate the identification problem of the linear subsystem from the complete nonlinear process. During the first test period, a simple step response data is utilized to estimate the linear subsystem dynamics. Then, the overall system response to sinusoidal input is used to estimate nonlinearity in the process. A single-pole fractional order transfer function with time delay is used to model the linear subsystem. In order to reduce the mathematical complexity resulting from the fractional derivatives of signals, a HWOM based algebraic approach is developed. The proposed method is proven to be simple and robust in the presence of measurement noises. The numerical study illustrates the efficiency of the proposed modeling technique through four different nonlinear processes and results are compared with existing methods.     

Supervisory multiple regime control

The objective of this work is to identify a control algorithm that is capable of handling nonlinear behaviour (operating point dependent) witnessed in most industrial processes. To this end, the proposed solution is that of a supervisory multiple model control scheme, SMMC. This work demonstrates that the multiple model methodology can be recast into a Supervisory approach, whereby the supervisor is employed as a selector. This selector (supervisor) identifies the appropriate local-controller from a fixed family set. Unlike other supervisory techniques a multiple model observer (MMO) is proposed for the selection mechanism. Switching between local-controllers is accomplished bumplessly through a multiple model bumpless transfer scheme. Consequently, producing a continuous control signal as the process transverses between different operating regimes. The key issue in this application is the unique interaction between the local-controllers and the supervisor. This interaction is necessary to ensure global stability is maintained at all times, especially during switching. In short, the SMMC scheme enables the implementation of linear control theory, which is well accepted in industry, to standard nonlinear processes. The SMMC approach warrants the control design to extend beyond normal operating conditions that breakdown when standard linear control techniques are applied. The above notion is applied to a pilot-scale binary distillation column. In this example the column's distinct operating points describe the nonlinear behaviour. The results illustrate that as the distillation column shifted between different operating points the SMMC self-regulates accordingly. This self-regulation ensures that global stability and performance are maintained at an optimum. The entire SMMC design was implemented within a PC Windows-NT environment that was interfaced to an industrial DCS system.     

双稳随机共振系统信号调制噪声效应用于弱信号检测

通过对双稳系统随机共振模型的数值分析，得出在双稳系统输出信号中，有一个正弦信号成分和一个表现为维纳过程的噪声成分分别与输入的正弦信号和白噪声相对应。通过选择合适的系统参数，可以减小系统输出中信号和噪声之间的耦合效应。该系统可以大大抑制噪声，并在双稳系统中产生信号调制噪声效应。然后对双稳系统的输出信号作功率谱分析。不但可以辨识出淹没在白噪声中的微弱正弦信号的频率，还可以较精确地估算出微弱正弦信号的幅值。数值仿真表明，双稳系统的信号调制噪声效应可用于多个微弱正弦信号的检测。     

Identification Input Design for Consistent Parameter Estimation of Linear Systems With Binary-Valued Output Observations

Input design is of essential importance in system identification for providing sufficient probing capabilities to guarantee convergence of parameter estimates to their true values. This paper presents conditions on input signals that characterize their probing richness for strongly consistent parameter estimation of linear systems with binary-valued output observations. Necessary and sufficient conditions on periodic signals are derived for sufficient richness. These conditions are further studied under different system configurations including open-loop and feedback systems, and different scenarios of noises including actuator noise, input measurement noise, and output measurement noise. In addition to system parameter estimation, essential properties of identifiability and input conditions are also derived when sensor thresholds or noise distribution functions are unknown. The findings of this paper provide a foundation to study identification of systems that either use binary-valued or quantized sensors or involve communication channels, which mandate quantization of signals.     

基于组合式信号源的Hammerstein-Wiener模型辨识方法

针对含有有色噪声的非线性Hammerstein-Wiener模型,提出一种基于组合式信号源的辨识方法.通过利用可分离信号和随机信号组成的组合信号源实现有色噪声干扰下Hammerstein-Wiener模型各串联模块参数辨识的分离,简化辨识过程.首先,基于可分离信号的输入和输出,采用相关分析方法抑制过程噪声的干扰,辨识输出静态非线性模块和动态线性模块的参数;然后,基于辅助模型技术,利用辅助模型的输出和残差的估计值分别取代辨识模型中的不可测中间变量和噪声变量,推导辅助模型递推增广最小二乘方法,根据随机信号的输入输出数据辨识输入静态非线性模块和噪声模型的参数;最后,通过理论分析和仿真结果表明,所提出方法能够有效辨识有色噪声干扰下的非线性Hammerstein-Wiener模型,具有较好的鲁棒性.     

Stability analysis of a multi-model predictive control algorithm with application to control of chemical reactors

We study a stabilizing multi-model predictive control strategy for controlling nonlinear process at different operating conditions. The control algorithm is a receding horizon scheme with a quasi-infinite horizon objective function that has finite and infinite horizon cost components. The finite horizon cost consists of free input variables that direct the system towards a terminal region which contains the desired operating point. The infinite horizon cost has an upper bound and steers the system to the desired operating point. The system is represented by a sequence of piecewise linear models. Based on the condition of the system states, the sequence of piecewise linear models is updated and the controller’s objective function switches form quasi-infinite to infinite horizon objective function. This results in a hybrid control structure. A recent approach in the analysis of hybrid systems that uses multiple Lyapunov functions is employed in the stability analysis of the closed-loop system. The stabilizing hybrid control strategy is illustrated on two examples and their closed-loop stability properties are studied.     

一种基于边界特征线且特征点可变的二阶非线性离散跟踪微分器及在测速定位系统中的应用

利用状态反推方法确定最速离散二阶系统的线性区域的边界特征线及控制特征线,以相平面上的点及边界曲线、控制线的相对位置按线性规则确定控制量的大小,区分可达区与线性区,并依此构造最速分段线性函数形式的跟踪微分器（Tracking-differentiator,TD）,这种算法可以方便地修改特征点,适应能力强,而且运算中不包含任何根号运算,使得控制综合函数的形式极大简化,有利于工程实现.对正弦信号及方波信号的仿真结果表明了上述结论的合理性.验证了特征点分段线性算法在适当修改特征点后得到的TD,与经典TD以及它的线性近似进行比较,跟踪能力和微分提取能力都得到了较大的提高.应用移动平均算法构成的跟踪微分器组,具有相位补偿功能,适当选取TD参数后,得到了滤波能力强、相位特性良好的滤波器,并应用于基于长定子齿槽检测的永磁电动磁悬浮列车的测速定位系统中.实验结果表明,本文提出的简化TD按相位补偿确定的方案能有效滤除脉冲和扰动等噪声,对过轨道接缝时的畸变信号进行修复,边界容易修改,算法简单有效,实时性强,易于工程实现.     

火电厂沸腾燃烧锅炉微机控制系统

本文在对沸腾燃烧锅炉动态特性作出分析的基础上，通过现场调研提出了符合实际的微机控制方案，现场运行收到满意效果。该控制系统由一台ＴＰ－８０５微型计算机及输入、输出接口、信号转换器等组成。本文主要介绍微机控制系统的研究及投运的基本情况，着重于动态特性分析和控制方案的确定。     

Adaptive Control of Piecewise Linear Systems with State Feedback for Output Tracking

A piecewise linear system consists of a set of linear time‐invariant (LTI) subsystems, with a switching sequence specifying an active subsystem at each time instant. This paper studies the adaptive control problem of single‐input, single‐output (SISO) piecewise linear systems. By employing the knowledge of the time instant indicator functions of system parameter switches, a new controller structure parametrization is proposed for the development of a stable adaptive control scheme with reduced modeling error in the estimation error signal used for parameter adaptive laws. This key feature is achieved by the new control scheme's ability to avoid a major parameter swapping term in the error model, with the help of indicator functions whose knowledge is available in many applications. A direct state feedback model reference adaptive control (MRAC) scheme is presented for such systems to achieve closed‐loop signal boundedness and small output tracking error in the mean square sense, under the usual slow system parameter switching condition. Simulation results on linearized NASA GTM models are presented to demonstrate the effectiveness of the proposed scheme.     

Identification of time-varying pH processes using sinusoidal signals

This paper presents an approach to the identification of time-varying, nonlinear pH processes based on the Wiener model structure. The algorithm produces an on-line estimate of the titration curve, where the shape of this static nonlinearity changes as a result of changes in the weak-species concentration and/or composition of the process feed stream. The identification method is based on the recursive least-squares algorithm, a frequency sampling filter model of the linear dynamics and a polynomial representation of the inverse static nonlinearity. A sinusoidal signal for the control reagent flow rate is used to generate the input-output data along with a method for automatically adjusting the input mean level to ensure that the titration curve is identified in the pH operating region of interest. Experimental results obtained from a pH process are presented to illustrate the performance of the proposed approach. An application of these results to a pH control problem is outlined.     

一种新型的数据采集系统性能量化方法的研究

考虑到数据采集系统的精度对应于系统对信号的不失真传输及系统本身的时间稳定性问题,提出了一种新型的数据采集系统性能量化方法。该方法将数据采集系统看作为一个开环的线性时不变系统,把采集系统本身看作滤波器,其输入为需要采集的信号,输出为采集到的信号,然后利用LMS算法的基本原理反推通道模型参数,最后利用求得的模型参数计算数据采集系统对正弦信号的传输特性,实现了对数据采集系统的性能考核。对系统模型和量化方法的数学仿真结果表明,所采取的量化方法和系统模型精确地反映了数据采集系统的正弦信号的响应,可以作为实际数据采集系统的精度考核手段。     

An iterative Kalman smoother/least-squares algorithm for the identification of delta-ARX models

Additive measurement noise on the output signal is a significant problem in the δ-domain and disrupts parameter estimation of auto-regressive exogenous (ARX) models. This article deals with the identification of δ-domain linear time-invariant models of ARX structure (i.e. driven by known input signals and additive process noise) by using an iterative identification scheme, where the output is also corrupted by additive measurement noise. The identification proceeds by mapping the ARX model into a canonical state-space framework, where the states are the measurement noise-free values of the underlying variables. A consequence of this mapping is that the original parameter estimation task becomes one of both a state and parameter estimation problem. The algorithm steps between state estimation using a Kalman smoother and parameter estimation using least squares. This approach is advantageous as it avoids directly differencing the noise-corrupted ‘raw’ signals for use in the estimation phase and uses different techniques to the common parametric low-pass filters in the literature. Results of the algorithm applied to a simulation test problem as well as a real-world problem are given, and show that the algorithm converges quite rapidly and with accurate results.     

Robust H-infinity control of uncertain stochastic time-delay linear repetitive processes

Repetitive processes are a distinct class of 2D systems of both theoretic and practical interest. The robust H-infinity control problem for uncertain stochastic time-delay linear continuous repetitive processes is investigated in this paper. First, sufficient conditions are proposed in terms of stochastic Lyapunov stability theory, Itˆo differential rule and linear matrix inequality technology. The corresponding controller design is then cast into a convex optimization problem. Attention is focused on constructing an admissible controller, which guarantees that the closed-loop repetitive processes are mean-square asymptotically stable and have a prespecified H-infinity performance γ with respect to all energy-bounded input signals. A numerical example illustrates the effectiveness of the proposed design scheme.     

Discrete model reference adaptive control with an augmented error signal

A method is developed for designing discrete model reference adaptive control systems when one has access to only the plant's input and output signals. Controllers for single-input, single-output, nonlinear, nonautonomous plants are developed via Lyapunov's second method. The augmented error signal method is employed to ensure that the normally used true error signal approaches zero asymptotically without requiring anticipative values of the plant output signal. Such anticipative signals are replaced by others easily obtained from low pass digital filters operating on the plant's input and output signals.     

具有输入输出约束的无人直升机预设性能安全跟踪控制

针对无人直升机姿态与高度系统存在未知外部干扰、输入饱和、姿态与高度约束等问题, 本文提出一种具 有输入输出约束的预设性能安全跟踪控制方法. 首先, 针对无人直升机的姿态与高度约束, 通过设计一类边界保护 算法, 构建了新的安全期望跟踪信号. 为了保证系统对于安全期望跟踪信号的跟踪性能, 将预设性能函数与边界保 护算法进行结合, 并对跟踪误差进行转换. 针对系统的输入饱和现象, 使用Sigmoid函数进行逼近; 同时, 针对饱和函 数的逼近误差与未知外部干扰构成的复合干扰, 采用参数自适应方法对其上界进行逼近. 然后, 结合反步控制方法 设计了安全跟踪控制器, 并通过Lyapunov稳定性理论证明了闭环系统所有信号的收敛性, 保证了无人直升机的安全 跟踪性能. 最终, 通过数值仿真验证了所提控制方法的有效性.     

Sinusoidal model-based analysis and classification of stressed speech

In this paper, a sinusoidal model has been proposed for characterization and classification of different stress classes (emotions) in a speech signal. Frequency, amplitude and phase features of the sinusoidal model are analyzed and used as input features to a stressed speech recognition system. The performances of sinusoidal model features are evaluated for recognition of different stress classes with a vector-quantization classifier and a hidden Markov model classifier. To find the effectiveness of these features for recognition of different emotions in different languages, speech signals are recorded and tested in two languages, Telugu (an Indian language) and English. Average stressed speech index values are proposed for comparing differences between stress classes in a speech signal. Results show that sinusoidal model features are successful in characterizing different stress classes in a speech signal. Sinusoidal features perform better compared to the linear prediction and cepstral features in recognizing the emotions in a speech signal.     

Stability analysis of periodic orbit of an adaptive notch filter for frequency estimation of a periodic signal

Online frequency estimation of a sinusoidal signal is a classical problem and has many practical applications. Recently an adaptive notch filter (ANF) with global convergence property has been developed for frequency estimation of a pure sinusoidal signal. This paper addresses a modified ANF structure that can estimate the fundamental frequency of any periodic signal including pure sinusoidal signals. To prove the stability of the modified ANF, the paper introduces a new theorem that shows for any periodic signal, there exists a locally asymptotically stable periodic orbit of this ANF by which the frequency estimation becomes feasible. This alternative stability proof is simple and uses widely known mathematical tools, and therefore alleviates the problem complexity even when the input signal is a pure sinusoidal signal. A further contribution of this paper is obtaining a necessary and sufficient condition in terms of design parameters for local asymptotical stability of the modified ANF. This condition, obtained from the numerical study of Floquet multipliers of a linear time-varying periodic system, provides a strict stability region in the modified ANF design parameters space.     

Probing signals for model reference identification

This paper examines certain properties of probing signals employed in a model reference identification procedure which guarantee identification of the parameters of a linear multivariable system. The property of persistent excitation is examined with respect to a new class of (persistently spanning) signals. In particular, this class of signals includes many (periodic or almost periodic) signals which have previously been considered as effective probing signals, The results yield concrete guidelines useful in the practical design of probing signals.