基于小波分解的非线性系统多模型自适应控制

提出了一种改进的基于小波分解的非线性系统辨识算法,利用小波函数的逼近能力在线辨识被控对象的非线性项.针对基于小波分解的辨识算法缺乏预测能力,提出了根据线性鲁棒自适应控制器提供的当前控制信息预测未来的非线性项值新方法,并结合多模型方法,根据所定义的切换指标自动切换到当前最优控制器.仿真结果表明,改进的基于小波分解的辨识算法能够有效逼近非线性系统,基于小波分解的非线性系统多模型自适应控制方法改善了系统性能,随着系统运行跟踪误差明显减小,说明了该方法的有效性和可行性.     

用B-样条神经网络设计非线性观测器

对线性部分已知、非线性部分未知的一类非线性系统,提出了一种新的状态观测器 的设计方法.首先针对线性部分设计线性观测器,随后在线性观测器中加入非线性补偿项.该 补偿项先由"反卷积"的方式确定,再用B-样条神经网络拟合.对三个非线性系统设计了观测 器,通过与已有的解析方法进行比较,说明了该方法的优越性.     

基于SVR的传感器Hammerstein模型辨识

提出一种基于支持向量回归机的非线性动态传感器Hammerstein模型辨识方法并给出了相关的数学理论及学习算法.在该模型中,用非线性静态子环节和线性动态子环节串联来描述传感器的非线性动态特性.再利用函数展开将模型的非线性传递函数转换为等价的线性中间模型,并通过SVR求取中间模型参数.最后,推导出中间模型参数与传感器Hammerstein模型参数之间的关系,并由该关系实现非线性静态环节和线性动态环节的同时辨识.用实际力传感器动态标定实验数据进行测试,结果表明与常规非线性传感器辨识方法不同,所提方法只需进行一次动态标定实验就能给出非线性动态模型的数学解析表达式.且建立的力传感器Hammerstein模型阶次为4,而线性动态系统模型则需要6阶才能达到相同的精度.因此该研究为传感器非线性动态系统辨识又提供了一种可选方法.     

Identification of Wiener models for dynamic and steady‐state performance with application to solid oxide fuel cell

This work is concerned with identification of Wiener models (a linear dynamic part connected in series with a nonlinear dynamic one). A neural network with one hidden layer is used as the nonlinear block of the model, two network configurations are considered. For model identification three algorithms are described. In the first case model accuracy only in transient conditions is considered, only the dynamic data is used for model training. In the next two algorithms model accuracy in both transient and steady‐state conditions is considered, dynamic and steady‐state data sets are used. The steady‐state model errors are taken into account by an additional term in the minimized cost‐function or by additional inequality constraints. For comparison of discussed algorithms and model structures, identification of a Wiener model of a solid oxide fuel cell (SOFC) process is considered. It is shown that the best results are obtained by the algorithm 2 which minimizes at the same time both dynamic and steady‐state model errors, additional constraints used in the algorithm 3 are computationally quite demanding.     

基于非线性自回归时序模型的振动系统辨识

针对线性和弱非线性振动系统进行了研究,提出采用非线性自回归时序(GNAR)模型进行系统频率辨识和判断系统性或非线性基本特征的方法。首先根据摄动法求解非线性微分方程的理论,论证GNAR模型与线性和弱非线性系统之间的本质联系,推导出GNAR模型系数与线性和非线性系统频率之间的解析关系,然后给出由GNAR模型系数和结构判断系统是否存在非线性,及辨识系统频率和非线性项基本特征的方法。最后,以单自由度线性振动系统和无阻尼Duffing振动系统为算例验证该辨识方法的有效性和准确性。实验结果表明,基于GNAR模型的振动系统基本特征辨识方法具有较好的识别精度,能用于估计系统的动力学特性。     

基于小波变换的非线性广义预测控制

提出了基于小波变换的非线性广义预测控制算法。预测模型采用Hammerstein模型,对于其静态非线性部分采用小波网络来辨识,动态线性部分用最小二乘法来辨识。这种辨识方法比传统的多项式拟合的模型误差要小得多。基于这种预测模型广义预测控制器弥补了传统广义预测控制的模型失配问题。以CSTR为例对所设计的控制器进行仿真研究,结果表明控制器能够取得良好的控制效果。     

Correlation analysis based MIMO neuro-fuzzy Hammerstein model with noises

A novel identification algorithm for neuro-fuzzy based MIMO Hammerstein system with noises by using the correlation analysis method is presented in this paper. A special test signal that contains independent separable signals and uniformly random multi-step signal is adopted to identify the MIMO Hammerstein system, resulting in the identification problem of the linear model separated from that of nonlinear part. As a result, it can circumvent the problem of initialization and convergence of the model parameters encountered by the existing iterative algorithms used for identification of MIMO Hammerstein model. Moreover, least square method based parameter identification algorithms of dynamic linear part and static nonlinear part are proposed to avoid the influence of noise. Examples are used to illustrate the effectiveness of the proposed method.     

Maximum likelihood‐based gradient estimation for multivariable nonlinear systems using the multiinnovation identification theory

This article considers the identification problems of multivariable input nonlinear systems with unmeasured disturbances. For the identification difficulty caused by the crossproducts between the parameters of the linear block and the nonlinear block, the key term separation technique is adopted to separate the parameters of the nonlinear block from the parameters of the linear block. By combining the model decomposition technique and the hierarchical identification principle, a key term separation‐based maximum likelihood recursive extended stochastic gradient algorithm with reduced computational complexity is presented to estimate all the parameters directly. By introducing the multiinnovation identification theory, a key term separation‐based maximum likelihood multiinnovation extended stochastic gradient algorithm is proposed to improve the parameter estimation accuracy. The simulation results illustrate the effectiveness of the proposed methods.     

Stabilization of a class of nonlinear uncertain ordinary differential equation by parabolic partial differential equation controller

This article is concerned with stabilization for a class of uncertain nonlinear ordinary differential equation (ODE) with dynamic controller governed by linear 1?d heat partial differential equation (PDE). The control input acts at the one boundary of the heat's controller domain and the second boundary injects a Dirichlet term in ODE plant. The main contribution of this article is the use of the recent infinite‐dimensional backstepping design for state feedback stabilization design of coupled PDE‐ODE systems, to stabilize exponentially the nonlinear uncertain systems, under the restrictions that (a) the right‐hand side of the ODE equation has the classical particular form: linear controllable part with an additive nonlinear uncertain function satisfying lower triangular linear growth condition, and (b) the length of the PDE domain has to be restricted. We solve the stabilization problem despite the fact that all known backstepping transformation in the literature cannot decouple the PDE and the ODE subsystems. Such difficulty is due to the presence of a nonlinear uncertain term in the ODE system. This is done by introducing a new globally exponentially stable target system for which the PDE and ODE subsystems are strongly coupled. Finally, an example is given to illustrate the design procedure of the proposed method.     

含有色噪声的神经模糊Hammerstein模型分离辨识

针对实际工业过程中普遍存在的有色噪声,本文提出一种基于递推增广最小二乘算法的神经模糊Hammerstein模型辨识方法,突破了传统的Hammerstein模型迭代分离算法.首先,利用多信号源实现Hammerstein模型中静态非线性环节和动态线性环节的分离,大大简化了辨识过程,提高了串联环节参数的分离精度.其次,利用长除法将噪声模型用有限脉冲响应模型逼近,采用增广递推最小二乘法进行线性环节的参数估计.最后,采用神经模糊模型拟合静态非线性环节,同时设计了神经模糊模型参数的非迭代优化算法,改善了模型的使用范围.该方法保证了模型的预测精度,对含有色噪声的非线性系统具有较好的拟合效果.仿真结果验证了上述方法的有效性.     

Auxiliary model multiinnovation stochastic gradient parameter estimation methods for nonlinear sandwich systems

This article studies the identification problem of the nonlinear sandwich systems. For the sandwich system, because there are inner variables which cannot be measured in the information vector of the identification models, it is difficult to identify the nonlinear sandwich systems. In order to overcome the difficulty, an auxiliary model is built to predict the estimates of inner variables by means of the output of the auxiliary model. For the purpose of employing the real‐time observed data, a cost function with dynamical data is constructed to capture on‐line information of the nonlinear sandwich system. On this basis, an auxiliary model stochastic gradient identification approach is proposed based on the gradient optimization. Moreover, an auxiliary model multiinnovation stochastic gradient estimation method is developed, which tends to enhance estimation accuracy by introducing more observed data dynamically. The numerical simulation is provided and the simulation results show that the proposed auxiliary model identification method is effective for the nonlinear sandwich systems.     

A nonlinear state‐feedback state‐feedforward tracking control strategy for a boiler‐turbine unit

A boiler‐turbine unit is a primary module for coal‐fired power plants, and an effective automatic control system is needed for the boiler‐turbine unit to track the load changes with the drum water level kept within an acceptable range. The aim of this paper is to develop a nonlinear tracking controller for the Bell‐Åström boiler‐turbine unit. A Takagi‐Sugeno fuzzy control system is introduced for the nonlinear modeling of the Bell‐Åström boiler‐turbine unit. Based on the Takagi‐Sugeno fuzzy models, a nonlinear tracking controller is developed, and the proposed control law is comprised of a state‐feedforward term and a state‐feedback term. The stability of the closed‐loop control system is analyzed on the basis of Lyapunov stability theory via the linear matrix inequality approach and Schur complement. Moreover, model uncertainties are also considered, and it is proved that with the proposed control law the tracking error converges to zero. To assess the performance of the proposed nonlinear state‐feedback state‐feedforward control strategy, a nonlinear model predictive control strategy and a linear strategy are presented as comparisons. The effectiveness and the advantages of the proposed nonlinear state‐feedback state‐feedforward control strategy are demonstrated by simulations.     

基于α阶逆的大时滞非线性动态矩阵控制

针对一类大时滞非线性系统,提出了基于α阶逆的动态矩阵控制新方法.该方法采用BP神经网络辨识逼近原非线性系统的α阶逆系统,并与原系统串联复合组成伪线性系统;采用基于线性系统的动态矩阵预测控制方法设计系统附加控制器.在系统存在建模误差、存在扰动和模型参数发生较大变化等情况下,采用该控制方法依然具有很好的动、静态性能和很强的鲁棒性.给出了详细的设计原理和步骤,并通过大量的仿真分析与已有的大时滞非线性系统内模控制研究结果进行了比较:内模控制依赖于系统模型,当模型出现严重失配的情况下,系统性能变坏,而采用提出的方法则不依赖系统精确的数学模型,计算量小,简化了非线性系统的设计;研究与仿真结果证明了所提控制方法的有效性.     

一类非线性离散时间动态系统的交替辨识算法及应用

表征产品在工业过程加工的质量、效率、成本、能耗或物耗等的运行指标与过程控制系统的输出密切相关,它们之间的动态模型往往机理不清,具有强非线性,难以用精确数学模型描述,但运行指标的预报对运行操作具有重要意义.本文利用工业过程在工作点附近工作的特点,将过程控制系统的输出与运行指标之间的动态模型描述成线性模型与高阶非线性项即未建模动态组成,对线性模型以及未建模动态提出了一种由改进的投影算法与未建模动态估计算法组成的交替辨识算法.最后,通过数值仿真实验和电熔镁炉的真实数据进行功率预报实验,实验结果表明了所提方法的有效性.     

Recursive identification for dynamic systems with backlash

A recursive algorithm for identification of nonlinear dynamic systems with backlash is proposed in this paper. In this method, the backlash, which is a non‐smooth function, is decomposed into a combination of a group of piecewise linearized models so that all the parameters of the backlash can be estimated separately. Moreover, the model of the backlash is embedded into a Hammerstein‐type model. Thus, a pseudo‐Hammerstein model with backlash is constructed. The estimation of the parameters for such a non‐smooth nonlinear system can be implemented through a so‐called recursive general identification algorithm (RGIA). Then, the corresponding convergence analysis of the RGIA for the model with backlash is also investigated. After that, two examples are presented to show the performance of the proposed method. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Continuous-time Wiener system identification

A continuous-time Wiener system is identified. The system consists of a linear dynamic subsystem and a memoryless nonlinear one connected in a cascade. The input signal is a stationary white Gaussian random process. The system is disturbed by stationary white random Gaussian noise. Both subsystems are identified from input-output observations taken at the input and output of the whole system. The a priori information is very small and, therefore, resulting identification problems are nonparametric. The impulse impulse of the linear part is recovered by a correlation method, while the nonlinear characteristic is estimated with the help of the nonparametric kernel regression method. The authors prove convergence of the proposed identification algorithms and examine their convergence rates     

Fractional‐Order Dynamic Output Feedback Sliding Mode Control Design for Robust Stabilization of Uncertain Fractional‐Order Nonlinear Systems

A robust fractional‐order dynamic output feedback sliding mode control (DOF‐SMC) technique is introduced in this paper for uncertain fractional‐order nonlinear systems. The control law consists of two parts: a linear part and a nonlinear part. The former is generated by the fractional‐order dynamics of the controller and the latter is related to the switching control component. The proposed DOF‐SMC ensures the asymptotical stability of the fractional‐order closed‐loop system whilst it is guaranteed that the system states hit the switching manifold in finite time. Finally, numerical simulation results are presented to illustrate the effectiveness of the proposed method.     

Asymptotic rejection of unknown sinusoidal disturbances in nonlinear systems

This paper deals with global disturbance rejection of nonlinear systems. The disturbance is assumed to be sinusoidal with completely unknown phases, amplitude, and frequencies, but the number of distinct frequencies or the order of the corresponding unknown linear exosystem is known. Different from the common structural assumptions of nonlinear systems needed in literature for disturbance rejection of nonlinear systems, the proposed method only requires the information of control design with a known Lyapunov function when the system is disturbance-free, and a mild assumption needed for internal model design. The proposed disturbance rejection algorithm extends complete global rejection of unknown sinusoidal disturbances for nonlinear dynamic systems beyond the common nonlinear models such as the strict feedback forms and the output feedback forms.