Statistic PID tracking control for non-Gaussian stochastic systems based on T-S fuzzy model

A new robust proportional-integral-derivative （PID） tracking control framework is considered for stochastic systems with non-Gaussian variable based on B-spline neural network approximation and T-S fuzzy model identification. The tracked object is the statistical information of a given target probability density function （PDF）, rather than a deterministic signal. Following B-spline approximation to the integrated performance function, the concerned problem is transferred into the tracking of given weights. Different from the previous related works, the time delay T-S fuzzy models with the exogenous disturbances are applied to identify the nonlinear weighting dynamics. Meanwhile, the generalized PID controller structure and the improved convex linear matrix inequalities （LMI） algorithms are proposed to fulfil the tracking problem. Furthermore, in order to enhance the robust performance, the peak-to-peak measure index is applied to optimize the tracking performance. Simulations are given to demonstrate the efficiency of the proposed approach.     

Fault diagnosis and fault-tolerant control for non-Gaussian nonlinear stochastic systems via entropy optimisation

ABSTRACT

In this paper, the fault diagnosis (FD) and fault tolerant control (FTC) problems are studied for non-linear stochastic systems with non-Gaussian disturbance and fault. Unlike classical FD algorithms, the minimum entropy FD is adopted to minimise the residual entropy and control the shape of the probability density function (PDF) of the residual signal. The observation error system can be proved to be locally and ultimately bounded in the mean square sense. Since entropy can be used to characteriSe the uncertainty of the tracking error for non-Gaussian stochastic systems, the FTC controller is obtained by minimising the performance function with regard to the entropy of the tracking error in this paper. The PDF of the output tracking error is approximated by the B-spline model. An illustrative example is utilised to demonstrate the effectiveness of the FD and FTC algorithm, and satisfactory results have been obtained.     

Constrained PID tracking control for output PDFs of non‐gaussian stochastic system based on LMIs

This paper presents a new PID tracking control strategy for general non‐Gaussian stochastic systems based on a square root B‐spline model for the output probability density functions (PDFs). Using the B‐spline expansion with modeling errors and the nonlinear weight model with exogenous disturbances, the PDF tracking is transformed to a constrained dynamical tracking control problem for weight vectors. Instead of the non‐convex design algorithms, the generalized PID controller structure and the improved convex linear matrix inequality (LMI) algorithms are proposed to fulfil the PDF tracking problem. Meanwhile, in order to enhance robustness, the robust peak‐to‐peak measure is applied to optimize the tracking performance. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

随机分布系统状态记忆保性能控制的研究

对于连续随机分布控制中的保守性问题,采用平方根B样条逼近建立系统静态模型（输出概率密度函数模型）,利用系统输入和输出概率密度函数权值之间的动态关系建立动态模型,提出状态记忆反馈保性能控制算法,并利用凸优化技术优化算法,通过计算机仿真验证,该算法能够实现系统输出概率密度函数追踪目标概率密度函数,并满足规定的性能指标。     

Constrained discrete-time PI controller design for output PDFs of stochastic systems with time delays

This article presents a new proportional-integral (PI) tracking control strategy for non-Gaussian stochastic systems based on a square root B-spline model for the output probability density functions (PDFs). Following the square root B-spline approximation to the measured output PDF, a non-linear discrete-time dynamical model can be established between the control input and the weights related to the PDFs. It is noted that the PDF tracking is transformed to a constrained dynamical tracking control problem for weight dynamics. For the non-linear discrete-time weight model including time-delay terms and exogenous disturbances, convex linear matrix inequality optimisation algorithms are used to design a generalised PI controller such that stabilisation, state constraint and tracking performance can be guaranteed simultaneously. Furthermore, in order to enhance the robustness, the peak-to-peak measure index is applied to optimise the tracking performance. Simulations are given to demonstrate the efficiency of the proposed approach.     

基于有理平方根逼近的非高斯随机分布系统的故障诊断和容错控制

随机分布系统指的是输入为常规向量而输出为系统输出的概率密度函数所描述的一类随机系统．该类系统控制算法的目标是选择一个控制输入使得系统的实际输出概率密度函数尽可能跟踪一个事先给定的概率密度函数．本文对采用有理平方根B样条逼近其输出概率密度函数的非高斯动态随机分布系统,提出了一种基于非线性自适应观测器的故障诊断方法．该方法可快速有效地诊断出非高斯随机分布系统故障．通过对故障系统的重组,使故障后系统的输出概率密度函数仍能跟踪给定的分布,实现了该随机系统的容错控制,提高了随机系统的可靠性．     

基于遗传优化的模糊PID控制在智能除草中的应用研究*

针对当前智能除草控制系统的非线性、时滞性及喷施精度过低等问题,设计了一种基于超代遗传算法(HG-GA)优化的模糊PID控制方案。在该方案中,针对智能除草装置的特点,设计了对应的模糊PID控制器,并对控制器的各因子进行遗传优化,从而提高系统的控制效果,同时加快了优化速度。实验结果表明这是一种有效的控制策略,尤其是在处理非线性及外部干扰方面有更好的鲁棒性。     

Robust fault diagnosis for non-Gaussian stochastic systems based on the rational square-root approximation model

The task of robust fault detection and diagnosis of stochastic distribution control （SDC） systems with uncertainties is to use the measured input and the system output PDFs to still obtain possible faults information of the system. Using the rational square-root B-spline model to represent the dynamics between the output PDF and the input, in this paper, a robust nonlinear adaptive observer-based fault diagnosis algorithm is presented to diagnose the fault in the dynamic part of such systems with model uncertainties. When certain conditions are satisfied, the weight vector of the rational square-root B-spline model proves to be bounded. Conver- gency analysis is performed for the error dynamic system raised from robust fault detection and fault diagnosis phase. Computer simulations are given to demon- strate the effectiveness of the proposed algorithm.     

Linearized controller design for the output probability density functions of non-Gaussian stochastic systems

1 Introduction There are many practical systems that require the control of the shape of the output probability den- sity function rather than just their mean values and variances. These systems are seen in papermaking processes[1,2], chemical engineering, material science, combustion ?ame distribution systems and food pro- cessing industries. For example, in chemical engineer- ing the control of particle size distribution has al- ways been regarded as an important area of research[3], whilst …     

基于自适应模糊PID控制的太阳光跟踪伺服系统

针对太阳光跟踪伺服系统中传统PID控制过程中的一些问题,通过对自适应模糊PID控制系统的分析,设计了一种双轴跟踪伺服系统自适应模糊PID控制器,同时在Simulink环境中建立了方位角跟踪传动机构仿真模型并完成了仿真。仿真结果表明,太阳光跟踪伺服系统自适应模糊PID控制器较传统PID控制器具有较强的稳定性、适应性与鲁棒性,在太阳光跟踪伺服系统控制领域具有重要的实用价值与应用空间。     

基于模糊自整定PID的主汽温串级控制系统的设计

火电厂主汽温具有大惯性、大迟延和时变特性等特性,采用常规的PID串级控制难以获得满意的控制效果.为此,提出一种基于模糊自整定PID控制器的串级控制系统,该系统将模糊控制、PID控制和串级控制三者有机地相结合,提高了主汽温控制系统的控制品质.仿真结果表明：系统超调量、调节时间和抗干扰能力明显优于常规的PID串级控制.     

Multi-objective control for stochastic model reference systems based on LMI approach and sliding mode control concept

In this article, a multi-objective control u(t) is designed for stochastic model reference systems to achieve the following three objectives simultaneously: the pole placement constraint, H _∞-norm constraint and individual error state variance constraint. Using the invariance property of sliding mode control, the reference model input and the plant error term will disappear on the sliding mode of the error system. By combining the upper bound covariance control theory, pole placement skill and H _∞-norm control theory, a controller, in which the control feedback gain matrix is synthesised utilising linear matrix inequality (LMI) approach, is derived to achieve the above multiple objectives. Furthermore, a practical example for the problem of ship yaw-motion systems is adopted to illustrate the proposed method.     

Feedback control of nonlinear stochastic systems for targeting a specified stationary probability density

In the present paper, an innovative procedure for designing the feedback control of multi-degree-of-freedom (MDOF) nonlinear stochastic systems to target a specified stationary probability density function (SPDF) is proposed based on the technique for obtaining the exact stationary solutions of the dissipated Hamiltonian systems. First, the control problem is formulated as a controlled, dissipated Hamiltonian system together with a target SPDF. Then the controlled forces are split into a conservative part and a dissipative part. The conservative control forces are designed to make the controlled system and the target SPDF have the same Hamiltonian structure (mainly the integrability and resonance). The dissipative control forces are determined so that the target SPDF is the exact stationary solution of the controlled system. Five cases, i.e., non-integrable Hamiltonian systems, integrable and non-resonant Hamiltonian systems, integrable and resonant Hamiltonian systems, partially integrable and non-resonant Hamiltonian systems, and partially integrable and resonant Hamiltonian systems, are treated respectively. A method for proving that the transient solution of the controlled system approaches the target SPDF as t→∞ is introduced. Finally, an example is given to illustrate the efficacy of the proposed design procedure.     

基于模糊PID控制的微型燃气轮机发电系统研究

根据微型燃气轮发电机系统的动态特性,将微型燃气轮机及其电气部分当作一个整体,建立了微型燃气轮机发电系统完整的数学模型,并在转速环加入模糊PID控制器,分析了微型燃气轮机系统孤网带负荷时的动态特性。仿真结果验证了基于模糊PID控制的微型燃气轮机发电系统具有良好的稳定性和灵活性。     

Fault tolerant sliding mode control for T-S fuzzy stochastic time-delay system via a novel sliding mode observer approach

In this paper, a fault estimation and fault-tolerant control problem for a class of T-S fuzzy stochastic time-delay systems with actuator and sensor faults is investigated. A novel sliding mode observer is proposed, which can simultaneously estimate the system states, actuator and sensor faults with good accuracy. Based on the state and actuator fault estimation, a new sliding mode control scheme is developed, which can effectively eliminate the influence of actuator fault. Sufficient conditions for the existence of the proposed observer and fault-tolerant sliding mode controller are provided in terms of linear matrix inequality, and moreover, the reachability of the sliding mode surface can be guaranteed under the proposed control scheme. The propose sliding mode observer and fault-tolerant sliding mode controller can overcome the restrictive assumption that the input matrix of all local modes is the same. Finally, a numerical example is provided to verify the effectiveness of the proposed sliding mode observer and fault-tolerant sliding mode control technique.     

随机部分可积拟哈密顿系统的概率密度追踪控制

目前非线性随机系统的控制方法存在设计复杂,计算成本高,以及缺乏稳定性或收敛性证明等缺点,针对这些问题,本文在作者前期研究的基础上发展了一种全新的针对部分可积的非线性随机系统的反馈控制,使得受控系统输出的稳态概率密度逼近事先给定的目标概率密度,并利用Lyapunov函数法证明受控系统的收敛性.数学仿真结果证明了这种方法的可行性和正确性.     

The PDF shape control of the state variable for a class of stochastic systems

The shape control of probability density function (PDF) is an important subject in stochastic systems. The PDF-shaping control study has ranged from linear systems to non-linear systems. In this paper we present a PDF-shaping control technique which is useful for a class of non-linear stochastic systems. Controlling the PDF shape requires designing a controller to make the state PDF follow the goal PDF; it is actually to determine the gains of the controller. As we know, the stationary PDF of the state variable is equivalent to the solution of the Fokker–Planck–Kolmogorov (FPK) equation arising from the stochastic system driven with Gaussian white noise. After designing the controller, we derive the solution with some parameters to the corresponding FPK equation, and then solve out the parameters in the solution by the linear-least-squares method, therefore obtaining the gains of the controller. Finally, simulation experiments have been carried out to verify the effectiveness of the approach.     

基于模糊PID的防烧伤红外理疗仪温控系统设计

红外理疗仪在疾病的辅助治疗中已经得到了广泛的应用。在红外理疗过程中,对红外辐照强度和辐照时间控制不当,就会造成患者被照射部位发生烧伤。根据患者产生低温烧伤的特点,提出了一种基于模糊PID的温度控制方法,并设计了以PIC16F877A单片机为核心的红外理疗仪温度测控系统。实验表明:该装置能够有效地避免患者被照射部位发生烧伤。     

Predictive functional control based on fuzzy T-S model for HVAC systems temperature control

In heating, ventilating and air-conditioning (HVAC) systems, there exist severe nonlinearity, time-varying nature, disturbances and uncertainties. A new predictive functional control based on Takagi-Sugeno (T-S) fuzzy model was proposed to control HVAC systems. The T-S fuzzy model of stabilized controlled process was obtained using the least squares method, then on the basis of global linear predictive model from T-S fuzzy model, the process was controlled by the predictive functional controller. Especially the feedback regulation part was developed to compensate uncertainties of fuzzy predictive model. Finally simulation test results in HVAC systems control applications showed that the proposed fuzzy model predictive functional control improves tracking effect and robustness. Compared with the conventional PID controller, this control strategy has the advantages of less overshoot and shorter setting time, etc.