Designs and analyses of various fuzzy controllers with region‐wise linear PID subcontrollers

To reduce the complexity of PID‐like fuzzy controllers with three inputs, designs and analyses of various fuzzy controllers with region‐wise linear PID subcontrollers are presented in this paper. The proposed region‐wise linear PID subcontrollers are composed of one dimensional fuzzy mechanism. And the triangular‐type membership functions are adopted for the input variables of the fuzzy controllers. All the possible structures of fuzzy controllers with region‐wise linear PID subcontrollers are discussed. According to the number of one‐dimensional fuzzy mechanisms included in the structure of the fuzzy controllers, the fuzzy controllers are classified into three main categories. An algorithm is provided to construct effective fuzzy controllers with lowest complexity among all the possible structures. Also, the properties of various designs of fuzzy controllers with region‐wise linear PID subcontrollers are compared. The simulation results are included to demonstrate the performances of three basic types of proposed fuzzy controllers with the linear, nonlinear, and delayed plants. © 2001 John Wiley & Sons, Inc.     

基于状态反馈的一类非线性系统动态输出反馈镇定

针对一类具有线性不可测量状态的非线性系统,基于状态反馈稳定控制器,利用不变流形和滑模变结构控制技术设计了动态输出反馈镇定控制器.这类控制器的结构类似于系统的状态反馈稳定控制器,在较简单的假定条件下,能够保证被控系统的状态得到渐近镇定.仿真算例表明该动态输出反馈控制器具有较强的镇定能力.     

Distributed optimal control of multiple systems

This article considers distributed optimal control of multiple linear systems. Distributed approximately optimal controllers are proposed for each system with the aid of communications between systems. The proposed controllers make the states of the closed-loop systems exponentially converge to the states of the closed-loop systems with the centralised optimal controllers if the communication digraph is strongly connected. If the communication digraph is switching and there are communication delays, the proposed controllers also make the states of the closed-loop systems exponentially converge to the states of the closed-loop systems with the centralised optimal controllers. Simulation results show effectiveness of the proposed controllers.     

一类不确定广义系统的分散容错控制

讨论一类不确定广义系统分散容错控制器设计问题.首先利用线性矩阵不等式(LMI)设计分散状态反馈控制器,使得广义系统执行器未出现故障时渐近稳定;接着针对广义系统的部分执行器出现故障的情况设计分散状态反馈控制器,使得闭环广义系统渐近稳定;进而利用LMI设计广义系统在分散状态反馈作用下具有完整性的容错控制器;同时对传感器故障情形设计了广义系统在分散输出反馈作用下具有完整性的容错控制器,得到了不确定广义系统关于执行器和传感器的分散容错控制器设计的方法.将所设计的控制器用于实际电子网络系统,验证了所提出方法的有效性.     

Designing fuzzy controllers from a variable structures standpoint

A procedure is presented for designing fuzzy controllers based upon variable structures techniques. Three such controllers are presented: the fuzzy equivalents of sliding-mode controllers, saturating controllers, and tanh controllers. By using an approach based upon variables structures (VSS) techniques, the stability of each of these controllers is assured. By using a sliding surface, the order of the rule base is reduced to size r×m, where r is the number of inputs and m is the number of fuzzification levels. This combination makes the proposed design procedure able to generate simple controllers with guaranteed stability properties. To illustrate the proposed design procedure, fuzzy controllers are designed for a ball-and-beam system. It is demonstrated that in spite of this system being a fourth-order unstable system, the proposed design procedure results in simple stable fuzzy controllers     

复合控制一种简便模糊切换方法

针对常见的FUZZY—PI和FUZZY-PID等复合控制常规切换的缺陷，提出一种简便的基于偏差量的模糊切换方法，仿真结果表明其性能优丁一般常规切换的复合控制。     

Neurofuzzy network based self-tuning control with offset eliminating

The design of nonlinear controllers involves first selecting the input and then determining the nonlinear functions for the controllers. Since systems described by smooth nonlinear functions can be approximated by linear models in the neighbourhood of the selected operating points, the input of the nonlinear controller at these operating points can be chosen to be identical to those of the local linear controllers. Following this approach, it is proposed that the input of the nonlinear controller are similarly chosen, and that the local linear controllers are designed based on the integrating and k-incremental suboptimal control laws for their ability to remove offsets. Neurofuzzy networks are used to implement the nonlinear controllers for their ability to approximate nonlinear functions with arbitrary accuracy, and to be trained from experimental data. These nonlinear controllers are referred to as neurofuzzy controllers for convenience. As the integrating and k-incremental control laws have also been applied to implement self-tuning controllers, the proposed neurofuzzy controllers can also be interpreted as self-tuning nonlinear controllers. The training target for the neurofuzzy controllers is derived, and online training of the neurofuzzy controllers using a simplified recursive least squares (SRLS) method is presented. It is shown that using the SRLS method, computing time to train the neurofuzzy controllers can be drastically reduced and the ability to track varying dynamics improved. The performance of the neurofuzzy controllers and their ability to remove offsets are demonstrated by two simulation examples involving a linear and a nonlinear system, and a case study involving the control of the drum water level in the boiler of a power generation system.     

The hierarchical expert tuning of PID controllers using tools ofsoft computing

We present soft computing-based results pertaining to the hierarchical tuning process of PID controllers located within the control loop of a class of nonlinear systems. The results are compared with PID controllers implemented either in a stand alone scheme or as a part of conventional gain scheduling structure. This work is motivated by the increasing need in the industry to design highly reliable and efficient controllers for dealing with regulation and tracking capabilities of complex processes characterized by nonlinearities and possibly time varying parameters. The soft computing-based controllers proposed are hybrid in nature in that they integrate within a well-defined hierarchical structure the benefits of hard algorithmic controllers with those having supervisory capabilities. The controllers proposed also have the distinct features of learning and auto-tuning without the need for tedious and computationally extensive online systems identification schemes.     

一种三对角结构非线性系统的稳定性及其应用

针对非线性系统的分析及综合问题, 提出了一种状态渐近稳定的三对角结构非线性系统, 并给出其应用--设计镇定控制器使原系统变换成该类三对角结构系统. 对移动机器人跟踪控制的仿真说明这种设计方法的有效性.     

常见模糊蕴涵算子的模糊系统及其响应函数

详细讨论了较常见的21种模糊蕴涵算子构成的模糊控制器及其响应函数.主要结果是,异常蕴涵算子模糊控制算法都可归结为某种插值方法,它们相应的模糊控制器均具有函数逼近的泛性且彼此等效;而正常蕴涵算子(包括正规蕴涵算子的导出算子)模糊控制算法均非插值方法,其模糊控制器都不具有函数逼近的泛性,除Zadeh蕴涵算子外,这些正常蕴涵算子的模糊控制器均只具备阶跃输出功能且在一定意义下相互等效.     

Modelling and motion control of a mechatronic system using BGM with intelligent controllers

In this research paper, a mechatronics system such as a pan tilt platform (PTP) has been considered for motion control under intelligent controllers. A proportional-derivative (PD) controller is considered for comparison of results obtained from fuzzy and hybrid controllers. The trajectory following performance of the mechatronics system is found against these controllers. The results of simulations show that hybrid fuzzy controller reduce the tracking error effectively in lesser settling time. The intelligent controllers require knowledge base of error and derivative of error to compensate the PTP dynamics. The intelligent controllers have similar trends as the PD controllers and compensated both electrical and mechanical dynamics. The PD controller requires position measurement. The intelligent controllers have knowledge base consisting of position and velocity data. Thus intelligent controllers have position measurement along with knowledge base for position control system. The best results were achieved with hybrid fuzzy controllers. They meet the desired specifications.     

Genetic synthesis of production-control systems for unreliable manufacturing systems with variable demands

The control of manufacturing systems with variable demands has attracted much research attention over the years. However, only limited results have been obtained due to the difficulty of this production-control problem. In this paper, genetically optimized short-run hedging points are used to construct gain-scheduled adaptive controllers for unreliable manufacturing systems with variable demands. The performance of such adaptive controllers is illustrated for unreliable systems subjected to piecewise-constant demands. It is demonstrated that the performance of these adaptive controllers is superior, in general, to that of genetically optimized non-adaptive controllers. However, such gain-scheduled adaptive controllers are designed for variable demands that are piecewise-constant. Therefore, in order to deal with more general classes of variable demands, a genetic rule-induction design methodology is used to synthesize robust fuzzy-logic controllers to provide automatic closed-loop control for unreliable manufacturing systems. Such robust fuzzy-logic controllers are shown to provide effective control for unreliable manufacturing systems with various kinds of variable demands.     

Static state feedback control of asynchronous sequential machines

Static controllers, which consist of logical gates with no memory elements, form the simplest class of controllers for asynchronous sequential machines. This paper presents necessary and sufficient conditions for the existence of static state feedback controllers that control a given asynchronous sequential machine so as to match a specified model. The process of designing static state feedback controllers is described.     

Interpolation of observer state feedback controllers for gainscheduling

The authors propose a method of interpolating linear time-invariant controllers with observer state feedback structure in order to generate a continuously varying family of controllers that stabilizes a family of linear plants. Gain scheduling is a motivation for this work, and the interpolation method yields guidelines for the design of gain scheduled controllers. The method is illustrated with the design of a missile autopilot using loop-shaping H-infinity controllers     

Optimal linear stochastic systems with independent controllers

The problem of synthesis of optimal controllers for linear stochastic systems with independent control channels is considered. In the considered systems two independent controllers with independent measurement devices are used. The equations for optimal cost function, covariance matrix of the state estimation error and for the controlled system output are derived. It is shown that the application of a well-known separation principle or certainty equivalence principle results in controllers which are not optimal and which can be far from the optimality. It is also shown that improvement of the estimation accuracy by means of manipulation of the controller parameters can significantly improve the control performance as a whole. The numerical examples of calculation of the optimal independent controllers are given to demonstrate the obtained theoretical results and superiorities over controllers based on the separation principle. It is also demonstrated that the optimal controllers have smaller control gains for the control loops with larger observation noises, which can be characterized as cautious properties of the controllers.     

非标准H∞控制问题的降价控制器

研究了具有无穷远零点的非标准H∞控制问题的降价控制器及无穷远零点所对应的特征 空间与H∞控制器族之间的关系.当广义对象满足一定条件时,可通过选取控制器族中的自 由参量函数,构造低于广义对象阶次的降价H∞控制器;还讨论了降价H∞控制器的参量化问 题,从而得到了两个降价的H∞控制器族.     

安全的混成系统神经网络控制器生成与验证

控制器生成是混成系统控制中的重要问题.生成具有安全保证的控制器,关系着混成系统在安全攸关领域的使用.提出了一种为混成系统生成具有安全保证的神经网络控制器的方法.神经网络控制器的安全性由与其同时生成的障碍证书保证.为了生成安全的神经网络控制器,首先确定控制器的网络结构,并基于混成系统构造训练数据集;然后,根据保证控制器安全的障碍证书条件编码神经网络训练时的损失函数.当训练完成后,学习到的神经网络控制器对于训练数据集中的数据是安全的,但对于整个混成系统可能并不安全.为了检验学习到的控制器在整个系统上的安全性,将其安全验证问题转化为一组混合整数规划问题,并使用数值优化器求解,以得到形式化保证的结果.工作实现了安全神经网络控制器生成工具SafeNC,并评估了它在8个基准系统上的性能.实验结果表明:SafeNC可以生成包含6个隐藏层的具有1 804个神经元的安全神经网络控制器;同时,与现有方法相比, SafeNC可为更复杂的系统生成安全的神经网络控制器,更有效且更具扩展性.     

Optimization of interval type-2 fuzzy logic controllers using evolutionary algorithms

A method for designing optimal interval type-2 fuzzy logic controllers using evolutionary algorithms is presented in this paper. Interval type-2 fuzzy controllers can outperform conventional type-1 fuzzy controllers when the problem has a high degree of uncertainty. However, designing interval type-2 fuzzy controllers is more difficult because there are more parameters involved. In this paper, interval type-2 fuzzy systems are approximated with the average of two type-1 fuzzy systems, which has been shown to give good results in control if the type-1 fuzzy systems can be obtained appropriately. An evolutionary algorithm is applied to find the optimal interval type-2 fuzzy system as mentioned above. The human evolutionary model is applied for optimizing the interval type-2 fuzzy controller for a particular non-linear plant and results are compared against an optimal type-1 fuzzy controller. A comparative study of simulation results of the type-2 and type-1 fuzzy controllers, under different noise levels, is also presented. Simulation results show that interval type-2 fuzzy controllers obtained with the evolutionary algorithm outperform type-1 fuzzy controllers.     

Periodic sampling: maximising the sampling period

The process of periodic sampling is investigated for a class of nonlinear systems. The objective is to achieve the longest sampling period that is compatible with a specified error bound. It is shown that there are robust optimal controllers that achieve this objective. It is also shown that the performance of such optimal controllers can be approximated by bang-bang controllers – controllers that are relatively easy to design and implement.     

Smith predictor based robust fractional order control: Application to water distribution in a main irrigation canal pool

This paper proposes a new methodology to design fractional integral controllers combined with Smith predictors, which are robust to high frequency model changes. In particular, special attention is paid to time delay changes. These controllers show also less sensitivity to high frequency measurement noise and disturbances than PI or PID controllers. This methodology is applied to design controllers for water distribution in a main irrigation canal pool. Simulated results of standard PI and PID controllers plus a Smith predictor, and the controller developed in this paper are compared when applied to the dynamical model of a real main irrigation canal pool showing that our controller exhibits better and more robust features than these. Moreover our controller is compared with other more complex control techniques as predictive control and robust H_∞ controllers, exhibiting better or similar performances than these.