Optimized fuzzy PD cascade controller: A comparative analysis and design

In this study, we develop a design methodology for a fuzzy PD cascade controller for a ball & beam system by using particle swarm optimization (PSO). The ball & beam system is a well-known control engineering experimental setup, which consists of servo motor, beam, and ball. This system exhibits a number of interesting and challenging properties when being considered from the control perspective. The ball & beam system determines the position of ball through the control of a servo motor. The displacement change of the position of ball leads to the change of the angle of the beam which determines the position angle of a servo motor. Consequently the variation of the position of the moving ball and the ensuing change of the angle of the beam results in the change of the position angle of a servo motor. We introduce a fuzzy PD cascade controller scheme which consists of the outer (1st) controller and the inner (2nd) controller arranged in a cascaded architecture. Auto-tuning of the parameters of the controller (scaling factors) as well as fuzzy rules of each fuzzy PD controller is realized with the use of the PSO. Moreover the comparative analysis of results of optimization realized by PSO and GA based on SGA (Serial Genetic Algorithms) is discussed from the viewpoint of control performance. The set-point value of the inner controller (the 2nd controller) corresponds to the position angle of a servo motor, and is given as reference value, which enters into the inner controller as the 2nd controller of the two cascaded controllers. The optimization process takes advantage of a rapid convergence of PSO being used here as a generic search mechanism. A detailed comparative analysis carried out from the viewpoint of the performance and the design methodology, is provided for the fuzzy PD cascade controller and the conventional PD cascade controller whose design exploited serial genetic algorithms.     

Synchronization of complex networks with coupling delays via adaptive pinning intermittent control

The problem of exponential synchronization for a class of general complex dynamical networks with nonlinear coupling delays by adaptive pinning periodically intermittent control is considered in this paper. We use the methods of the adaptive control, pinning control and periodically intermittent control. Based on the piecewise Lyapunov stability theory, some less conservative criteria are derived for the global exponential synchronization of the complex dynamical networks with coupling delays. And several corresponding adaptive pinning feedback synchronization controllers are designed. These controllers have strong robustness against the coupling strength and topological structure of the network. Using the delayed nonlinear system as the nodes of the networks, a numerical example of the complex dynamical networks with nonlinear coupling delays is given to demonstrate the effectiveness of the control strategy.     

The design of a fuzzy cascade controller for ball and beam system: A study in optimization with the use of parallel genetic algorithms

In this study, we introduce a design methodology for an optimized fuzzy cascade controller for ball and beam system by exploiting the use of hierarchical fair competition-based genetic algorithm (HFCGA). The ball and beam system is a well-known control engineering experimental setup which consists of servo motor, beam and ball and exhibits a number of interesting and challenging properties when considered from the control perspective. The position of ball is determined through the control of a servo motor. The displacement change of the position of ball requires the change of the angle of the beam which determines the position angle of a servo motor. Consequently, the variation of the position of the moving ball and the ensuing change of the angle of the beam results in the change of the position angle of a servo motor. We introduce the fuzzy cascade controller scheme which consists of the outer (1st) controller and the inner (2nd) controller in a cascaded architecture. Auto-tuning of the parameters of the controller (viz. scaling factors) of each fuzzy controller is realized with the use of the HFCGA. The set-point value of the inner controller (the 2nd controller) corresponds to the position angle of a servo motor, and is given as a reference value which enters into the inner controller as the 2nd controller of the two cascaded controllers. HFCGA is a kind of a parallel genetic algorithm (PGA), which helps alleviate an effect of premature convergence being a potential shortcoming present in conventional genetic algorithms (GAs). A detailed comparative analysis carried out from the viewpoint of the performance and the design methodology, is provided for the fuzzy cascade controller and the conventional PD cascade controller whose design relied on the use of the serial genetic algorithms.     

Bidirectional active control of structures with type-2 fuzzy PD and PID

Proportional-derivative and proportional-integral-derivative (PD/PID) controllers are popular algorithms in structure vibration control. In order to maintain minimum regulation error, the PD/PID control require big proportional and derivative gains. The control performances are not satisfied because of the big uncertainties in the buildings. In this paper, type-2 fuzzy system is applied to compensate the unknown uncertainties, and is combined with the PD/PID control. We prove the stability of these fuzzy PD and PID controllers. The sufficient conditions can be used for choosing the gains of PD/PID. The theory results are verified by a two-storey building prototype. The experimental results validate our analysis.     

板球系统的T-S模糊多变量控制方案

板球系统是一个典型的多变量、非线性控制对象，它是杆球系统的扩展，适合用以 检验各种控制方案．本文介绍了板球系统及其数学模型，就轨迹跟踪问题提出了基于T-S模 型的模糊多变量控制方案，并验证了这种控制方案能使系统全局渐进稳定．仿真实验结果表 明本文所采用的控制方案明显优于传统的PD控制方案．     

航天器近距离相对轨道的滑模控制

基于滑模控制原理,研究了近距离追踪航天器与目标航天器交会对接时,相对运动轨道的控制问题.首先,建立非线性航天器相对运动模型;其次,利用滑模控制原理和分数阶导数的相关性质,设计了整数阶PD控制器和分数阶PD~α控制器;最后,分别运用整数阶和分数阶控制器对未扰和受扰系统实施控制.数值仿真结果表明,整数阶与分数阶控制器均能实现对未扰和受扰系统的控制,验证了方法的有效性.同时发现,在时效性上,分数阶控制器明显优于整数阶控制器;在能效性上,达到相同控制目标时,分数阶控制器的能量消耗大于整数阶控制器.     

基于非线性牵制控制的分数阶混沌网络聚同步

针对分数阶混沌复杂网络,提出一种非线性牵制控制策略实现网络聚同步.根据网络结点的不同属性,只对群间点施加非线性控制,然后基于分数阶系统稳定性理论,给出了实现聚同步的充分条件.数值仿真验证了该聚同步方案的有效性和正确性,同时深入讨论了控制增益和耦合强度等对聚同步的影响.     

Design and implementation of a hybrid fuzzy logic controller for a quadrotor VTOL vehicle

Helicopters have generated considerable interest in both the control community due to their complex dynamics, and in military community because of their advantages over regular aerial vehicles. In this paper, we present the modeling and control of a four rotor vertical take-off and landing (VTOL) unmanned air vehicle known as quadrotor aircraft. This model has been generated using Newton-Euler equations. In order to control the helicopter, classical PD (proportional derivative) and Hybrid Fuzzy PD controllers have been designed. Although fuzzy control of various dynamical systems has been presented in literature, application of this technology to quadrotor helicopter control is quite new. A quadrotor helicopter has nonlinear characteristics where classical control methods are not adequate especially when there are time delays, disturbances and nonlinear vehicle dynamics. On the other hand, Fuzzy control is nonlinear and it is thus suitable for nonlinear system control. Matlab Simulink has been used to test, analyze and compare the performance of the controllers in simulations. For the evaluation of the autonomous flight controllers, some experiments were also performed. For this purpose, an experimental test stand has been designed and manufactured. This study showed that although, both of the classical PD and the Fuzzy PD controllers can control the system properly, the Fuzzy PD controllers performed slightly better than the classical PD controllers, and have benefits such as better disturbance rejection, ease of building the controllers.     

类Chen-Qi混沌系统的固定时间自适应同步控制

类Chen-Qi四维混沌系统的渐近稳定控制的同步误差不能在有限时间内收敛到零,有限时间控制的同步误差收敛到零的状况与初值有关.因此,本文应用固定时间控制技术,设计了自适应控制器和参数估计律,试图使得驱动系统与同类型的参数未知的响应系统在固定时间内达到同步,完成了理论证明.应用数值仿真考察同步误差收敛到零的状况.选取不同参数值,不同状态初值,考察状态时程图、同步误差曲线等.结果表明：混沌运动时,固定时间内同步误差收敛到零的效果较好,与状态初值无关,收敛时间符合理论计算值;周期运动时,固定时间内前三个状态的同步误差收敛到零的效果较好,收敛时间符合理论计算值,但第四个状态的同步误差的收敛时间不符合理论计算值,其原因是系统存在的三次非线性项的不平衡、不匹配.     

多自由度机械臂的饱和输出反馈有限时间同步位置控制EI北大核心CSCD

针对输入受限的多自由度机械臂高精度位置控制问题,本文充分考虑驱动器饱和非线性的影响,提出了多自由度机械臂输出反馈饱和有限时间比例–微分(PD)+同步位置控制策略,应用Lyapunov稳定性理论和几何齐次性技术证明了闭环系统的全局有限时间稳定性.非线性饱和函数的恰当引入,使得所提出的控制器具有清晰明确的上界,可以通过预先选择满足特定条件的控制器参数有效避免驱动器饱和问题;同步控制项的恰当引入,使得所提出的控制器兼顾了多自由度机械臂各轴间的同步协调性,从而获得更快的收敛速度和更好的系统整体性能,满足工程实际对机械臂的高精度要求.本文的数值仿真结果验证了所提出的控制方法的有效性和可行性.     

Synchronization of a class of nonlinear network flow systems

In this paper, we consider the synchronization of a class of nonlinear network flow systems. Motivated by air distribution problem in air conditioning and mechanical ventilation (ACMV) systems, we propose a class of coupled nonlinear multi‐agent systems that can model a wide class of network flow systems, including air flow in ACMV systems, water flow in irrigation systems, traffic flow in transportation systems, and so on. Then we consider the synchronization problem for the class of nonlinear multi‐agent systems and propose cooperative controllers for the system. Based on graph theory, we derive conditions on the initial values of the state and the control input such that synchronization can be achieved. An application to air ventilation is provided to demonstrate the effectiveness of the cooperative controllers. Copyright © 2015 John Wiley & Sons, Ltd.     

Multi machine power system excitation control design via theories of feedback linearization control and nonlinear robust control

The dynamics of a large-scale power system are both nonlinear and interconnected. The equilibrium of such a system is typically unknown and uncertain, and the controllers within are also subject to physical limitations. In this paper, a new application of nonlinear robust control is presented for power system control design. It is assumed that the controllers are designed as a part of generator excitation system design. First, a customized exact feedback linearization scheme is developed for the power system under investigation. This new linearization scheme allows one to transform the power system with a single-axis system model into a linear uncertain system with an unknown equilibrium. Based on the latest development of nonlinear robust control theory, a novel control design is then applied to stabilize the resulting linearized uncertain system. Finally, a nonlinear decentralized excitation control is obtained by the inverse transformation. Compared with existing control schemes, the proposed control is free from such common deficiencies of power system nonlinear controllers as network dependence and equilibrium dependence. Detailed stability analysis and engineering judgment in the control design are provided. The results of simulation studies are presented.     

Stable Switching PD Control Using Hunt-Crossley Model for a Press Platform

This study proposes a switching proportional-derivative (PD) controller for a press platform for inspecting the surfaces of a wind turbine blade. We use the Hunt-Crossley model to represent the probe shape or the nonlinearity of the inspection platform. This model consists of a nonlinear spring and a damper; therefore, it is more accurate than linear spring-damper models. We prove the global asymptotic stability of a PD force feedback controller and a PD position feedback (force) controller. However, both the controllers suffer from implementation-related problems. Specifically, the PD force feedback controller makes the impact force large, and the PD position feedback controller cannot easily measure small position changes when the platform contacts the surface. These problems of each controller are solved by switching the two controllers. The PD force feedback control and PD position feedback control are used when the platform is in the contact and noncontact states, respectively. We prove that the proposed switching PD force/position feedback controller is globally asymptotically stable. Further, simulations show satisfactory performance resulting from stable switching between the two control schemes.

     

欺骗攻击环境下具有执行器故障的跳变耦合信息物理系统的同步控制

针对一类离散Markov跳变耦合信息物理系统(CPS)的同步控制问题,在考虑系统参数跳变、耦合参数跳变、控制信息不完全和人为攻击的情况下,设计同步控制器实现CPS的同步.首先,给出具有随机欺骗攻击和执行器故障的Markov跳变耦合CPS模型.其次,基于矩阵Kronecker积,得到同步误差系统,将CPS的同步控制问题转化为同步误差系统的稳定性分析问题.再次,通过构造合适的Lyapunov-Krasovskii泛函,并利用Lyapunov稳定性理论和线性矩阵不等式方法得到使同步误差系统稳定的充分条件,在此基础上,设计同步控制器实现对Markov跳变耦合CPS的同步控制.最后,通过数值仿真例子说明该同步控制器设计方法的有效性.     

Control of nonlinear, continuous, dynamic systems via finite elements, sensitivity analysis, and optimization

A general methodology to design open loop controllers for nonlinear, dynamic, continuous systems is presented and applied to control a single flexible link (SFL). In this application, the partial differential equations that describe the beam system are first analyzed via the finite element method (FEM) and Newmark integration method. Two open loop control inputs to achieve specified system performance criteria are then computed by posing and solving inverse dynamics problems. These analyses use nonlinear programming (NLP) algorithms and analytical gradients that are computed by the direct sensitivity method. The open loop control is verified experimentally. Closed loop controller synthesis for linear time invariant (LTI) and linear time varying systems (LTV) is relatively well understood. To apply this knowledge base to the control of the SFL, the nonlinear finite element plant model is linearized and recast in standard state space form.     

Structural analysis of fuzzy controllers with nonlinear input fuzzy sets in relation to nonlinear PID control with variable gains

The popular linear PID controller is mostly effective for linear or nearly linear control problems. Nonlinear PID controllers, however, are needed in order to satisfactorily control (highly) nonlinear plants, time-varying plants, or plants with significant time delay. This paper extends our previous papers in which we show rigorously that some fuzzy controllers are actually nonlinear PI, PD, and PID controllers with variable gains that can outperform their linear counterparts. In the present paper, we study the analytical structure of an important class of two- and three-dimensional fuzzy controllers. We link the entire class, as opposed to one controller at a time, to nonlinear PI, PD, and PID controllers with variable gains by establishing the conditions for the former to structurally become the latter. Unlike the results in the literature, which are exclusively for the fuzzy controllers using linear fuzzy sets for the input variables, this class of fuzzy controllers employs nonlinear input fuzzy sets of arbitrary types. Our structural results are thus more general and contain the existing ones as special cases. Two concrete examples are provided to illustrate the usefulness of the new results.     

Nonlinear variable structure excitation and steam valving controllers for power system stability

A set of novel nonlinear variable structure excitation and steam-valving controllers are proposed in this paper. On the basis of the classical dynamic equations of a generator, excitation control and steam valving control are simultaneously considered. Design of these controllers combines the differential geometry theory with the variable structure controlling theory. The mathematical model in the form of ＂an affine nonlinear system＂ is set up for the control design of a large-scale power plant. The dynamic performance of the nonlinear variable structure controllers proposed for a single machine connected to an infinite bus power system is simulated. Simulation results show that the nonlinear variable structure excitation and steam-valving controllers give satisfactory dynamic performance and good robustness.     

Constructing nonlinear variable gain controllers via theTakagi-Sugeno fuzzy control

We investigated the analytical structure of the Takagi-Sugeno (TS) type of fuzzy controllers, which was unavailable in the literature. The TS fuzzy controllers we studied employ a new and simplified TS control rule scheme in which all the rule consequent use a common function and are proportional to one another, greatly reducing the number of parameters needed in the rules. Other components of the fuzzy controllers are general: arbitrary input fuzzy sets, any type of fuzzy logic, and the generalized defuzzifier, which contains the popular centroid defuzzifier as a special case. We proved that all these TS fuzzy controllers were nonlinear variable gain controllers and characteristics of the gain variation were parametrized and governed by the rule proportionality. We conducted an in-depth analysis on a class of nonlinear variable gain proportional-derivative (PD) controllers. We present the results to show: (1) how to analyze the characteristics of the variable gains in the context of control; (2) why the nonlinear variable gain PD controllers can outperform their linear counterpart; and (3) how to generate various gain variation characteristics through the manipulation of the rule proportionality     

A new class of nonlinear PID controllers with robotic applications

This paper introduces a new class of simple nonlinear PID controllers and provides a formal treatment of their stability analysis. These controllers are comprised of a sector-bounded nonlinear gain in cascade with a linear fixed-gain P, PD, PI, or PID controller. Three simple nonlinear gains are proposed: the sigmoidal function, the hyperbolic function, and the piecewise–linear function. The systems to be controlled are assumed to be modeled or approximated by second-order transfer functions, which can represent many robotic applications. The stability of the closed-loop systems incorporating nonlinear P, PD, PI, and PID controllers are investigated using the Popov stability criterion. It is shown that for P and PD controllers, the nonlinear gain is unbounded for closed-loop stability. For PI and PID controllers, simple expressions are derived that relate the controller gains and system parameters to the maximum allowable nonlinear gain for stability. A numerical example is given for illustration. The stability of partially-nonlinear PID controllers is also discussed. Finally, the nonlinear PI controller is implemented as a force controller on a robotic arm and experimental results are presented. These results demonstrate the superior performance of the nonlinear PI controller relative to a fixed-gain PI controller. © 1998 John Wiley & Sons, Inc. 15: 161–181, 1998     

具有控制约束的分数阶混沌系统柔性同步控制

研究具有控制约束的两个相同分数阶混沌系统的同步问题.首先,在不消除非线性项的情况下,基于比例控制与自适应控制理论,设计线性自适应切换控制器,实现分数阶混沌系统的同步;其次,考虑到控制器存在约束,利用能够提供无限子控制器的柔性变结构控制策略对线性控制器进行改进,设计柔性变结构控制器,以应对控制的约束,并对线性控制器进行优化;同时,基于分数阶系统Mittag-Leffler稳定判定定理对误差系统的稳定性进行证明.在兼顾系统稳定性与鲁棒性的情况下,可以缩短系统的调整时间,并有效抑制抖振.最后,利用所设计的自适应柔性控制器实现分数阶Chen系统的混沌同步,并通过仿真对比两控制器控制效果,从而验证柔性变结构方法在具有约束的分数阶混沌系统同步控制中的优越性.