三轴液压仿真转台非线性多输入多输出QFT控制器设计

三轴液压仿真转台本质上是非线性变参数多输入多输出系统.系统负载、油源压力、增益的变化及耦合作用随速度,加速度的变化造成很大的参数不确定性.针对液压转台提出一种基于SIMULINK模型线性化的多输入多输出非线性定量反馈设计方法.其本质是找到液压伺服系统一系列控制特性最差的运行点,直接用它们的频率响应集合来综合非线性定量反馈控制器.这种方法简化了目前的QFT多输入多输出控制系统设计方法,显示了很大的优越性.文中举例说明这种方法的效果.     

基于速度反馈分数阶PID控制的达芬振子的主共振.

与传统整数阶比例-积分-微分(PID)控制器相比,分数阶比例-积分-微分控制器由于增加了两个控制参数,因此能够更灵活地控制受控对象.研究了基于速度反馈分数阶比例-积分-微分控制的达芬振子的主共振,利用平均法获得了系统的近似解析解.研究发现分数阶比例-积分-微分控制器的比例环节以等效线性阻尼的形式影响系统的共振振幅,积分环节以等效线性阻尼和等效线性刚度的形式影响系统的动力学特性,微分环节以等效线性阻尼和等效质量的形式影响系统的动力学特性.建立了主共振幅频响应方程的解析表达式和稳定性判断准则,并对主共振幅频响应的近似解析解和数值解进行了比较,二者吻合良好,验证了求解过程和近似解析解的正确性.分析了分数阶比例-积分-微分控制器的比例环节系数、积分环节系数、微分环节系数以及分数阶阶次变化时,对系统主共振幅频响应的影响.对分数阶比例-积分-微分控制器与传统整数阶比例-积分-微分控制器的控制效果进行了对比,发现当控制器各个环节的系数相同时,基于速度反馈的分数阶比例-积分-微分控制对达芬振子主共振的控制效果要优于传统整数阶比例-积分-微分控制.      

A novel framework to design and compare limit cycle minimizing controllers: demonstration with integer and fractional-order controllers

In this paper, a constrained optimization problem is formulated to tune the limit cycle minimizing controllers meeting additional loop-shaping performances such as phase margin and gain crossover frequency. A graphical approach is proposed so as to determine the superior controller in terms of better limit-cycle suppression. The framework is illustrated with a suitable case of elementary servo plant which has separable static backlash nonlinearity in its model. For this plant, integer-order controllers and their fractional counterparts (PI and \( PI ^\alpha , [ PI ]^\alpha \) ; PID and \( PI ^\alpha D^\beta \) ) are designed and compared. Interestingly, it is found that the fractional controllers produce better limit-cycle responses than their integer counterparts while both meeting the rest of the specifications. Correspondingly, the better sustained oscillations in the plant output response are obtained with fractional controllers. Such a ‘fractional superiority’ is further verified with the closed-loop nonlinear simulation.     

Application of Takagi–Sugeno fuzzy model to a class of chaotic synchronization and anti-synchronization

In this study, we investigate a class of chaotic synchronization and anti-synchronization with stochastic parameters. A controller is composed of a compensation controller and a fuzzy controller which is designed based on fractional stability theory. Three typical examples, including the synchronization between an integer-order Chen system and a fractional-order Lü system, the anti-synchronization of different 4D fractional-order hyperchaotic systems with non-identical orders, and the synchronization between a 3D integer-order chaotic system and a 4D fractional-order hyperchaos system, are presented to illustrate the effectiveness of the controller. The numerical simulation results and theoretical analysis both demonstrate the effectiveness of the proposed approach. Overall, this study presents new insights concerning the concepts of synchronization and anti-synchronization, synchronization and control, the relationship of fractional and integer order nonlinear systems.     

Adaptive neural network control of bilateral teleoperation with constant time delay

This paper proposes a novel approach for bilateral teleoperation systems with a multi degrees-of-freedom (DOF) nonlinear robotic system on the master and slave side with constant time delay in a communication channel. We extend the passivity based architecture to improve position and force tracking and consequently transparency in the face of offset in initial conditions, environmental contacts and unknown parameters such as friction coefficients. The proposed controller employs a stable neural network on each side to approximate unknown nonlinear functions in the robot dynamics, thereby overcoming some limitations of conventional controllers such as PD or adaptive controllers and guaranteeing good tracking performance. Moreover, we show that this new neural network controller preserves the control passivity of the system. Simulation results show that NN controller tracking performance is superior to that of conventional controllers.     

Seismic-vibration mitigation of a nonlinear structural system with an ATMD through a fuzzy PID controller

This paper discusses the design of fuzzy PID type controllers (FPIDC) to improve seismic control performance of a nonlinear structural system with an active tuned mass damper (ATMD) against earthquakes. Since structural systems have nonlinearities and uncertainties, fuzzy-based controllers are adequate because of their robust character and satisfactory performance in active structural control. The main advantages of this controller are the ability to handle nonlinearities and uncertainties effectively. In the literature, various structures for fuzzy PID (including PI and PD) controllers have been proposed. In order to obtain proportional, integral and derivative control actions altogether, it is intuitive and convenient to combine PI and PD actions to form a fuzzy PID controller. The simulated system has fifteen degrees of freedom and is modeled using nonlinear behavior of the base–structure interaction. The system is then simulated against the ground motion of the Northridge earthquake (M _w =6.7) in USA on 17 January, 1994. Finally, the time history of the storey displacements, accelerations, ATMD displacements, control voltage and frequency responses of both the uncontrolled and controlled cases are presented. The ground motion recorded of the El-Centro and Kocaeli earthquakes has been used to evaluate the effectiveness of the proposed control algorithm. The robustness of the controller has been checked through the uncertainty in stiffness of the structure. Simulation results exhibit that superior vibration suppression is achieved by the use of designed fuzzy PID type controllers.     

岩石流变分数阶模型研究

以Kelvin流变模型为研究对象,提出了一种分数阶Kelvin流变模型。首先,把Kelvin模型中的整数阶导数改为分数阶导数,考虑到岩石材料的频率通常不超过1000 Hz,在分数阶拟合时,拟合频段选取为[0 1000],进而利用Oustalop滤波算法把分数阶表示为整数阶模式;其次,利用试验数据对分数阶模型进行参数识别,考虑到分数阶Kelvin模型具有强非线性的特点,引入了Levenberg-Marquardt优化算法来确定未知参数;最后,对于频域表示的流变方程,利用Laplace逆变换获得流变精确表达式。仿真实例表明本文方法可以很好地反映岩石流变特性。     

Stochastic synchronization of complex network via a novel adaptive nonlinear controller

In this paper, a novel adaptive nonlinear controller is designed to achieve stochastic synchronization of complex networks. We find that this novel adaptive nonlinear controller is less conservative and may be more widely used than the traditional adaptive linear controller. By using the properties of Weiner process, the stochastic synchronization of complex networks with stochastic perturbation via the proposed novel adaptive nonlinear controller can be achieved. Experimental tests demonstrate the superior performance of this novel adaptive nonlinear controller as compared to a conventional adaptive linear controller.     

Adaptive neural novel prescribed performance control for non-affine pure-feedback systems with input saturation

An error constraint control problem is considered for pure-feedback systems with non-affine functions being possibly in-differentiable. A new constraint variable is used to construct virtual control that guarantees the tracking error within the transient and steady-state performance envelopment. The new error transformation avoids non-differentiable problems and complex deductions caused by traditional error constraint approaches. A locally semi-bounded and continuous condition for non-affine functions is employed to ensure the controllability and transform the closed-loop system into a pseudo-affine form. An auxiliary system with bounded compensation term is proposed for nonlinear systems with input saturation. On the basis of backstepping technique, an adaptive neural controller is designed to handle unknown terms and circumvent repeated differentiations of virtual controls. The boundedness and convergence of the closed-loop system are proved by Lyapunov theory. Asymptotic tracking is achieved without violating control input constraint and error constraint. Two examples are performed to verify the theoretical findings.     

A linear approach to generalized minimum variance controller design for MIMO nonlinear systems

Designing minimum variance controllers (MVC) for nonlinear systems is confronted with many difficulties. The methods which are able to identify MIMO nonlinear systems are scarce, and linear models are not accurate in modeling nonlinear systems. In this paper, Vector ARX (VARX) models are proposed for designing MVC and generalized minimum variance controller (GMVC) for linear and nonlinear systems, and the accuracy of these models in approximating the nonlinear MIMO system is studied. However, the VARX is a linear model. It is shown that this model can identify some kinds of nonlinear systems with any desired accuracy. Therefore, the controller designed by the VARX is accurate, even for these nonlinear systems. The proposed controller is tested on a both linear system and a nonlinear four-tank benchmark process. In spite of the simplicity of designing GMVCs for the VARX models, the results show that the proposed method is accurate and implementable.     

Nonlinear Input-Shaping Controller for Quay-Side Container Cranes

Input-shaping is one of the most practical open-loop control strategies for gantry cranes, especially those having predefined paths and operating at constant cable lengths. However, when applied to quay-side container cranes, its performance is far from satisfactory. A major source of the poor performance can be linked to the significant difference between the gantry crane model and the quay-side container crane model. Gantry cranes are traditionally modeled as a simple pendulum. However, a quay-side container crane has a multi-cable hoisting mechanism.In this paper, a two-dimensional four-bar-mechanism model of a container crane is developed. For the purpose of controller design, the crane model is reduced to a double pendulum with two fixed-length links and a kinematic constraint. The method of multiple scales is used to develop a nonlinear approximation of the oscillation frequency of the simplified model. The resulting frequency approximation is used to determine the switching times for a bang-off-bang input-shaping controller. The performance of the controller is numerically simulated on the full model of the container crane, and is compared to the performance of similar controllers based on a nonlinear frequency approximation of a simple pendulum and a linear frequency approximation of a constraint double pendulum. Results demonstrate a superior performance of the controller based on the nonlinear frequency approximation of the constraint double pendulum.The effect of the oscillation frequency on the controller performance is investigated by varying the model's frequency around the design value. Simulations revealed that the performance of the controller suffers serious degradation due to small changes in the model frequency. To alleviate the shortcomings of the input-shaping controller, a delayed-position feedback controller is successfully applied at the end of each transfer maneuver to eliminate residual oscillations without affecting the commands of the input-shaping controller.     

Comparison of Quasi Bang-Bang and Sliding Mode Controls for a DC Shunt Motor with Time Delay

We propose a hybrid fuzzy-linear controller for a nonlinearterminal voltage-controlled DC motor. The nonlinearity includes theeffect of magnetization saturation and a nonlinear fan load. The inputto the proposed Fuzzy Logic Controller (FLC) is an 'aggregate' errorbetween the required and the actual rpm and its time derivatives. TheFLC is designed to approximate a bang-bang controller and itscoefficients are chosen as a tradeoff between short rise time, smallsteady-state errors, and control chattering. The FLC performance wascompared to that of a well-known design; namely a sliding modecontroller with a boundary layer. Although the FLC design procedure iseasier, the performance of the two controllers are quite similar.Unfortunately, the FLC design was not robust enough to counter theeffect of large time delays introduced by the power electronicsinterface.     

Dynamics and optimal control of multibody systems using fractional generalized divide-and-conquer algorithm

In this paper, a new framework is presented for the dynamic modeling and control of fully actuated multibody systems with open and/or closed chains as well as disturbance in the position, velocity, acceleration, and control input of each joint. This approach benefits from the computed torque control method and embedded fractional algorithms to control the nonlinear behavior of a multibody system. The fractional Brunovsky canonical form of the tracking error is proposed for a generalized divide-and-conquer algorithm (GDCA) customized for having a shortened memory buffer and faster computational time. The suite of a GDCA is highly efficient. It lends itself easily to the parallel computing framework, that is used for the inverse and forward dynamic formulations. This technique can effectively address the issues corresponding to the inverse dynamics of fully actuated closed-chain systems. Eventually, a new stability criterion is proposed to obtain the optimal torque control using the new fractional Brunovsky canonical form. It is shown that fractional controllers can robustly stabilize the system dynamics with a smaller control effort and a better control performance compared to the traditional integer-order control laws.

     

Global stabilization of high-order nonlinear systems under multi-rate sampled-data control

This paper studies the sampled-data control problem for a class of high-order nonlinear systems. Based on exact discrete-time equivalent model of the sampled-data system, a multi-rate sampled-data controller with the form of a power series expansion is designed to achieve the global asymptotic stability of the closed-loop system under some assumptions. Approximate solutions of the proposed controller are proved to be effective by a theoretical analysis. The results show that, compared with the emulated control scheme, the approximate controllers allow considering larger sampling periods and enlarge the domain of attraction for a given sampling period. Finally, a simulation example is given to show the effectiveness of the proposed control scheme.     

FPGA implementation of novel fractional-order chaotic systems with two equilibriums and no equilibrium and its adaptive sliding mode synchronization

This paper introduces two novel fractional-order chaotic systems with cubic nonlinear resistor and investigates its adaptive sliding mode synchronization. Firstly the novel two equilibrium chaotic system with cubic nonlinear resistor (NCCNR) is derived and its dynamic properties are investigated. The fractional-order cubic nonlinear resistor system (FONCCNR) is then derived from the integer-order model and its stability and fractional-order bifurcation are discussed. Next a novel no-equilibrium chaotic cubic nonlinear resistor system (NECNR) is derived from NCCNR system. Dynamic properties of NECNR system are investigated. The fractional-order no equilibrium cubic nonlinear resistor system (FONECNR) is derived from NECNR. Stability and fractional-order bifurcation are investigated for the FONECNR system. The non-identical adaptive sliding mode synchronization of FONCCNR and FONECNR systems are achieved. Finally the proposed systems, adaptive control laws, sliding surfaces and adaptive controllers are implemented in FPGA.     

Dynamic control for permanent magnet synchronous generator system using novel modified recurrent wavelet neural network

Because permanent magnet synchronous generator (PMSG) system driven by permanent magnet synchronous motor (PMSM) based on wind turbine emulator (WTE) is a nonlinear and time-varying system with high complication, an accurate dynamic model of the PMSG system directly driven by WTE is difficult to establish for the linear controller design. In order to conquer this difficulty and improve the robustness of dynamic system, the PMSG system controlled by the online-tuned parameters of the novel modified recurrent wavelet neural network (NN)-controlled system is proposed to control output voltages and powers of controllable rectifier and inverter in this study. First, a closed-loop PMSM-driven system based on WTE is designed for driving the PMSG system to generate output power. Second, the rotor speeds of the PMSG, the voltages, and currents of the two power converters are detected simultaneously to yield maximum power output. In addition, two sets of the online-tuned parameters of the modified recurrent wavelet NN controllers in the controllable rectifier and inverter are developed for the voltage-regulating controllers in order to improve output performance. Finally, some experimental results are verified to show the effectiveness of the proposed novel modified recurrent wavelet NN controller for the power output of the PMSG system driven by WTE.     

Robust predictive scheme for input delay systems subject to nonlinear disturbances

The predictor-based control is known as an effective method to compensate input delays. Yet the traditional predictors, like Smith predictor, have poor robustness with respect to system disturbances. In this paper, with the consideration of future disturbances, a novel robust predictive scheme is developed for input delay systems subject to nonlinear disturbances. The Artstein reduction method is used to provide performance analysis of different predictor-based controllers, which shows that the proposed predictor-based controller can provide better disturbance attenuation than previous approaches in the literature for a wide range of disturbances.     

A criterion of robustness intelligent nonlinear control for multiple time-delay systems based on fuzzy Lyapunov methods

A control system with state feedback controllers, in which the fuzzy Lyapunov approach is developed for the stability criterion, is studied. The proposed intelligent design provides a systematic and effective framework for the control systems. The global nonlinear controller is constructed based on T–S (Takagi–Sugeno) fuzzy controller design techniques, blending all such local state feedback controllers. Based on this design, the stability conditions of a multiple time-delay system are derived in terms of the fuzzy Lyapunov theory. The effectiveness and the feasibility of the proposed controller design method are demonstrated through numerical simulations.     

Path tracking design based on Davidson–Cole prefilter using a centralized CRONE controller applied to multivariable systems

To perfectly govern MIMO (Multi-Input Multi-Output) processes, a fully populated matrix controller has been developed due to its flexibility. Taking into account the plant uncertainties, the CRONE (Commande Robuste d’Ordre Non Entier) control approach is used with the non-diagonal quantitative feedback theory (QFT) procedure. The MIMO-QFT robust synthesis methodology has been used in order to generate the appropriate equivalent MISO (Multi-Input Single-Output) system structure from the MIMO plant. For each MISO structure, the CRONE control approach based on third-generation CRONE methodology is used to find the diagonal elements of the controller of the plant while considering the plant uncertainties. The non-diagonal part of the controller is determined to reach the aim of minimizing the coupling effects. After that, a fractional prefilter synthesis approach is developed to find the non-integer prefilter expression satisfying the tracking specifications. A SCARA robot manipulator has been used to verify the designed controller performances.     

Self-tuning fuzzy logic control of a non-linear structural system with ATMD against earthquake

Self-tuning fuzzy logic controllers (STFLC) for the active control of Marmara Kocaeli earthquake excited building structures are studied in this paper. Vibration control using intelligent controllers, such as fuzzy logic has attracted the attention of structural control engineers during the last few years, because fuzzy logic can handle nonlinearities, uncertainties, and heuristic knowledge effectively and easily. The improved seismic control performance can be achieved by converting a simply designed static gain into a real time variable dynamic gain through a self-tuning mechanism. Self-tuning fuzzy logic controller is designed to reduce the story-drift of each floor. The simulated system has a nine-degree-of-freedom, which is modeled using nonlinear behavior of the base-structure interaction. Modeled system was simulated against the ground motion of the Marmara Kocaeli earthquake (M _w=7.4) in Turkey on 17 August, 1999. At the end of the study, the time history of the story displacements, accelerations, ATMD displacements, control voltage, and frequency responses of the both uncontrolled and controlled cases are presented. The robustness of the controller has been checked through the uncertainty in stiffness of the structure. Performance of the designed STFLC has been demonstrated for the different disturbance using ground motion of the Kobe earthquake. Simulations of an earthquake excited nine story structure are performed to prove the validity of proposed control strategy.