Incremental harmonic balance method for nonlinear flutter of an airfoil with uncertain-but-bounded parameters

The limit cycle oscillation of a two-dimensional airfoil with parameter variability in an incompressible flow is investigated using the incremental harmonic balance (IHB) method. The variable parameters, such as the wind speed, the cubic plunge and pitch stiffness coefficients, are modeled as either bounded uncertain or stochastic parameters. In the solution process of the IHB method, the bounded parameters are considered as an active increment. Taking all values over the considered bounded regions of the active parameters provides us with a series of IHB solutions of limit cycle oscillations of the airfoil. With the aid of the attained solutions, the bounds and some statistical properties of the limit cycle oscillations are determined and compared with Monte Carlo simulation (MCS) results. Numerical examples show that the proposed approach is valid and effective for analyzing strongly nonlinear vibration problems with bounded uncertainties.     

Sliding mode control of hyperchaos in Rössler systems

In this paper, an extended sliding mode controller is applied to control a hyperchaotic motion in Rössler system. The sliding surface of this paper used is one dimension higher than traditional sliding surface and guarantees it passing through the activated initial states of controlled system. Therefore, using the characteristic of this sliding mode to design a controller not only can meet the desired specification but also without chattering phenomenon and abrupt state change. By comparing with the result in the existed literatures, the results show that the proposed controller can steer Rössler system to the desired state accurately. It also provides a good characteristic for disturbance rejection.     

Dynamics and chaos control in nonlinear electrostatic transducers

In this paper, we analyze the dynamics of a system consisting of two coupled nonlinearly Duffing oscillators, obtained from a nonlinear electrostatic device which is a prototype of emitters and receivers in communication engineering. Inverse or backward period doubling cascades and sudden transition to chaos are observed. A sliding mode controller is applied to control the electrostatic transducers system. The sliding surface used is one dimension higher than the traditional surface and guarantees its passage through the initial states of the controlled system. By means of the design of sliding mode dynamics characteristics, the controlled system performance is arbitrarily determined by assigning the switching gain of the sliding mode dynamics. Therefore, using the characteristic of this sliding mode we aim to design a controller that can meet the desired specification and use less control energy by comparing with the result in the current literature. The results show that the proposed controller can steer electrostatic transducers to the desired reference trajectory without chattering phenomenon and abrupt state change.     

基于滑模方法的倒立摆台车系统的非线性控制

以倒立摆台车系统为研究对象，将系统状态分成两组，构造出一种双层滑动面，给出一种基于滑模控制的非线性控制律，并设计了控制器参数．然后采用Lyapunov方法，证明了各级滑动平面的稳定性，实现了台车在水平方向位置及摆角的渐近跟踪．     

Chaos control in AFM system using sliding mode control by backstepping design

This paper presents a robust algorithm to control the chaotic atomic force microscope system (AFMs) by backstepping design procedure. The proposed feedback controller is composed by a sliding mode control (SMC) and a backstepping feedback, so its implementation is quite simple and can be made on the basis of the measured signal. The developed control scheme allows chaos suppression despite uncertainties in the model as well as system external disturbances. The concept of extended system is used such that a continuous sliding mode control effort is generated using backstepping scheme. It is guaranteed that under the proposed control law, uncertain AFMs can asymptotically track target orbits. The converging speed of error states can be arbitrary turned by assigning the corresponding dynamics of the sliding surfaces. Numerical simulations demonstrate its advantages by stabilizing the unstable periodic orbits of the AFMs and this method can also be easily extended to elimination chaotic motion in any types of chaotic AFMs.     

Suppression of chaotic behavior in horizontal platform systems based on an adaptive sliding mode control scheme

This work presents an adaptive sliding mode control scheme to elucidate the robust chaos suppression control of non-autonomous chaotic systems. The proposed control scheme utilizes extended systems to ensure that continuous control input is obtained in order to avoid chattering phenomenon as frequently in conventional sliding mode control systems. A switching surface is adopted to ensure the relative ease in stabilizing the extended error dynamics in the sliding mode. An adaptive sliding mode controller (ASMC) is then derived to guarantee the occurrence of the sliding motion, even when the chaotic horizontal platform system (HPS) is undergoing parametric uncertainties. Based on Lyapunov stability theorem, control laws are derived. In addition to guaranteeing that uncertain horizontal platform chaotic systems can be stabilized to a steady state, the proposed control scheme ensures asymptotically tracking of any desired trajectory. Furthermore, the numerical simulations verify the accuracy of the proposed control scheme, which is applicable to another chaotic system based on the same design scheme.     

A light wing

In a development of the results obtained previously in [1] a version of the design scheme for a low-mass wing is proposed. It takes the form of a system of spars with each of which a system of cantilevers is linked which participate in the formation of the upper and lower surfaces of the wing. Here, the axes of the spars and the rods forming the wing surfaces are arranged in such a way that there are no torques in the cross-sections of these elements. The dimensions of the sections of each element are chosen so as to ensure equal strength. It is shown that, in the case of this wing scheme, the flexural vibration of the wing which randomly arise does not develop into bending-torsional vibration and does not lead to flutter. The mass of a wing for a light aircraft is estimated.     

Unidirectional synchronization for Hindmarsh–Rose neurons via robust adaptive sliding mode control

This paper presents an adaptive neural network (NN) based sliding mode control for unidirectional synchronization of Hindmarsh–Rose (HR) neurons in a master–slave configuration. We first give the dynamics of single HR neuron which may exhibit spike-burst chaotic behaviors. Then we formulate the problem of unidirectional synchronization control of two HR neurons and propose a NN based sliding mode controller. The controller consists of two simple radial basis function (RBF) NNs which are used to approximate the desired sliding mode controller and the uncertain nonlinear part of the error dynamical system, respectively. The control scheme is robust to the uncertainties such as approximate errors, ionic channel noise and external disturbances. The simulation results demonstrate the validity of the proposed control method.     

The sliding mode control for an airfoil system driven by harmonic and colored Gaussian noise excitations

This paper addresses a sliding mode control (SMC) for an airfoil model excited by a combination of harmonic force and colored Gaussian noise. Firstly, to reveal effects of random factors, the airfoil model with colored Gaussian noise is established. Next, via a perturbation technique and the stochastic averaging method, an analytical expression for the time-averaging mean square response is derived, which agrees well with results by Monte Carlo simulations. Additionally, we uncover that colored noise can induce a stochastic jump phenomenon, which can cause a catastrophic structural failure of the airfoil or even a disintegration of the aircraft. Subsequently, the SMC strategy is employed to design an effective controller for suppressing such a jump phenomenon of the stochastic airfoil system. In the case of the proposed stochastic airfoil system, we introduce concepts of ultimately reachability with an arbitrary small bound and a mean square practical stability to realize the reachability of the sliding mode and the stability of the system state. Finally, several numerical results are presented to demonstrate the effectiveness of the proposed SMC algorithm. We show that the jump phenomenon can be suppressed efficiently to avoid a catastrophic failure of the wing structure due to large deformation/deflection, and the energy cost is discussed to analyze the SMC approach.     

Positioning control for a linear actuator with nonlinear friction and input saturation using output‐feedback control

This article deals with the positioning control problem via the output feedback scheme for a linear actuator with nonlinear disturbances. In this study, the proposed controller accounts for not only the nonlinear friction, force ripple, and external disturbance but also the input saturation problem. In detail, the energy consumption for conquering friction and disturbance rejection is estimated and used as compensation based on the hybrid controller including and sliding‐mode‐based adaptive algorithms, which ensures the tracking performance and robustness of electromechanical servo system. Moreover, to confront the input saturation, a saturation observer and an anti‐windup controller are designed. The global robustness of the controller is guaranteed by an output feedback robust law. Theoretically, the designed controller can guarantee a favorable tracking performance in the presence of various disturbance forces and input saturation, which is essential for high accuracy motion plant in industrial application. The simulation results verify the robustness and effectiveness for the motion system with the proposed control strategy under various operation conditions. © 2016 Wiley Periodicals, Inc. Complexity 21: 191–200, 2016     

不同类型近破波作用下沉箱式防波堤的振动-提离摇摆运动

倾覆失稳是沉箱式防波堤的主要破坏形式之一,是稳定性验算的基本内容．采用质量-弹簧-阻尼器集总参数模型模拟沉箱式防波堤在单峰值冲击型、双峰值冲击型和冲击-振荡衰减型等不同类型近破波作用下的振动-提离摇摆运动过程,研究了不同类型近破波和沉箱的提离摇摆运动对沉箱式防波堤动力响应的影响．结果表明,在近破波冲击力幅值相同的条件下,近破波类型对沉箱的动力响应影响很大;提离摇摆运动虽然会使沉箱的转角幅值增大,但可有效地减小沉箱的位移、滑移力和倾覆力矩幅值．研究成果为允许沉箱式防波堤出现提离摇摆运动的设计概念提供了理论基础．     

The existence of the exponentially stable limit cycle for a class of nonlinear systems

In this paper, the exponentially stable limit cycle phenomenon for a class of nonlinear systems is investigated. Based on the analytic method, the existence and uniqueness of the exponentially stable limit cycle for such systems can be guaranteed. Moreover, the amplitude of oscillation, the period of oscillation, and guaranteed convergence rate can be correctly estimated. Finally, two numerical examples are provided to illustrate the use of the main result.     

Exponential stabilization using sliding mode control for singular systems with time-varying delays and nonlinear perturbations

This paper considers a sliding mode control (SMC) of singular systems. The systems under consideration involve nonlinear perturbations and time-varying delays. The aim of this paper is to design a sliding mode controller such that the nonlinear singular system is exponentially stable and its trajectory can be driven onto the sliding surface in finite time. By using the Lyapunov–Krasovskii functional and some specified matrices, conditions on exponential stabilization are obtained in the form of strict linear matrix inequalities (LMIs). A numerical example is given to illustrate the effectiveness of the proposed main results. All these results are expected to be of use in the study of singular time-varying delay systems with nonlinear perturbations.     

Fuzzy fractional order sliding mode controller for nonlinear systems

In this paper, an intelligent robust fractional surface sliding mode control for a nonlinear system is studied. At first a sliding PD surface is designed and then, a fractional form of these networks PD^α, is proposed. Fast reaching velocity into the switching hyperplane in the hitting phase and little chattering phenomena in the sliding phase is desired. To reduce the chattering phenomenon in sliding mode control (SMC), a fuzzy logic controller is used to replace the discontinuity in the signum function at the reaching phase in the sliding mode control. For the problem of determining and optimizing the parameters of fuzzy sliding mode controller (FSMC), genetic algorithm (GA) is used. Finally, the performance and the significance of the controlled system two case studies (robot manipulator and coupled tanks) are investigated under variation in system parameters and also in presence of an external disturbance. The simulation results signify performance of genetic-based fuzzy fractional sliding mode controller.     

Standard passivity-based control for multi-hydro-turbine governing systems with surge tank

This paper addresses the problem of control design for hydro-turbine governing systems with surge tanks from the perspective of standard passivity-based control. The dynamic model of a synchronous machine is considered in conjunction with a model of the hydro-turbine to generate an eleventh-order nonlinear set of differential equations. An Euler–Lagrange representati of the system and its open-loop dynamics is developed. Then, the standard passivity-based control is applied to design a global and asymptotically stable controller in closed-loop operation. The proposed control is decentralized to avoid challenges of communication between the hydro-turbine governing systems. The proposed standard passivity-based control approach is compared with two control approaches. First, a classical standard cascade proportional-integral-derivative controller is applied for the governing system, the automatic voltage regulator, and the excitation system. Second, a sliding mode control is also implemented in the governing system. Two test systems were used to validate the performance of the proposed controller. The first test system is a single machine connected to an infinite bus, and the second test system is the well-known Western System Coordinating Council’s multimachine system. Overall, simulation results show that the proposed controller exhibits a better dynamic response with shorter stabilization times and lower peaks during the transient periods.     

Nonlinear sliding surface based second order sliding mode controller for uncertain linear systems

A second order sliding mode (SOSM) controller using nonlinear sliding surface is proposed in this paper. The aim of the proposed controller is to guarantee stability as well as enhance the transient performance of uncertain linear systems with parametric uncertainty. The nonlinear sliding surface consists of a linear term and a nonlinear term. The linear term comprises a gain matrix which has a very low value of damping ratio and thereby facilitates fast response. The nonlinear term is introduced to accommodate a variable damping ratio to reduce overshoot and settling time of the closed loop system as the output reaches nearer the desired reference position. A major gain of the proposed SOSM controller is the elimination of chattering in the control input. The proposed nonlinear sliding surface based SOSM controller achieves fast rise, low overshoot and low settling time. Simulation results demonstrate the effectiveness of the proposed SOSM controller.     

Composite nonlinear feedback based discrete integral sliding mode controller for uncertain systems

In this paper, a discrete integral sliding mode (ISM) controller based on composite nonlinear feedback (CNF) method is proposed. The aim of the controller is to improve the transient performance of uncertain systems. The CNF based discrete ISM controller consists of a linear and a nonlinear term. The linear control law is used to decrease the damping ratio of the closed-loop system for yielding a quick transient response. The nonlinear feedback control law is used to increase the damping ratio with an aim to reduce the overshoot of the closed-loop system as it approaches the desired reference position. It is observed that the discrete CNF-ISM controller produces superior transient performance as compared to the discrete ISM controller. The closed-loop control system remains stable during the sliding condition. Simulation results demonstrate the effectiveness of the proposed controller.     

Control and synchronize a novel hyperchaotic system

The control and hybrid projective synchronization (HPS) strategies for a novel hyperchaotic system are investigated. Firstly, the novel hyperchaotic system is controlled to the unsteady equilibrium point or limit cycle via only one scalar controller which includes two state variables. Secondly, based on Lyapunov’s direct method HPS between two novel hyperchaotic systems is studied. A new nonlinear feedback vector controller is designed to guarantee HPS, which can be simplified ulteriorly into a single scalar controller to achieve complete synchronization between two novel hyperchaotic systems. Finally, numerical simulations are given to verify the effectiveness of these strategies. The proposed methods have certain significances for reducing the cost and complexity for controller implementation.     

Finite-time chaos control via nonsingular terminal sliding mode control

This paper considers the nonsingular terminal sliding mode control for chaotic systems with uncertain parameters or disturbances. The switching surface is designed technically to realize fast convergence. The controller derived from such switching surface is nonsingular and it can stabilize the chaotic systems in a finite time. Besides the second-order system and the triangular system, the proposed method can also be applied to a general class of uncertain nonlinear system. Finally, simulation results are presented to illustrate the effectiveness of the design.     

Robust control of a spatial robot using fuzzy sliding modes

In order to improve the performance of the sliding mode controller, fuzzy logic sliding mode controller is proposed in this study. The control gain of the conventional sliding mode controller is tuned by a fuzzy logic rule base and, also dynamic sliding surfaces are obtained by changing their slopes using the error states of the system in another fuzzy logic algorithm. These controllers are then combined in order to enhance the performance. Afterwards, proposed controllers were used in trajectory control of a three degrees of freedom spatial robot, which is subjected to noise and parameter variations. Finally, the controllers introduced are compared with a PID controller which is commonly used for control of robotic manipulators in industry. The results indicate the superior performance of the proposed controller.