Robust disturbance rejection method for uncertain system with disturbances of unknown frequencies

In this paper, we discuss a robust disturbance rejection method for dealing with disturbances of unknown frequencies. Unlike many other approaches, the method proposed here does not require the disturbance frequencies of the separate harmonics to be estimated. The current approach is based on disturbance reduction and disturbance suppression. This novel disturbance reduction controller consists of an inverse of the nominal model with an input deduction and a high gain integral term. The proposed controller can reduce both periodic and nonperiodic unknown disturbances with uncertainties in both stable and unstable systems. In addition, undesired responses caused by residual disturbances and residual modeling uncertainties are suppressed by combining the novel disturbance reduction controller with a sliding mode controller. The simulation results demonstrate that the proposed disturbance rejection method performs well under different disturbance inputs including random signals.     

Distributed coordinated tracking of multiple autonomous underwater vehicles

This paper considers the distributed coordinated tracking problem of multiple autonomous underwater vehicles with a time-varying reference trajectory. Each vehicle is subject to model uncertainty and time-varying ocean disturbances. A novel predictor-based neural dynamic surface control design approach is proposed to develop the node controllers, under which synchronization between vehicles can be reached on condition that the augmented graph induced by the vehicles and the reference trajectory contains a spanning tree. The prediction errors are used to update the neural adaptive laws, which enable fast identifying the vehicle dynamics without excessive knowledge of their dynamical models. Further, this result is extended to the output-feedback case where only position-yaw information can be measured. A local predictor, based on its own position-yaw information, is constructed, not only to recover the unmeasured velocity information, but also to identify the unknown dynamics for each vehicle. A linear matrix inequality-based analysis is performed for the stability of the predictor. Then, distributed output-feedback tracking controllers are developed to achieve synchronization between vehicles in the presence of unknown dynamics and unmeasured velocities. For both cases, the stability properties of the closed-loop network are established via Lyapunov analysis. Simulation results demonstrate the effectiveness of the proposed methods.     

UDE-based decoupled full-order sliding mode control for a class of uncertain nonlinear MIMO systems

In this paper, a generalized control scheme for the class of nonlinear multiple-input multiple-output (MIMO) uncertain system with cross-coupling and nonlinearity in their input channels under the influence of external disturbances is presented. This is accomplished using full-order model following sliding mode control based on uncertainty and disturbance estimator (UDE) technique. The fourth-order uncertain nonlinear MIMO system is separated into multiple single-input single-output double integrator subsystems by considering the effect of input coupling and nonlinearity as a disturbance. The UDE is designed to estimate the plant uncertainties as well as external disturbances without the knowledge of the bounds on the uncertainties. The proposed method decouples the system and overcomes the problem of high initial control which ultimately eliminates the reaching phase and the chattering phenomenon which is generally occurred in sliding mode control. The effectiveness of the proposed control scheme is demonstrated through numerical simulation of two-link manipulator.     

AIRSHIP ATTITUDE TRACKING SYSTEM

The attitude tracking control problem for an airship with parameter uncertainties and external disturbances was considered in this paper. The mathematical model of the airship attitude is a multi-input/multi-output uncertain nonlinear system. Based on the characteristics of this system, a design method of robust output tracking controllers was adopted based on the upper-bounds of the uncertainties. Using the input/output feedback linearization approach and Liapunov method, a control law was designed, which guarantees that the system output exponentially tracks the given desired output. The controller is easy to compute and complement. Simulation results show that, in the closed-loop system, precise attitude control is accomplished in spite of the uncertainties and external disturbances in the system.     

Optimally growing boundary layer disturbances in a convergent nozzle preceded by a circular pipe

We report the findings from a theoretical analysis of optimally growing disturbances in an initially turbulent boundary layer. The motivation behind this study originates from the desire to generate organized structures in an initially turbulent boundary layer via excitation by disturbances that are tailored to be preferentially amplified. Such optimally growing disturbances are of interest for implementation in an active flow control strategy that is investigated for effective jet noise control. Details of the optimal perturbation theory implemented in this study are discussed. The relevant stability equations are derived using both the standard decomposition and the triple decomposition. The chosen test case geometry contains a convergent nozzle, which generates a Mach 0.9 round jet, preceded by a circular pipe. Optimally growing disturbances are introduced at various stations within the circular pipe section to facilitate disturbance energy amplification upstream of the favorable pressure gradient zone within the convergent nozzle, which has a stabilizing effect on disturbance growth. Effects of temporal frequency, disturbance input and output plane locations as well as separation distance between output and input planes are investigated. The results indicate that optimally growing disturbances appear in the form of longitudinal counter-rotating vortex pairs, whose size can be on the order of several times the input plane mean boundary layer thickness. The azimuthal wavenumber, which represents the number of counter-rotating vortex pairs, is found to generally decrease with increasing separation distance. Compared to the standard decomposition, the triple decomposition analysis generally predicts relatively lower azimuthal wavenumbers and significantly reduced energy amplification ratios for the optimal disturbances.     

Interaction of weak free-stream disturbance with an oblique shock:validation of the shock-capturing method

Transition prediction is of great importance for the design of long distance flying vehicles. It starts from the problem of receptivity, i.e., how external disturbances trigger instability waves in the boundary layer. For super/hypersonic boundary layers,the external disturbances first interact with the shock ahead of the flying vehicles before entering the boundary layer. Since direct numerical simulation(DNS) is the only available tool for its comprehensive and detailed investigation, an important problem arises whether the numerical scheme, especially the shock-capturing method, can faithfully reproduce the interaction of the external disturbances with the shock, which is so far unknown.This paper is aimed to provide the answer. The interaction of weak disturbances with an oblique shock is investigated, which has a known theoretical solution. Numerical simulation using the shock-capturing method is conducted, and results are compared with those given by theoretical analysis, which shows that the adopted numerical method can faithfully reproduce the interaction of weak external disturbances with the shock.     

Adaptive neural network-based saturated control of robotic exoskeletons

In this paper, novel adaptive neural network (NN) controllers with input saturation are presented for n-link robotic exoskeletons. The controllers consist of a state feedback controller and an output feedback controller. Through utilizing auxiliary dynamics, the controllers provide a new framework for input saturated control of these robotic systems which can feature the global stability for state feedback control. To compensate for the unknown dynamics of the system, adaptive schemes based on NNs are exploited. Furthermore, adaptive robust terms are utilized to deal with unknown external disturbances. Stability studies show that the closed-loop system is globally uniformly ultimately bounded (UUB) with the state feedback controller, where the global property of the NN-based controller is achieved exploiting a smooth switching function and a robust control term. Also, the system is semi-globally UUB with the output feedback controller. Effectiveness of the controllers is validated by simulations and experimental tests.     

Dynamic modeling and vibration control of a three-dimensional flexible string with variable length and spatiotemporally varying parameters subject to input constraints

In this paper, a three-dimensional dynamic model is developed for a flexible string system with variable length as well as spatiotemporally varying parameters. The dynamic system model is described by coupled partial differential equations and ordinary differential equations. On the basis of the established model, a boundary control method is proposed via backstepping technology and Nussbaum functions to eliminate the vibration of the three-dimensional string with input constraints and disturbances. Deformations of the three-dimensional string system can be verified to converge to small neighborhoods of zero under the proposed control. Input constraints can also be guaranteed by applying smooth hyperbolic tangent function. Simulation results present that the vibration suppression of the flexible string can be achieved and input constraints can be ensured with the proposed control scheme.

     

Observer-based model reference adaptive control for unknown time-delay chaotic systems with input nonlinearity

Existence of unknown time-delay in the systems is a drastic restriction that it can menace the stability criteria and even deteriorate the performance system. This undesired case would be more intensified if that the uncertain input nonlinearity effects are also considered. To handle the input nonlinearities effects (results in dead-zone and/or hysteresis phenomena) and also unknown time-delay in the chaotic systems, this paper presents an observer-based Model Reference Adaptive Control (MRAC) scheme for a class of unknown time-delay chaotic systems with disturbances. This new method is a delay-independent variable-structure control method which is integrated with an observer system. The main task of the proposed approach is to accomplish a perfect tracking procedure such that unknown parameters are adapted via output estimation error. Furthermore, stability of the closed-loop system is achieved by means of the Lyapunov stability theory. Finally, the proposed methods are applied to some famous chaotic systems to verify the effectiveness of the proposed methods.     

Sensitivity Analysis Using Adjoint Parabolized Stability Equations for Compressible Flows

An input/output framework is used to analyze the sensitivity of two- and three-dimensional disturbances in a compressible boundary layer for changes in wall and momentum forcing. The sensitivity is defined as the gradient of the kinetic disturbance energy at a given downstream position with respect to the forcing. The gradients are derived using the parabolized stability equations (PSE) and their adjoint (APSE). The adjoint equations are derived in a consistent way for a quasi-two-dimensional compressible flow in an orthogonal curvilinear coordinate system. The input/output framework provides a basis for optimal control studies. Analysis of two-dimensional boundary layers for Mach numbers between 0 and 1.2 show that wall and momentum forcing close to branch I of the neutral stability curve give the maximum magnitude of the gradient. Forcing at the wall gives the largest magnitude using the wall normal velocity component. In case of incompressible flow, the two-dimensional disturbances are the most sensitive ones to wall inhomogeneity. For compressible flow, the three-dimensional disturbances are the most sensitive ones. Further, it is shown that momentum forcing is most effectively done in the vicinity of the critical layer. This revised version was published online in July 2006 with corrections to the Cover Date.     

Adaptive fuzzy formation control for a swarm of nonholonomic differentially driven vehicles

In this paper, an adaptive fuzzy robust H ^∞ controller is proposed for formation control of a swarm of differential driven vehicles with nonholonomic dynamic models. Artificial potential functions are used to design the formation control input for kinematic model of the robots and matrix manipulations are used to transform the nonholonomic model of each differentially driven vehicle into equivalent holonomic one. The main advantage of the proposed controller is the robustness to input nonlinearity, external disturbances, model uncertainties, and measurement noises, in a formation control of a nonholonomic robotic swarm. Moreover, robust stability proof is given using Lyapunov functions. Finally, simulation results are demonstrated for a swarm formation problem of a group of six unicycles, illustrating the effective attenuation of approximation error and external disturbances, even in the case of robot failure.     

Finite-time consensus tracking of second-order multi-agent systems via nonsingular TSM

The finite-time consensus tracking problem for second-order multi-agent system is investigated in this paper. The multi-agent system here is composed of a leader with bounded input signal and n followers with bounded disturbances. A new continuous nonlinear distributed consensus tracking protocol is constructed via nonsingular terminal sliding mode (TSM) scheme. It is proved that the overall system will reach consensus in finite time via Lyapunov theory when appropriately choosing the parameters under directed connected topology. Finally, simulations are performed, and results show that the method is robust and efficient.     

Robust adaptive sliding mode attitude maneuvering and vibration damping of three-axis-stabilized flexible spacecraft with actuator saturation limits

This paper presents a dual-stage control system design method for flexible spacecraft attitude maneuvering control by use of on-off thrusters and active vibration suppression by embedded smart material as actuator. As a stepping stone, an adaptive sliding mode controller with the assumption of knowing the upper bounds of the lumped perturbation is designed that ensures exponential convergence or uniform ultimate boundedness (UUB) of the attitude control system in the presence of bounded parameter variation/disturbances and control input saturation as well. Then this adaptive controller is redesigned such that the need for knowing the upper bound in advance is eliminated. Lyapunov analysis shows that this modified adaptive controller can also guarantee the exponential convergence or UUB of the system. For actively suppressing the induced vibration, linear quadratic regulator (LQR) based positive position feedback control method is presented. Numerical simulations are performed to show that rotational maneuver and vibration suppression are accomplished in spite of the presence of disturbance torque/parameter uncertainty and saturation input.     

Seeding of helical modes in the initial region of an axisymmetric jet

Active control of fundamental two- and three-dimensional amplified modes in an axisymmetric jet is presented. This is done by introducing localized acoustic disturbances produced by an azimuthal array of miniature speakers placed in the close proximity of the jet lip on the exit face. The independent control of each speaker output allows different azimuthal amplitude and phase distributions of periodic input pressure disturbances. Coupled with this was the development and use of a circular smoke-wire for visualizing shear layer modes around the complete jet circumference.     

Output feedback controller for hysteretic time-delayed MIMO nonlinear systems

In this paper, an H ^?? output feedback controller is developed for a class of time-delayed MIMO nonlinear systems, containing backlash as an input nonlinearity. Particularly, a state observer is proposed to estimate unmeasurable states. The control law can be divided into two elements: An adaptive interval type-2 fuzzy part which approximates the uncertain model. The second part is an H ^??-based controller, which attenuates the effects of external disturbances and approximation errors to a prescribed level. Furthermore, the Lyapunov theorem is used to prove stability of proposed controller and its robustness to external disturbance, hysteresis input nonlinearity, and time varying time-delay. As an example, the designed controller is applied to address the tracking problem of 2-DOF robotic manipulator. Simulation results not only verify the robust properties but also in comparison with an existing method reveal the ability of the proposed controller to exclude the effects of unknown time varying time-delays and hysteresis input nonlinearity.     

Decentralized adaptive neural network control for mechanical systems with dead-zone input

We propose a decentralized adaptive robust controller for trajectory tracking of mechanical systems with dead-zone input in this paper. The considered mechanical systems are with high-order interconnections and unknown non-symmetric nonlinear input. In each local controller, the neural network control is introduced to estimate the uncertainties and disturbances, meanwhile the siding mode control and adaptive technical are designed to compensate for the approximation errors. A nonlinear function is chosen to deal with the interconnections. Following, the stability and robustness are verified by using Lyapunov stability theorem. Finally, simulations are provided to support the theoretical results     

Model predictive control of rigid spacecraft with two variable speed control moment gyroscopes

In this paper, an attitude maneuver control problem is investigated for a rigid spacecraft using an array of two variable speed control moment gyroscopes(VSCMGs)with gimbal axes skewed to each other. A mathematical model is constructed by taking the spacecraft and the gyroscopes together as an integrated system, with the coupling interaction between them considered. To overcome the singular issues of the VSCMGs due to the conventional torque-based method, the first-order derivative of gimbal rates and the second-order derivative of the rotor spinning velocity, instead of the gyroscope torques, are taken as input variables. Moreover, taking external disturbances into account,a feedback control law is designed for the system based on a method of nonlinear model predictive control(NMPC). The attitude maneuver can be realized fast and smoothly by using the proposed controller in this paper.     

Three-dimensional schlieren measurements using inverse tomography

The “synthetic schlieren” method has been used to measure the amplitude of internal waves that are two-dimensional and axisymmetric. Here it is adapted to reconstruct fully three-dimensional perturbations. This non-intrusive technique, which uses inverse tomography methods, shows accurate results when a sufficient number of perspectives taken from the same experiment are provided to the inversion code. We demonstrate the effectiveness of the wavefield reconstruction from three idealized disturbances in the form of a Gaussian function, a Gaussian multiplied in amplitude by a sine function and a sinusoidal plane wave with an elliptical envelope. The consequences of noisy data input are also investigated.     

Boundary control of an Euler–Bernoulli beam with input and output restrictions

Nonlinear Dynamics - In this study, boundary control is considered for an Euler–Bernoulli beam subject to bounded input, bounded output, and external disturbances. Through utilizing the...