A feedback linearization design for the control of vehicle’s lateral dynamics

In this paper, the feedback linearization scheme is applied to the control of vehicle’s lateral dynamics. Based on the assumption of constant driving speed, a second-order nonlinear lateral dynamical model is adopted for controller design. It was observed in (Liaw, D.C., Chung, W.-C. in 2006 IEEE International Conference on Systems, Man, and Cybernetics, 2006) that the saddle-node bifurcation would appear in vehicle dynamics with respect to the variation of the front wheel steering angle, which might result in spin and/or system instability. The vehicle dynamics at the saddle node bifurcation point is derived and then decomposed as an affine nominal model plus the remaining term of the overall system dynamics. Feedback linearization scheme is employed to construct the stabilizing control laws for the nominal model. The stability of the overall vehicle dynamics at the saddle-node bifurcation is then guaranteed by applying Lyapunov stability criteria. Since the remaining term of the vehicle dynamics contains the steering control input, which might change system equilibrium except the designed one. Parametric analysis of system equilibrium for an example vehicle model is also obtained to classify the regime of control gains for potential behavior of vehicle’s dynamical behavior.     

Nonlinear dynamics in mechanics and engineering: 40 years of developments and Ali H. Nayfeh’s legacy

Nonlinear Dynamics - Nonlinear dynamics of engineering systems has reached the stage of full maturity in which it makes sense to critically revisit its past and present in order to establish an...     

T–S fuzzy control design for a class of nonlinear networked control systems

This paper is devoted to controlling a class of nonlinear systems over a communication network in the presence of packet transmission delays, packet losses, quantization errors, and sampling-related phenomena. Specifically, based on the Takagi–Sugeno (T–S) fuzzy approach, this paper presents a way of designing a quantized controller that allows all the states of nonlinear NCSs to converge exponentially to a bounded ellipsoid. In particular, this paper provides a method capable of exploiting fully the time-varying delay term d(t), induced by Jensen inequality, for nonlinear NCSs.     

Nonlinear dynamic analysis and sliding mode control for?a?gyroscope system

This paper employs differential transformation (DT) method to analyze and control the dynamic behavior of a gyroscope system. The analytical results reveal a complex dynamic behavior comprising periodic, subharmonic, quasiperiodic, and chaotic responses of the center of gravity. Furthermore, the results reveal the changes which take place in the dynamic behavior of the gyroscope system as the external force is increased. The current analytical results by DT method are found to be in good agreement with those of Runge?CKutta (RK) method. In order to suppress the chaotic behavior in gyroscope system, the sliding mode controller (SMC) is used and guaranteed the stability of the system from chaotic motion to periodic motion. Numerical simulations are shown to verify the results. The proposed DT method and controlling scheme provide an effective means of gaining insights into the nonlinear dynamics and controlling of gyroscope systems.     

Longitudinal–lateral velocity control design and implementation for a model-scaled unmanned helicopter

In this paper, a nonlinear controller is designed and implemented for longitudinal–lateral motion of a model-scaled helicopter. The underlying principle of controller design is the backstepping technique with slight modifications to accommodate the helicopter model. It is proved theoretically that, under the proposed controller, velocities and yaw angle of the closed-loop system are capable of tracking reference signals. A practical helicopter testbed is constructed to test the performances of the closed-loop system. Experimental results of practical flight tests demonstrate that performances of the closed-loop system are satisfactory.     

Optimal control of the transmission dynamics of tuberculosis

This paper deals with the problem of optimal control for the transmission dynamics of tuberculosis (TB). A tuberculosis model which incorporates the essential biological and epidemiological features of the disease such as exogenous reinfection and chemoprophylaxis of latently infected individuals, and treatment of the infectious is developed and rigorously analyzed. Based on this continuous model, the tuberculosis control is formulated and solved as an optimal control theory problem, indicating how a control term on the chemoprophylaxis should be introduced in the population to reduce the number of individuals with active TB. The feedback control law has been proved to be capable of reducing the number of individuals with active TB. An advantage is that the proposed scheme accounts for the energy wasted by the controller and the closed-loop performance on tracking. Numerical results show the performance of the optimization strategy.     

Nonlinear dynamics of a planar beam–spring system: analytical and numerical approaches

The multiple timescales method is applied to the exact partial differential equations of the planar motion of a hinged–simply supported beam with a linear axial spring of arbitrary stiffness. The forced-damped and free oscillations of the system around frequencies corresponding to nth natural bending mode are examined thoroughly and compared with numerical simulations as well as with already published results obtained by Lindstedt–Poincaré method. A special numerical technique using explicit finite element method to draw the frequency–response curves is appositely developed. The well-known jump phenomena between resonant and non-resonant branches, as well as superharmonic resonances, have been detected numerically.     

“Simple” solutions of the equations of dynamics for a polytropic gas

The notion of a “simple” solution of a system of differential equations that admit a local Lie group G of transformations of the basic space is considered as an invariant H-solution of type (0, 0) with respect to the subgroup HυG. Such solutions are attractive since they are described by explicit formulas that provide a clear physical interpretation for them. For gas-dynamic equations with a polytropic gas law, all simple solutions that are not related to special forms of gas flow are listed. Examples of simple solutions are given and the collapse phenomenon, which has been previously studied for barochronic flows, is described. Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 2, pp. 5–12, March–April, 1999.     

Nonlinear dynamics of a delayed Leslie predator–prey model

The present paper is concerned with a delayed Leslie predator–prey model. The conditions of boundedness of the solutions of the system, existence, and stability of the equilibrium of the system are investigated. Meanwhile, we find that the system can also undergo a Hopf bifurcation of nonconstant periodic solution at the positive equilibrium when the delay crosses through a sequence of critical values. The extensive simulations carried out show that the bifurcations arise around the positive equilibrium.     

Impulsive control induced effects on dynamics of single and coupled ODE systems

The dynamics of differential system can be changed very obviously after inputting impulse signals. Previous studies show that the single chaotic system can be controlled to periodic motions using impulsive control method. It was well known that the dynamics of hyper-chaotic and coupled systems are very important and more complex than those of a single system. In this paper, particular impulsive control of the hyper-chaotic Lü system was proposed, which is with outer impulsive signals. It can be seen that such impulsive strategy can generate chaos from periodic orbit or control chaos to periodic orbit etc. For the first time, impulsive control induced effects on dynamics of coupled systems are considered in this paper, where the impulse effect has outer input signals. Many interesting and useful results are obtained. The coupled system can realize synchronization and its synchronization manifold can be changed with such impulsive control signals. Strict theories are given, and numerical simulations confirm the correctness of theoretical results.     

Nonlinear dynamics of hardware-in-the-loop experiments on stick–slip phenomena

A single degree-of-freedom nonlinear mechanical model of the stick–slip phenomenon is studied when the Stribeck-type friction force is emulated by means of a digitally controlled actuator. The relative velocity of the slipping contact surfaces is considered as bifurcation parameter. The original physical system presents subcritical Hopf bifurcation with a wide bistable parameter region where stick–slip and steady-state slipping are both stable locally. Hardware-in-the-loop experiments are performed with a physical oscillatory system subjected to the emulated Stribeck forces. The effect of sampling time is studied with respect to the stability and nonlinear behavior of this experimental system. The existence of subcritical Neimark–Sacker bifurcations are proven in the digital system, the stability and bifurcation characteristics of the continuous and the digital systems are compared, and the counter-intuitive stabilizing effect of sampling time is shown both analytically and experimentally. The conclusions draw the attention to the limitations of hardware-in-the-loop experiments when the corresponding systems are strongly nonlinear.     

Nonlinear dynamics and conformational changes of linear entangled polymers using the Rolie-Poly model with an “effective” maximum contour length

The extended Rouse-CCR tube model for linear entangled polymers recently proposed by the authors (Kabanemi and Hétu, J Non Newtonian-Fluid Mech 160:113–121, 2009), designed to capture the progressive changes in the average internal structure (kinked state) of polymer chains, is here used to analyze, by means of a time-dependent three-dimensional finite element method, chain segment dynamics, pressure drop, and stability of flow through a 4:1:4 constriction in a tube. The model predicts an enhancement of the pressure drop in the stretch-dominated flow regime, which is also observed experimentally. This excess pressure drop was not associated with the onset of flow instability. The model also predicts kinked configurations within chain segments in the entry section to the constriction tube, at the inception of flow, and prior to the development of upstream vortices. It is also shown how these kinked configurations within chain segments influence pressure drop transients.     

Nonlinear incidence rate of a pest management SI model with biological and chemical control concern

A pest management SI model with impulsive releases of infective pests and spraying pesticides is proposed and investigated. We prove that all solutions of the model are uniformly ultimately bounded. We also obtain the sufficient conditions of globally asymptotic stability periodic solution of pest-extinction and permanence of the model. The approach of combining impulsive releasing infective pests with impulsive spraying pesticides provides reliable tactical basis for the practical pest management.     

Preface： Aerodynamics,dynamics and control of animal（insects,birds and bats） flight

Animal flight and swimming have long been of great interest to people.Besides curiosity about how their sophisticated aero-and hydrodynamic feats are performed,researches are very interested in the mechanics of animal flight and swimming for the following two reasons.One is that biologists need to understand the effects of aero-and hydrodynamic force production and energy expenditure on the physiology,behavior,evolution and other aspects of the animals.     

Nonlinear dynamics of a non-autonomous network with coupled discrete–continuum oscillators

A network model of a multi-modular floating platform incorporated with a runway structure, viewed as a non-autonomous network with discrete–continuum oscillators, is developed for a general purpose of dynamic analysis. Numerical analysis shows the coupling effect between the two different types of oscillators on various complex dynamics, including sudden leaps, torus motions, beating vibrations, the synergetic effect of phase lock and anti-phase synchronizations. The amplitude death phenomenon, a suppressed weak oscillation state, is studied by using the fundamental solution derived by the averaging method. The parametric domain of the onset of amplitude death is illustrated to show the great significance to the stability design of the floating platform. The effect of the flexural rigidity of the runway on the distribution of amplitude death state is also discussed.     

Nonlinear dynamics of axially moving beam with coupled longitudinal–transversal vibrations

In this study, the nonlinear vibrations of an axially moving beam are investigated by considering the coupling of the longitudinal and transversal motion. The Galerkin method is used to truncate the governing partial differential equations into a set of coupled nonlinear ordinary differential equations. By detuning the axially velocity, the exact parameters with which the system may turn to internal resonance are detected. The method of multiple scales is applied to the governing equations to study the nonlinear dynamics of the steady-state response caused by the internal–external resonance. The saturation and jump phenomena of such system have been reported by investigating the nonlinear amplitude–response curves with respect to external excitation, internal, and external detuning parameters. The longitudinal external excitation may trigger only longitudinal response when excitation amplitude is weak. However, beyond the critical excitation amplitude, the response energy will be transferred from the longitudinal motion to the transversal motion even the excitation is employed on the longitudinal direction. Such energy transfer due to saturation has the potential to be used in the vibration suppression.     

Homogenization of aligned “fuzzy fiber” composites

The aim of this work is to study composites in which carbon fibers coated with radially aligned carbon nanotubes are embedded in a matrix. The effective properties of these composites are identified using the asymptotic expansion homogenization method in two steps. Homogenization is performed in different coordinate systems, the cylindrical and the Cartesian, and a numerical example are presented.