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.     

Soliton interaction control through dispersion and nonlinear effects for the fifth-order nonlinear Schrödinger equation

Nonlinear Dynamics - Optical fiber communication has developed rapidly because of the needs of the information age. Here, the variable coefficients fifth-order nonlinear Schrödinger equation...     

Vertical vibration control using nonlinear energy sink with inertial amplifier

To reduce additional mass, this work proposes a nonlinear energy sink(NES)with an inertial amplifier(NES-IA) to control the vertical vibration of the objects under harmonic and shock excitations. Moreover, this paper constructs pure nonlinear stiffness without neglecting the gravity effect of the oscillator. Both analytical and numerical methods are used to evaluate the performance of the NES-IA. The research findings indicate that even if the actual mass is 1% of the main oscillator, the NES-IA...     

Vibration control of nonlinear Absorber–Isolator-Combined structure with time-delayed coupling

A nonlinear combined structure consisted of isolator and absorber with time-delayed coupling active control is proposed in this study, whose vibration suppression effectiveness and control mechanism are investigated. The mathematical model of the combined structure is obtained and stability analysis for different structural parameters and time delay are firstly carried out, which provides a general guideline for the ranges of active control parameters. Then the combined effect of nonlinearity and time delay on vibration suppression and energy transfer is discussed in details based on the analysis of control mechanism by the method of multiple scales. Since the time-delayed nonlinear absorber can induce internal resonance between different modes, the vibration energy at low frequencies can be transferred to high frequency mode and the vibration of the fundamental frequency range is thus suppressed. This paper provides a novel application of internal resonance in vibration suppression of an Absorber–Isolator-Combined structure.     

A nonlinear high gain observer based input–output control of flexible link manipulator

The input–output control strategy needs all of the states feedback. However, in flexible link robot manipulators, measuring the time rate of elastic degrees of freedom is practically impossible. In this paper, a new nonlinear high gain observer has been developed to estimate the elastic degrees of freedom and their time derivatives. The control strategy is based on an output redefinition approach which stabilizes the zero dynamics of the manipulator. Finally, the results are presented by implementing the proposed observer and controller on a single link flexible manipulator. Numerical simulations will support the validity of our research results.     

Dynamic model based nonlinear tracking control of a planar parallel manipulator

Based on the dynamic model, a novel nonlinear tracking controller is developed to overcome the nonlinear dynamics and friction of a planar parallel manipulator. The dynamic model is formulated in the active joint space, and the active joint friction is described with the Coulomb + viscous friction model. A nonlinear tracking controller is designed to eliminate the tracking error by using the power function. The nonlinear tracking controller is proven to guarantee asymptotic convergence to zero of both the tracking error and error rate with the Barbalat’s lemma. The trajectory tracking experiment of the proposed controller is implemented on an actual five-bar planar parallel manipulator both at the low-speed and high-speed motion. Moreover, the control performances of the proposed controller are compared with the results of the augmented PD (APD) controller.     

Sliding-mode control of switched delay systems with nonlinear perturbations: average dwell time approach

This paper investigates the robust sliding-mode control (SMC) problem for a class of uncertain switched systems with a time delay. The design process of sliding-mode control is divided into two steps. First, a sliding surface is constructed such that the reduced-order equivalent sliding mode restricted to the sliding surface is completely invariant to all admissible uncertainties under switching laws with an average dwell-time property. Second, variable structure controllers are developed to drive the states of the switched delay system to reach the sliding surface in finite time and remain on it thereafter. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.     

Finite-time output feedback control for a class of second-order nonlinear systems with application to DC–DC buck converters

The problem of output feedback control for a class of second-order nonlinear systems is investigated in this paper. Using the techniques of finite-time control and finite-time convergent observer, an observer-based finite-time output feedback controller is proposed which can guarantee that the system’s state converges to the equilibrium in a finite time. As an application of the proposed theoretical results, the problem of finite-time control without current signal for the DC–DC buck converters is solved. Simulation results are given to demonstrate the effectiveness of the proposed method.     

Fractional nonlinear energy sinks

The cubic or third-power(TP) nonlinear energy sink(NES) has been proven to be an effective method for vibration suppression, owing to the occurrence of targeted energy transfer(TET). However, TET is unable to be triggered by the low initial energy input, and thus the TP NES would get failed under low-amplitude vibration. To resolve this issue, a new type of NES with fractional nonlinearity, e.g., one-third-power(OTP)nonlinearity, is proposed. The dynamic behaviors of a linear oscillator(LO) with...     

Comments and modifications on: “Pragmatical adaptive synchronization of different orders chaotic systems with all uncertain parameters via nonlinear control”

In Ref. Li and Ge (Nonlinear Dyn. 64:77?C87, 2011), the authors proposed a new adaptive synchronization scheme by pragmatical asymptotically stability theorem. However, there are a few errors in the proof of the stability, and the controller cannot be implemented. In this letter, a modified control law is proposed, and the corresponding proof is given. Simulation results show the effectiveness of the modified method.     

Substructures’ coupling with nonlinear connecting elements

Nonlinear Dynamics - The analysis of complex structures is often very challenging since reliable data can only be obtained if the underlying model represents properly the real case. Thus,...     

Global solution for coupled nonlinear Klein-Gordon system

The globed solution for a coupled nonlinear Klein-Gordon system in two-dimensional space was studied. First, a sharp threshold of blowup and global existence for the system was obtained by constructing a type of cross-constrained variational problem and establishing so-called cross-invariant manifolds of the evolution flow. Then the result of how small the initial data for which the solution exists globally was proved by using the scaling argument.     

Finite-time synchronization control for a class of perturbed nonlinear systems with fixed convergence time and hysteresis quantizer: applied to Genesio–Tesi chaotic system

In the present article, a terminal sliding mode control strategy has been proposed in order to address the synchronization problem for a class of perturbed nonlinear systems with fixed convergence time and input quantization. The proposed protocol guarantees the fixed-time convergence of the sliding manifold to the origin, which means that the convergence time of the proposed sliding manifold does not change on the variations of initial values, different from typical control methods. Here, the hysteresis quantizer, as a specific type of quantizer with nonlinear sector-bounded, is applied in order to quantize the input signal. The proposed quantized control scheme vigorously prevents the potential adverse chattering phenomenon which is experienced in the common quantization methods. The proposed controller does not need the limiting criteria related to considered parameters of quantization compared to recent control approaches. Finally, the designed controller is implemented on the perturbed Genesio–Tesi (G–T) chaotic systems to verify effectiveness and strength of the proposed method.

     

The effect of blade vibration on the nonlinear characteristics of rotor–bearing system supported by nonlinear suspension

In this paper, the complicated nonlinear dynamics of the harmonically forced quasi-zero-stiffness SD (smooth and discontinuous) oscillator is investigated via direct numerical simulations. This oscillator considered that the gravity is composed of a lumped mass connected with a vertical spring of positive stiffness and a pair of horizontally compressed springs providing negative stiffness, which can achieve the quasi-zero stiffness widely used in vibration isolation. The local and global bifurcation analyses are implemented to reveal the complex dynamic phenomena of this system. The double-parameter bifurcation diagrams are constructed to demonstrate the overall topological structures for the distribution of various responses in parameter spaces. Using the Floquet theory and parameter continuation method, the local bifurcation patterns of periodic solutions are obtained. Moreover, the global bifurcation mechanisms for the crises of chaos and metamorphoses of basin boundaries are examined by analysing the attractors and attraction basins, exploring the evolutions of invariant manifolds and constructing the basin cells. Meanwhile, additional nonlinear dynamic phenomena and characteristics closely related to the bifurcations are discussed including the resonant tongues, jump phenomena, amplitude–frequency responses, chaotic seas, transient chaos, chaotic saddles, and also their generation mechanisms are presented.     

On Hashin–Shtrikman-type bounds for nonlinear conductors

For linear composite conductors, it is known that the celebrated Hashin–Shtrikman bounds can be recovered by the translation method. We investigate whether the same conclusion extends to nonlinear composites in two dimensions. To that purpose, we consider two-phase composites with perfectly conducting inclusions. In that case, explicit expressions of the various bounds considered can be obtained. The bounds provided by the translation method are compared with the nonlinear Hashin–Shtrikman-type bounds delivered by the Talbot–Willis (1985) [2] and the Ponte Castañeda (1991) [3] procedures.     

Homogeneous diffusion in ℝ with power-like nonlinear diffusivity

We study the nonnegative solutions of the initial-value problem u_t=(u^r|u_x|^p-1u_x)_x,u(x, 0)L ¹(), where p>0, r+p>0. The local velocity of propagation of the solutions is identified as V = -v_x| v_x|^p-1 where v =cu (with r +p - 1)/p and c (r +p/(r +p- 1)) is the nonlinear potential. Our main result is the a priori estimate (v_x|v_x|^p-1)_x-

On ‘roller-coaster’ experiments for nonlinear oscillators

We consider the dynamics of roller-coaster type experimental models used as analog devices for nonlinear oscillators. It is shown how to chose the shape of the track in order to achieve a desired oscillator equation, in terms of the are length coordinate or its projection onto the horizontal. Explicit calculations are carried out for the linear oscillator, the so-called escape equation, the two-well Duffing oscillator, and the pendulum.     

Quantized state feedback-based $$\varvec{\mathcal {H}_\infty }$$ H ∞ control for nonlinear parabolic PDE systems via finite-time interval

Nonlinear Dynamics - In this paper, the finite-time $${\mathcal {H}}_\infty $$ control problem of nonlinear parabolic partial differential equation (PDE) systems with parametric uncertainties is...     

Isogeometric analysis of nonlinear Euler–Bernoulli beam vibrations

In this paper we analyze the vibrations of nonlinear structures by means of the novel approach of isogeometric finite elements. The fundamental idea of isogeometric finite elements is to apply the same functions, namely B-Splines and NURBS (Non-Uniform Rational B-Splines), for describing the geometry and for representing the numerical solution. In case of linear vibrational analysis, this approach has already been shown to possess substantial advantages over classical finite elements, and we extend it here to a nonlinear framework based on the harmonic balance principle. As application, the straight nonlinear Euler–Bernoulli beam is used, and overall, it is demonstrated that isogeometric finite elements with B-Splines in combination with the harmonic balance method are a powerful means for the analysis of nonlinear structural vibrations. In particular, the smoother k-method provides higher accuracy than the p-method for isogeometric nonlinear vibration analysis.