Nonsingular Terminal Sliding Mode Control With Ultra-Local Model and Single Input Interval Type-2 Fuzzy Logic Control for Pitch Control of Wind Turbines

As wind energy is becoming one of the fastestgrowing renewable energy resources,controlling large-scale wind turbines remains a challenging task due to its system model nonlinearities and high external uncertainties.The main goal of the current work is to propose an intelligent control of the wind turbine system without the need for model identification.For this purpose,a novel model-independent nonsingular terminal slidingmode control(MINTSMC)using the basic principles of the ultralocal model(ULM)and combined with the single input interval type-2 fuzzy logic control(SIT2-FLC)is developed for non-linear wind turbine pitch angle control.In the suggested control framework,the MINTSMC scheme is designed to regulate the wind turbine speed rotor,and a sliding-mode(SM)observer is adopted to estimate the unknown phenomena of the ULM.The auxiliary SIT2-FLC is added in the model-independent control structure to improve the rotor speed regulation and compensate for the SM observation estimation error.Extensive examinations and comparative analyses were made using a real-time softwarein-the-loop(RT-SiL)based on the dSPACE 1202 board to appraise the efficiency and applicability of the suggested modelindependent scheme in a real-time testbed.

Precise robust motion control of cell puncture mechanism driven by piezoelectric actuators with fractional-order nonsingular terminal slidingmode control

A novel robust controller is proposed in this study to realize the precise motion control of a cell puncture mechanism(CPM)driven by piezoelectric ceramics(PEAs).The entire dynamic model of CPM is constructed based on the Bouc–Wen model,and the nonlinear part of the dynamic model is optimized locally to facilitate the construction of a robust controller.A model-based,nonlinear robust controller is constructed using time-delay estimation(TDE)and fractional-order nonsingular terminal sliding mode(FONTSM).The proposed controller does not require prior knowledge of unknown disturbances due to its real-time online estimation and compensation of unknown terms by using the TDE technology.The controller also has finite-time convergence and high-precision trajectory tracking capabilities due to FONTSM manifold and fast terminal sliding mode-type reaching law.The stability of the closed-loop system is proved by Lyapunov stability theory.Computer simulation and hardware-in-loop simulation experiments of CPM verify that the proposed controller outperforms traditional terminal sliding mode controllers,such as the integer-order or model-free controller.The proposed controller can also continuously output without chattering and has high control accuracy.Zebrafish embryo is used as a verification target to complete the cell puncture experiment.From the engineering application perspective,the proposed control strategy can be effectively applied in a PEA-driven CPM.

Construction of nonsingular formulae of variance and covariance function of disturbing gravity gradient tensors

When the computational point is approaching the poles, the variance and covariance formulae of the disturbing gravity gradient tensors tend to be infinite, and this is a singular problem. In order to solve the problem, the authors deduced the practical non-singular computational formulae of the first- and second-order derivatives of the Legendre functions and two kinds of spherical harmonic functions, and then constructed the nonsingular formulae of variance and eovarianee function of disturbing gravity gradient tensors.

Nonsingular terminal sliding mode approach applied to synchronize chaotic systems with unknown parameters and nonlinear inputs

This paper deals with the design of a novel nonsingular terminal sliding mode controller for finite-time synchro-nization of two different chaotic systems with fully unknown parameters and nonlinear inputs. We propose a novel nonsingular terminal sliding surface and prove its finite-time convergence to zero. We assume that both the master＇s and the slave＇s system parameters are unknown in advance. Proper adaptation laws are derived to tackle the unknown parameters. An adaptive sliding mode control law is designed to ensure the existence of the sliding mode in finite time. We prove that both reaching and sliding mode phases are stable in finite time. An estimation of convergence time is given. Two illustrative examples show the effectiveness and usefulness of the proposed technique. It is worthwhile noticing that the introduced nonsingular terminal sliding mode can be applied to a wide variety of nonlinear control problems.

SIMPLE SUFFICIENT CONDITIONS OF NONSINGULAR H-MATRICES

1 IntroductionH-matrices have important role in numerical analysis and matrix theory,etc.In thispaper,several practical criteria for H-matrices are obtained,to which the matrix is notnecessary be a diagonally dominant matrix,and the numbers of rows which are not diago-nal dominant can be n-1.We introduce the concept of α-diagonally dominant matrix,andby using the concept to investigate H-matrices.

Nonsingular Fast Terminal Sliding Mode Control Based on Nonlinear Disturbance Observer for a Quadrotor

Given external disturbances and system uncertainties,a nonsingular fast terminal sliding mode control(NFTSMC)method integrated a nonlinear disturbance observer(NDO)is put forward for quadrotor aircraft.First,a NDO is proposed to estimate the actual values of uncertainties and disturbances.Second,the NFTSM controller based on the reaching law is designed for the attitude subsystem(inner loop),and the control strategy can ensure Euler angles’fast convergence and stability of the attitude subsystem.Moreover,the NFTSMC strategy combined with backstepping is proposed for the position subsystem(outer loop),which can ensure subsystem tracking performance.Finally,comparative simulations show the trajectory tracking performance of the proposed method is superior to that of the traditional sliding mode control(SMC)and the SM integral backstepping control under uncertainties and disturbances.

Adaptive Neural Observer-Based Nonsingular Super-Twisting Terminal Sliding-Mode Controller Design for a Class of Hovercraft Nonlinear Systems

Designing a controller to stabilize maneuvering hovercrafts is an important challenge in amphibious vehicles.Hovercrafts are implemented in several applications,such as military missions,transportation,and scientific tasks.Thus.to improve their performance,it is crucial to control the system and compensate uncertainties and disruptions.In this paper,both classic and intelligent approaches are combined to design an observer-based controller.The system is assumed to be both controllable and observable.An adaptive neural network observer with guaranteed stability is derived for the nonlinear dynamics of a hovercraft,which is controlled via a nonsingular super-twisting terminal sliding-mode method.The main merits of the proposed method are as follows:(1) the Lyapunov stability of the overall closed-loop system,(2) the convergence of the tracking and observer errors to zero,(3) the robustness against uncertainties and disturbances,and(4) the reduction of the chattering phenomena.The simulation results validate the excellent performance of the derived method.

Decoupled nonsingular terminal sliding mode control for affine nonlinear systems

A decoupled nonsingular terminal sliding mode control（DNTSMC） approach is proposed to address the tracking control problem of affine nonlinear systems.A nonsingular terminal sliding mode control（NTSMC） method is presented,in which the nonsingular terminal sliding surface is defined as a special nonsingular terminal function and the convergence time of the system states can be specified.The affine nonlinear system is firstly decoupled into linear subsystems via feedback linearization.Then,a nonsingular terminal sliding surface is defined and the NTSMC method is applied to each subsystem separately to ensure the finite time convergence of the closed-loop system.The verification example is given to demonstrate the effectiveness and robustness of the proposed approach.The proposed approach exhibits a considerable advantage in terms of faster tracking error convergence and less chattering compared with the conventional sliding mode control（CSMC）.

ACCURATE COMPUTATION FOR IRREDUCIBLE NONSINGULAR M-MATRIX

Computing the eigenvalue of smallest modulus and its corresponding eigneveclor of an irreducible nonsingular M-matrix A is considered, It is shown that if the entries of A are known with high relative accuracy, its eigenvalue of smallest modulus and each component of the corresponding eigenvector will be determined to much higher accuracy than the standard perturbation theory suggests. An algorithm is presented to compute them with a small componentwise backward error, which is consistent with the perturbation results.

A SYMMETRICAL NONSINGULAR BOUNDARY ELEMENT METHOD

In this paper, on the basis of the theory of functional analysis, by the use of the complete orthogonal eigenfunction system, a fundamental solution of the control equation is constructed. By this method, a symmetrical nonsingular boundary element method is derived.

A DECOMPOSITION DEPENDED ON DIRECTIONS FOR NONSINGULAR LINEAR TRANSFORMATION

In this paper. we give a decomposition depending on p(1≤p≤n-2) orthonormaldirections assigned for nonsingular linear transformation F on a n-dimension (n≥3)Euclidean space En, and then prove foal there exist q(q=n-p) quasi-Principaldirections.for F depending on the preceding p orthonormal directions. As applicance ofthe preceding result, we derive that there exist at least two orthonormal principaldirections of strain in arbitrary plane of body which is in homogeneous deformation,and strain energy density is.function of 5 real numbers under arbitrary quasi-principalbase.for the preceding nonsingular linear transformation.

Nearfield acoustic holography in a moving medium based on particle velocity input using nonsingular propagator

Nearfield acoustic holography in a moving medium is a technique which is typically suitable for sound sources identification in a flow.In the process of sound field reconstruction,sound pressure is usually used as the input,but it may contain considerable background noise due to the interactions between microphones and flow moving at a high velocity.To avoid this problem,particle velocity is an alternative input,which can be obtained by using laser Doppler velocimetry in a non-intrusive way.However,there is a singular problem in the conventional propagator relating the particle velocity to the pressure,and it could lead to significant errors or even false results.In view of this,in this paper,nonsingular propagators are deduced to realize accurate reconstruction in both cases that the hologram is parallel to and perpendicular to the flow direction.The advantages of the proposed method are analyzed,and simulations are conducted to verify the validation.The results show that the method can overcome the singular problem effectively,and the reconstruction errors are at a low level for different flow velocities,frequencies,and signal-to-noise ratios.

Sufficient Conditions of Nonsingular H-matrices

From the concept of α diagonally dominant matrix, two sufficient conditions of nonsingular H-matrices were obtained in this paper. An example was given to show that these results improve the known results.

High-Precision Nonsingular Integrator of Guiding-Center Orbit Close to Magnetic Axis in Tokamak Equilibrium Configuration

Equations of guiding-center motion without the coordinate singularity at the magnetic axis have been derived from the guiding-center Lagrangian.The poloidal magnetic flux is suggested to be included as one of the nonsingular coordinates for the computation of the guidingcenter orbit.The numerical results based on different nonsingular coordinates are verified using the GCM code which is based on canonical variables.A comparison of numerical performance among these nonsingular coordinates and canonical coordinates has been carried out by checking the conservation of energy and toroidal canonical momentum.It is found that by using the poloidal magnetic flux in the nonsingular coordinate system,the numerical performance of nonsingular coordinates can be greatly improved and is comparable to that of canonical variables in long-time simulations.

Notes on Phase Transition of Nonsingular Black Hole

On the belief that a black hole is a thermodynamic system, we study the phase transition of nonsingular black holes. If the black hole entropy takes the form of the Bekenstein-Hawking area law, the black hole mass M is no longer the internal energy of the black hole thermodynamic system. Using the thermodynamic quantities, we calculate the heat capacity, thermodynamic curvature and free energy. It is shown that there will be a larger black hole/smaller black hole phase transition for the nonsingular black hole. At the critical point, the second-order phase transition appears.

Nonsingularity on Level-k (r_1, r_2,…, r_k)-circulant Matrices of Type (n_1, n_2,…, n_k)

In this paper,it is given that the new equivalent definition of level-k (r1,r2, …,rk)-cir culant matrices of type (n1,n2,…,nk) in [1] and we give the explicit expression of its the eigenval ues and four methods of discriminations its nonsingularity by utilizing only parameter r1,r2, …,rk and elements of the first row of the sorts matrices.

A DIRECT ALGORITHM FOR DISTINGUISHING NONSINGULAR M-MATRIX AND H-MATRIX

A direct algorithm is proposed by which one can distinguish whether a matrix is an M-matrix (or H-matrix) or not quickly and effectively. Numerical examples show that it is effective and convincible to distinguish M-matrix (or H-matrix) by using the algorithm.

H-tensors and nonsingular H-tensors

The H-matrices are an important class in the matrix theory, and have many applications. Recently, this concept has been extended to higher order H-tensors. In this paper, we establish important properties of diagonally dominant tensors and H-tensors. Distributions of eigenvalues of nonsingular symmetricH-tensors are given. An J（t%-tensor is semi-positive, which enlarges the area of semi-positive tensor from H-tensor to H＋-tensor. The spectral radius of Jacobi tensor of a nonsingular （resp. singular） H-tensor is less than （resp. equal to） one. In particular, we show that a quasi-diagonally dominant tensor is a nonsingular H-tensor if and only if all of its principal sub-tensors are nonsingular H-tensors. An irreducible tensor H is an H-tensor if and only if it is quasi-diagonally dominant.

Design of two dimensional nonsingular internal-external cloaks with arbitrary cross-section

According to the combination of the complementary medium and transformation optics, the shape of two-dimensional (2D) internal-external cloaks has been generalized into any geometry to adapt to the variety of object shapes. In order to adapt to the practical application, some approximations have been introduced to eliminate the infinite singularity of the parameters in the compressed region by adjusting the principle sketch out of the plane. Firstly, the general parameter equations of the nonsingular cloak with arbitrary cross-section are deduced strictly by the mathematical method based on coordinate transformations in the cylindrical coordinate system. Secondly, taking into account the discontinuous property of the curve functions of arbitrary polygons, a supplementary investigation is given for the nonsingular cloak with arbitrary polygonal cross-section. The transformations in the supplementary study are carried out in the Cartesian coordinate system directly and referred to the coordinates of the polygon's vertices rather than the curve function of the polygon. Last, the invisibility effect of the corresponding cloak is studied by full-wave simulations based on the finite element method. The applicable scope of the 2D internal-external cloak is expanded greatly by the methods and results given in this paper.

Improved Nonsingular Fast Terminal Sliding Mode Control of Unmanned Underwater Hovering Vehicle

An improved nonsingular fast terminal sliding mode manifold based on scaled state error is proposed in this paper.It can significantly accelerate the convergence rate of the state error which is initially far from the origin and achieve the fixed-time convergence.In addition,conventional double power term based reaching law is improved to ensure the convergence of sliding state in the presence of disturbances.The proposed approach is applied to the hovering control of an unmanned underwater vehicle.The controller exhibits both fast convergence and strong robustness to model uncertainty and external disturbances.