Nonlinear State Research Articles

Accurate voltage regulation for a DC microgrid using nonlinear state feedback controller

AbstractThe high penetration of distributed generation systems poses challenges in effectively managing both DC bus voltage and power‐sharing in DC microgrids (MGs). To ensure precise voltage regulation across various distributed generation systems and maintain overall system stability, this paper studies the modelling and control of an islanded DC MG described by a set of nonlinear‐nonaffine differential equations. In the proposed DC MG, a battery storage, a photovoltaic (PV) power plant, and a back‐end power converter with DC loads have been connected to a common DC bus. First, a dynamic model of a DC MG was developed. Then, to find the maximum power point of solar PV, a straightforward method based on an artificial neural net is employed. Afterward, a nonlinear local state feedback controller through output regulation theory is applied to achieve voltage stability, overcoming the drawbacks of droop‐based techniques. Moreover, partial state feedback capability simplifies controller design. To verify the effectiveness of the proposed approach, various scenarios, including sudden load variation, illumination change, and changes in the MG configuration, have been examined. Finally, numerical studies were carried out in a simulation environment to demonstrate the superiority of the proposed nonlinear control scheme over constant feedback control.

In-Plane Chemical Ordering (Mo2/3R1/3)2AlB2 (R = Tb, Dy, Ho, Er, Tm, and Lu) i-MAB Phases and their Two-Dimensional Derivatives (MBene): Synthesis, Structure, Magnetic, and Supercapacitor Performance.

A family of hexagonal in-plane chemical ordering (Mo2/3R1/3)2AlB2 (R = Tb, Dy, Ho, Er, Tm, and Lu) i-MAB phases are synthesized with R-3m hexagonal structure. The i-MAB phases with R = Tb to Tm are considered to have a nonlinear ferromagnetic-like coupling magnetic ground state with gradually weakened magnetocrystalline anisotropy due to variant R-R distances and 4f electrons. Their 2D derivatives (2D-MBene) with rare-earth (R) atom vacancies are obtained by chemical etching. The delamination solvent, surface functional terminations, and chemical bond of 2D-MBene can be modified by one-step nitridation in environment-friendly nitrogen instead of ammonia. A phase conversion is caused by nitridation at 973 K from 2D-MBene to Mo2N, leading to the optimized specific capacitance of 229 F g-1. Besides exploring more rare-earth-containing laminated boride systems, this work also demonstrates the promising application of their 2D derivatives with R vacancies in supercapacitors.

Identification of structured nonlinear state–space models for hysteretic systems using neural network hysteresis operators

Hysteretic system behavior is ubiquitous in science and engineering fields including measurement systems and applications. In this paper, we put forth a nonlinear state–space system identification method that combines the state–space equations to capture the system dynamics with a compact and exact artificial neural network (ANN) representation of the classical Prandtl–Ishlinskii (PI) hysteresis. These ANN representations called PI hysteresis operator neurons employ recurrent ANNs with classical activation functions, and thus can be trained with classical neural network learning algorithms. The structured nonlinear state–space model class proposed in this paper, for the first time, offers a flexible interconnection of PI hysteresis operators with a linear state–space model through a linear fractional representation. This results in a comprehensive and flexible model structure. The performance is validated both on numerical simulation and on measurement data.

On error-driven nonlinear ESO based control design with application to air–fuel ratio control of engines

In this paper, the tracking control problem of the uncertain control system is studied in the frame of uncertainties estimation and compensation. To eliminate the influence of external disturbances and internal uncertainties on the control system, the error-driven nonlinear extended state observer (EDN-ESO), whose gain is set as an increasing function with respect to the absolute value of estimation error of the system output, is proposed to improve the estimation performance for the “total disturbance”. Next, both the estimation error of proposed ESO and the tracking error of system output are proven to be bounded by selecting the lower bound and variation range of ESO’s bandwidth. Moreover, the convergence of the estimation error as well as the tracking error to zero is proven under certain conditions. Finally, the proposed design method is applied to the air–fuel ratio control system of gasoline engines, and the experimental results show that the proposed EDN-ESO can effectively adjust the observer gain, so as to enhance the tracking performance.

One new composite control based smooth nonlinear fractional order sliding mode algorithm and disturbance compensation for PMSM with parameter uncertainties

To achieve high-quality control of PMSM with parameter uncertainties, a nonlinear smooth fractional order sliding mode composite control (NSFOSMCC) strategy is designed in this paper. This approach incorporates a novel nonlinear smooth fractional order sliding mode controller, a novel adaptive super-twisting (AST) algorithm, and a modified nonlinear extended state observer (ESO) to achieve enhanced motor performance. To effectively overcome the disadvantages of simplicity and toughness associated with the conventional fractional order sliding mode controller, a novel nonlinear smooth fractional order sliding mode controller is designed. A novel AST technique is introduced to effectively weaken chattering issues. The modified nonlinear ESO is used to estimate the uncertainty parameters of the PMSM. By combining the modified nonlinear ESO with the latest sliding mode controller, a new composite controller called NSFOSMCC strategy is developed for PMSM. The proposed NSFOSMCC strategy, utilizing a combination of “feedforward plus feedback,” is implemented for PMSM with parameter uncertainties. The reliability and stability of the controller are thoroughly established through the utilization of the Lyapunov stability theorem. Furthermore, comparative results show strong evidence supporting the effectiveness of the novel composite control strategy.

Symbiotic Ocean Modeling Using Physics‐Controlled Echo State Networks

AbstractWe introduce a “symbiotic” ocean modeling strategy that leverages data‐driven and machine learning methods to allow high‐ and low‐resolution dynamical models to mutually benefit from each other. In this work we mainly focus on how a low‐resolution model can be enhanced within a symbiotic model configuration. The broader aim is to enhance the representation of unresolved processes in low‐resolution models, while simultaneously improving the efficiency of high‐resolution models. To achieve this, we use a grid‐switching approach together with hybrid modeling techniques that combine linear regression‐based methods with nonlinear echo state networks. The approach is applied to both the Kuramoto–Sivashinsky equation and a single‐layer quasi‐geostrophic ocean model, and shown to simulate short‐term and long‐term behavior better than either purely data‐based methods or low‐resolution models. By maintaining key flow characteristics, the hybrid modeling techniques are also able to provide higher quality initial conditions for high‐resolution models, thereby improving their efficiency.

Nonlinear Extended State Observer Based Super-Twisting Terminal Sliding Mode Synchronous Control for Parallel Drive Systems

Addressing the issue to restrain the nonlinear coupling disturbance in the multimotor parallel drive system and acquiring perfect driving control performance, a novel super-twisting terminal sliding mode synchronous control (STSC) is proposed. In this control scheme, a lumped error (LE) with a synchronization coefficient is designed to transform coupled control into LE convergence. Then, a recursive terminal sliding mode function with two layers is introduced. Based on this sliding mode function, the STSC scheme is proposed, and it can guarantee the LE finite-time convergence and the continuous control action in nature. A nonlinear extended state observer (NESO) is introduced to enhance robustness. Moreover, the NESO not only provides an estimation of disturbance but also provides a smooth velocity signal. Therefore, differential operations and filtering operations are avoided. Finally, a compound control scheme is obtained. Compared with conventional super-twisting algorithm (STA), the robustness is enhanced by embedding NESO-based disturbance compensation, and the advantage of continuous control action is inherited. The major advantages of this scheme are characterized by output-based information only used, good model adaptability, and strong disturbance rejection ability. Experimental results show the effectiveness of the proposed control law.

Beyond Battery State of Charge Estimation: Observer for Electrode-Level State and Cyclable Lithium With Electrolyte Dynamics

This paper presents a provably convergent battery estimation scheme based on a single particle model with electrolyte dynamics (SPMe), by proposing a systematic methodology to estimate critical information such as electrode-level states, electrolyte dynamics, and cyclable lithium. Electrode-level state estimation suffers from weak observability originating from two standalone electrode dynamics, which is then aggravated by the addition of electrolyte dynamics. This lack of observability can be alleviated by exploiting lithium inventory conservation enabled by Kalman decomposition, allowing one to separate out the unobservable subspace. Assuming the knowledge of cyclable lithium, a nonlinear state observer with provable convergence can be constructed for the SPMe model, using voltage and current measurements. To relax this strong assumption, a sensitivity-based parameter estimation scheme is also deployed to track cyclable lithium – a crucial physical variable for capacity fade. Ultimately, the estimation framework can perform finer monitoring and diagnosis of battery charge and health down to the level of individual electrode and the electrolyte. Experimental validation demonstrates <1% estimation error for cyclable lithium inventory. Solid phase lithium concentration estimates, especially in the negative electrode, can be sensitive to disturbances in cyclable lithium.

DC‐Link Voltage Control Strategy of High‐Gain Bidirectional Quasi‐Z Source Inverter

This article presents an improved method combining active disturbance rejection control (ADRC) and sliding mode control (SMC) to address the problem of non‐minimum phase characteristics of high‐gain bidirectional quasi‐Z source inverters. The present study is specifically targeting the robustness of the DC‐link voltage. Firstly, a high‐gain bidirectional quasi‐Z source inverter is proposed, enabling high‐gain and bidirectional energy flow. The operation principle is analyzed, and the topology with non‐minimum phase characteristics is obtained through small signal modeling. To overcome the non‐minimum phase characteristic, the active disturbance rejection control‐sliding mode control (ADRC‐SMC) method is employed to control the DC‐link voltage indirectly by controlling the capacitor voltage. Building upon the principles of ADRC using the FAL function, an improved nonlinear function called HFAL function is proposed. The nonlinear state error feedback law is implemented using a designed sliding‐mode controller that introduces an exponential convergence law. Simulation and experimental results demonstrate the superior robustness of the improved ADRC‐SMC method in controlling the DC‐link voltage of the high‐gain bidirectional quasi‐Z source inverter, effectively avoiding system jitter and enhancing the overall system immunity. © 2023 Institute of Electrical Engineer of Japan and Wiley Periodicals LLC.

Dirac solitons and topological edge states in the β-Fermi-Pasta-Ulam-Tsingou dimer lattice.

We consider a dimer lattice of the Fermi-Pasta-Ulam-Tsingou (FPUT) type, where alternating linear couplings have a controllably small difference and the cubic nonlinearity (β-FPUT) is the same for all interaction pairs. We use a weakly nonlinear formal reduction within the lattice band gap to obtain a continuum, nonlinear Dirac-type system. We derive the Dirac soliton profiles and the model's conservation laws analytically. We then examine the cases of the semi-infinite and the finite domains and illustrate how the soliton solutions of the bulk problem can be glued to the boundaries for different types of boundary conditions. We thus explain the existence of various kinds of nonlinear edge states in the system, of which only one leads to the standard topological edge states observed in the linear limit. We finally examine the stability of bulk and edge states and verify them through direct numerical simulations, in which we observe a solitonlike wave setting into motion due to the instability.

Passive bias-free non-reciprocal metasurfaces based on thermally nonlinear quasi-bound states in the continuum

Passive bias-free non-reciprocal metasurfaces based on thermally nonlinear quasi-bound states in the continuum

Teleportation of superposed nonlinear coherent states

In this paper, we study the teleportation of nonlinear coherent cat states assuming even and odd nonlinear quasi-Bell states as the channel. Odd nonlinear quasi-Bell states are shown to be maximally entangled independent of the coherent parameter and also nonlinear function but the entanglement of the even nonlinear coherent states depends on the parameters involved. Subsequently, the teleportation probability is evaluated for some nonlinear functions. Our research reveals that when even and odd nonlinear quasi-Bell states are assumed as the quantum channel, the probabilities for successful teleportation are oppositely varied by increasing coherent parameter. For the special case of nonlinear harmonious states, the teleportation probability is a decreasing (increasing) function of the coherent parameter if even (odd) nonlinear quasi-Bell state is used as the channel.

Observer-Based Adaptive Control for Trajectory Tracking of AUVs with Input Saturation

In this paper, an observer-based adaptive control method is investigated for the horizontal trajectory tracking of autonomous underwater vehicles (AUV) with input saturation and system disturbances. Firstly, the desired surge speed and trajectory angle are established, which could decouple the tracking error subsystem and avoid the complex form. Secondly, the input saturation is approximated by a smooth function, and a nonlinear extended states observer (NESO) is designed for estimating system disturbances. Based on the command filtered backstepping technique, which can avoid the explosion caused by the derivative of the virtual control, an observer-based adaptive output feedback control method is developed, and an auxiliary system is applied to compensate for filtered tracking errors, input saturation bias, and observer errors. Finally, simulation results show the proposed method has good robustness in the face of system uncertainties, and the error is nearly 33.3% smaller than that of other control methods when meeting sudden trajectory changes. A good control performance is guaranteed.

Active Disturbance Rejection Control Algorithm for the Driven Branch Chain of a Polishing Robot

To overcome poor error suppression performance and low control accuracy in the polishing robot-driven branch chain control system, this paper proposes an improved active disturbance rejection control (ADRC) from the design of the derived nonlinear function. Subsequently, the tracking differentiator (TD), extended state observer (ESO) and nonlinear state error feedback (SEF) are designed in the ADRC, and the driven branch’s ADRC servo-control system is established based on the permanent magnet synchronous motor (PMSM) with each driven branch. Meantime, by establishing first-order and second-order ADRC, current-loop control, and speed-and-position-loop control are realized, respectively. Finally, this study analysed differences in the speed and motor rotor error performance between the proportional-integral-derivative (PID)control and ADRC control strategy by using Simulink. Furthermore, an experiment platform, including hardware and software, is built to validate some inclusions. The results show that the ADRC not only realises high-precision trajectory tracking control but also ensures the rapid response performance of the system.

Output tracking for nonlinear stochastic systems driven by bounded and colored noises

In this paper, we consider practical tracking problem for a class of nonlinear stochastic systems driven by bounded and colored noises by means of active disturbance rejection control approach. The nonlinear extended state observer with homogeneous weighted functions is constructed to estimate in real time the unmeasurable state and the total stochastic disturbance that affects system performance. An observer-based output feedback is designed to guarantee the almost surely practical convergence of the tracking errors. The existence of the global weak solution of the closed-loop system is proved and the tracking convergence accuracy is shown to be higher than that of linear one under the same tuning parameters. Some numerical simulations are carried out to validate the effectiveness of the proposed controller.

Novel Active Disturbance Rejection‐Based Sliding‐Mode Control for Permanent Magnet Linear Synchronous Motor Drives

Active disturbance rejection control (ADRC) has been widely used in the permanent magnet linear synchronous motor (PMLSM) drive system for its strong anti‐disturbance ability and fast response speed. However, a large number of adjustment parameters add difficulties to its application. To solve this problem, a novel sliding mode‐based active disturbance rejection control (SM‐ADRC) with autotuned parameters is proposed in this paper. In this control strategy, the SM is incorporated with extended state observer (ESO) and nonlinear state error feedback (NLSEF) to reduce the number of adjustment parameters. The simulated annealing particle swarm optimization (SAPSO) algorithm is carried out to achieve the optimal configuration and realize parameter self‐tuning. The experimental results of the PMLSM speed servo system demonstrate the proposed control method has better suppression of chattering effect, disturbance rejection ability and fast dynamic response. © 2023 Institute of Electrical Engineer of Japan and Wiley Periodicals LLC.

Gap solitons and nonlinear Bloch states in Bose-Einstein condensates with current-dependent interactions

Gap solitons and nonlinear Bloch states in Bose-Einstein condensates with current-dependent interactions

Robust adaptive output feedback for the formation control of heterogeneous ships based on a nonlinear extended state observer

This study considers the formation control problem of heterogeneous ships with unknown time-varying disturbances, dynamic uncertainties, and unmeasurable speeds, a robust adaptive output feedback formation control scheme for the heterogeneous ships based on nonlinear extended state observer is developed. In order to solve the heterogeneous ships formation control problem with leader-following structure, transforming the formation control problem into a class of ship trajectory tracking problem by improving the design of the virtual ship. Firstly, a nonlinear extended state observer is designed for estimating ship speeds due to technical limitations and external disturbances. Then, combining the adaptive neural networks with disturbances adaptive law to deal with the unknown time-varying disturbances and dynamic uncertainties. Meanwhile, the second-order tracking differentiator is designed to calculate the derivative of the virtual control law, which has higher precision comparing to the first-order filter. Stability theory is proved that all the signal of closed-loop control system are uniformly ultimately bounded, and the tracking errors can converge into arbitrary small neighborhoods around zero. Finally, comparative simulations were performed to demonstrate the effectiveness of the proposed controller.

Nonclassicality of entangled Schrödinger cat states associated to generalized displaced Fock states

In this paper, we introduce some distinct classes of entangled cat states associated to generalized displaced Fock states. For this purpose, we use the formalism of nonlinear coherent states corresponding to nonlinear oscillator algebra which yields various kinds of f-deformed entangled states. We also take a particular class of Gilmore-Perelomov-type of SU(1, 1) and a class of SU(2) coherent states. We then obtain the amount of entanglement between subsystems of the quantum states of interest by applying the measure of concurrence. Furthermore, examining some of the most important criteria, such as Mandels Q parameter, quadrature squeezing and Vogels characteristic function, we study the nonclassicality of the introduced quantum states. The numerical results show remarkable values of entanglement, sub-Poissonian statistics of the field, and squeezing indicating that the introduced states can be regarded as possible candidates for nonclassical entangled states. Afterwards, we see that the Vogel function for quantum states of interests goes beyond the value of characteristic function of the ground state, which shows the nonclassicality of the introduced states.

Stationary states and switching dynamics of the self-defocusing nonlinear coupled system with PT-symmetric [formula omitted]-wavenumber Scarf II potential

The stationary states and switching dynamics of the parity-time (PT) symmetric coupled system with k-wavenumber Scarf II potential in the self-defocusing nonlinear regime have been analysed. The eigenmodes with central peaks are evolved in the linear regime, whereas those with central dips are evolved in the defocusing nonlinear regime, for ground, 2nd, and 4th excited states. The threshold condition of the PT-symmetry breaking and the effect of coupling, self-defocusing nonlinearity, and width of the potential on the high and low-frequency modes of the ground and excited states have been analysed. The stability of the eigenmodes is verified using the linear stability analysis. The power-switching dynamics between the gain and lossy channels of the system has been analysed. The input power-dependent switching and the effects of gain/loss and potential width on the switching are discussed.