Perturbation Estimation Research Articles

Design of adaptive sliding mode controllers for perturbed nonlinear systems with partial unmeasurable states and state constraints

A sliding mode control (SMC) strategy is proposed in this paper for a class of perturbed nonlinear systems with unmeasurable states and state constraints to deal with the state tracking problems. First of all, a partial states observer is designed for solving the problems due to unmeasurable states. The estimation errors will approach zero in a finite time. Secondly, based on a designed barrier Lyapunov function, one designs the sliding surface function and an adaptive sliding mode tracking controller to ensure that the states have the ability to track the desired signals. Moreover, the tracking error is capable of converging to zero in a finite time without violating the given state’s constraints. Perturbation estimator and adaptive mechanisms are also utilized so that there is no need to know the upper bounds of perturbations and perturbation estimation errors in advance. Finally, a numerical example and a practical application are provided to demonstrate the effectiveness and applicability of the proposed control strategy.

Strong Relativistic Effects in Lanthanide-Based Single-Molecule Magnets.

Lanthanide-based single-molecule magnets (SMMs) are promising building blocks for quantum memory and spintronic devices. Designing lanthanide-based SMMs with long spin relaxation time requires a detailed understanding of their electronic structure, including the crucial role of the spin-orbit coupling (SOC). While traditional calculations of SOC using the perturbation theory applied to a solution of the nonrelativistic Schrödinger equation are valid for light atoms, this approach is questionable for systems containing heavy elements such as lanthanides. We investigate the accuracy of the perturbation estimates of SOC by variationally solving the Dirac equation for the [DyO]+ molecule, a prototype of a lanthanide-based SMM. We show that the energy splittings between the states involved in spin relaxation depend on the interplay between strong SOC and dynamic electron correlation. We demonstrate that this interplay affects the resonances between the spin and vibrational transitions and, therefore, the spin relaxation time.

Improved Active Disturbance Rejection Control Strategy for LCL-Type Grid-Connected Inverters Based on the Backstepping Method

In the process of grid connection of an LCL inverter, sudden changes in load, high harmonics of the grid voltage, sudden changes in power, and other disturbances often occur. These will cause sharp degradation of the grid-connected power quality, so this paper proposes a new solution to the problem of how to reduce and eliminate disturbances in power quality by using a first-order linear active disturbance rejection control (LADRC) strategy with precise compensation via splitting the total disturbance term. An improved overall direct compensation method for total disturbance was proposed. The use of a subdivision compensation term could avoid the misjudgment arising from the estimation of the overall perturbation by the linear expanded state observer (LESO) within the first few weeks of the feedback when the overall compensation was applied. It aimed to reduce the overshooting caused by the overcompensation of the estimated disturbance term and to shorten the system convergence speed. Backstepping control was introduced to optimize the intermediate quantities of LADRC to estimate the error design outer-loop control law. The controlled quantity tracking the input quantity had excellent characteristics, and could set the desired error range quantity as the purpose of approximation. Therefore, backstepping control was suitable as a feedforward control of the system to preprocess the error in the estimated total disturbance of LESO and feed it into the inner loop improvement LADRC. Secondly, an improved control cascade PWM modulation with a PLL phase-locked loop to regulate the inverter output resulted in the elimination of the effects of internal and external disturbances on the grid-connected current and voltage. Finally, the amplitude–frequency characteristics were analyzed and compared for the trackability and antidisturbance of the improved linear active disturbance rejection controller, showing a good performance of the improved active disturbance rejection. At the same time, comparative simulations were conducted to confirm that the grid-connected current of the LCL inverter could obtain a better stability and grid entry quality in the first-order improved linear active disturbance rejection control.

Robust Nonlinear Control of DFIG-Based Wind Farms for Damping Inter-Area Oscillations of Power Systems

This article presents a perturbation observer–based robust nonlinear damping control (RNDC) scheme for a doubly fed induction generator (DFIG)–based wind farm to damp the inter-area oscillations of multi-area power systems. In the RNDC scheme, the perturbation term is introduced to describe the combined effects of nonlinearities, uncertainties, and disturbances of multi-area power systems with wind farms. The feedback linearization control is realized for reactive power control loops of the DFIG based on state estimation and perturbation estimation derived from a perturbation observer, thus achieving the damping control of the DFIG. The proposed RNDC scheme only needs one measurement signal, and it does not require any model parameters of the power grid and wind farm. Simulation studies are carried out on a two-area power system model connected with the wind farm to validate the control performance of the RNDC scheme under the conditions of three-phase-to-ground faults, parameter variations, and time delays.

Robust nonlinear adaptive pressure control of polymer electrolyte membrane fuel cells considering sensor failures based on perturbation compensation

The large deviations between the partial pressure of oxygen and hydrogen can lead to severe membrane damage, which reduces the life of the polymer electrolyte membrane fuel cell (PEMFC). The deviation of pressure can be restrained by effective control of partial pressure. Considering the actual operating environment of PEMFC, its control system is not only affected by load changes, but also affected by some unknown disturbances, such as system parameter variations, failures, etc. Considering the above factors, this paper has proposed a robust nonlinear adaptive pressure control (RNAPC) employing the perturbation estimation technique to suppress the deviations. The proposed controller does not need to identify or estimate the system parameters in real time like the conventional controller based on parameter estimation technology, nor does it need to rely on the fault diagnosis and isolation technology to detect and estimate the failures in real time. It only uses the variations of system state variables caused by failures to provide the required failure information for the controller. In the design of RNAPC, an observer is designed to estimate a perturbation term containing system uncertainties, nonlinearities, and disturbances. The estimation of perturbation is used for the compensation of actual perturbation. Then, an adaptive FLC of PEMFC system can be realized. Therefore, the RNAPC requires only a few state measurements and is independent of an accurate system model. Simulation results show that the RNAPC method has smaller deviations of partial pressure of oxygen and hydrogen and better dynamic performance than traditional PI control under load disturbance, and obtains higher robustness against uncertainties and sensor failures than traditional PI control and FLC. The maximum error of partial pressure can be limited within 0.5% under four different simulation scenarios under the RNAPC.

Condition numbers of the mixed least squares-total least squares problem revisited

A recent study on the condition numbers of the mixed least squares-total least squares (MTLS) problem is due to Zheng and Yang (Numer Linear Algebra Appl. 2019;26(4):e2239). However, the associated expressions are not compact and the Kronecker-product operations make the computation costly. In this paper, we first present new and alternative closed formula for the first order perturbation estimate and condition numbers of the MTLS solution. Then we reveal the relationship between the new formula and Zheng and Yang's result. Several new computable formulae and perturbation bounds for the normwise condition number of the MTLS solution are also provided. Finally, mixed and componentwise condition numbers, structured condition numbers are investigated. Through a number of tests, they are shown to be tighter than the normwise condition numbers for sparse and structured problems.

Ultraperipheral production of lepton pairs (perturbative and nonperturbative effects)

Perturbative and nonperturbative terms of the cross-sections of ultraperipheral production of lepton pairs in ion collisions are taken into account. It is shown that production of low-mass [Formula: see text] pairs is strongly enhanced (compared to perturbative estimates) due to the nonperturbative Sommerfeld–Gamow–Sakharov (SGS) factor. Coulomb attraction of the nonrelativistic components of those pairs leads to the finite value of their mass distribution at lowest masses. Their annihilation can result in an increased intensity of 511 keV photons. It can be recorded at the NICA collider and is especially crucial in astrophysical implications regarding the 511 keV line emitted from the Galactic center. The analogous effect can be observed in lepton pairs production at LHC. Energy spectra of lepton pairs created in ultraperipheral nuclear collisions and their transverse momenta are calculated.

Stabilization of the Linearized Water Tank System

In this article we study the so-called water tank system. In this system, the behavior of water contained in a 1-D tank is modelled by Saint-Venant equations, with a scalar distributed control. It is well-known that the linearized systems around uniform steady-states are not controllable, the uncontrollable part being of infinite dimension. Here we will focus on the linearized systems around non-uniform steady states, corresponding to a constant acceleration of the tank. We prove that these systems are controllable in Sobolev spaces, using the moments method and perturbative spectral estimates. Then, for steady states corresponding to small enough accelerations, we design an explicit Proportional Integral feedback law (obtained thanks to a well-chosen dynamic extension of the system) that stabilizes these systems exponentially with arbitrarily large decay rate. Our design relies on feedback equivalence/backstepping.

Perturbation estimation based nonlinear adaptive control of VSC flexible excitation system

A new type of flexible excitation system (FES) is proposed by using fully-controlled power electronic devices such as IGBTs to replace the half controlled devices in the conventional static excitation system, which has the merit of independent control of rotor angle and terminal voltage of the synchronous generator. This paper proposes nonlinear adaptive control (NAC) strategies for synchronous generator with FES in a single machine infinite bus system. External disturbances and the uncertainties of all parameters as well as modelling are defined as lumped perturbation terms and estimated by perturbation observers or state and perturbation observer. The estimated perturbation terms are used to compensate the real perturbations and achieve a model-independent and robust NAC. Merits of the FES against the conventional static excitation system and effectiveness of the proposed NAC scheme against the accurate model based multi-variable feedback linearisation control are verified via small-signal stability analysis and simulation studies. The simulation results have shown that the proposed NAC can achieve superior control performance with less states feedback during a three-phase short circuit and better robustness against parameter uncertainties, compared with linear control and multi-variable feedback linearisation control.

Speed sensorless nonlinear adaptive control of induction motor using combined speed and perturbation observer

High performance induction motors (IM) require a robust and reliable speed controller to maintain the speed tracking performance under various uncertainties and disturbances. This paper presents a sensorless speed controller for IM based on speed and perturbation estimation and compensation. By defining a lumped perturbation term to include all unmodeled nonlinear dynamics and external disturbances, two state and perturbation observers are designed with combining the model reference adaptive system (MRAS) based speed observer to estimate the flux and speed states and the flux- and speed-loop related lumped perturbation terms. The estimated flux, speed and perturbation terms are used to design an output feedback, speed sensorless nonlinear adaptive controller (SSNAC) for IM. The stability of the closed-loop system is addressed in Lyapunov theory. Effectiveness of the SSNAC is verified via simulation and experiment tests. Comparing with the standard vector control plus MRAS speed observer (VC-MRAS), the proposed SSNAC reduces the speed tracking error by 20% to 30% on average under model uncertainties and unknown load disturbance due to the estimation and compensation of perturbation terms. The combined observer can estimate the real rotor speed under speed varying and load changes and thus makes SSNAC achieve high performance robust speed drive without using speed sensors.

Non-Singular Finite Time Tracking Control Approach Based on Disturbance Observers for Perturbed Quadrotor Unmanned Aerial Vehicles.

In this paper, a disturbance observer based on the non-singular terminal sliding mode control method was presented for the quadrotor in the presence of wind perturbation. First, the position and attitude dynamical equation of the quadrotor was introduced in the existence of windy perturbation. It was difficult to exactly determine the upper bound of the perturbations in the practical systems such as robot manipulators and quadrotor UAVs. Then, a disturbance observer was designed for the estimation of wind perturbation which was entered to the quadrotor system at any moment. Afterward, a non-singular terminal sliding surface was proposed based on the disturbance observer variable. Furthermore, finite time convergence of the closed-loop position and attitude models of the quadrotor was proved using Lyapunov theory concept. Unlike the existing methods, the new adaptive non-singular terminal sliding mode tracker for quadrotor unmanned aerial vehicles enabled accurate tracking control, robust performance, and parameter tuning. Through the combination of the finite time tracker and disturbance observer, the position and attitude tracking of quadrotor UAVs could be accurately performed not only in the nominal environment but also in the existence of different types of perturbations. Finally, simulation results based on the recommended method were provided to validate the proficiency of the suggested method. Moreover, comparison results with another existing study were presented to prove the success of the proposed method.

Complete Synchronization and Partial Anti-Synchronization of Complex Lü Chaotic Systems by the UDE-Based Control Method

The presence of uncertainty and disturbance can lead to asymmetric control of nonlinear systems, and this asymmetric control can lead to a decrease in the productivity of the engineered system. In order to improve the control speed of the improved nonlinear system, complete synchronization and partial anti-synchronization of complex Lü chaotic systems with uncertainty and disturbance are investigated in the present paper. First, a new UDE-based dynamic feedback control method is proposed for the complete synchronization problem of the system. The method unites the dynamic gain feedback control method and the uncertainty and perturbation estimator (UDE) control method, where the dynamic gain feedback controller is used to achieve asymptotic stability of the nominal system and the UDE controller is used to handle a given controlled system with uncertainty and disturbance. Second, for the partial desynchronization problem of this system, a new UDE-based linear-like feedback control method is proposed, which consists of two controllers: a linear-like feedback controller used to achieve the asymptotic stabilization of the nominal system and the other UDE controller is designed to handle the given controlled system with uncertainty and disturbance. Finally, numerical simulations are performed to verify the correctness and stability of the theoretical results.

Equation of state of cold and dense QCD matter in resummed perturbation theory

We discuss the hard dense loop resummation at finite quark mass and evaluate the equation of state (EoS) of cold and dense QCD matter in $\ensuremath{\beta}$ equilibrium. The resummation in the quark sector has an effect of lowering the baryon number density and the EoS turns out to have much smaller uncertainty than the perturbative QCD estimate. Our numerical results favor smooth matching between the EoS from the resummed QCD calculation at high density and the extrapolated EoS from the nuclear matter density region. We also point out that the speed of sound in our EoS slightly exceeds the conformal limit.

Force/Torque-Based Impedance Control With Perturbation Observer—Toward High Payload System Robust Trajectory Tracking

This paper presents a robust force/torque-based impedance control that reacts to deviated motion by generating forces to achieve the desired impedance, particularly for high payload systems. One of the special cases of such systems is an assistive robot for paraplegics (ARP) with a sit-stand mechanism (STSM) and, therefore, its control is investigated. Recently, a nonlinear robust position control known as sliding mode control with sliding perturbation observer (SMCSPO) was implemented on STSM and proven its effectiveness. However, with increasing subject body mass, high switching control gains are required which consequently either result in increased tracking error or chattering in control performance. In this regard, a new framework of integrated control was proposed which combines the feature of impedance control with estimated information from SMCSPO resulting in an enhanced control algorithm. The advantage of this impedance control is that because of SMCSPO, it utilizes the linear system information with position feedback only to estimate the states and perturbation (nonlinearities, uncertainties, and disturbance). This estimated perturbation then helps in compensating the actual perturbation effect from the system response. Moreover, the impedance control excludes the saturation function which helps prevent the chattering with low control gains. The comparison simulation and experiment results of the proposed impedance control with SMCSPO validated the proposed algorithm which enhances the transient response with minimized estimation error and better perturbation estimation.

Modelling and predictive control for a RTM mold

The objective of this work is the control of a Resin Transfer Moulding (RTM) mold trying to obtain a temperature in the whole cavity as much homogeneous as possible. This is a complex process, mainly because of two factors: temperature distribution in a complex geometry and variability of the system parameters. In order to solve these difficulties, a design procedure based on models is carried out. Firstly, the detailed modelling of the thermal system, discretized and solved by means of finite elements (FEM) and validated by thermal tests in the physical mold. Then, a simplified reduced-order model (ROM) is obtained by means of ARX approach based on the former model. Finally, the design of a  robust MPC (Model Predictive Control) which is able to take the system variability, the geometry complexity and the limitations of the actuation systems (resistances) into account. In order to afford the nonlinearities intrinsically present in the system, in addition to the controller, a perturbation estimator is implemented, which evaluates the changes produced in the mold with regard to the expected behaviour according to the ROM. In this way, the control system is able to detect the variations and compensate them in real time. These algorithms are validated both by simulation and experimentally. From this verification, it follows that the application of these modelling, estimation and control techniques allows to control the mold with temperature variations much tighter than for PID standard controllers.

Time-Harmonic Solutions for Maxwell\u2019s Equations in Anisotropic Media and Bochner\u2013Riesz Estimates with Negative Index for Non-elliptic Surfaces

We solve time-harmonic Maxwell’s equations in anisotropic, spatially homogeneous media in intersections of L^p-spaces. The material laws are time-independent. The analysis requires Fourier restriction–extension estimates for perturbations of Fresnel’s wave surface. This surface can be decomposed into finitely many components of the following three types: smooth surfaces with non-vanishing Gaussian curvature, smooth surfaces with Gaussian curvature vanishing along one-dimensional submanifolds but without flat points, and surfaces with conical singularities. Our estimates are based on new Bochner–Riesz estimates with negative index for non-elliptic surfaces.

A=4-7varXi hypernuclei based on interactions from chiral effective field theory

We investigate the existence of bound varXi states in systems with A=4-7 baryons using the Jacobi NCSM approach in combination with chiral NN and varXi N interactions. We find three shallow bound states for the NNNvarXi system (with (J^pi ,T)=(1^+,0), (0^+,1) and (1^+,1)) with quite similar binding energies. The ^5_{varXi }mathrm {H}(frac{1}{2}^+,frac{1}{2}) and ^7_{varXi }mathrm {H}(frac{1}{2}^+,frac{3}{2}) hypernuclei are also clearly bound with respect to the thresholds ^4mathrm {He} + varXi and ^6mathrm {He} +varXi , respectively. The binding of all these varXi systems is predominantly due to the attraction of the chiral varXi N potential in the ^{33}S_1 channel. A perturbative estimation suggests that the decay widths of all the observed states could be rather small.

Quantum estimation of a time-dependent perturbation

We analyze the estimation of a time-dependent perturbation acting on a continuously monitored quantum system. We describe the temporal fluctuations of the perturbation by a hidden Markov model, and we combine quantum measurement theory and classical filter theory into a time-evolving hybrid quantum and classical trajectory. The forward-backward analysis that permits smoothed estimates of classical hidden Markov models has a counterpart in the theory of retrodiction and past quantum states. As a specific example, we apply our hybrid trajectory and past-quantum-state theory to the sensing of a fluctuating magnetic field by microwave interrogation of a single quantum spin.

Error Estimates for the Smagorinsky Turbulence Model: Enhanced Stability Through Scale Separation and Numerical Stabilization

In the present work we show some results on the effect of the Smagorinsky model on the stability of the associated perturbation equation. We show that in the presence of a spectral gap, such that the flow can be decomposed in a large scale with moderate gradient and a small amplitude fine scale with arbitratry gradient, the Smagorinsky model admits stability estimates for perturbations, with exponential growth depending only on the large scale gradient. We then show in the context of stabilized finite element methods that the same result carries over to the approximation and that in this context, for suitably chosen finite element spaces the Smagorinsky model acts as a stabilizer yielding close to optimal error estimates in the L^2-norm for smooth flows in the pre-asymptotic high Reynolds number regime.

A satellite-data-driven framework to rapidly quantify air-basin-scale NO<sub><i>x</i></sub> emissions and its application to the Po Valley during the COVID-19 pandemic

Abstract. The evolving nature of the COVID-19 pandemic necessitates timely estimates of the resultant perturbations to anthropogenic emissions. Here we present a novel framework based on the relationships between observed column abundance and wind speed to rapidly estimate the air-basin-scale NOx emission rate and apply it at the Po Valley in Italy using OMI and TROPOMI NO2 tropospheric column observations. The NOx chemical lifetime is retrieved together with the emission rate and found to be 15–20 h in winter and 5–6 h in summer. A statistical model is trained using the estimated emission rates before the pandemic to predict the trajectory without COVID-19. Compared with this business-as-usual trajectory, the real emission rates show three distinctive drops in March 2020 (−42 %), November 2020 (−38 %), and March 2021 (−39 %) that correspond to tightened COVID-19 control measures. The temporal variation of pandemic-induced NOx emission changes qualitatively agrees with Google and Apple mobility indicators. The overall net NOx emission reduction in 2020 due to the COVID-19 pandemic is estimated to be 22 %.