Nonlinear Observer Research Articles

Saturation-Tolerant Prescribed Control for Nonlinear Systems With Unknown Control Directions and External Disturbances.

In this article, saturation-tolerant prescribed control (SPC) is investigated for a class of multiinput-multioutput (MIMO) nonlinear systems. The key challenge lies in how to guarantee both input and performance constraints simultaneously for nonlinear systems especially under external disturbance and unknown control directions. We propose concise finite-time tunnel prescribed performance (FTPP) for better tracking performance, which features tight allowable set and user-specified settling time. To comprehensively tackle the conflict between the above two constraints, an auxiliary system is designed to explore their interconnections instead of neglecting their contradictions. By introducing its generated signals into FTPP, the obtained saturation-tolerant prescribed performance (SPP) has the ability to degrade or recover the performance boundaries in the light of different saturation conditions. Consequently, the developed SPC, together with nonlinear disturbance observer (NDO), can effectively improve the robustness and reduce the conservatism against external disturbances, input, and performance constraints. Finally, comparative simulations are presented to showcase these theoretical findings.

Fixed time containment control of multi-agent system under multi-source mismatched disturbance

Aiming at the cooperative control problem of multi-agent system, the fixed-time containment control of general second-order multi-agent system under mismatched disturbances is studied. Firstly, the problem of multi-agent system fixed-time containment control in ideal state is analyzed, and a distributed control protocol based on variable structure control is proposed. Then, a nonlinear fixed-time disturbance observer is designed, aiming at the mismatched disturbance, and a fixed-time control protocol based on the nonlinear disturbance observer is proposed. Finally, the effectiveness of the proposed control protocol under switching topology and multi-source disturbance is verified by numerical simulation.

Continuous–discrete derivative-free extended Kalman filter based on Euler–Maruyama and Itô–Taylor discretizations: Conventional and square-root implementations

In this paper, we continue to study the derivative-free extended Kalman filtering (DF-EKF) framework for state estimation of continuous–discrete nonlinear stochastic systems. Having considered the Euler–Maruyama and Itô–Taylor discretization schemes for solving stochastic differential equations, we derive the related filters’ moment equations based on the derivative-free EKF principal. In contrast to the recently derived MATLAB-based continuous–discrete DF-EKF techniques, the novel DF-EKF methods preserve an information about the underlying stochastic process and provide the estimation procedure for a fixed number of iterates at the propagation steps. Additionally, the DF-EKF approach is particularly effective for working with stochastic systems with highly nonlinear and/or nondifferentiable drift and observation functions, but the price to be paid is its degraded numerical stability (to roundoff) compared to the standard EKF framework. To eliminate the mentioned pitfall of the derivative-free EKF methodology, we develop the conventional algorithms together with their stable square-root implementation methods. In contrast to the published DF-EKF results, the new square-root techniques are derived within both the Cholesky and singular value decompositions. A performance of the novel filters is demonstrated on a number of numerical tests including well- and ill-conditioned scenarios.

Improvement of real-time state estimation performance in HVDC systems using an adaptive nonlinear observer

This paper proposes a novel adaptive nonlinear observer design for a voltage source converter based on high-voltage direct current (VSC-HVDC) transmission systems. We consider a system consisting of a power grid, and a converter station connected to an unknown load through a long HVDC cable. The primary contribution of this work is the development of a global high-gain observer that facilitates the estimation of all system states. Specifically, it encompasses the estimation of power grid parameters, such as the angular frequency and the voltage at the point of common coupling (PCC), as well as the states of the HVDC cable and the current absorbed by the load. The performance of the proposed observer is assessed through theoretical analysis and simulations. Additionally, we implemented our observer on a digital signal processor (DSP) eZdsp in a processor-in-the-loop (PIL) quasi-real-time setting. Experimental results, coupled with numerical simulations, showcase the outstanding performance of our proposed observer.

Sensorless AC Current Control with Backstepping Design for a PWM AC-DC Converter

In this paper, a novel sensorless AC current control scheme is proposed for the design of PWM AC-DC converter. This design strategy deals with nonlinear backstepping controllers and AC current observer to achieve the purpose of current following. In general, PWM AC-DC converter design requires AC current measurement to achieve control goals, the backstepping observer employed estimates the AC current, and then nonlinear controllers based on backstepping design algorithm are developed to realize the sensorless AC current for the PWM AC-DC converter system. The proposed control scheme is not only to stabilize the PWM AC-DC converter system, but also to drive the current tracking error to converge to zero asymptotically. Furthermore, some simulation results are shown to illustrate excellent performances of the nonlinear backstepping control design scheme applied to a PWM AC-DC converter

Adaptive fuzzy anti-saturation tracking control for uncertain nonlinear systems with external disturbance

In this paper, a predictive-based adaptive anti-saturation tracking control scheme is designed for uncertain multiple-input and multiple-output (MIMO) nonlinear systems subject to input constraints and external disturbance. Taking the safety of the MIMO nonlinear systems into account, a safety saturation threshold, which is less than the physical device saturation threshold, is given. In addition, since all signals of the auxiliary systems are not immediately employed to the systems when the input saturation happens, a new predictive-based auxiliary system is designed. Furthermore, to estimate the compound disturbance, with the help of the fuzzy control technology, the nonlinear disturbance observer (NDO) is used. Then, the stability of the closed-loop systems is proved under the designed controller. Finally, a simulation example is given to illustrate the feasibility of the designed anti-saturation controller.

Robust collision-free formation control of quadrotor fleets: Trajectory generation and tracking with experimental validation

This paper addresses the problem of formation control of multiple quadrotor vehicles, focusing on ensuring inter-vehicle collision avoidance in the presence of time-varying external disturbances. The problem is divided into two sub-problems: (i) the generation of collision-free trajectories; and (ii) trajectory tracking. Initially, by employing the Lyapunov-based backstepping technique, a set of collision-free trajectories is generated based on a potential function. Additionally, a trajectory tracking controller is developed for each individual quadrotor, ensuring accurate tracking of their respective trajectories. Furthermore, to attain robust tracking performance, nonlinear disturbance observers are developed and incorporated into the control inputs to compensate for time-varying external disturbances. Comprehensive simulation and experimental results are provided and analyzed to demonstrate the effectiveness and performance of the proposed strategy.

Predictor-based observer and controller for nonlinear systems with input/output delays

This letter addresses the problem of asymptotic stabilization by output feedback for nonlinear systems with delays in the input and output. Under stabilizability and detectability of the linearized time-delay system, we show that asymptotic stabilization is solvable by predictor-based nonlinear observer and dynamic output compensator. The proof is based on the linearization method, the design of local nonlinear observers and observer-based controllers, as well as the Razumikhin theorem.

Nonlinear Control Structure of Grid Connected Modular Multilevel Converters

This paper implements nonlinear control structure based on Adaptive Fuzzy Sliding Mode (AFSM) Current Control and Unscented Kalman Filter (UKF) to estimate the capacitor voltages from the measurement of arm currents of Modular Multilevel Converter (MMC). UKF use nonlinear unscented transforms in the prediction step in order to preserve the stochastic characteristics of a nonlinear system. In order to design adaptive robust control strategy and nonlinear observer, mathematical model of MMC using rotating d-q theory has been used. Digital time-domain simulation studies are carried out in the Matlab/Simulink environment to verify the performance of the overall proposed control structure during different case studies.

Fault estimation for nonlinear uncertain time‐delay systems based on unknown input observer

AbstractIn this paper, a novel nonlinear unknown input observer is proposed in order to fault estimation for nonlinear uncertain systems with time delays. By the estimation of the faults, the features are detected such as shape, size occurrence time etc. The time delay is considered a constant and known parameter in the states. The disturbances are investigated in the states and outputs and also, and sensor and actuator faults are considered. The stability of the closed‐loop system is guaranteed by Lyapunov–Krasovskii theory and some feasible Linear matrix inequalities (LMI). The proposed method is simulated on a continuous‐stirred tank reactor (CSTR) with uncertainties and time delay. Simulation results show the appropriate efficiency of the proposed method.

Fault-tolerant control of underactuated MSVs based on neural finite-time disturbance observer: An Event-triggered Mechanism

This paper deals with the problem of fault-tolerant control synthesis for underactuated marine surface vessels (MSVs) with dynamic uncertainties, external time-varying disturbances, and input saturation. In control design, with the help of neural networks (NNs) to reconstruct the dynamic uncertainty of the system, a novel nonlinear finite-time disturbance observer (FTDO) is established to reconstruct the compound uncertainty online, including unknown time-varying disturbances, approximation errors, bias faults and parts of loss-of-effectiveness (LOE) faults. Combining finite-time control (FTC) theory, event-triggered control (ETC) technology and backstepping design method, a new fault-tolerant control scheme for underactuated MSVs is designed. Based on the Lyapunov stability theory, it is proved that all signals in the closed-loop tracking system are bounded, and the tracking error of the underactuated MSVs converges to a small set near the origin in finite-time. The effectiveness of the proposed novel fault-tolerant control scheme is verified by computer simulation.

Predictor‐based continuous‐discrete nonlinear observer design subject to aperiodic sampled and delayed measurement

AbstractIn this paper, a predictor‐based continuous‐discrete nonlinear observer is proposed for a class of nonaffine Lipschitz nonlinear systems with aperiodic sampled delayed output measurements and external disturbance. Firstly, this study introduces a class of delayed sampling hybrid nonlinear systems. By employing Lyapunov techniques and trajectory‐based stability theory, sufficient conditions are established for ensuring input‐to‐state stability of the delayed sampling hybrid nonlinear system with respect to external disturbances. Then the predictor‐based continuous‐discrete nonlinear observer is designed which consists of a continuous‐time observer, a compensating injector and a predictor. The continuous‐time observer is utilized to obtain continuous and delay‐free state estimation. The compensating injector is designed to compensate for output errors that occur between sampling instants. Furthermore, the predictor is employed to obtain delay‐free output error information, which is then utilized by the continuous‐time observer for feedback correction. The proposed observer's exponential input‐to‐state property against the disturbance is proved via the proposed hybrid system stability theory. The effectiveness of the proposed observers has been demonstrated through numerical simulations and performance comparisons with the zero‐order holder‐based observer and the output predictor‐based observer designs in order to highlight the effectiveness and advantages of the proposed observer.

Disturbance-observer-based event-triggered model predictive control of nonlinear input-affine systems

This paper proposes a novel disturbance-observer-based event-triggered model predictive control (DEMPC) framework for a class of nonlinear input-affine systems with state and control input constraints as well as unmatched disturbances to simultaneously enhance the robustness of standard MPC and reduce computational resource utilization. First, a nonlinear disturbance observer is designed to compensate for disturbances actively. Next, a constant-threshold-type event-triggering mechanism (CTETM) is designed in terms of the state prediction deviation caused by the remaining disturbances. Subsequently, a DEMPC algorithm is constructed using the disturbance estimation information, the CTETM, and the so-called dual-mode scheme. Furthermore, rigorous theoretical analysis is provided, involving robust constraint fulfillment, Zeno phenomenon prevention, recursive feasibility, and stability. Particularly for systems with only matched disturbances, it is proven that continuous disturbance compensation would result in a possibly lower triggering frequency and enhanced control performance for the DEMPC compared to conventional EMPC without introducing additional conservatism into the state constraints. In the end, simulation studies are performed to illustrate the effectiveness of the proposed framework.

Comprehensive wheel cylinder pressure estimation based on systematic hydraulic control unit model

Wheel cylinder pressure (WCP) is a crucial state for vehicles, directly influencing safety, comfort, and fuel economy. Serving as the foundation for sensor-less control and sensor redundancy, WCP estimation is a promising work for brake-by-wire systems (BBW). Nevertheless, WCP estimation is a challenging problem due to the nonlinear characteristics and intricate coupling within the hydraulic control unit (HCU). To enhance the performance of BBW, this paper proposes a comprehensive WCP estimation scheme based on the systematic HCU model. Component models including direct current (DC) motor pump and normally open valve (NOV) are established first. Considering the pulsation of the plunger pump, a modified nonlinear observer (MNO) is used to observe the angular speed of the DC motor. Inspired by the critical state, the linear pressure-drop relationship of NOV is analyzed and the NOV is simplified as a relief valve model expressed by algebraic equations. Dividing the HCU into the pump front part, pump rear part, and cylinder part, the systematic HCU model is then established, based on which, the comprehensive cause-based WCP estimation scheme is proposed. Next, simulations utilizing Amesim validate the angular speed estimator, while bench experiments prove the NOV model. Finally, vehicle tests under active and passive pressure regulating conditions are conducted. The results indicate the proposed scheme exhibits satisfactory performance while preserving computational efficiency.

The Non-Singular Terminal Sliding Mode Control of Underactuated Unmanned Surface Vessels Using Biologically Inspired Neural Network

Underactuated Unmanned Surface Vessels (USVs) are widely used in civil and military fields due to their small size and high flexibility, and trajectory tracking control is a critical research area for underactuated USVs. This paper proposes a trajectory tracking control strategy using the Biologically Inspired Neural Network (BINN) for USVs to improve tracking speed and accuracy. A virtual control law is designed to obtain the required virtual velocity for trajectory tracking control, in which the velocity error is calibrated to ensure that the position error converges to zero. To observe and compensate for unknown and complex environmental disturbances such as wind, waves, and currents, a nonlinear extended state observer (NESO) is designed. Then, a controller based on Non-singular Terminal Sliding Mode (NTSM) is designed to resolve the problems of singular value and controller chattering and to improve the controller response speed. A BINN is introduced to simplify the process of differentiation, reduce the input values of the initial state, and solve the problem of thruster input saturation. Finally, the Lyapunov stability theory is utilized to analyze the stability of the proposed algorithm. The simulation results show that the proposed algorithm has a higher trajectory tracking accuracy and speed than traditional methods.

A Bayesian Kalman filter algorithm for quantifying estimation uncertainty of track irregularity on bridges with randomness in system parameters

Vehicle on-board monitoring methods use responses of running vehicles to identify track irregularity in real time. But the parameters of both the bridges and the vehicles in such processes may have a non-negligible degree of uncertainty or randomness that will inevitably lead to uncertainty in the track irregularity identification. Quantifying such uncertainty is a great challenge as the vehicle-bridge system (VBS) to be treated with is time-dependent and random. This paper proposes an on-board track irregularity identification algorithm that realizes an inverse random dynamic analysis of the VBS to quantify estimation uncertainty by using a Bayesian Kalman filter technology. The proposed algorithm utilizes sigma point sets to simulate the random parameters and the noises, and is therefore capable of implementing high-fidelity probability density propagation in the nonlinear state transfer and observation functions describing the VBS. The proposed algorithm is validated by numerical examples with various running states and parameter uncertainty levels.

Adaptive type-2 fuzzy output feedback control using nonlinear observers for permanent magnet synchronous motor servo systems

This paper investigates the accurate servo position control of the permanent magnet synchronous motor (PMSM)-driven system under varying external disturbance and unknown mechanical friction. Firstly, to overcome the difficulty of state observer design caused by uncertainties, the interval type-2 fuzzy logic system (IT2 FLS) is introduced to approximate the nonlinear friction. Meanwhile, the nonlinear disturbance observer (NDO) is employed to estimate the lumped disturbance. Then aiming to solve the problem of explosion of complexity and filtering error, a finite-time (FT) adaptive IT2 fuzzy output feedback controller is proposed by combining the error compensation mechanism and FT control. In addition, to further improve the performance of the closed-loop system, the adaptive law is updated by the compensation error signal. By means of Lyapunov stability theory, all signals in the closed loop system can be guaranteed to be finite-time stable. Numerical simulations and real-time experiments are presented to demonstrate the effectiveness and superiority of the proposed controller.

Leveraging digital twin for autonomous docking of a container truck with stabilization control

AbstractThis paper describes the design, development, and implementation of a high‐precision autonomous docking control system for a container truck based on a digital twin approach. The digital twin is used to simulate the dynamic behavior of the physical truck and to design the controller by providing a virtual platform to test, validate, and optimize control strategies and algorithms before their deployment in the actual system. To this end, a cascade of a nonlinear observer and an unscented Kalman filter is used to estimate the state variables of the physical truck for point‐stabilization and orientation controls during the autonomous docking process. The docking motion involves two stabilization problems: point stabilization for smooth motion from the initial configuration to the docking slot, and orientation control to deliver the container truck to the final docking position with a margin of error of 5 cm for position and 0.0087 rad for orientation. The stability of both controllers is investigated, and simulations and experiments are conducted to demonstrate the accuracy of the proposed method in a container terminal environment.

Robust Braking Pressure Control for an Electrohydraulic Brake System under Friction and Disturbance Conditions

This paper addresses the challenges in hydraulic pressure control for an electrohydraulic brake (EHB), considering nonlinearities and uncertainties such as friction and parameter variations. The proposed solution is a robust integral backstepping control (IBC) strategy, which incorporates motor current dynamics and the LuGre friction model. A nonlinear observer is introduced to estimate the unmeasurable internal state of the LuGre model. The IBC is applied to pressure control for the EHB, resulting in improved steady-state behavior and robustness. The paper concludes with a global stability analysis using Lyapunov theory and performance validation through simulation using MATLAB/Simulink.

A Robust Backstepping Controller Based on Nonlinear Observer for Shunt Active Filters to Improve Power Quality in Four-Wire Distribution Systems

This article introduces a novel approach to enhance the performance of LCL based active power filters (APFs) in four-wire distribution systems by employing a nonlinear current control strategy. The strategy combines backstepping control (BSC) and a nonlinear disturbance observer (NDOB) to effectively manage harmonic and interharmonic grid currents. By situating the shunt active power filter (SAPF) at the point of common coupling (PCC) via the LCL filter, the technique ensures that grid connected currents remain balanced and purely sinusoidal. The integration of NDOB with BSC aims to fortify the resilience of BSC against disturbances. Consequently, any disturbances occurring within the system are precisely estimated by the NDOB and subsequently mitigated through the BSC mechanism. Notably, this approach showcases robust adaptability across diverse scenarios, encompassing external disturbances, variations in filter parameters, nonlinear loads laden with harmonics and interharmonics, load imbalances, and non-ideal grid voltages. Its performance remains robust and stable even when disturbances are present. Comparative analysis with linear-based methodologies underscores the advantages of this approach, revealing quicker and smoother transient responses. The efficacy of the proposed technique is demonstrated through comprehensive simulation studies, substantiating its potential for significantly advancing power quality in complex distribution systems.