Nonlinear Observer Research Articles

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.

Self-triggered formation control for multi-spacecraft attitude coordination with communication delays

This article addresses the event-triggered formation control problem for multi-spacecraft systems subject to time-varying delays. Firstly, a formation attitude dynamics model considering communication delays is proposed, and two auxiliary trigger instants are designed to transform the event-based control problem subject to delays into the conventional event-triggered control problem. Next, a nonlinear observer based on the triggering information of neighbors is developed to estimate the lumped nonlinear term. To avoid continuous communication, a dynamic event-based formation control strategy is proposed based on the nonlinear observer. To avoid continuous computation of the trigger mechanism, a self-triggered function is developed based on the current trigger information. Moreover, the system is Zeno-free under the proposed event-based control algorithms. Finally, simulation results show that compared with the dynamic triggering function, the self-triggered function avoids continuous computation and improves the control accuracy by nearly one order of magnitude while increasing communication frequency by 67.8 %.

Attitude tracking control of hypersonic vehicle based on an improved prescribed performance dynamic surface control

AbstractIn this paper, we investigate the constrained attitude control problem of hypersonic vehicles (HVs). An improved prescribed performance dynamic surface control method is proposed based on an adaptive scaling strategy. Because of the uncertain time-varying disturbances, the controlled state may violate the constraint in the prescribed performance control (PPC) framework. An adaptive scaling strategy is introduced in the PPC method to avoid state violation. The performance function is scaled with respect to the state adaptively. Moreover, a nonlinear disturbance observer is used to compensate the sum of external and other internal disturbances of the system. The proposed method improves the system dynamic performance while ensuring the system robustness. Furthermore, the stability of the closed-loop system is proved by Lyapunov analysis. Finally, numerical simulations are implemented to verify the effectiveness of the PPC method and superiority over other methods.

Disturbance Observer-Based Event-Triggered Adaptive Command Filtered Backstepping Control for Fractional-Order Nonlinear Systems and Its Application

This paper considers the disturbance observer-based event-triggered adaptive fuzzy tracking control issue for a class of fractional-order nonlinear systems (FONSs) with quantized signals and unknown disturbances. To improve the disturbance rejection ability, a fractional-order nonlinear disturbance observer (FONDO) is designed to estimate the unknown composite disturbances. Furthermore, by combining an improved fractional-order command-filtered backstepping control technique and an event-triggered control mechanism, an event-triggered adaptive fuzzy quantized control scheme is established, which guarantees the desired tracking performance can be achieved even in the presence of network constraint. Finally, the validity and superiority of the theoretic results are verified by a fractional-order horizontal platform system.

Angle demand control of steer-by-wire system by disturbance estimation–based generalized predictive control approach

In this article, a disturbance estimation–based robust generalized predictive control approach is proposed for angle demand control of a steer-by-wire system. It consists of a generalized predictive controller and a nonlinear disturbance observer. First, the nonlinear disturbance observer is used to estimate the effects of the lumped disturbances, including model uncertainties, unmodeled dynamics, and external disturbances. Second, the estimate of the nonlinear disturbance observer is integrated into the generalized predictive controller design for front-wheel angle output prediction. Then, an explicit analytical form of the disturbance estimation–based robust generalized predictive controller is derived. In addition, rigorous stability analysis proves that the closed-loop system under the proposed control is stable. Finally, the developed control approach has been downloaded into a steering control unit and tested in real-world conditions using a vehicle test bench to fully realize steering by wire in engineering practice. Extensive simulations and experiments have been performed, and results show that the proposed control approach outperforms the comparative controllers regarding disturbance rejection, robust tracking performance under model uncertainties, and disturbances.

Adaptive Anti-Disturbance Control of Dissolved Oxygen in Circulating Water Culture Systems

In the three-dimensional culture model, the breeding basket of the culture area is symmetrical and it is important to control the dissolved oxygen in the symmetrical region to improve the culture efficiency. Practical engineering issues, such as the influence of flow rate, pH, water temperature, and biological oxygen consumption on the dissolved oxygen content in the circulating water culture system, must be considered along with the presence of modeling errors in the control model. The authors propose an adaptive anti-disturbance control strategy for dissolved oxygen that combines nonlinear disturbance observation with an adaptive sliding model control. Initially, a dynamic model for controlling dissolved oxygen in a recirculating water aquaculture system was developed. The model considers external disturbances like artificial oxygenation, abrupt changes in system flow, and variations in culture oxygen consumption. Secondly, to enhance the robustness and accuracy of controlling dissolved oxygen concentration, the paper introduces a nonlinear adaptive disturbance observer for real-time estimation and observation of external disturbances and system uncertainties. This is accompanied by a sliding-mode control-based adaptive anti-disturbance strategy. Lastly, the simulation results demonstrate that the control strategy proposed in this paper shows resistance to system uncertainties and unknown external disturbances. Furthermore, it reduces the model accuracy requirements for the controller and proves to be suitable for accurately controlling dissolved oxygen in circulating water systems.

Brunovsky Decomposition for Dynamic Interval Localization

This paper proposes a new set-membership method for estimating the trajectories of dynamical systems, when the states are completely unknown and only non-linear observations are available. The first part of the proposed method is symbolic and follows the decomposition of Brunovsky, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i.e.</i> , it decomposes the set of differential equations describing the dynamical system into two blocks of constraints: one block gathers non-linear analytical equations that do not involve differential operators, while the other block is composed of linear chains of integrators. The second part of the method, that relies on the symbolic decomposition, is numerical and based on a contractor approach. It involves a specific optimal operator for narrowing the sets of feasible solutions. This approach is shown to be efficient on a difficult problem of dynamic localization of a mobile robot, without any prior knowledge about its states.

Improved finite-time prescribed performance super-twisting sliding mode united control framework for underwater vehicle-manipulator system

This paper investigates the trajectory tracking control problem for underwater vehicle-manipulator system (UVMS) with model uncertainties, dynamic coupling effects and external disturbances. Firstly, an improved finite-time performance function (IFTPF) is proposed to ensure the prescribed tracking accuracy with predefined convergence time while avoiding singularities in the system and enhancing robustness. Additionally, to reduce the controller’s dependence on the system model and compensate for unknown external disturbances, a neural network (NN) estimator is proposed to estimate the combination of system uncertainties and dynamic coupling effects, while a neural network-based nonlinear disturbance observer (NNDO) addresses the unknown external disturbances. Furthermore, an improved finite-time prescribed performance super-twisting sliding mode control framework using neural network-based disturbance observer (NNDO-IFTPPSTSMC) is proposed to ensure control accuracy and robustness while reducing chattering phenomenon. Theoretical analysis demonstrates that corresponding error variables of the system are bounded, and the trajectory tracking errors satisfy the prescribed performance constraints. Finally, simulation results validate the effectiveness and feasibility of the proposed method.

Learning-Based Approaches for Voltage Regulation and Control in DC Microgrids with CPL

This article introduces a novel approach to voltage regulation in a DC/DC boost converter. The approach leverages two advanced control techniques, including learning-based nonlinear control. By combining the backstepping (BSC) algorithm with artificial neural network (ANN)-based control techniques, the proposed approach aims to achieve accurate voltage tracking. This is accomplished by employing the nonlinear distortion observer (NDO) technique, which enables a fast dynamic response through load power estimation. The process involves training a neural network using data from the BSC controller. The trained network is subsequently utilized in the voltage regulation controller. Extensive simulations are conducted to evaluate the performance of the proposed control strategy, and the results are compared to those obtained using conventional BSC and model predictive control (MPC) controllers. The simulation results clearly demonstrate the effectiveness and superiority of the suggested control strategy over BSC and MPC.

Real-Time Attitude Estimation for Spinning Projectiles by Magnetometer Based on an Adaptive Extended Kalman Filter.

The attitude measurement system based on geomagnetic information offers advantages such as small space requirements, fast response times, excellent resistance to high-overload conditions, and cost-effectiveness. However, during the flight process of a high-mobility guided spinning projectile, calculating attitude based on geomagnetic information often leads to non-unique solutions. To address this challenge, this paper proposes the Adaptive Extended Kalman Filter (AEKF) attitude estimation algorithm, based on geomagnetic vector information. Based on the analysis of the short-term attitude motion characteristics of the projectile, the Kalman state system equation and the nonlinear observation equation are established, along with real-time correction of the yaw angle and adaptive updates of parameters. The effectiveness of the algorithm is verified by simulations and experiments, demonstrating its ability to eliminate the dual solution problem inherent in traditional Single-Epoch algorithms. It notably improves the accuracy of pitch and roll angle estimation while providing precise estimates of attitude angular rates. Furthermore, the algorithm effectively mitigates the impact of magnetic disturbances on attitude determination. The proposed method has many potential applications in attitude measurement and navigation using geomagnetic data.

Estimation of Process Variables in a Steam Distillation Plant

The on-line supervision of the process variables in a steam distillation plant is the main objective of this work. For this end, a nonlinear observer is designed based on the mathematical model proposed by Cerpa et al. (2008). The model has three differential equations, which reproduce the dynamics of the oil mass throughout the three stages of the process: (i) Loss of oil from plant material, (ii) Biphasic (oil-water) layer, (iii) Colected essential oil. The purpose of this work is to estimate the mass flow of oil lost by the plant material and the mass flow in the two-phase layer called the aqueous layer. Both process variables are difficult to measure physically, but it is important to know them because they can have an impact on the performance of the process. However, the mass of oil collected is considered to be an available variable to measure. By taking this consideration into account, a nonlinear Luenberger type observer is designed that takes as available output the mass of oil collected, and from this variable is able to estimate the dynamics of the unavailable variables.

Fault compensations in resonant grounded power systems with residual current compensation inverters using an adaptive nonlinear extended state observer‐based model predictive controller

AbstractThis paper proposes a new adaptive nonlinear extended state observer‐based model predictive controller (ANLESO‐MPC) for residual current compensation (RCC) inverters to compensate fault characteristics in resonant grounded power systems (RGPSs). In the proposed scheme, the adaptation feature is used to adapt the adjustable inductor appearing in the dynamical model of RGPSs by satisfying the desired fault current compensation requirement which in turn will ensure the resonance condition. Since the adapted parameter is used in the control signal, the ANLESO‐MPC offers robustness against parameter sensitivity. The neutral voltage is considered as a disturbance and the change in this voltage as an extended state to estimate this disturbance while incorporating the adapted parameter so that the adaptive nonlinear extended state observer (ANLESO) provides robustness against disturbances. Finally, the model predictive controller (MPC) is designed for the RCC inverter utilizing estimated disturbances and adapted parameters to fully achieve the fault current compensation. The performance of the controller is evaluated using simulations in MATLAB/Simulink and OPAL‐RT real‐time platforms under varying fault impedances as the fault characteristics change with variations in the fault impedance. Results are also compared with a conventional MPC where the proposed ANLESO‐MPC seems more effective to compensate fault characteristics.

High precision control of direct-drive permanent magnet linear motor with adaptive friction compensation

To improve the control precision and stability of Direct-Drive Permanent Magnet Linear Motor (DPMLM) with frictional nonlinearity and uncertain disturbances at a low speed, an adaptive robust integral sign error control algorithm based on friction compensation of dual nonlinear observer is proposed in this study. An improved LuGre friction model is established to describe the friction phenomena of the system. The dual nonlinear observer is designed to observe the internal frictional state of the model. A parameter adaptive law is designed to perform parameter estimation of structured uncertainty. Robust integral of the sign of the error (RISE) term is designed to overcome the frictional nonlinear disturbances. The friction nonlinearity and parameter uncertainty are compensated by feedforward compensation. The bounded stability of the proposed controller is proved by Lyapunov stability theory. As suggested by the experimental results, RMSE index decreased by 10.8% and the control precision was improved effectively by the proposed control algorithm at a low speed.

Zero-Voltage Ride-Through Scheme of PMSG Wind Power System Based on NLESO and GFTSMC

In this paper, a scheme for zero-voltage ride through of a permanent magnet synchronous generator wind power system is proposed. Maintaining the stability of DC-link voltage is the key to realizing zero-voltage ride through. A braking chopper is used to dissipate the active power to restrain the rise of DC-link voltage during a grid fault. However, the braking chopper-caused disturbance to the double closed-loop control of the grid side converter makes the control effect on DC-link voltage worse. Therefore, a robust current feedforward control, based on a nonlinear extended state observer and global fast terminal sliding mode control is proposed. A nonlinear extended state observer estimates the total disturbance in the system and compensates for the control law. Global fast terminal sliding mode control enables the system to reach the sliding mode surface in a finite time, and its control law is continuous without switching terms, thereby eliminating the chattering phenomenon. A nonlinear extended state observer and global fast terminal sliding mode control change the current feedforward control into a nonlinear robust current feedforward control. The control effect is improved, and the use of current transformers is reduced in practical applications, thereby reducing costs. The validity of this scheme has been verified by simulation.

Predictive digital twins for autonomous surface vessels

This paper presents an approach to improve the reliability and efficiency of autonomous surface vessels (ASV) by leveraging predictive digital twin and state estimation techniques. The predictive digital twin is based on a graphical model that shows the relationship between variables, and it is implemented and tested in an ASV based on a nonlinear discrete-time model and an adaptive exogenous Kalman filter to estimate the states and parameters associated with faults in the system. The state estimation method consists of a cascade of a nonlinear adaptive observer and a linearized adaptive Kalman filter, and the predictive algorithm is developed by creating a discrete-time state-space model from measured data and using the validated model to forecast the system response for a future time span. Experimental results in the Otter ASV developed by Maritime Robotics demonstrate the potential of the predictive digital twin as a decision support system for the predictive maintenance of ASVs.

A GES joint position trajectory tracking smooth controller of torque‐driven robot manipulators affected by disturbances

SummaryThis paper presents a controller for joint position tracking of torque‐driven robot manipulators affected by torque disturbances. In particular, the proposed approach allows concluding global exponential stability (GES) of the state‐space origin of the closed‐loop system when constant disturbances affect the robot dynamics. Besides, when time‐varying disturbances are presented, the trajectories of the closed‐loop system are proven to be bounded as result of the input‐to‐state stability. The main contribution is the design of the control law and a nonlinear observer based on an alternative energy shaping approach. The nonlinear observer is designed to compute and compensate for unknown disturbances, whether they are constant or time‐varying. Furthermore, a detailed stability analysis of the closed‐loop system based on Lyapunov theory and input‐to‐state stability is presented. As far as the authors know, this is the first energy‐shaping controller for trajectory tracking control of robot manipulators affected by constant disturbances that achieves global exponential stability. Real‐time experiments on a manipulator arm of two degrees‐of‐freedom illustrate the performance of the proposed controller.

Active Control for an Electric Vehicle with an Observer for Torque Energy-Saving

Vehicle dynamics play an important role in determining a vehicle’s stability. It is necessary to identify and obtain models related to vehicle dynamics to evaluate the performance of electric vehicles, as well as how to control them. This paper presents fundamentals of vehicle dynamics, proposing a three-degree-of-freedom nonlinear observer and controller to control lateral velocity and tire torque in comparison to a PID control, while also utilizing a Lyapunov function to determine the stability of the controlled state feedback system concerning the observer, which estimates state errors. This work demonstrates the mathematical development of estimations that will be fed into the algorithms of two active nonlinear controls (state feedback and PID), utilizing the results from Matlab-Simulink simulations of tire torque, lateral and angular velocities based on longitudinal velocity measurements, and employing dynamic gains, such as response to a steering maneuver by the driver following the international standards ISO 7401/2011 and ISO 3888-2. It is concluded that the observer is robust and exhibits energy-saving efficiency in tire torque, even under conditions of variable tire-ground friction.

Numerical and experimental investigation on the synthesis of extended Kalman filters for cable-driven parallel robots modeled through DAEs

Cable-driven parallel robots are parallel robots where light-weight cables replace rigid bodies to move an end-effector. Their peculiar design allows obtaining large workspaces, high-dynamic handlings, ease of reconfigurability and, in general, low-cost architecture. Knowing the full state variables of a cable robot may be essential to implement advanced control and monitoring strategies and imposes the development of state observers. In this work a general approach to develop nonlinear state observers based on an extended Kalman filter (EKF) is proposed and validated both numerically and experimentally by referring to a cable-suspended parallel robot. The state observer is based on a system model obtained by converting a set of differential algebraic equations into ordinary differential equations through different formulations: the penalty formulation, the Udwadia–Kalaba formulation, and the Udwadia–Kalaba–Phohomsiri formulation, which have been chosen since they can handle the presence of redundant constraints as often happens in cable-driven parallel robots. In the numerical investigation, the EKF is validated simulating encoders heavily affected by quantization errors to demonstrate the filtering capabilities of EKF. In the experimental investigation, a very challenging validation is proposed: only two sensors measuring the rotations of two motors are used to estimate the actual position and velocity of the end-effector. This result cannot be achieved by sole forward kinematics and clearly proves the effectiveness of the proposed observer.

Effective Energy Management Strategy with Model-Free DC-Bus Voltage Control for Fuel Cell/Battery/Supercapacitor Hybrid Electric Vehicle System

This article presents a new design method of energy management strategy with model-free DC-Bus voltage control for the fuel-cell/battery/supercapacitor hybrid electric vehicle (FCHEV) system to enhance the power performance, fuel consumption, and fuel cell lifetime by considering regulation of DC-bus voltage. First, an efficient frequency-separating based-energy management strategy (EMS) is designed using Harr wavelet transform (HWT), adaptive low-pass filter, and interval type–2 fuzzy controller (IT2FC) to determine the appropriate power distribution for different power sources. Second, the ultra-local model (ULM) is introduced to re-formulate the FCHEV system by the knowledge of the input and output signals. Then, a novel adaptive model-free integral terminal sliding mode control (AMFITSMC) based on nonlinear disturbance observer (NDO) is proposed to force the actual values of the DC-link bus voltage and the power source’s currents track their obtained reference trajectories, wherein the NDO is used to approximate the unknown dynamics of the ULM. Moreover, the Lyapunov theorem is used to verify the stability of AMFITSMC via a closed-loop system. Finally, the FCHEV system with the presented method is modeled on a Matlab/Simulink environment, and different driving schedules like WLTP, UDDS, and HWFET driving cycles are utilized for investigation. The corresponding simulation results show that the proposed technique provides better results than the other methods, such as operational mode strategy and fuzzy logic control, in terms of the reduction of fuel consumption and fuel cell power fluctuations.

Virtual coupling of permanent magnetic maglev trains: An improved cooperative tracking and collision avoidance control protocol

AbstractIn the cooperative tracking task of multiple permanent magnetic maglev trains, system uncertainty, external disturbances, and collision avoidance control are issues that must be considered. Therefore, the cooperative tracking and collision avoidance control for train virtual coupling with external disturbances are studied. First, according to the idea of multi‐agent consensus control and active disturbance rejection control, a cooperative tracking controller based on a novel nonlinear extended state observer (NESO) is designed. Second, a collision avoidance control method based on an improved artificial potential field (APF) is designed. Finally, an improved cooperative tracking and collision avoidance control protocol is proposed, and the stability proof is given. Compared with the conventional protocol, the proposed protocol can achieve smooth coupling and high‐precision cruise while ensuring safe collision avoidance. It has the advantages of higher tracking accuracy and stronger anti‐interference performance.