Nonlinear State Observer Research Articles

Adaptive coupled attitude-servo control for moving mass flight vehicles with high-mass-ratio

Moving mass flight vehicles (MMFVs) with high-mass-ratio suffer from a more severe nonlinear attitude-servo coupling than the traditional configurations that are under particle moving mass hypothesis. Therefore, the coupled attitude-servo control problem is investigated in this paper, and an adaptive backstepping sliding mode controller with extended state observers and neural-networks (ABSMC-ENN) is proposed. Based on the formulated control model with strict-feedback form, a sliding mode control law (SMC) with exponential reaching rate and a nonsingular terminal sliding mode control law (NTSMC) are combined to perform the fast and robust tracking of the command angle-of-attack. Considering the disturbances and uncertainties existing in the coupled dynamics, two nonlinear extended state observers (ESOs) are utilized to estimate the total disturbances online for compensation. To further enhance the adaptiveness and dynamic response performances of the controller in various flight conditions, two radial basis function neural networks (RBFNNs) are exploited to optimize the switching gains of the controller in real-time with performance indexes being the functions of tracking errors. Closed-loop stability of the whole system is proved via Lyapunov methodology. Comparison simulation studies considering multiple disturbances, various flight conditions, and different controllers successfully demonstrate the superiority of the ABSMC-ENN in robustness and adaptiveness.

Nonlinear State Observer and Control Design for Triangular Tethered Satellite Formation

This article researches the control of triangular tethered satellite formation (TTSF) system and nonlinear state observer (NSO) design when velocity vector is unmeasured. First, the stability around the equilibrium of open-loop system is discussed, which is stable around certain equilibrium pairs. To improve the system performance, linear feedback control is designed using Jacobian matrix of original nonlinear system, which is locally stable around linearized point. Besides, nonlinear control is designed subsequently which owns global stability domain. Then in case of the unmeasured velocity states, NSO is designed which contains a nonlinear function of estimation error to regulate the observation bias. With the designed nonlinear control and NSO, the simulation of the deployment of TTSF is made thereafter. Compared with linear feedback control and general observer with linear regulation, the proposed nonlinear control together with NSO has global stability domain and less chattering, which is promising in practical application.

Design of an nonlinear extended state observer to estimate unmeasurable information on the problem of flying objects guidance

Design of an nonlinear extended state observer to estimate unmeasurable information on the problem of flying objects guidance

Effective dynamic disturbance rejection scheme based on higher order sliding mode control for DC-AC inverter under load variation

In this paper, a dynamic super twisting sliding mode controller(ST-SMC) is proposed to resolve the problems associated with sudden load changes in AC-DC inverter system such that a high-quality output can be obtained. By developing a non-linear extended state observer (NLESO), both system states and lumped parameter disturbances are estimated and incorporated into controller design. This dynamic disturbance estimation and rejection algorithm not only increases the control loop reliability by eliminating the current sensor dependency, but it also allows the ST-SMC to be implemented with a small switching gain that minimizes the chattering effect. Optimal observer gain parameters design has been achieved by adopting the particle swarm optimization approach. The stability of the entire closed-loop system is proven based on the Lyapunov stability criterion. The effectiveness of the proposed dynamic ST-SMC algorithm has been validated in MATLAB Simulink environment where, the control strategy exhibit rapid dynamic response with a steady-state error of [Formula: see text]. The total harmonic distortion (THD) is also reduced to 0.02%[Formula: see text] and 0.08[Formula: see text]% for linear and non-linear loads, respectively.

Numerical Analyses and a Nonlinear Composite Controller for a Real-Time Ground Aerodynamic Heating Simulation of a Hypersonic Flying Object

This paper contains two parts: numerical analyses and a control method. The numerical analyses of a hypersonic flying object’s aerodynamic heating environment are based on three different two-dimensional outflow fields via finite element calculations. Then, the reference temperature trajectories of a hypersonic flying object are obtained. The other one is an intelligent proportional-derivative (IPD) with a nonlinear global sliding mode control (NGSMC) based on a nonlinear extended state observer (NESO) for a real-time ground aerodynamic heating simulation of a hypersonic flying object, named a thermal-structural test with quartz lamp heaters. The composite controller is made of three sub-components: a model free frame that is independent of the system dynamic model along with an ultra-local model; a NESO for the lumped disturbances observation; and an integral sliding mode control with a nonlinear function for the observation errors compensation. The flight environment of the hypersonic flying object is from Mach number 0.6 to Mach number 5.0, with between flight altitude of 31,272 m and flight altitude of 13,577 m. The comparative results demonstrate some superiorities of the proposed composite controller in terms of tracking errors and robustness.

Development of an accumulator liquid-level estimator to enable zero-superheat control and active charge management in vapor-compression systems

Vapor-compression system efficiency increases with reduced superheat but excessively low superheat settings may cause wet compression and jeopardize reliable system operations. Accumulators are commonly used to intercept liquid refrigerant before it reaches the compressor and can also be used as a refrigerant reservoir to assist active charge management. For zero-superheat and active charge control, accurate measurement or estimation of the accumulator liquid level is required. This paper presents an accumulator liquid level estimation approach based on a nonlinear state observer combined with a gray-box dynamic model of the evaporator and accumulator. This approach affords virtual detection of the liquid level in real-time from refrigerant pressure and temperature measurements, which are readily available in modern vapor-compression systems, and supports zero-superheat and dynamic charge control to maximize system efficiency. Both numerical and experimental tests of the proposed liquid level estimation and charge control strategies were carried out with a 3-ton variable-speed heat pump. The tests have demonstrated the accuracy of the accumulator liquid level estimator and shown that the zero-superheat and active charge control strategy could improve the system efficiency by up to 10.5%.

Formation tracking control for underactuated surface vehicles with actuator magnitude and rate saturations

In this paper, a formation tracking problem with collision avoidance is investigated for underactuated surface vehicles (USVs) with actuator magnitude and rate saturations. The USVs are subject to model uncertainties and external disturbances. A nonlinear extended state observer (NESO) is used to recover the linear velocity and yaw rate as well as unknown uncertainties and disturbances. A distributed control law is designed by artificial potential functions (APFs), the NESO and a backstepping technique. The APFs combined with a strategy are employed to achieve collision avoidance. Additional controllers are employed to deal with the underactuated problem, actuator magnitude and rate saturations. The stability of formation control system and simulation results are performed to illustrate the effectiveness of the proposed strategy.

Robust trajectory tracking control for a quadrotor using recursive sliding mode control and nonlinear extended state observer

The trajectory tracking performance of a quadrotor is affected by the load variations, wind gusts, inaccurate model parameters, etc. This study proposes a novel robust trajectory tracking controller for a quadrotor via a nonlinear extended state observer and recursive sliding mode control (NESO-RSMC). First, a novel NESO is applied to observe the lumped disturbance in quadrotor dynamics, and the parameter design of the NESO does not rely on the information of the unknown lumped disturbance. Subsequently, based on NESO, the RSMC scheme is constructed in detail, which reduces chattering and ensures a fast response. In addition, the finite-time convergence of tracking errors based on the NESO-RSMC scheme was rigorously proved. The numerical simulation results verify the robustness of the proposed NESO-RSMC scheme in the case of external disturbances and model parameter uncertainties. Ultimately, the NESO-RSMC scheme was implemented on a real quadrotor, and its effectiveness was further proven by outdoor flight experiments.

Nonlinear Optimization-Based Robust Control Approach for a Two-Stage Anaerobic Digestion Process

A two-stage anaerobic digestion (AD) process has been applied to improve the efficiency of methane production from various organic materials. However, the performance of traditional process controllers may be limited by differences in the rate of biochemical reactions, process uncertainties, and the consequences of interconnection between the two bioreactors. In this work, a nonlinear optimization-based control strategy that applies an analytical model predictive control (AMPC) scheme with an adaptive optimal set-point is proposed for the control of the two-stage AD system. The objectives of the proposed control system are to stabilize the system under uncertain operating conditions and maximize biomethane production. The optimal set-points for the controller are adapted in real-time operation, and then the control system is performed to manipulate the controlled output to the optimal trajectories. Compensators and nonlinear state observers are applied to handle the process/model mismatch and estimate unmeasured variables. The proposed control system is applied to the process with disturbances, fluctuations of inlet stream concentrations, and changes in the bacterial growth rate, and the control performance is investigated. Simulation results show that the developed control scheme automatically adjusts the optimal set-points and provides adequate control actions to maintain the maximum rate of methane production. The results of this investigation demonstrate that the control strategy promotes different biochemical reactions, avoids the inhibition effect, and handles the mutual effects between acidogenic and methanogenic bioreactors for methane production effectively.

Nonlinear Extended State Observer Based Prescribed Performance Control for Quadrotor UAV with Attitude and Input Saturation Constraints

In this paper, a prescribed performance control scheme of the quadrotor unmanned aerial vehicle (UAV) under attitude and input saturation constraints is introduced. According to the underactuated feature, the quadrotor UAV system can be decomposed into an underactuated subsystem and a fully actuated subsystem. With the feedback linearization technique, a single nonlinear extended state observer (ESO) is proposed, and multiple observations are utilized to estimate both matched and unmatched disturbances, which not only can obtain a uniform convergence, but also reduces the complexity of the observer’s parameter adjustment. To improve system stability, an input saturation algorithm for each single rotor is introduced to modify the final control output. In addition, the limited attitude for the quadrotor UAV is also considered as a saturation constraint in the control scheme with a compensation auxiliary system. On this basis, dynamic surface control (DSC) with prescribed performance is adopted to guarantee the bounded convergence and steady-state error. All state errors of the closed-loop system are proven to be uniformly bounded using the Lyapunov theory, and the simulation results are given to demonstrate the stability, effectiveness, and superiority of the proposed control strategies at last.

Safe cooperative path following with relative-angle-based collision avoidance for multiple underactuated autonomous surface vehicles

This paper addresses the safe cooperative path following for multiple autonomous surface vehicles (ASVs) in the presence of static and dynamic obstacles. The positions and velocities of the obstacles are unknown, and only the relative angle is measured. The ASVs are subject to uncertain kinetics and unknown disturbances induced by wind, waves and currents. Switching cooperative guidance laws with collision avoidance are designed at the kinematic level, and a collision avoidance strategy based on the relative angle is introduced into the desired yaw rate design. A smooth switch between the cooperative path following and the collision avoidance is achieved by using an exponential-function-based weighted coefficient. At the kinetic level, nonlinear switching extended state observers (NSESOs) based on fractional power functions are developed to estimate the model uncertainties and environmental disturbances. Anti-disturbance kinetic control laws are designed based on the nonlinear switching extended state observers and finite-time convergent differentiators. A salient feature of the proposed cooperative path following method is that both the static and dynamic obstacles can be avoided by using the relative angle only. Through theoretical analysis, it is proven that the closed-loop system is input-to-state stable, and a safe distance can be maintained between the ASVs and the obstacles. Simulation and hardware-in-loop (HIL) experiment results are given to substantiate the effectiveness of the proposed safe cooperative path following control method for multiple ASVs based on relative angles.

Mathematical Modeling and Control of COVID-19 Using Super Twisting Sliding Mode and Nonlinear Techniques.

Since the outbreak of the COVID-19 epidemic, several control strategies have been proposed. The rapid spread of COVID-19 globally, allied with the fact that COVID-19 is a serious threat to people's health and life, motivated many researchers around the world to investigate new methods and techniques to control its spread and offer treatment. Currently, the most effective approach to containing SARS-CoV-2 (COVID-19) and minimizing its impact on education and the economy remains a vaccination control strategy, however. In this paper, a modified version of the susceptible, exposed, infectious, and recovered (SEIR) model using vaccination control with a novel construct of active disturbance rejection control (ADRC) is thus used to generate a proper vaccination control scheme by rejecting those disturbances that might possibly affect the system. For the COVID-19 system, which has a unit relative degree, a new structure for the ADRC has been introduced by embedding the tracking differentiator (TD) in the control unit to obtain an error signal and its derivative. Two further novel nonlinear controllers, the nonlinear PID and a super twisting sliding mode (STC-SM) were also used with the TD to develop a new version of the nonlinear state error feedback (NLSEF), while a new nonlinear extended state observer (NLESO) was introduced to estimate the system state and total disturbance. The final simulation results show that the proposed methods achieve excellent performance compared to conventional active disturbance rejection controls.

Parameterization of a Novel Nonlinear Estimator for Uncertain SISO Systems with Noise Scenario

Dynamic observers are commonly used in feedback loops to estimate the system’s states from available control inputs and measured outputs. The presence of measurement noise degrades the performance of the observer and consequently degrades the performance of the controlled system. This paper presents a novel nonlinear higher-order extended state observer (NHOESO) for efficient state and disturbance estimation in presence of measurement noise for nonlinear single-input–single-output systems. The proposed nonlinear function allows a fast reconstruction of the system’s states and is robust against uncertainties and measurement noise. An analytical parameterization technique is proposed to parameterize the coefficients of the proposed nonlinear higher-order extended state observer in the case of measurement noise in the output signal. Several scenarios are simulated to demonstrate the effectiveness of the proposed observer.

Non-Linear Bandwidth Extended-State-Observer Based Non-Smooth Funnel Control for Motor-Drive Servo Systems

This article proposes a non-smooth funnel control (NSFC) strategy based on the extended state observer (ESO) for motor-drive servo systems with unknown dynamics. These unknown dynamics, including the modeling error, the external disturbances, and the non-linear friction, are considered as a lumped disturbance. For estimating the unknown states and the lumped disturbance, a non-linear bandwidth extended state observer (NLB-ESO) is developed. The NLB designed using the Gaussian function and the position observation error can deal with the “peaking value problem” caused by the high observer gains. Furthermore, a funnel error surface is proposed based on the non-smooth error transformation (NSET) and incorporated into the dynamic surface control design procedure, where the NSFC can prescribe the position tracking error in a funnel region with small steady-state error and overshoot and short adjustment time. The non-smooth funnel error surface also avoids the singular problem in controller design by selecting the non-smooth parameter. Moreover, the stability of the closed-loop control system with the NLB-ESO is guaranteed by the Lyapunov theory. Comparative simulations and experiments show that the proposed NSFC can prescribe the tracking error in a funnel and ensure better tracking performance.

Extended State Observer Based Interval Type-2 Fuzzy Neural Network Sliding Mode Control With Its Application in Active Power Filter

Aiming at the difficulties in modeling the active power filter (APF) system and the susceptibility to parameter perturbation and external disturbance, this article proposes a new adaptive sliding mode controller with using a nonlinear extended state observer (NESO) based on an interval type-2 fuzzy neural network (IT2FNN) structure. The IT2FNN is designed to estimate the unknown control coefficient, so that the NESO can estimate the state of the system and the total disturbance including the unmodeled dynamics and external disturbances, and then perform feedforward compensation to achieve active disturbance rejection. Simulation and experimental results show that the proposed control strategy is effective in the harmonic suppression of the APF system and has better steady-state and dynamic performance compared with the existing methods.

Fuzzy linear extended states observer‐based iteration learning fault‐tolerant control for autonomous underwater vehicle trajectory‐tracking system

To deal with thrusters’ faults of autonomous underwater vehicle (AUV), an iterative learning algorithm fault-tolerant control (FTC) based on the linear extended states observer (LESO) is proposed. In this control scheme, the non-linear feedback mechanism of the LESO is transplanted into iterative learning processes to estimate fault. Compared to our previous work, LESO is used to substitute classic non-linear extended state observer to make the establishment of the whole system more structured; moreover, the number of parameters need to be tuned can be reduced by the conception of observer bandwidth of LESO. To enhance the controllability and robustness of whole scheme, a new saturated sliding mode controller is proposed based on the Lyapunov theory. Then to achieve online parameter self-tuning for the control system, fuzzy logic controllers are introduced to find optimal relationship between LESO's parameter and tracking errors. The performance of the proposed controller is tested by some comparison experiments on Zhuhai A18D AUV; the results show that the proposed control scheme can ensure better stability than classical control and our previous control scheme when AUV suffers faults.

Dynamic surface control for formation control of quadrotors with input constraints and disturbances

In this paper, a novel formation control scheme is presented by integrating the dynamic surface control for multi-quadrotor subject with model uncertainties and external disturbances. First, according to requirements of formation control, the target trajectories of followers are obtained by the designed virtual quadrotors. Then, the formation control problem is transformed into the trajectory tracking control problem. Second, the saturation function and the auxiliary system are developed to make up for nonlinear terms arising from input saturation. A nonlinear extended state observer (ESO) is proposed to estimate and compensate for model uncertainties and external disturbances, and a dynamic surface controller based on the nonlinear ESO is constructed for the desired formation performance. In addition, the amount of communications between the quadrotors is decreased by the constructed distributed speed estimator. And the uniformly ultimately bounded is proved by using the Lyapunov method. Finally, the numerical example is used to demonstrate that the designed controller is effective.

Design of Improved Nonlinear Active Disturbance Rejection Controller for Hybrid Microgrid With Communication Delay

In this paper, an improved nonlinear active disturbance rejection control (INLADRC) approach is proposed for load frequency control of hybrid microgrid with communication delay. The INLADRC technique includes a nonlinear extended state observer (NESO) to estimate the system states and a nonlinear controller for the cancellation of the generalized disturbance acting on system. The effect of communication delay in the hybrid microgrid system is alleviated via the incorporation of an auxiliary structure that also restores the synchronization between the inputs of NESO. The efficacy of the proposed approach is validated via a comprehensive analysis, wherein step variations as well as random perturbations are considered in solar power, wind power and load demand. Further, the performance of proposed technique is also corroborated via consideration of real time solar and wind data. Moreover, the robustness of INLADRC technique is investigated in presence of parametric uncertainty, model-plant mismatch, delay time mismatch as well as varying communication delay. An extensive comparative analysis is a testimony to the effectiveness of INLADRC approach.

2D Magnetic Actuation and Localization of a Surface Milli-Roller in Low Reynolds Numbers

Magnetic actuation of minimally invasive medical tetherless devices holds great promise in several biomedical applications. However, there are still several challenges in noninvasive localization, both in terms of sensing detectable signals of these devices and estimating their states. In this work, a magnetic milli-roller is actuated in a viscous fluid under the influence of a rotating magnetic field. A Lyapunov-based nonlinear state observer is designed and implemented to estimate the position of the roller using a 2D array of Hall-effect sensors. We show that the local stability of the state observer yields convergence to one of the local equilibria, for pre-defined levels of sensor noise, initial conditions, and modeling errors. Performance is quantified using redundant measurements of the fields and we investigate the influence of the number of magnetic field measurements on the observability of the system. Open-loop actuation and state estimation are demonstrated and experimental results show that the localization of a 5 mm diameter roller along sinusoidal, circular and square trajectories achieve a steady-state mean absolute position error of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$2.3 \,\mathrm{m}\mathrm{m}$</tex-math></inline-formula> , <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$1.67 \,\mathrm{m}\mathrm{m}$</tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$1.73 \,\mathrm{m}\mathrm{m}$</tex-math></inline-formula> , respectively.

Modeling and Cascade Control of a Pneumatic Positioning System

Abstract A robust cascade control system based on active disturbance rejection controller (ADRC) is originally developed for accurate position control of a pneumatic servo system, which is usually characterized by nonlinearity, uncertainty, and disturbance. The proposed control system consists of inner and outer control loops. Particularly, a linear ADRC (LADRC) is utilized to adjust valve position for a linear spool valve dynamics in the inner loop. A nonlinear ADRC (NADRC) is designed to control the position of a nonlinear pneumatic actuator subsystem in the outer loop. LADRC and NADRC contain linear and nonlinear extended state observers (ESOs), respectively. The ESO can estimate both unknown nonlinear dynamics and external disturbances and thus make the ADRC robust against system uncertainties and disturbances. Simulation results successfully demonstrate the effectiveness and robustness of the proposed cascade control system. The stabilities of the inner and outer control loops were proved separately using a Lyapunov approach.