Extended State Observer Design Research Articles

Extended state observer design for uncertainty estimation in electronic throttle valve system

AbstractThe Electronic Throttle Valve (ETV) is the core part of automotive engines which are recently used in control-by-wire cars. The estimation of its states and uncertainty is instructive for control applications. This study presents the design of Extended State Observer (ESO) for estimating the states and uncertainties of Electronic Throttle Valve (ETV). Two versions of ESOs have been proposed for estimation: Linear ESO (LESO) and Nonlinear ESO (NESO). The model of ETV is firstly developed and extended in state variable form such that the extended state stands for the uncertainty in system parameters. The design of both structures of ESOs are developed and a comparison study has been conducted to show the effectiveness of the proposed observers. Numerical simulation has been conducted to assess the performance of observers in estimating the states and uncertainties of ETV. The simulated results showed that both full order and reduced order models of ETV have the same transient characteristics. Moreover, the effectiveness of two versions of observers has been examined based on Root Mean Square of Error (RMSE) indicator. The results showed that the NESO has less estimation errors for both states and uncertainties than LESO.

Internal Model Principle-Based Extended State Observer for the Uncertain Systems with Nonconstant Disturbances

Existing traditional expansion state observers exhibit good tracking performance for constant and low-frequency disturbances. However, their ability to track non-constant disturbances such as ramp and high-frequency harmonics is inadequate. This paper proposes an extended state observer design method based on the internal model principle. This method achieves precise tracking of non-constant disturbances in the system, effectively addressing the issue of disturbance estimation errors in conventional expansion state observers. When applied to control systems, this approach significantly mitigates or suppresses system vibrations caused by non-constant disturbances, thereby enhancing control accuracy. Furthermore, it demonstrates the stability of the controlled system and the active disturbance rejection controller parameters over a wide range of variations. Simulation results indicate that the ADRC controller based on the proposed observer in this paper offers notable advantages, including high tracking accuracy, strong disturbance rejection capability, and good stability, leading to commendable control performance.

Nested extended state observer design for uncertain nonlinear systems under time‐varying disturbance

AbstractWith rising demands on system performance and reliability in engineering practice, researchers are increasingly interested in disturbance rejection control, of which state and disturbance observation is the essential element. The extended state observer (ESO, or extended high‐gain observer) is extensively utilized to compensate disturbance, nevertheless, the neglect of lumped disturbance's first derivative and peak phenomenon in classical ESO design impose obstacles to further promotion. In this article, nested ESO (NestedESO) is proposed to estimate states and disturbance simultaneously for general uncertain nonlinear systems under time‐varying disturbance. In NestedESO framework, low‐gain generalized ESO is implemented to obtain a rough estimation of lumped disturbance in the first stage. Then, a novel proportion‐filter‐derivative disturbance estimation refinement mechanism is introduced to provide accurate disturbance estimation. With refined disturbance estimation, modified Luenburger observer is put forward to reconstruct state. Besides, extension to sampled‐data systems is investigated to adapt the networked signal transmission scenario. Numerical examples are given to illustrate the validity and effectiveness of the proposed method.

Improving Tracking Accuracy for Repetitive Learning Systems by High-Order Extended State Observers.

For systems executing repetitive tasks, how to realize the perfect tracking objective is generally desirable, for which an effective method called "iterative learning control (ILC)" emerges thanks to the incorporation of the repetitive execution of systems into an ILC design framework. However, nonrepetitive (iteration-varying) uncertainties are often inevitable in practice and greatly degrade the tracking accuracy of ILC, which has not been treated well, regardless of considerable robust ILC results. This motivates this article to develop a new design method to improve the tracking accuracy of ILC by adopting a high-order extended state observer (ESO) to address ill effects of nonrepetitive uncertainties and uncertain system models. With the designed ESO-based ILC, the robust tracking of any desired trajectory can be achieved such that the tracking error can be decreased to vary in a small bound depending continuously on the bounds of high-order variations of nonrepetitive uncertainties with respect to the iteration. It makes the tracking accuracy of ILC possible to be regulated through the design of ESO, of which the validity is demonstrated by including a simulation example.

Nonlinear Functional Observer Design for Robot Manipulators

In this paper, a nonlinear functional observer (NFO) is first proposed for the control design of robot manipulators under model uncertainties, external disturbances, and a lack of joint velocity information. In principle, the proposed NFO can estimate not only lumped disturbances and uncertainties but also unmeasurable joint velocities, which are then fed back into the main controller. Compared to the well-known ESO design, the proposed NFO has a simpler structure, more accurate estimations, and less computational effort, and consequently, it is easier for practical implementation. Moreover, unnecessary observations of joint displacements are avoided when compared to the well-known extended state observer (ESO). Based on the Lyapunov theory, globally uniformly ultimately bounded estimation performance is guaranteed by the proposed NFO. Consequently, it is theoretically proven that the estimation performances of the NFO are better than those of the ESO. Simulations with a two-degree-of-freedom (2-DOF) robot manipulator are conducted to verify the effectiveness of the proposed algorithm in terms of not only the estimation performance but also the closed-loop control performance.

Discrete-Time Active Disturbance Rejection Current Control of PM Motor at Low Speed Using Resonant Sliding Mode

A discrete-time active disturbance rejection control (ADRC) method using resonant sliding mode is proposed to solve the disturbance characteristics of the current loop of permanent magnet (PM) motor at low speed. The extended state observer (ESO) is used to estimate the disturbance, but there is a contradiction between disturbance rejection and noise rejection in parameter design of ESO, which will affect the accuracy of the estimation, especially at low speed. In order to solve the problem, sliding mode control is combined with ADRC, while traditional integral sliding mode control still has poor rejection effect on the specific frequency harmonics. The resonant sliding mode is proposed to add resonance term to the integral sliding mode surface, which mitigates the impact of the disturbance that ESO fails to estimate on the tracking accuracy. Therefore, resonant sliding mode in the feedback control law of ADRC (RSM-ADRC) is employed to current loop to reduce the steady-state error. Meanwhile, the stability of the proposed algorithm is verified by discretization method. The steady and dynamic performances of the four control methods are compared through experiments to verify the feasibility and effectiveness of the proposed method. For example, when the reference current of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</i> - and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</i> -axis is 0A and 1A respectively at 50rpm, the total harmonic distortion of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</i> -axis current decreases from 1.68% to 0.64% and the 6th harmonic of current also drops to 0.135%. Despite the sudden change of inductance parameters, the steady-state current response is largely unaffected.

Distributed extended state observer design and output feedback anti‐disturbance control for nonlinear interconnected systems: A dynamic memory event‐triggered mechanism

AbstractThis paper investigates a distributed extended state observer design and output feedback anti‐disturbance control for nonlinear interconnected systems (ISs) with multiple disturbances. First, a distributed extended state observer with a sparse observer communication network is established to estimate the system states and external disturbances. Then, an output feedback controller with a disturbance compensation (DC) item is designed, where a novel dynamic memory event‐triggered mechanism (DMETM) is proposed to save communication resources. Third, under the proposed controller, the closed‐loop signals are bounded and the system states and the estimation errors converge to zero. Additionally, the system outputs satisfy performance. Finally, the simulation examples demonstrate the effectiveness of the DMETM in reducing the number of data transmissions compared to the dynamic event‐triggered mechanism (ETM).

Tansig type NLESO-based integral terminal sliding mode control for modular robot manipulators with uncertain disturbance: Theory and experimental verification

To overcome the mutual constraints between the system chattering and the arrival time in conventional sliding mode control in this paper, a tangent excitation function (tansig) type nonlinear extended state observer (NLESO)-based integral terminal sliding mode control is proposed to solve the trajectory tracking control task of the modular robot manipulators (MRMs) possessing strong coupling and complex time-varying properties. Through the joint torque feedback technology, the MRM system dynamic model is formulated; on this basis, the proposed NLESO based on tansig is utilized to estimate and compensate the system uncertain information, which are consisted of the friction, interconnected dynamic coupling, and external disturbance. The proposed NLESO can simplify the traditional extended state observer design parameters for theoretical analysis and practical application. The proposed tansig-type NLESO-based integral terminal sliding mode control integrated adaptive term exponential reaching law for MRMs is designed to diminish the arrival time when the system state converges to the equilibrium point. The presented algorithm improves the robotic system antidisturbance ability. Furthermore, the Lyapunov theory is utilized to verify stability of the proposed NLESO and closed-loop robotic system. Finally, the availability of the proposed algorithm is demonstrated by experiments.

Composite anti-unwinding attitude control of spacecraft under actuator saturation and angular velocity limits

Spacecraft attitude control employs quaternion representation to avoid singularity issues and obtain global maneuver stability. However, it has redundancy associated, resulting in dual equilibrium points. The attitude control may confront the unwinding phenomenon due to the presence of the equilibria. In this paper, an anti-unwinding controller for spacecraft stabilization in the presence of external disturbances and inertial uncertainties, angular velocity limit, actuator saturation and faults is presented. Specifically, a modified extended state observer (ESO) is designed to obtain total disturbance estimates of the rigid-body spacecraft. Auxiliary parameters are added in the design to avoid initial high estimates in the proposed ESO design resulting in faster convergence. The proposed disturbance observer is to release the assumption that requires the estimated disturbance to be constant or varying at slow rates. Using the ESO estimates, a particular back-stepping-SMC (ESO-BTSMC) controller is devised to formulate anti-unwinding control law for spacecraft stabilization. Lyapunov stability theory is employed to prove closed-loop stability of system and estimation error convergence. Comparative simulations are performed to demonstrate the performance of the proposed control scheme. It is found that the proposed control scheme gives smooth and precise control performance along with faster transient response. Additionally, it also alleviates the chattering phenomenon.

Wave-filtering finite-time self-learning extended state observers for robotic surface vehicles

This paper presents wave-filtering finite-time self-learning extended state observers for robotic surface vehicles subject to unknown control gains and ocean disturbances. By incorporating wave filtering technique and concurrent learning into the extended state observer design, the low-frequency motion components and wave-frequency motion components of robotic surface vehicles can be estimated, in addition to the unknown control gains, total disturbance and unmeasured velocity. A salient feature of the proposed approach is that wave-frequency motion components are filtered from the position and yaw angle sensor measurements to avoid mechanical wear and tear of the propulsion system components caused by wave-frequency motion signals. The result is extended to a wave-filtering finite-time self-learning extended state observer which improves the estimation performance considerably. The efficacy of the proposed two wave-filtering self-learning extend state observers for robotic surface vehicles with unknown control gains is substantiated via simulations.

Novel Extended State Observer Design for Uncertain Nonlinear Systems via Refined Dynamic Event-Triggered Communication Protocol.

In this article, an extended state observer (ESO) design problem is investigated for uncertain nonlinear systems subject to limited network bandwidth. First, for rational information exchange scheduling, a dynamic event-triggered (DET) communication protocol is proposed. Different from the traditional static event-triggered strategies with fixed thresholds, an internal dynamic variable is introduced to be adaptively adjusted by a dual-directional regulating mechanism. Thus, more desirable tradeoff between observation performance and communication resource efficiency is achieved. Second, inspired by our early work on Takagi-Sugeno fuzzy ESO (TSFESO), a novel paradigm of event-triggered TSFESO is initially proposed. Third, under the DET mechanism, the TSFESO design approach is derived to carry out exponential convergence for estimation error dynamics. Finally, the effectiveness of the proposed method is verified by numerical examples. The nonlinear estimating efficiency and linear numerical tractability are integrated in TSFESO. In addition, a generalized ESO formulation is developed to allow some nonadditive uncertainties incompatible with total disturbance, such as improved event-triggered strategy, and thus, the application sphere of ESO is further expanded.

Finite-time ESO-based cascade-free FCS-MPC for NNPC converter

This article addresses a novel finite control-set model predictive control solution for nested neutral point-clamped converter. More specifically, it is formed by incorporating a finite-time extended state observer design into a cascade-free finite control-set model predictive control architecture. In this architecture, a finite-time extended state observer is developed to estimate the total disturbances, and an integral error term and a dynamic reference design point of view are embedded into the proposed design so as to improve the performance. The main features of this proposal are: first of all, the detailed knowledge of the physical structure of the controlled plant is not required; second, a cascade-free structure is achieved in finite control-set model predictive control solution without weighting factors and steady-state error; and third, the proposed methodology can operate with different systems not just power converters, while keeping the fast transient response. In contrast to existing finite control-set model predictive control approaches, it can be found that our modification not only can track fast to their references but also can have superior robustness performance. Finally, the proposed solution is verified by comprehensive results that prove the theoretical researches for nested neutral point-clamped converter, while meeting the harmonic standards.

Generalized Fuzzy Extended State Observer Design for Uncertain Nonlinear Systems: An Improved Dynamic Event-Triggered Approach

This article is concerned with extended state observer (ESO) design for uncertain nonlinear systems. First, different from standard ESO exclusively applicable for integral chain systems, a ESO formation including nonlinear and linear types is proposed for general state-space models. Inspired by our previous work, a event-triggered generalized fuzzy ESO (GFESO) is developed. Second, in order to schedule transmission rationally, an improved total disturbance-resilient dynamic event-triggered mechanism (TDRDETM) is put forward. Third, under TDRDETM, the GFESO design approach is presented in sense of exponential convergence. Finally, numerical examples illustrate the effectiveness of the given methods.

Adaptive fast-finite-time extended state observer design for uncertain electro-hydraulic systems

This paper presents the design of an adaptive fast-finite-time extended state observer for electro-hydraulic actuator systems. First, state variables and subsequently the system model are divided into three independent parts, and fast-finite-time state observers with adaptive gains are designed independently for each part, guaranteeing the fast uniformly ultimate boundedness of the estimation errors. Then, based on the designed state observers and without any knowledge about the upper bounds of uncertainties or their derivatives, supplementary adaptive observers are presented to estimate the uncertainties. Besides, the adaptive gains of both observers are adjusted based on the evaluation of the absolute value of the observation errors in a straightforward manner, where rigorous analyses of the proposed strategy are provided through the Lyapunov approach. Finally, comparative simulations with respect to some leading strategies are presented to analyze the effectiveness of the proposed observers, where the convergence of the estimation errors to a small neighborhood of zero can be achieved almost regardless of the initial conditions. Indeed, in contrast to the earlier finite-time approaches which only have a relatively fast convergence rate around the equilibrium points, the proposed adaptive framework can also improve the convergence rate for zones far from the equilibrium points. It is concluded that the proposed scheme can compete with other leading strategies, making it a qualified alternative approach in the observer design with noteworthy potential.

Extended state observer design with fractional order Bode’s ideal cut-off filter in a linear motor motion control system

A desired output tracking motion control scheme of a new type of self-made linear motor is proposed in the presence of parameter uncertainties and external disturbance. An extended state observer is designed with a fractional order Bode’s ideal cut-off filter to suppress the high-frequency measurement noise. Characteristics of the linear motor are analyzed, including its working principle, mathematical model, and mechanical structure. A fractional order Bode’s ideal cut-off filter, a second-order extended state observer, a reference acceleration feedforward control scheme, and a normal proportional–derivative algorithm constitute the linear-motion control system in this article. The effectiveness of the control scheme has been verified by comparative simulations and experimental results. The proposed method is an effective way to obtain desired output tracking control performance in actual motion control engineering.

Flatness-Based Active Disturbance Rejection Control for a PVTOL Aircraft System with an Inverted Pendular Load

This paper presents a systematic procedure for the control scheme design for a PVTOL aircraft system with an inverted pendular load, which is a nonlinear underactuated system. The control scheme is based on the use of angular movement as an artificial control in order to propose new auxiliary control inputs. This is achieved by a linear extended state observer-based active disturbance rejection control to reject both nonmodeled dynamics and external disturbances. The flying planar inverted pendulum is then linearized around an unstable equilibrium point, and the resulting system is subdivided into two subsystems: (1) the height system, and (2) the horizontal pendulum system. For the height system, a linear extended state observer-based active disturbance rejection control is proposed in order to accomplish a take-off and landing task in the presence of external disturbances and non-linearities neglected in the linearization process. The flatness property in the horizontal-pendulum system is exploited in order to propose another active disturbance rejection control of linear nature. The flatness of the tangentially linearized model provides a unique structural property that results in an advantageous low-order cascade decomposition of the linear extended state observer design. Numerical simulations show the effectiveness of the proposed control scheme in trajectory tracking tasks in the presence of disturbances caused by crosswinds with random amplitudes.

Aperiodic Sampled-Data Takagi–Sugeno Fuzzy Extended State Observer for a Class of Uncertain Nonlinear Systems With External Disturbance and Unmodeled Dynamics

For the extended state observer (ESO) design, the most challenging issue is to exploit efficient nonlinear observation performance, while maintaining desirable linear numerical tractability under noncontinuous transmission. In this article, in order to address this issue, the sampled-data ESO design is investigated for a class of uncertain nonlinear systems. First, based on the fuzzy modeling approach with reasonable fuzzy rules and sets, the nonlinear functions of the ESO are suitably approximated by several local linear models weighted by membership functions. Then, a novel methodology of Takagi–Sugeno fuzzy extended state observer (TSFESO) is developed for the first time. By virtue of fuzzy membership functions, the estimating action is implemented in a nonlinear pattern, while taking advantages of Takagi–Sugeno fuzzy formulation, the observer gains can be calculated in a linear manner. As a result, the nonlinear estimating efficiency and linear numerical tractability are integrated in a unified framework. Second, for the aperiodic sampling case, the exponential convergence criterion for the TSFESO is presented by constructing a sampling- and time-dependent Lyapunov functional, in which the information on sampling action is taken into full consideration for desirable feasibility. Moreover, the observer design approach is also put forward. Finally, the superiorities and effectiveness of the proposed approaches are demonstrated by numerical examples.

Continuous finite-time extended state observer design for electro-hydraulic systems

This paper presents a novel framework towards a time-varying observer design for nonlinear electro-hydraulic actuators. The key idea of this paper is to employ a positive-increasing function associated with the observer objective to improve the estimation performance. An extended state observer is designed to estimate the full state variables and the uncertainties without any knowledge about the upper bounds of the uncertainties and their derivatives. First, without loss of generality, the system model is divided into three parts, and the extended state observers are designed for each part, independently. Then, the time-varying gains of each observer are designed to make the observation errors uniformly bounded. Finally, the simulated performance of the presented framework is compared with two valid approaches including high-order sliding mode and high-gain extended state observers.

Data-driven adaptive extended state observer design for autonomous surface vehicles with unknown input gains based on concurrent learning

This paper is concerned with the disturbance estimation and velocity recovery of autonomous surface ve hicles subject to unknown input gains, in addition to lumped uncertainties composed of unknown internal dynamics and external disturbances. Existing extended state observer design methods are not applicable due to the fact that some prior knowledge on model parameters such as the control input gains are assumed to be known in advance. By incorporating a concurrent learning approach into the extended state observer design, a three-order data-driven adaptive extended state observer based on position and acceleration information is proposed to estimate the unknown input gains, lumped disturbance, and unmeasured velocities. An advantage of the proposed data-driven adaptive extended state observer is that the unknown input gains, lumped disturbance, and unknown velocities can be simultaneously estimated with guaranteed convergence thanks to concurrent learning. The result is extended to a data-driven adaptive extended state observer with finite-time convergence. The efficacy of the proposed two data-driven adaptive extended state observers for autonomous surface vehicles is substantiated via simulations.

A new extended state observer for uncertain nonlinear systems

Extended state observer (ESO) is a class of high-gain observers and a powerful tool for output feedback control of uncertain nonlinear systems. In this paper, we propose a new ESO design technique which is based on cascading a series of first-order ESOs. Benefited from the cascade design, saturations can be inserted into the observer internal variables to limit the maximal implemented gain. The convergence of the new ESO with a class of nonlinear gain functions is established, and it is shown that adopting appropriate nonlinear gain mechanisms leads to improvement in measurement noise tolerance. What is more, the new ESO based output feedback control has stronger uncertainty estimation and compensation capability than the standard ESO based output feedback control. Specifically, the proposed approach only relies on the knowledge of the control direction of the uncertain nonlinear system. Finally, the obtained results are applied to suppress the wing rock motion of a slender delta wing.