Survey on methods of increasing the efficiency of extended state disturbance observers

Active disturbance rejection control with fractional-order model-aided extended state observer

Increasing the observer bandwidth of the extended state observer (ESO) can significantly enhance the disturbance rejection performance of the active disturbance rejection control (ADRC). However, a large observer bandwidth can also amplify the noise and degrade the control quality. This study proposes a novel fractional-order ADRC (FOADRC) approach. A fractional-order model-aided extended state observer (FOMESO) is designed by leveraging available plant information. Under a given observer bandwidth, the disturbance estimation performance of FOMESO is improved, while noise sensitivity is not aggravated. Additionally, FOMESO transforms a typical second-order plant into a fractional-order double-integrator model, reducing the phase lag to below 180∘. Consequently, the derivative component, which is sensitive to noise, is unnecessary in the feedback controller. Simulation and comprehensive comparisons demonstrate that the proposed FOADRC scheme outperforms the traditional ADRC in tracking, noise sensitivity, disturbance rejection, and stability. Furthermore, the proposed FOADRC approach is robust to plant parameter variations. The proposed method is validated through experiments on a permanent magnet synchronous motor speed servo system, confirming its superiority and effectiveness.

Modified Active Disturbance Rejection Predictive Control: A fixed-order state-space formulation for SISO systems

This paper presents a novel control strategy that provides active disturbance rejection predictive control on constrained systems with no nominal identified model. The proposed loop relaxes the modelling requirement to a fixed discrete-time state-space realisation of a first-order plus integrator plant despite the nature of the controlled process. A third-order discrete Extended State Observer (ESO) estimates the model mismatch and assumed plant states. Moreover, the constraints handling is tackled by incorporating the compensation term related to the total perturbation in the definition of the optimisation problem constraints. The proposal merges in a new way state-space Model Predictive Control (MPC) and Active Disturbance Rejection Control (ADRC) into an architecture suitable for the servo-regulatory operation of linear and non-linear systems, as shown through validation examples.

Active disturbance rejection control of drag-free satellites considering the effect of micro-propulsion noise

The space gravitational wave detection mission requires a super "static and precise" scientific experiment environment. In order to solve the non-conservative force disturbance variation and the actuator noise and measurement noise, this paper designs a drag-free control scheme based on active disturbance rejection control (ADRC) framework to achieve the high-precision index. According to the ultra-high accuracy, low bandwidth limitation, and robustness requirements of drag-free satellite, the H_∞ controller satisfying the robustness constraint is designed as an active disturbance rejection feedback controller to achieve the high-precision index. Meanwhile, the non-conservative force disturbance with a wide range of variations is estimated and feedforward compensated by an extended state observer to improve the system robustness. Simulation results show that the control system can achieve the relative displacement of 2 nm/Hznm/Hz^1/2 for the drag-free satellite platform and the residual acceleration of 1 × 10^-15 m/sm/s²/Hz^1/2 for the test mass.

On convergence of extended state observers for nonlinear systems with non-differentiable uncertainties

The analysis of convergence of extended state observers (ESOs) requires the total disturbance to be differentiable. However, this requirement is not satisfied in many control engineering practices. In this paper, we attempt to analyze the convergence of ESOs for nonlinear systems with non-differentiable uncertainties. A decomposition method is first presented to divide the non-differentiable total disturbance into a differentiable signal and a bounded but non-differentiable signal. Based on this decomposition, we give out the convergence of both nonlinear and linear ESOs (NLESO/LESO), low- and high-power ESOs (LPESO/HPESO), and fixed-time ESO (FxESO). We also derive the explicit formulas for the estimation errors of these ESOs. Simulations and experiments demonstrate the correctness of the analysis results.

Data-driven adaptive compensation control for a class of nonlinear discrete-time system with bounded disturbances

This paper considers the compensation control problem for a class of nonlinear discrete-time systems subject to bounded disturbances. With the help of the dynamic linearization technique (DLT), an equivalent data model to the unknown disturbed controlled plant is first established. Based on the data model, two data-driven controllers are designed through novel disturbance-related compact-form and partial-form DLT, which are equivalent to the unknown ideal compensation controller in theory. Adaptive gains designed for the proposed controllers are time-varying and are adaptively updated by directly utilizing the I/O data without involving any model information of the controlled plant, making both controllers purely data-driven adaptive disturbance compensation controllers. Further, in practice, unmeasurable disturbances are commonly encountered due to expensive measuring instruments, unreliable performance or large lags. Therefore, both proposed control laws provide solutions for measurable disturbance (MD) and unmeasurable disturbance (UD) in a unified framework, where the time-varying adaptive gains fuse more system dynamics when disturbance is completely unknown except for some boundedness. The stability of the proposed controllers are strictly guaranteed, and their effectiveness and applicability are verified by a numerical simulation and a distillation column.

On the equivalence between Generalized Proportional Integral Observer and Disturbance Observer

This paper presents the equivalence between generalized proportional integral observer (GPIO) and disturbance observer (DOB), which is applicable to reduced-order GPIO (ROGPIO), full-order GPIO (FOGPIO), and extended state observer (ESO). From this equivalence, established in frequency-domain, comprehensive analyses are performed regarding the influence of the system order, the number of extended states, the uncertain control gain, and the tuning method on the robustness and performance of GPIO. In addition, the equivalence allows a detailed comparison between ROGPIO and FOGPIO in the active disturbance rejection control (ADRC) framework. Finally, experimental validation of the main results is presented for the study case of a synchronous buck converter.

ADRC-Based Habituating Control of Double-Heater Heat Source

This paper deals with the proposition of improvement in the performance of a heat source by modification of its structure and by deriving a dedicated control system. Traditional heat sources consist of a single heater of high nominal power, but slow dynamics, that is regulated by a single closed loop control system. In this paper, an existing heater serially-connected with a supplemental heater with low nominal power but fast dynamics is proposed. A dedicated control system was derived with two active disturbance rejection controllers (ADRC) implemented in the habituating control structure. The proposed solution was validated using a virtual commissioning procedure where the heating system was simulated in the SIEMENS® Simit v10.3 industrial software, and ADRC controllers were implemented in SIEMENS® PLCSIM Advanced using dedicated library function blocks. The results showed the superiority of the proposed approach in comparison with the traditional single closed loop solution. The proposed dedicated habituating control system provided better robustness to the changes in dynamics of a heat source and to the measurement noise. At the same time, it will ensure lower (or in some cases comparable) values of popular closed loop performance indices.

On the stability of active disturbance rejection control for first-order plus delay time processes

The paper presents a stability analysis of a closed-loop system with an active disturbance rejection control (ADRC) algorithm and a reduced-order extended state observer (RESO). The controller is designed for first-order plus delay time processes, and one of the input signals to the RESO is delayed to compensate for the effect of the system delay. If the process delay is known, perfect synchronization between the observer input signals can be achieved. In a more realistic case, the process delay is not precisely known, and the resulting imperfect synchronization may lead to instability of the closed-loop system. The perfect synchronization case shows that the closed-loop system can be stabilized for any delay. For the imperfect synchronization case, delay-dependent stability conditions are derived for a simple tuning method.

Active Disturbance Rejection Control of Euler-Lagrange Systems Exploiting Internal Damping

Active disturbance rejection control (ADRC) is an efficient control technique to accommodate both internal uncertainties and external disturbances. In the typical ADRC framework, however, the design philosophy is to "force" the system dynamics into a double-integral form by an extended state observer (ESO) and then the controller is designed. Especially, the systems' physical structure has been neglected in such a design paradigm. In this article, a new ADRC framework is proposed by incorporating at a fundamental level the physical structure of the Euler-Lagrange (EL) systems. In particular, the differential feedback gain can be selected considerably small or even 0, due to the effective exploitation of the system's internal damping. The design principle stems from an analysis of the energy balance of EL systems, yielding a physically interpretable design. Moreover, the exploitation of the system's internal damping is thoroughly discussed, which is of practical significance for applications of the proposed design. Besides, a sliding-mode ESO is designed to improve the estimation performance over traditional linear ESO. Finally, the proposed control framework is illustrated through tracking control of an omnidirectional mobile robot. Extensive experimental tests are conducted to verify the proposed design as well as the discussions.

Novel Adaptive Extended State Observer for Dynamic Parameter Identification with Asymptotic Convergence

In this paper, a novel method of parameter identification of linear in parameter dynamic systems is presented. The proposed scheme employs an Extended State Observer to online estimate a state of the plant and momentary value of total disturbance present in the system. A notion is made that for properly redefined dynamics of the system, this estimate can be interpreted as a measure of modeling error caused by the parameter uncertainty. Under this notion, a disturbance estimate is used as a basis for classic gradient identification. A global convergence of both state and parameter estimates to their true values is proved using the Lyapunov approach under an assumption of a persistent excitation. Finally, results of simulation and experiments are presented to support the theoretical analysis. The experiments were conducted using a compliant manipulator joint and obtained results show the usefulness of the proposed method in drive control systems and robotics.

Cascade extended state observer for active disturbance rejection control applications under measurement noise

The extended state observer (ESO) plays an important role in the design of feedback control for nonlinear systems. However, its high-gain nature creates a challenge in engineering practice in cases where the output measurement is corrupted by non-negligible, high-frequency noise. The presence of such noise puts a constraint on how high the observer gains can be, which forces a trade-off between fast convergence of state estimates and quality of control task realization. In this work, a new observer design is proposed to improve the estimation performance in the presence of noise. In particular, a unique cascade combination of ESOs is developed, which is capable of fast and accurate signals reconstruction, while avoiding over-amplification of the measurement noise. The effectiveness of the introduced observer structure is verified here while working as a part of an active disturbance rejection control (ADRC) scheme. The conducted numerical validation and theoretical analysis of the new observer structure show improvement over standard solution in terms of noise attenuation.

A novel fuzzy extended state observer

In designing the extended state observer (ESO), one of the most challenging issues is its performance improvement. In this paper, a simple fuzzy system is proposed to improve the performance of ESO and changes this observer into fuzzy extended state observer (FESO). This FESO is an intelligent linear form of the ESO. The fuzzy system, which is applied to tune the observer gains in an intelligent manner, directs the observer to deliver an appropriate estimation performance. To design this fuzzy system, a simple input-output form is applied to reduce the number of fuzzy rules. The linear form of FESO simplifies the convergence analysis of this observer, which is analyzed through a Lyapunov function. The performance of FESO in the fields of fault diagnosis and active disturbance rejection control (ADRC) are shown by simulation examples and compared with traditional forms of ESO. In this paper, it is revealed that this new proposed ESO embodies advantages of the simple linear structure and provides a good performance, confirmed by its results.

Suppressions of vibration in the Tip-Tilt mirror control system by add-on controller

Tip-Tilt mirrors play an important role in astronomical telescopes requiring the tracking performance at the level of microradian or sub-microradian. However, the closed-loop performance suffers a lot from the low-sample rate and time delay of image sensors. Especially, this issue is under the condition of vibrations, because dynamic behaviors are complex and the models are difficult to be obtained accurately. Another challenging issue comes from the measurement of vibrations and its extraction for the closed-loop control. This paper proposes a new method based on an add-on controller of the Tip-Tilt mirror to mitigate telescope vibrations. The proposed method only uses Tip-Tilt errors from an image sensor to implement a disturbance observer, which is not being restricted by an accurate model. As a result, the closed-loop performance can be optimized by designing of a proper Q-filter. To suppress the low-frequency and high-frequency vibrations, a novel Q-filter combining a lowpass filter and a bandpass filter is proposed here. The improved control method is validated by both simulation and experiment in the tip-tilt mirror control system under the condition of vibrations.

On the stability of ADRC for manipulators with modelling uncertainties

The Active Disturbance Rejection Control (ADRC) is an object of the ever growing interest in the latest years due to its limited requirements concerning knowledge of a plant's mathematical model. In this paper, a problem of system stability in presence of modelling uncertainties is investigated. Precisely, imperfect knowledge of the manipulator dynamics and an inertia matrix is considered by the means of the Lyapunov analysis and conditions are formulated which guarantees convergence of the errors in the system to some finite boundary. Influence of the unknown inertia matrix is thoroughly investigated. It is shown, that if the third derivative of the desired trajectory is small enough then an intentional increase of the input matrix estimation error may lead to a reduction of the tracking error boundary. Obtained results are supported by presented simulations and experiments.

Anti-Disturbance Control for Quadrotor UAV Manipulator Attitude System Based on Fuzzy Adaptive Saturation Super-Twisting Sliding Mode Observer

Aerial operation with unmanned aerial vehicle (UAV) manipulator is a promising field for future applications. However, the quadrotor UAV manipulator usually suffers from several disturbances, such as external wind and model uncertainties, when conducting aerial tasks, which will seriously influence the stability of the whole system. In this paper, we address the problem of high-precision attitude control for quadrotor manipulator which is equipped with a 2-degree-of-freedom (DOF) robotic arm under disturbances. We propose a new sliding-mode extended state observer (SMESO) to estimate the lumped disturbance and build a backstepping attitude controller to attenuate its influence. First, we use the saturation function to replace discontinuous sign function of traditional SMESO to alleviate the estimation chattering problem. Second, by innovatively introducing super-twisting algorithm and fuzzy logic rules used for adaptively updating the observer switching gains, the fuzzy adaptive saturation super-twisting extended state observer (FASTESO) is constructed. Finally, in order to further reduce the impact of sensor noise, we invite a tracking differentiator (TD) incorporated into FASTESO. The proposed control approach is validated with effectiveness in several simulations and experiments in which we try to fly UAV under varied external disturbances.

Water Pump Control: A Hybrid Data-Driven and Model-Assisted Active Disturbance Rejection Approach

Water pump control, prevalent in various industrial plants, such as wastewater treatment and steam generator facilities, plays a significant role in maintaining economic efficiency and stable plant operation. Due to its slow dynamics, strong nonlinearity, and various disturbances, it is also widely studied as a typical benchmark problem in process control. The current control strategies can be categorized into two aspects: one branch resorts to model-based design and the other to data-driven design. To merge the merits and overcome the deficiencies of each paradigm, this paper proposes a hybrid data-driven and model-assisted control strategy, namely modified active disturbance rejection control (MADRC). The model information regarding water dynamics is incorporated into an extended state observer (ESO), which is used to estimate and mitigate the limitations of slow dynamics, strong nonlinearity, and various disturbances by analyzing the real-time data. The tuning formula is given in terms of the desired closed-loop performance. It is shown that MADRC is able to produce a satisfactory control performance while maintaining a low sensitivity to the measurement noise under general parametric setting conditions. The simulation results verify the clear superiority of MADRC over the proportional-integral (PI) controller and the conventional ADRC, and the results also evidence its noise reduction effects. The experimental results agree well with the simulation results based on a water tank setup. The proposed MADRC approach is able to improve the control performance while reducing the actuator fluctuation. The results presented in this paper offer a promising methodology for the water control loops widely used in the water industry.

Extended state observer based output control for spacecraft rendezvous and docking with actuator saturation

This paper investigates the relative position tracking and attitude synchronization problem of a chaser spacecraft rendezvous and docking with an uncontrolled tumbling target in the presence of external disturbances and actuator saturation. By combining the extended state observer technique with backstepping control methodology, a robust output-feedback control strategy with no precise motion information of the tumbling target is proposed. Moreover, a particular Nussbaum-type function is introduced to compensate for the nonlinear terms arising for actuator saturation. Within the Lyapunov framework, it is then shown that the proposed control strategy can guarantee the relative position and attitude errors converge into small regions containing the origin. Finally, numerical simulations are carried out to verify the effectiveness of the designed control strategy.

Robust control of uncertain feedback linearizable systems based on adaptive disturbance estimation

In this paper, an adaptive disturbance estimation-based control of a class of uncertain feedback linearizable systems with the presence of, both, external perturbations as well as non-modeled dynamics is considered. The aim of the control design was to solve the tracking trajectory problem for a class of output-based linearizable uncertain systems. An adaptive scheme is proposed for developing a state estimator of the uncertain dynamics. The estimation of both, the states and the uncertain dynamics is attained despite the limited knowledge of the plant and the information contained in the output signal. The uncertain section in the linearized system was approximated by a class of time-dependent combination of the system states. The observer implemented a parametric identifier to obtain the time varying parameters associated to the estimation of the uncertain section. This method ensured the adequate estimation process of the uncertainties/perturbations, measured in terms of the mean square error. Simultaneously, an adaptive gain associated to the observer adjusts its trajectories to provide the ultimate boundedness of the estimation error. Once the states of the uncertain system are obtained, a feedback controller rejects actively the perturbations that affect the system by a compensation scheme. Two numerical examples were developed to show the observer-based control performance.

On the Flexible Operation of Supercritical Circulating Fluidized Bed: Burning Carbon Based Decentralized Active Disturbance Rejection Control

Supercritical circulating fluidized bed (CFB) is one of the prominent clean coal technologies owing to the advantages of high efficiency, fuel flexibility, and low cost of emission control. The fast and flexible load-tracking performance of the supercritical CFB boiler-turbine unit presents a promising prospect in facilitating the sustainability of the power systems. However, features such as large inertia, strong nonlinearity, and multivariable coupling make it a challenging task to harmonize the boiler’s slow dynamics with the turbine’s fast dynamics. To improve the operational flexibility of the supercritical CFB unit, a burning carbon based decentralized active disturbance rejection control is proposed. Since burning carbon in the furnace responds faster than throttle steam pressure when the fuel flow rate changes, it is utilized to compensate the dynamics of the corresponding loop. The parameters of the controllers are tuned by optimizing the weighted integrated absolute error index of each loop via genetic algorithm. Simulations of the proposed method on a 600 MW supercritical CFB unit verify the merits of load following and disturbance rejection in terms of less settling time and overshoot.

A Sustainable Power Plant Control Strategy Based on Fuzzy Extended State Observer and Predictive Control

The control of an ultra-supercritical (USC) boiler–turbine power plant is critical in maintaining the safety of the sustainable power grid. However, it is challenging due to the internal nonlinearity, hard manipulation constraints, and widespread uncertainties. To this end, a fuzzy extended state observer (FESO)-based stable fuzzy predictive control (SFPC) approach is developed in this paper. First, the control difficulties of the USC boiler–turbine unit are analyzed. Then, based on a Takagi–Sugeno (T–S) fuzzy model, a new FESO is developed for nonlinear systems to achieve a more precise observation performance. The gain of FESO is determined by solving a series of linear matrix inequalities, while guaranteeing the stability of FESO. Then, by combining the proposed FESO with the SFPC, an integrated FESO–SFPC algorithm is devised. The disturbance rejection ability of the FESO–SFPC algorithm is analyzed theoretically. Simulation results on a 1000 MW USC boiler–turbine power plant model further validate the effectiveness of the proposed method.

Extended state observer-based robust non-linear integral dynamic surface control for triaxial MEMS gyroscope

This paper reports an extended state observer (ESO)-based robust dynamic surface control (DSC) method for triaxial MEMS gyroscope applications. An ESO with non-linear gain function is designed to estimate both velocity and disturbance vectors of the gyroscope dynamics via measured position signals. Using the sector-bounded property of the non-linear gain function, the design of an $\mathcal{L}_2$-robust ESO is phrased as a convex optimization problem in terms of linear matrix inequalities (LMIs). Next, by using the estimated velocity and disturbance, a certainty equivalence tracking controller is designed based on DSC. To achieve an improved robustness and to remove static steady-state tracking errors, new non-linear integral error surfaces are incorporated into the DSC. Based on the energy-to-peak ($\mathcal{L}_2$-$\mathcal{L}_\infty$) performance criterion, a finite number of LMIs are derived to obtain the DSC gains. In order to prevent amplification of the measurement noise in the DSC error dynamics, a multi-objective convex optimization problem, which guarantees a prescribed $\mathcal{L}_2$-$\mathcal{L}_\infty$ performance bound, is considered. Finally, the efficacy of the proposed control method is illustrated by detailed software simulations.

An AHP based optimized tuning of Modified Active Disturbance Rejection Control: An application to power system load frequency control problem

This paper presents Modified Active Disturbance Rejection Control (MADRC) scheme and a systematic procedure to tune its tuning variables via. observer and controller gains. The problem of tuning is formulated as a constrained multi-objective optimization problem. Depending upon the application appropriate objective functions are chosen, and a unified objective is developed based on weighted sum approach. Five different weight combinations are considered, which result in five objective functions. Each objective function is individually optimized using Teaching-Learning Based Optimization (TLBO), this leads to five sets of tuning variables. Best among five alternatives will be selected based on Analytical Hierarchy Process (AHP). The effectiveness of this approach is validated through its application to a power system with load frequency control problems. Different simulation examples involving single-area and multi-area power systems are considered in the presence of sudden load disturbances, model uncertainties, and parameter variations. Further stability analyses are carried out in a standard two-degree of freedom Internal Model Control (IMC) framework.

Super-Twisting Extended State Observer and Sliding Mode Controller for Quadrotor UAV Attitude System in Presence of Wind Gust and Actuator Faults

This article addresses the problem of high precision attitude control for quadrotor unmanned aerial vehicle in presence of wind gust and actuator faults. We consider the effect of those factors as lumped disturbances, and in order to realize the quickly and accurately estimation of the disturbances, we propose a control strategy based on the online disturbance uncertainty estimation and attenuation method. Firstly, an enhanced extended state observer (ESO) is constructed based on the super-twisting (ST) algorithm to estimate and attenuate the impact of wind gust and actuator faults in finite time. And the convergence analysis and parameter selection rule of STESO are given following. Secondly, in order to guarantee the asymptotic convergence of desired attitude timely, a sliding mode control law is derived based on the super-twisting algorithm. And a comprehensive stability analysis for the entire system is presented based on the Lyapunov stability theory. Finally, to demonstrate the efficiency of the proposed solution, numerical simulations and real time experiments are carried out in presences of wind disturbance and actuator faults.

Modified reduced order observer based linear active disturbance rejection control for TITO systems

This paper proposes an observer based control approach for two input and two output (TITO) plant affected by the lumped disturbance which includes the undesirable effect of cross couplings, parametric uncertainties, and external disturbances. A modified reduced order extended state observer (ESO) based active disturbance rejection control (ADRC) is designed to estimate the lumped disturbance actively as an extended state and compensate its effect by adding it to the control. The decoupled mechanism has been used to determine the controller parameters, while the proposed control technique is applied to the TITO coupled plant without using decoupler to show its efficacy. Simulation results show that the proposed design is efficiently able to nullify the interactions within the loops in the multivariable process with better transient performance as compared to the existing proportional-integral-derivative (PID) control methods. An experimental application of two tanks multivariable level control system is investigated to present the validity of proposed scheme.

Control of unstable processes with time delays via ADRC

Active disturbance rejection control (ADRC) treats the external disturbance and internal uncertainties as a general disturbance, and uses an extended state observer (ESO) to estimate it in real-time and feeds it back in the control loop, thus can achieve good disturbance rejection performance. However, ADRC is not quite suitable for unstable delayed processes due to its inherent structure. In this paper, a two-degree-of-freedom (2DOF) control structure is proposed for unstable time- delayed systems. Set-point tracking and disturbance rejection are separated in this structure and ADRC is solely responsible for disturbance rejection. A method to tune the ADRC parameters using all the information of the system is proposed, and robustness and performance of the proposed method are analyzed. Simulation examples show that 2DOF-ADRC can achieve good tracking and disturbance rejection performance.

Nonlinear adaptive control based on fuzzy sliding mode technique and fuzzy-based compensator

It is difficult to efficiently control nonlinear systems in the presence of uncertainty and disturbance (UAD). One of the main reasons derives from the negative impact of the unknown features of UAD as well as the response delay of the control system on the accuracy rate in the real time of the control signal. In order to deal with this, we propose a new controller named CO-FSMC for a class of nonlinear control systems subjected to UAD, which is constituted of a fuzzy sliding mode controller (FSMC) and a fuzzy-based compensator (CO). Firstly, the FSMC and CO are designed independently, and then an adaptive fuzzy structure is discovered to combine them. Solutions for avoiding the singular cases of the fuzzy-based function approximation and reducing the calculating cost are proposed. Based on the solutions, fuzzy sliding mode technique, lumped disturbance observer and Lyapunov stability analysis, a closed-loop adaptive control law is formulated. Simulations along with a real application based on a semi-active train-car suspension are performed to fully evaluate the method. The obtained results reflected that vibration of the chassis mass is insensitive to UAD. Compared with the other fuzzy sliding mode control strategies, the CO-FSMC can provide the best control ability to reduce unwanted vibrations.

Direct energy balance based active disturbance rejection control for coal-fired power plant

The conventional direct energy balance (DEB) based PI control can fulfill the fundamental tracking requirements of the coal-fired power plant. However, it is challenging to deal with the cases when the coal quality variation is present. To this end, this paper introduces the active disturbance rejection control (ADRC) to the DEB structure, where the coal quality variation is deemed as a kind of unknown disturbance that can be estimated and mitigated promptly. Firstly, the nonlinearity of a recent power plant model is analyzed based on the gap metric, which provides guidance on how to set the pressure set-point in line with the power demand. Secondly, the approximate decoupling effect of the DEB structure is analyzed based on the relative gain analysis in frequency domain. Finally, the synthesis of the DEB based ADRC control system is carried out based on multi-objective optimization. The optimized ADRC results show that the integrated absolute error (IAE) indices of the tracking performances in both loops can be simultaneously improved, in comparison with the DEB based PI control and H_∞ control system. The regulation performance in the presence of the coal quality variation is significantly improved under the ADRC control scheme. Moreover, the robustness of the proposed strategy is shown comparable with the H_∞ control.

Methodology to assess quality of estimated disturbances in active disturbance rejection control structure for mechanical system

A methodology to assess the quality of estimation of disturbances in mechanical systems, by state observers, in the control structure with active compensation of disturbances (ADRC) is presented. Evaluation is carried out by four performance indices that depend on the steady-state error between reference signals and output of the plant. These indices are related with the accuracy and precision of the closed loop system in the sense of norms L₂ and L_∞, for a set of reference signals representing the typical operating conditions of the mechanism. The effectiveness of the methodology is illustrated with the quality assessment of the estimated disturbance of five state observers to control of a simple pendulum and validated on a SCARA robot arm.

Robust state estimation for a class of uncertain nonlinear systems: Comparison of two approaches

In this paper, two approaches for robust state estimation of a class of Lipschitz nonlinear systems are proposed. First, a novel Unknown Input Observer (UIO) is designed without observer matching condition satisfaction. Then, an H_∞ observer for approximate disturbance decoupling is proposed. Sufficient conditions for the existence of both proposed observers are derived based on a Lyapunov function. The achieved conditions are formulated in terms of a set of linear matrix inequalities (LMIs) and optimal gain matrices are obtained. The minimum values of the disturbance attenuation levels for both methods are obtained through solving optimization problems. Finally, the proposed approaches are compared by simulation studies of an automated highway system.

Extended observer based on adaptive second order sliding mode control for a fixed wing UAV

This paper addresses the design of attitude and airspeed controllers for a fixed wing unmanned aerial vehicle. An adaptive second order sliding mode control is proposed for improving performance under different operating conditions and is robust in presence of external disturbances. Moreover, this control does not require the knowledge of disturbance bounds and avoids overestimation of the control gains. Furthermore, in order to implement this controller, an extended observer is designed to estimate unmeasurable states as well as external disturbances. Additionally, sufficient conditions are given to guarantee the closed-loop stability of the observer based control. Finally, using a full 6 degree of freedom model, simulation results are obtained where the performance of the proposed method is compared against active disturbance rejection based on sliding mode control.

Hybrid controller with observer for the estimation and rejection of disturbances

In this paper, a hybrid controller with observer is introduced for the estimation and rejection of a disturbance. It is based on the combination of the sliding mode technique and the output feedback strategy. It is divided into two designs: (1) the observer and (2) the controller with observer. The observer is selected to reach two objectives: (a) to assure its stability and (b) for the estimation of a disturbance. The controller with observer is selected to reach three objectives: (a) to assure its stability, (b) for the rejection of a disturbance, and (c) for the decreasing of chattering in the sliding mode behavior. The proposed method is applied for the estimation and rejection of the disturbance in a plotter and a suspension system.

A nonlinear updated gain observer for MIMO systems: Design, analysis and application to marine surface vessels

In this paper, the state estimation problem of a class of multi-input-multi-output nonlinear systems with measurement noise is studied. We develop an extended updated-gain high gain observer to make a tradeoff between reconstruction speed and measurement noise attenuation. The designed observer, whose gains are driven by nonlinear functions of the available output estimation errors, has the ability to reconstruct system states quickly and reduce the effect of measurement noise. We establish that, if there exists a state feedback law exponentially stabilizing the system with respect to an invariant set, the estimations and estimation errors are bounded. Besides, the trajectories of state- and output-feedback (based on the proposed observer) are sufficiently close, namely performance recovery. The observer performance is illustrated by various examples in marine control, including a case of transformation into the predefined structure.

Combined feedforward and model-assisted active disturbance rejection control for non-minimum phase system

Control of the non-minimum phase (NMP) system is challenging, especially in the presence of modelling uncertainties and external disturbances. To this end, this paper presents a combined feedforward and model-assisted Active Disturbance Rejection Control (MADRC) strategy. Based on the nominal model, the feedforward controller is used to produce a tracking performance that has minimum settling time subject to a prescribed undershoot constraint. On the other hand, the unknown disturbances and uncertain dynamics beyond the nominal model are compensated by MADRC. Since the conventional Extended State Observer (ESO) is not suitable for the NMP system, a model-assisted ESO (MESO) is proposed based on the nominal observable canonical form. The convergence of MESO is proved in time domain. The stability, steady-state characteristics and robustness of the closed-loop system are analyzed in frequency domain. The proposed strategy has only one tuning parameter, i.e., the bandwidth of MESO, which can be readily determined with a prescribed robustness level. Some comparative examples are given to show the efficacy of the proposed method. This paper depicts a promising prospect of the model-assisted ADRC in dealing with complex systems.

Composite disturbance rejection control based on generalized extended state observer

Traditional extended state observer (ESO) design method does not focus on analysis of system reconstruction strategy. The prior information of the controlled system cannot be used for ESO implementation to improve the control accuracy. In this paper, composite disturbance rejection control strategy is proposed based on generalized ESO. First, the disturbance rejection performance of traditional ESO is analyzed to show the essence of the reconstruction strategy. Then, the system is reconstructed based on the equivalent disturbance model. The generalized ESO is proposed based on the reconstructed model, while convergence of the proposed ESO is analyzed along with the outer loop feedback controller. Simulation results on a second order mechanical system show that the proposed generalized ESO can deal with the external disturbance with known model successfully. Experiment of attitude tracking task on an aircraft is also carried out to show the effectiveness of the proposed method.

Extended State Observer based control for coaxial-rotor UAV

This paper considers the problem of controlling the position and the orientation of a Coaxial-Rotor Unmanned Aerial Vehicle -CRUAV- despite unknown aerodynamic efforts. A hierarchical flight controller is designed, allowing the trajectory tracking and the stabilization of the vehicle. The designed controller is build through a hierarchical approach yielding two control loops, an inner one to control the attitude and an outer one to control the translational trajectory of the rotorcraft. An Extended State Observer -ESO- is used to estimate the state and the unknown aerodynamic disturbances. The analysis further extends to the design of a control law that takes the disturbance estimation procedure into account. Numerical simulations are carried out to demonstrate the efficiency of the proposed control strategy.

Sliding mode control based impact angle control guidance considering the seeker׳s field-of-view constraint

The problem of impact angle control guidance for a field-of-view constrained missile against non-maneuvering or maneuvering targets is solved by using the sliding mode control theory. The existing impact angle control guidance laws with field-of-view constraint are only applicable against stationary targets and most of them suffer abrupt-jumping of guidance command due to the application of additional guidance mode switching logic. In this paper, the field-of-view constraint is handled without using any additional switching logic. In particular, a novel time-varying sliding surface is first designed to achieve zero miss distance and zero impact angle error without violating the field-of-view constraint during the sliding mode phase. Then a control integral barrier Lyapunov function is used to design the reaching law so that the sliding mode can be reached within finite time and the field-of-view constraint is not violated during the reaching phase as well. A nonlinear extended state observer is constructed to estimate the disturbance caused by unknown target maneuver, and the undesirable chattering is alleviated effectively by using the estimation as a compensation item in the guidance law. The performance of the proposed guidance law is illustrated with simulations.

A novel extended state observer

A novel extended state observer, which feeds back the output estimation error via both nonlinear and switching terms, is put forward for the first time in this paper. No longer neglecting the lumped uncertainty׳s first time derivative, the problem of disturbance observer design is transformed into the problem of state observer design in the presence of external disturbance. The switching term of the output estimation error is employed to counteract the adverse effect of external disturbance. The newly developed extended state observer provides an attractive solution to the issue of high precision motion control system. Both numerical simulation and experimentation on a speed turntable with temperature box are implemented to verify the performance of the proposed newly developed extended state observer.