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.     

基于扩张状态观测器的快速步进/凝视成像机构控制

提出一种基于扩张状态观测器并引入加速度补偿策略的控制器设计方案,以实现快速步进/凝视成像机构对控制性能的高要求。首先,阐述了扩张状态观测器理论,对其特性进行了详细分析,并设计了以成像机构为被控对象的三阶线性扩张状态观测器。通过将观测器置于速度内环反馈通道,设计了基于扩张状态观测器的位置和速度双回路控制器。在此基础上,利用观测器输出的加速度估计值,提出加速度补偿策略,并设计了补偿环节。实验结果表明,与无加速度补偿环节相比,引入加速度补偿后,成像机构每次步进调节时间由76ms减小到33ms,凝视期间的角位置精度由约0.07°减小到0.01°以内,速度波动减小约2~3倍,成像机构的控制性能明显改善。控制器设计简单,需整定参数少,对于提高同类控制系统性能具有较高的实用价值。     

Sampled data observer based inter-sample output predictor for Electro-Hydraulic Actuators

In this paper, a Sampled Data Disturbance Observer which simultaneously estimates the unmeasurable states and the uncertainties for the Electro-Hydraulic Actuators systems are presented. The novelty of our approach is the use of an inter-sample output predictor which allows the user to increase the frequency acquisition of the piston position sensor without affecting the convergence performance. The stability analysis of the proposed observer is proved using the Lyapunov function adapted to hybrid systems. To show the efficiency of the proposed observer, numerical simulations of a control application which combine the proposed observer and a Proportional Integral controller for the purpose of piston position tracking problem are presented.     

Output feedback model predictive control of hydraulic systems with disturbances compensation

Enhancing the robustness of output feedback control has always been an important issue in hydraulic servo systems. In this paper, an output feedback model predictive controller (MPC) with the integration of an extended state observer (ESO) is proposed for hydraulic systems. The ESO was designed to estimate not only the unmeasured system states but also the disturbances, which will be synthesized into the design of the output prediction equation. Based on the mechanism of receding horizon and repeating optimization of MPC, the output prediction equation will be updated in real time and the future behavior of the system will be accurately predicted since the disturbances are compensated effectively. Hence, the ability of the traditional MPC to suppress disturbances will be improved evidently. The experiment results show that the proposed controller has high-performance nature and strong robustness against various model uncertainties, which verifies the effectiveness of the proposed control strategy.     

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.     

Distributed output-feedback consensus control of multi-agent systems with dynamically changing directed interaction topologies

This paper considers the distributed output-feedback consensus control problem for a multi-agent system with higher order linear dynamics and subject to external disturbance, under dynamically changing directed topologies and weighting factors. An extended state observer (ESO) is first designed to estimate not only the unmeasurable agent states but also the external disturbance. Based on the output of the ESO, a novel distributed control protocol is proposed. We show that, with the application of the proposed control protocol, the consensus can be achieved asymptotically by the group of agents if the union of the directed interaction graphs contains a spanning tree frequently enough. A numerical example is given to verify the effectiveness of the theoretical results.     

Robust partial integrated guidance and control for missiles via extended state observer

A novel extended state observer (ESO) based control is proposed for a class of nonlinear systems subject to multiple uncertainties, and then applied to partial integrated guidance and control (PIGC) design for a missile. The proposed control strategy incorporates both an ESO and an adaptive sliding mode control law. The multiple uncertainties are treated as an extended state of the plant, and then estimate them using the ESO and compensate for them in the control action, in real time. Based on the output of the ESO, the resulting adaptive sliding mode control law is inherently continuous and differentiable. Strict proof is given to show that the estimation error of the ESO can be arbitrarily small in a finite time. In addition, the adaptive sliding mode control law can achieve finite time convergence to a neighborhood of the origin, and the accurate expression of the convergent region is given. Finally, simulations are conducted on the planar missile–target engagement geometry. The effectiveness of the proposed control strategy in enhanced interception performance and improved robustness against multiple uncertainties are demonstrated.     

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.     

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.     

基于扩张状态观测器的炮控系统串联滑模控制

针对坦克炮控系统中存在齿圈间隙、摩擦力矩和参数漂移等多种非线性因素造成系统驱动延时、换向振荡和低速“爬行”等问题,设计了一种基于扩张状态观测器(ESO)的炮控系统串联滑模控制器.首先,利用系统内部可测信息,将炮控系统分解为n个串联的一阶子系统;然后,引入ESO估计各子系统的不确定性.在此基础上,基于backsteppi...     

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.     

基于ESO及NTD的PMSM无机械传感器位置控制

在分析永磁同步电机(PMSM)系统模型的基础上,提出了一种基于扩张状态观测器(ESO)及非线性跟踪微分器(NTD)的PMSM无机械传感器位置控制系统。控制系统通过基于ESO及NTD的观测器实时观测出电机转子位置及转速,在此基础上实现PMSM无机械传感器位置控制。仿真和实验结果表明该系统结构简单,控制快速、准确、无超调,对于外界干扰具有较强的鲁棒性。     

Performance analysis of active disturbance rejection tracking control for a class of uncertain LTI systems

The paper considers the tracking problem for a class of uncertain linear time invariant (LTI) systems with both uncertain parameters and external disturbances. The active disturbance rejection tracking controller is designed and the resulting closed-loop system׳s characteristics are comprehensively studied. In the time-domain, it is proven that the output of closed-loop system can approach its ideal trajectory in the transient process against different kinds of uncertainties by tuning the bandwidth of extended state observer (ESO). In the frequency-domain, different kinds of parameters׳ influences on the phase margin and the crossover frequency of the resulting control system are illuminated. Finally, the effectiveness and robustness of the controller are verified through the actuator position control system with uncertain parameters and load disturbances in the simulations.     

Disturbance observer based hierarchical control of coaxial-rotor UAV

This paper propose an hierarchical controller based on a new disturbance observer with finite time convergence (FTDO) to solve the path tracking of a small coaxial-rotor-typs Unmanned Aerial Vehicles (UAVs) despite of unknown aerodynamic efforts. The hierarchical control technique is used to separate the flight control problem into an inner loop that controls attitude and an outer loop that controls the thrust force acting on the vehicle. The new disturbance observer with finite time convergence is intergated to online estimate the unknown uncertainties and disturbances and to actively compensate them in finite time.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.     

Robust disturbance rejection control of a biped robotic system using high-order extended state observer

This study addressed the problem of robust control of a biped robot based on disturbance estimation. Active disturbance rejection control was the paradigm used for controlling the biped robot by direct active estimation. A robust controller was developed to implement disturbance cancelation based on a linear extended state observer of high gain class. A robust high-gain scheme was proposed for developing a state estimator of the biped robot despite poor knowledge of the plant and the presence of uncertainties. The estimated states provided by the state estimator were used to implement a feedback controller that was effective in actively rejecting the perturbations as well as forcing the trajectory tracking error to within a small vicinity of the origin. The theoretical convergence of the tracking error was proven using the Lyapunov theory. The controller was implemented by numerical simulations that showed the convergence of the tracking error. A comparison with a high-order sliding-mode-observer-based controller confirmed the superior performance of the controller using the robust observer introduced in this study. Finally, the proposed controller was implemented on an actual biped robot using an embedded hardware-in-the-loop strategy.     

Active disturbance rejection control based human gait tracking for lower extremity rehabilitation exoskeleton

This paper presents an active disturbance rejection control (ADRC) based strategy, which is applied to track the human gait trajectory for a lower limb rehabilitation exoskeleton. The desired human gait trajectory is derived from the Clinical Gait Analysis (CGA). In ADRC, the total external disturbance can be estimated by the extended state observer (ESO) and canceled by the designed control law. The observer bandwidth and the controller bandwidth are determined by the practical principles. We simulated the proposed methodology in MATLAB. The numerical simulation shows the tracking error comparison and the estimated errors of the extended state observer. Two experimental tests were carried out to prove the performance of the algorithm presented in this paper. The experiment results show that the proposed ADRC behaves a better performance than the regular proportional integral derivative (PID) controller. With the proposed ADRC, the rehabilitation system is capable of tracking the target gait more accurately.     

Generalized proportional integral control for periodic signals under active disturbance rejection approach

Conventional repetitive control has proven to be an effective strategy to reject/track periodic signals with constant frequency; however, it shows poor performance in varying frequency applications. This paper proposes an active disturbance rejection methodology applied to a large class of uncertain flat systems for the tracking and rejection of periodic signals, in which the possibilities of the generalized proportional integral (GPI) observer-based control to address repetitive control problems are studied. In the proposed scheme, model uncertainties and external disturbances are lumped together in a general additive disturbance input that is estimated and rejected on-line. An illustrative case study of mechatronic nature is considered. Experimental results show that the proposed GPI observer-based control successfully rejects periodic disturbances even under varying speed conditions.     

High pressure common rail injection system modeling and control

In this paper modeling and common-rail pressure control of high pressure common rail injection system (HPCRIS) is presented. The proposed mathematical model of high pressure common rail injection system which contains three sub-systems: high pressure pump sub-model, common rail sub-model and injector sub-model is a relative complicated nonlinear system. The mathematical model is validated by the software Matlab and a virtual detailed simulation environment. For the considered HPCRIS, an effective model free controller which is called Extended State Observer – based intelligent Proportional Integral (ESO-based iPI) controller is designed. And this proposed method is composed mainly of the referred ESO observer, and a time delay estimation based iPI controller. Finally, to demonstrate the performances of the proposed controller, the proposed ESO-based iPI controller is compared with a conventional PID controller and ADRC.     

Tuning of linear active disturbance rejection controller with robustness specification

Active disturbance rejection control (ADRC) treats all the model uncertainties and all the external disturbances as a generalized disturbance. It uses an extended state observer (ESO) to estimate the generalized disturbance in real time, and compensate it using a state-feedback control law, thus can achieve good disturbance rejection performance. For linear ADRC (LADRC), the parameters can be tuned via the bandwidths of the ESO and the feedback control, thus an LADRC can be regarded as a fixed-structured controller with several parameters to tune, just like a PID controller. To help tuning the parameters of LADRC, a tuning rule is proposed in this paper, with the aim to minimize the load disturbance attenuation performance in the integral of time square error sense, under the constraint of a specified robustness measure for the first-order processes with deadtime. The tuning rule is tested for a variety of benchmark systems and the gravity drained tanks case, and the performances are compared with the well-known PID tuning methods.     

Robust control for rotational inverted pendulums using output feedback sliding mode controller and disturbance observer

This paper presents a system modeling, controller design and implementation for a rotational inverted pendulum system (RIPS), which is an under-actuated system and has the problem of unattainable velocity state. Two control strategies are applied to theRIPS. One is a sliding mode control method using the parameterization of both the hyperplane and the compensator for output feedback. The other is the disturbance observer which estimates disturbance and some modeling errors of RIPS with less computational effort. Some simulations and various kinds of experiments are performed in order to verify that the proposed controller has the ability to control RIPS whose velocity is assumed to be unavailable. The results of the simulations and experiments show that the proposed control system has superior performance for disturbance rejection and regulation at certain initial conditions as well as the robustness to model uncertainties.