This is the last part of four series papers, aiming at stabilization for signal-input-signaloutput (SISO) linear finite-dimensional systems corrupted by general input disturbances. A new observer, referred to as Extended Dynamics Observer (EDO), is proposed to estimate both the state and disturbance simultaneously. The working mechanism of EDO consists of two parts: The disturbance with known dynamics is canceled completely by its dynamics and the disturbance with unknown dynamics is absorbed by high-gain. It is found that the high-gain is always working as long as the control plant with unknown input disturbance is observable which is the only assumption for the observer design. When the disturbance dynamics are completely unknown except some boundedness, the EDO is reduced to an extension of the well-known extended state observer or high-gain observer. The main advantage of the developed method is that the prior information about both the control plant and the disturbance can be utilized as much as possible. The more the prior information we have, the better performance the observer would be. An EDO based stabilizing output feedback is also developed in the spirit of estimation/cancellation strategy. The stability of the resulting closed-loop system is established and some of the theoretical results are validated by numerical simulations.
Disturbance observer is an inner-loop output-feedback controller whose role is to reject external disturbances and to make the outer-loop baseline controller robust against plant's uncertainties. Therefore, the closed-loop system with the DOB approximates the nominal closed-loop by the baseline controller and the nominal plant model with no disturbances. This article presents how the disturbance observer works under what conditions, and how one can design a disturbance observer to guarantee robust stability and to recover the nominal performance not only in the steady-state but also for the tr…
This work provides formal safety guarantees for control systems with disturbance. A disturbance observer-based robust safety-critical controller is proposed, that estimates the effect of the disturbance on safety and utilizes this estimate with control barrier functions to attain provably safe dynamic behavior. The observer error bound - which consists of transient and steady-state parts - is quantified, and the system is endowed with robustness against this error via the proposed controller. An adaptive cruise control problem is used as illustrative example through simulations including real …
Repetitive operations are widely conducted by automatic machines in industry. Periodic disturbances induced by the repetitive operations must be compensated to achieve precise functioning. In this paper, a periodic-disturbance observer (PDOB) based on the disturbance observer (DOB) structure is proposed. The PDOB compensates a periodic disturbance including the fundamental wave and harmonics by using a time delay element. Furthermore, an adaptive PDOB is proposed for the compensation of frequency-varying periodic disturbances. An adaptive notch filter (ANF) is used in the adaptive PDOB to esti…
Yet Another Tutorial of Disturbance Observer: Robust Stabilization and Recovery of Nominal Performance
ASRI, Department of Electrical and Computer Engineering, Seoul National University（首尔国立大学电气与计算机工程系自动系统研究室）；Department of Electrical Engineering and Computer Science, University of Central Florida（中佛罗里达大学电气与计算机科学系）；School of Robotics, Kwangwoon University（光云大学机器人学院）；Department of Electrical Engineering, Soongsil University（崇实大学电气工程系）
The position and the orientation of a rigid body object pushed by a robot on a planar surface are extremely difficult to predict. In this paper, the prediction problem is formulated as a disturbance observer design problem. The disturbance observer provides accurate estimation of the total sum of model errors and external disturbances acting on the object. From the estimation results, it is revealed that there is a strong linear relationship between the applied force or torque and the estimated disturbances. The proposed prediction algorithm has two phases: the identification & the prediction.…
This paper proposes a new fraction-order active disturbance rejection controller based on an improved fraction-order extended state observer (IFESO) for a class of fraction-order systems. Applying the IFESO, the fraction-order system can be approximated as an integer-order integrator (1/s). The parameters that ensure the stability of the IFESO and closed-loop system are provided. The frequency-domain analysis shows that the IFADRC has a stronger disturbance estimation performance for the fraction-order system than an integer-order active disturbance rejection controller (IADRC). The simulation…
This paper proposes a disturbance-observer-based control (DOBC) scheme for frequency and voltage regulation for a renewable energy sources (RES) integrated power systems. The proposed approach acts a feed-forward control which improves the dynamic performance of the conventional proportional-integral-derivative (PID) controller. Robustness of the proposed control scheme has been validated through simulations under worst-case and stochastic uncertainties to mitigate real-time variability in RES output and load. The performance of the proposed control technique is compared to well established te…
This work develops a data-based construction of inverse dynamics for LTI systems. Specifically, the problem addressed here is to find an input sequence from the corresponding output sequence based on pre-collected input and output data. The problem can be considered as a reverse of the recent use of behavioral approach, in which the output sequence is obtained for a given input sequence by solving an equation formed by pre-collected data. The condition under which the problem gives a solution is investigated and turns out to be L-delay invertibility of the plant and a certain degree of persist…
Control systems are inevitably affected by external disturbances, and a major objective of the control design is to attenuate or eliminate their adverse effects on the system performance. This paper presents a disturbance rejection approach with two main improvements over existing results: 1) it relaxes the requirement of calculating or measuring the state derivatives, which are not available for measurement, and their calculation is corrupted by noise, and 2) it achieves finite-time disturbance rejection and control. To this end, the disturbance is first modeled by an unknown dynamics, and an…
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…
King Fahd University of Petroleum and Minerals（法赫德石油和矿产大学）
In this work, the autonomous control of a quadrotor-manipulator unmanned aerial vehicle is treated using an extended dynamic model. Due to persistent aerodynamic disturbances and dynamic couplings, the control of a quadrotor-manipulator unit is cumbersome. Active disturbance rejection control (ADRC) is proposed for the cancellation of the undesirable dynamics while a PD controller is developed for set-point tracking. Parameters were tuned using Gradient Descent-Sequential Quadratic Programming in Simulink design optimization
In a complex real-time operating environment, external disturbances and uncertainties adversely affect the safety, stability, and performance of dynamical systems. This paper presents a robust stabilizing safety-critical controller synthesis framework with control Lyapunov functions (CLFs) and control barrier functions (CBFs) in the presence of disturbance. A high-gain input observer method is adapted to estimate the time-varying unmodelled dynamics of the CBF with an error bound using the first-order time derivative of the CBF. This approach leads to an easily tunable low order disturbance es…
This paper presents a novel Sliding Mode Control (SMC) algorithm to handle mismatched uncertainties in systems via a novel Self-Learning Disturbance Observer (SLDO). A computationally efficient SLDO is developed within a framework of feedback-error learning scheme in which a conventional estimation law and a Neuro-Fuzzy Structure (NFS) work in parallel. In this framework, the NFS estimates the mismatched disturbances and becomes the leading disturbance estimator while the former feeds the learning error to the NFS to learn system behavior. The simulation results demonstrate that the proposed S…
In this paper, adaptive prescribed finite time stabilization of uncertain single-input and single-output nonlinear systems is considered in the presence of unknown states, unknown parameters, external load disturbance, and non-symmetric input saturation. A prescribed finite time disturbance observer is designed to approximate the unmeasured external disturbance. Also, a nonsingular prescribed finite time terminal sliding mode control is proposed for the closed-loop control of the system with the non-symmetric input saturation. Extended Kalman filter algorithm is employed for the real-time esti…
Eindhoven University of Technology（埃因霍温理工大学）；Technical University of Munich（慕尼黑工业大学）
This paper proposes a novel observer-based disturbance estimation method for high degree-of-freedom Euler-Lagrangian systems using an unknown input-output (UIO) sliding mode observer (SMO). Different from the previous SMO methods, this approach does not assume the matching condition of the disturbances. Besides, compared to the conventional disturbance estimation methods, the proposed method does not require the calculation of the inverse inertia matrices and accurate measurement of system velocities. This advantage resolves the concerns of heavy computational load and amplified noise for prac…
The goal of this paper is to clarify the robustness and performance constraints in the design of control systems based on disturbance observer (DOB). Although the bandwidth constraints of a DOB have long been very well-known by experiences and observations, they have not been formulated and clearly reported yet. In this regard, the Bode and Poisson integral formulas are utilized in the robustness analysis so that the bandwidth constraints of a DOB are derived analytically. In this paper, it is shown that the bandwidth of a DOB has upper and lower bounds to obtain good robustness if the plant h…
In this paper, a novel adaptive smooth disturbance observer-based fast finite-time adaptive backstepping control scheme is presented for the attitude tracking of the 3-DOF helicopter system subject to compound disturbances. First, an adaptive smooth disturbance observer (ASDO) is proposed to estimate the composite disturbance, which owns the characteristics of smooth output, fast finite-time convergence, and adaptability to the disturbance of unknown derivative boundary. Then, a finite-time backstepping control protocol is construct to drive the elevation and pitch angles to track reference tr…
This paper represents a novel online self-learning disturbance observer (SLDO) by benefiting from the combination of a type-2 neuro-fuzzy structure (T2NFS), feedback-error learning scheme and sliding mode control (SMC) theory. The SLDO is developed within a framework of feedback-error learning scheme in which a conventional estimation law and a T2NFS work in parallel. In this scheme, the latter learns uncertainties and becomes the leading estimator whereas the former provides the learning error to the T2NFS for learning system dynamics. A learning algorithm established on SMC theory is derived…
In this paper, we present a Nonlinear-Proportional Integrator (N-PI) disturbance observer (DOB) to enhance the motion tracking of the performance of a surface-mounted Permanent Magnet Synchronous Motor (SPMSM) in rapidly speed varying regions. By presenting an N-PI-DOB for load torque estimation with torque modulation technique, we show that the tracking error dynamics of angular position/velocity are coupled with tracking errors of currents loop and estimation errors. After analyzing disturbances of currents tracking error dynamics, we design the N-PI-DOB and Lyapunov-based nonlinear currents…
Disturbance-Observer-Based Grid-Forming Control for Unbalanced Grids
Aalto University School of Electrical Engineering（阿尔托大学电气工程学院）；ABB Oy Drives（ABB驱动器公司）；ABB Corporate Research（ABB企业研究院）；Aix Marseille Univ, CNRS, LIS（艾克斯-马赛大学、法国国家科学研究中心、LIS实验室）
This paper deals with the problem of predicting the future state of discrete-time input-delayed systems in the presence of unknown disturbances that can affect both the state and the output equations of the plant. Since the disturbance is unknown, computing an exact prediction of the future plant states is not possible. To circumvent this problem, we propose using a high-order extended Luenberger-type observer for the plant states, disturbances, and their finite difference variables, combined with a new equation for computing the prediction based on Newton's series from the calculus of finite …
This paper analyses and synthesises the Disturbance Observer (DOb) based motion control systems in the discrete-time domain. By employing Bode Integral Theorem, it is shown that continuous-time analysis methods fall-short in explaining the dynamic behaviours of the DOb-based robust motion controllers implemented by computers and microcontrollers. For example, continuous-time analysis methods cannot explain why the robust stability and performance of the digital motion controller deteriorate as the bandwidth of the DOb increases. Therefore, unexpected dynamic responses (e.g., poor stability and…
In data-driven predictive cloud control tasks, the privacy of data stored and used in cloud services could be leaked to malicious attackers or curious eavesdroppers. Homomorphic encryption technique could be used to protect data privacy while allowing computation. However, extra errors are introduced by the homomorphic encryption extension to ensure the privacy-preserving properties, and the real number truncation also brings uncertainty. Also, process and measure noise existed in system input and output may bring disturbance. In this work, a data-driven predictive cloud controller is develope…
Robust time-varying formation design problems for second-order multi-agent systems subjected to external disturbances are investigated. Firstly, by constructing an extended state observer, the disturbance compensation is estimated, which is a critical term in the proposed robust time-varying formation control protocol. Then, an explicit expression of the formation center function is determined and impacts of disturbance compensations on the formation center function are presented. With the formation feasibility conditions, robust time-varying formation design criteria are derived to determine …
University of Technology Sydney（悉尼科技大学）；Centre for Autonomous Systems（自主系统中心）；Centre for Artificial Intelligence（人工智能中心）
This paper presents an observer-integrated Reinforcement Learning (RL) approach, called Disturbance OBserver Network (DOB-Net), for robots operating in environments where disturbances are unknown and time-varying, and may frequently exceed robot control capabilities. The DOB-Net integrates a disturbance dynamics observer network and a controller network. Originated from conventional DOB mechanisms, the observer is built and enhanced via Recurrent Neural Networks (RNNs), encoding estimation of past values and prediction of future values of unknown disturbances in RNN hidden state. Such encoding…
This paper proposes new practical design tools for the robust motion control systems based on disturbance observer (DOB). Although DOB has long been used in several motion control applications, it has insufficient analysis and design tools. The paper proposes a new practical robustness constraint, which improve the robustness at high frequencies, on the bandwidth of a DOB and nominal inertia. Although increasing the bandwidth of a DOB and nominal inertia improves the performance and stability, they are limited by the robustness constraint. Besides, a novel stability analysis method is proposed…
