In this paper, an optimal output consensus problem is studied for discrete-time linear multiagent systems subject to external disturbances. Each agent is assigned with a local cost function which is known only to itself. Distributed protocols are to be designed to guarantee an output consensus for these high-order agents and meanwhile minimize the aggregate cost as the sum of these local costs. To overcome the difficulties brought by high-order dynamics and external disturbances, we develop an embedded design and constructively present a distributed rule to solve this problem. The proposed control includes three terms: an optimal signal generator under a directed information graph, an observer-based compensator to reject these disturbances, and a reference tracking controller for these linear agents. It is shown to solve the formulated problem with some mild assumptions. A numerical example is also provided to illustrate the effectiveness of our proposed distributed control laws.
In this work, an advanced motion controller is proposed for buck converter-fed DC motor systems. The design is based on an idea of active disturbance rejection control (ADRC) with its key component being a custom observer capable of reconstructing various types of disturbances (including complex, harmonic signals). A special formulation of the proposed design allows the control action to be expressed in a concise and practically appealing form reducing its implementation requirements. The obtained experimental results show increased performance of the introduced approach over conventionally us…
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…
This paper presents an improved active disturbance rejection control scheme (IFO-ADRC) with an improved fractional-order extended state observer (IFO-ESO). The structural information of the system is utilized in IFO-ESO rather than buried as in the typical fractional-order extended state observer (FO-ESO) and help significantly improve the performance of IFO-ESO and closed-loop system. Compared with the integer-order active disturbance rejection controller (IO-ADRC), the auxiliary tracking controller of IFO-ADRC has a simpler form and fewer parameters need to be tuned. Frequency-domain analysi…
This paper solves the problem of station-keeping control of a surface vessel under conditions of sinusoidal disturbances with unknown parameters. The proposed control algorithm is based on the geometric approach with the use of the adaptive internal model and the extended observer. The paper analytically proves the boundedness of the trajectories of the system and their semiglobal convergence to an arbitrarily small set. The performance of the algorithm is illustrated by computer simulation.
A new tuning rule is introduced for linear active disturbance rejection control (ADRC), which results in similar closed-loop dynamics as the commonly employed bandwidth parameterization design, but with lower feedback gains. In this manner the noise sensitivity of the controller is reduced, paving the way for using ADRC in more noise-affected applications. It is proved that the proposed tuning gains, while rooted in the analytical solution of an algebraic Riccati equation, can always be obtained from a bandwidth parameterization design by simply halving the gains. This establishes a link betwe…
The high tech industry which requires fast stable motion with nanometer precision continues to mainly use PID which is limited by fundamental linear control limitations. Floor vibrations as disturbance significantly affect performance and their rejection is particularly affected by these limitations. Reset control has provided a promising alternative to surpass these, while simultaneously allowing the use of industry standard loop-shaping during design. However, the reset action introduced higher order harmonics can induce unwanted dynamics and negatively influence performance. This paper inve…
Considering the control problem for nonlinear uncertain systems, the tolerable range of uncertain control input gain is a fundamental issue. The paper presents the necessary and sufficient condition for the well-performed closed-loop system based on active disturbance rejection control (ADRC) design. Via the proposed necessary and sufficient condition, the maximum tolerable range of the uncertain control gain is quantitatively presented, which reveals the capability of ADRC to handle the uncertainties related with control input. Moreover, under the proposed necessary and sufficient condition, …
The increasing demand for target tracking, environmental surveys, surveillance and mapping requires multi-axis gimbal systems with high tracking and stabilization performance. In this paper, first, computed torque model is generated to estimate the complex disturbances acting on the system. Then, two different control strategies based on active disturbance rejection control (ADRC) and computed torque model are implemented on a two-axis gimbal system. The purpose is to improve the robustness, environmental adaptability and tracking accuracy of the system and reduce the tuning effort of ADRC by …
Practical applications of controllers often impose further requirements on the implementation beyond the actual control performance, such as the ability to switch between manual and automatic control or between different control laws or controller parameter settings, known as bumpless transfer. Another common requirement is to limit the control signal in magnitude and/or rate. This article examines and extends several discrete-time variants of active disturbance rejection control (ADRC), which is increasingly being applied especially in the field of power electronics and drives, in this regard…
This paper presents an active disturbance rejection control (ADRC) scheme with an improved fractional-order extended state observer (IFO-ESO).Based on the new ADRC scheme, the open-loop transfer function of a high-order system can be approximately rendered to a so-called Weighed Bode's ideal transfer function, whose closed-loop performance is less prone to the controller parameter variations. The design of the IFO-ESO helps reduce the number of system states to be estimated and improves the performance of closed-loop system over %the previously proposed the fractional-order active disturbance …
A general controller scheme for stabilizing a non-linear system, which has its origin from the linear system theory, is proposed in this paper. The proposed controller can stabilize the non-linear system subjected to initial conditions. An effective way to obtain the controller parameters is presented with the knowledge of the system model. The controller is designed for the linear time-invariant (LTI) system, which can reject any disturbance acting on it. Paper emphasis the idea of an integrator controller in disturbance rejection. The concept is extended to the application to non-linear syst…
Universidad Complutense de Madrid（马德里康普顿斯大学）；School of Automation, Nanjing University of Science and Technology（南京理工大学自动化学院）
This paper addresses the problem of end-effector formation control for manipulators that are subjected to external disturbances: input disturbance torques and disturbance forces at each end-effector. The disturbances are assumed to be non-vanishing and are superposition of finite number of sinusoidal and step signals. The formation control objective is achieved by assigning virtual springs between end-effectors, by adding damping terms at joints, and by incorporating internal model-based dynamic compensators to counteract the effect of the disturbances; all of which presents a clear physical i…
We consider the task of motion control for non-prehensile manipulation using parallel kinematics mechatronic setup, in particular, stabilization of a ball on a plate under unmeasured external harmonic disturbances. System parameters are assumed to be unknown, and only a ball position is measurable with a resistive touch sensor. To solve the task we propose a novel passivity-based output control algorithm that can be implemented for unstable linearized systems of an arbitrary relative degree. In contrast to previous works, we describe a new way to parametrize harmonic signal generators and an e…
The robust disturbance rejection controller has been the subject of intensive research due to its undeniable importance for automation. Modern control theory tends to use model-based approaches versus model-free approaches, especially when it comes to highly modern applications. The backbone of the dissertation is based on the systematic modeling of dynamic systems and the development of advanced control methods. Accordingly, the dissertation begins with the investigation of nonlinearities in dynamic systems. The extension of classic subspace algorithms for linear systems in the frequency doma…
This thesis is concerned with the rejection of time-varying disturbances in linear model predictive control of discrete-time systems. In the literature, disturbances are widely rejected by using velocity models, disturbance model with observer approach or a scheme that combines the compensation of a disturbance observer and the feedback regulation of MPC. Contrary to the widely used methods, the technique proposed in this research utilises the increment model of plants, with the assumption of fast-changing disturbances, to formulate a control law to reject the varying-disturbances. The uniquen…
Matched disturbance rejection for energy-shaping controlled underactuated mechanical systems
The University of Newcastle（纽卡斯尔大学）；PRC CDSC（过程控制与系统研究中心）；University of Naples Federico II（那不勒斯费德里科二世大学）；PRISMA Lab（PRISMA实验室）；Queensland University of Technology（昆士兰科技大学）；Laboratoire des Signaux et Systèmes（信号与系统实验室）；CNRS-SUPELEC（法国国家科学研究中心-苏佩莱克）
The performance of active disturbance rejection control (ADRC) algorithms can be limited in practice by high-frequency measurement noise. In this work, this problem is addressed by transforming the high-gain extended state observer (ESO), which is the inherent element of ADRC, into a new cascade observer structure. Set of experiments, performed on a DC-DC buck power converter system, show that the new cascade ESO design, compared to the conventional approach, effectively suppresses the detrimental effect of sensor noise over-amplification while increasing the estimation/control performance. Th…
In this paper the stability of a closed-loop cascade control system in the trajectory tracking task is addressed. The considered plant consists of underlying second-order fully actuated perturbed dynamics and the first order system which describes dynamics of the input. The main theoretical result presented in the paper concerns stability conditions formulated based on the Lyapunov analysis for the cascade control structure taking advantage of the active rejection disturbance approach. In particular, limitations imposed on a feasible set of an observer bandwidth are discussed. In order to illu…
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…
Noticing that both the absolute and relative velocity protocols can solve the second-order consensus of multi-agent systems, this paper aims to investigate which of the above two protocols has better anti-disturbance capability, in which the anti-disturbance capability is measured by the L2 gain from the disturbance to the consensus error. More specifically, by the orthogonal transformation technique, the analytic expression of the L2 gain of the second-order multi-agent system with absolute velocity protocol is firstly derived, followed by the counterpart with relative velocity protocol. It i…
Active disturbance rejection control for unmanned tracked vehicles in leader-follower scenarios: discrete-time implementation and field test validation
