A sliding mode observer design for uncertain fractional Ito stochastic systems with state delay

This paper addresses the robust observer design problem for uncertain time-delay fractional Ito stochastic systems. A sliding surface is proposed and it is shown that state estimates converge towards it and remain there for the subsequent time. Additionally, by constructing a novel Lyapunov functional, a sufficient condition for the stability of the sliding motion of the estimated states is given in the form of Linear Matrix Inequalities (LMIs). It is demonstrated that the state estimates are stabilizable in probability provided that the LMI is feasible. Moreover, a finite-time sliding mode control law based on the estimated states is proposed. Simulation examples are given to show the validity and effectiveness of the results.     

Almost Disturbance Decoupling for a Class of Nonlinear Systems Subject to Time‐Delays Via Sampled‐Data Output Feedback Control

This paper considers the problem of almost disturbance decoupling (ADD) via sampled‐data output feedback control for a class of uncertain nonlinear systems subject to time‐delays. Based on output feedback domination approach, a sampled‐data output feedback controller is designed to globally stabilize the system under a lower‐triangular linear growth condition. Gronwall‐Bellman‐like inequality and inductive method are introduced to estimate the state growth in the presence of time‐delays, uncertain nonlinearities and unknown disturbances. The proposed controller can attenuate the influence of disturbances on the output to an arbitrary degree in the L₂ gain sense. Finally, simulation results show the effectiveness of the control method.     

Design of Optimal Petri Net Supervisors for Flexible Manufacturing Systems via Weighted Inhibitor Arcs

This paper develops an approach to the design of an optimal Petri net supervisor that enforces liveness to flexible manufacturing systems. The supervisor contains a set of observer places with weighted inhibitor arcs. An observer place with a weighted inhibitor arc is used to forbid a net from yielding an illegal marking by inhibiting the firing of a transition at a marking while ensuring that all legal markings are preserved. A marking reduction technique is presented to decrease the number of considered markings, which can dramatically lower the computational burden of the proposed approach. An integer linear program is presented to simplify the supervisory structure by minimizing the number of observer places. Finally, several examples are used to shed light on the proposed approach which can lead to an optimal supervisor for the net models that cannot be optimally controlled via pure Petri net supervisors.     

Stabilization of Uncertain Multi‐Order Fractional Systems Based on the Extended State Observer

The extended state observer (ESO) based controller has been used successfully with integer‐order systems involving large uncertainties. In this paper, the robust control of uncertain multi‐order fractional‐order (FO) systems based on ESO is investigated. First, we transform the multi‐order FO system into an equivalent system in the form of a same‐order state‐space equation. Then, the ESO for the new system is established for estimating both the state and the total disturbance. Sufficient conditions for bounded‐input and bounded‐output stability are derived, and the asymptotic stability of the closed loop system is analyzed, based on whether the states are available or not. Finally, numerical simulations are presented to demonstrate the validity and feasibility of the proposed methodology.     

基于卷积神经网络的永磁同步电机转矩观测器

内嵌式永磁同步电机具有高功率密度、高可靠性和弱磁性等诸多优点,但由于电动机参数具有非线性化特征,导致电磁转矩难以精确估算。该文提出了一种基于卷积神经网络的电磁转矩估算方 法,即转矩观测器。首先,基于所搭建的高保真非线性内嵌式永磁同步电机模型,获得用于神经网络训练的转矩观测器数据;然后,基于所提出的卷积神经网络转矩观测器实现内嵌式永磁同步电机的精确控制;最后,为获取最优的转矩估算误差,在仿真实验阶段对不同参数和结构的卷积神经网络进行了对比和分析。结果表明,该神经网络可以实现电磁转矩的准确估算,所建立的转矩观测器具有良好的性能参数和泛化能力。     

Modeling and vibration control for a flexible pendulum inverted system based on a PDE observer

This study addresses the problem of trajectory control of a flexible pendulum inverted system on the basis of the partial differential equation (PDE) and ordinary differential equation (ODE) dynamic model. One of the key contributions of this study is that a new model is proposed to simplify the complex system. In addition, this study proposed a nonlinear PDE observer to estimate distributed positions and velocities along flexible pendulum. Singular perturbation method is proposed to solve the coupling system of nonlinear PDE observer. The nonlinear PDE observer is divided into a fast subsystem and a slow subsystem by the use of the singular perturbation method. To stabilise this fast subsystem, a boundary controller is proposed at the free end of the beam. The sliding-mode control method is proposed to design controller for slow subsystems. The asymptotic stability of both the proposed nonlinear PDE observer and controller is validated by theoretical analysis. The results are illustrated by simulation.     

On the conditions of exponential stability in active disturbance rejection control based on singular perturbation analysis

Stability of active disturbance rejection control (ADRC) is analysed in the presence of unknown, nonlinear, and time-varying dynamics. In the framework of singular perturbations, the closed-loop error dynamics are semi-decoupled into a relatively slow subsystem (the feedback loop) and a relatively fast subsystem (the extended state observer), respectively. It is shown, analytically and geometrically, that there exists a unique exponential stable solution if the size of the initial observer error is sufficiently small, i.e. in the same order of the inverse of the observer bandwidth. The process of developing the uniformly asymptotic solution of the system reveals the condition on the stability of the ADRC and the relationship between the rate of change in the total disturbance and the size of the estimation error. The differentiability of the total disturbance is the only assumption made.     

Extended state observer-based motion synchronisation control for hybrid actuation system of large civil aircraft

Hybrid actuation system with dissimilar redundant actuators, which is composed of a hydraulic actuator (HA) and an electro-hydrostatic actuator (EHA), has been applied on modern civil aircraft to improve the reliability. However, the force fighting problem arises due to different dynamic performances between HA and EHA. This paper proposes an extended state observer (ESO)-based motion synchronisation control method. To cope with the problem of unavailability of the state signals, the well-designed ESO is utilised to observe the HA and EHA state variables which are unmeasured. In particular, the extended state of ESO can estimate the lumped effect of the unknown external disturbances acting on the control surface, the nonlinear dynamics, uncertainties, and the coupling term between HA and EHA. Based on the observed states of ESO, motion synchronisation controllers are presented to make HA and EHA to simultaneously track the desired motion trajectories, which are generated by a trajectory generator. Additionally, the unknown disturbances and the coupling terms can be compensated by using the extended state of the proposed ESO. Finally, comparative simulation results indicate that the proposed ESO-based motion synchronisation controller can achieve great force fighting reduction between HA and EHA.     

Consensus of linear multi-agent systems with exogenous disturbance generated from heterogeneous exosystems

This paper addresses the consensus tracking problem for multi-agent linear systems subject to exogenous disturbances generated from heterogeneous exosystems. For the case that the disturbances are generated from linear heterogeneous exosystems, a linear disturbance observer and distributed control law are proposed, and sufficient condition for consensus tracking is established by combining the input-to-state stability and Lyapunov analysis methods. For the case when the disturbances are generated from non-linear heterogeneous exosystems, a non-linear disturbance observer is presented to estimate such disturbance by using the dynamic gain technique; then, a distributed control law is designed, and sufficient condition is also presented for achieving consensus tracking. Two simulation examples are provided to demonstrate the effectiveness of the proposed consensus protocols.