Active Disturbance Rejection in Affine Nonlinear Systems Based on Equivalent‐Input‐Disturbance Approach

This paper presents a disturbance rejection method for an affine nonlinear system. The control system is constructed based on the equivalent‐input‐disturbance (EID) approach. An affine nonlinear state observer is used to reconstruct the state of the affine nonlinear system and to estimate an EID. The well‐known differential mean value theorem enables us to describe the closed‐loop system in the state space as a linear‐parameter‐varying system. This makes it easy to derive sufficient conditions of global uniform ultimate boundedness in term of linear matrix inequalities (LMIs) by using a Lyapunov function and convexity theory. Controllers are designed based on the LMIs. A numerical example is used to illustrate the design of the control system. And a comparison between the EID‐based control and the sliding‐mode control demonstrates the effectiveness and advantages of the EID‐based control method.     

四旋翼无人机时延模糊自抗扰容错控制

针对四旋翼无人机系统执行器故障问题,为改善飞行控制系统性能,提出一种时延模糊自抗扰容错控制。首先,根据四旋翼无人机系统非线性数学模型和执行器故障模型,选择模糊自抗扰控制器作为基准控制器,在未发生执行器故障的情况下,使飞行控制系统保持稳定;其次,在发生执行器故障的情况下,利用时延控制技术估计故障信息,并与模糊自抗扰控制相结合,实现容错控制;最后,对所研究的容错控制算法进行数值仿真分析,仿真结果表明:把时延控制与模糊自抗扰控制相结合,能有效调节执行器故障,使飞行控制系统对故障产生的干扰具有良好的鲁棒性。     

Robust Repetitive Control and Disturbance Rejection Based on Two‐Dimensional Model and Equivalent‐Input‐Disturbance Approach

A new configuration of a modified repetitive‐control system has been devised for a class of strictly proper plants that suppresses exogenous disturbances and uncertainties in the dynamics of the plant. It extends the applicability of the control system. The system consists of four parts: a two‐dimensional augmented model of the plant, which takes into account the difference in characteristics between continuous control and discrete learning in repetitive control; an equivalent‐input‐disturbance estimator; a state observer; and a state‐feedback controller. A robust‐stability condition expressed in terms of a linear matrix equality is used to determine the gains of the observer and the controller. Finally, a comparison of our method with repetitive control based on linear active disturbance rejection control (LADRC) shows how effective our method is and that it is superior to LADRC‐based repetitive control.     

A Discrete‐Time Global Quasi‐Sliding Mode Control Scheme with Bounded External Disturbance Rejection

A global quasi‐sliding mode control (GQSMC) scheme is introduced to ensure zigzag motion with a smaller bound than that offered by Gao's method and to provide disturbance rejection throughout the entire response in discrete time. The design of an augmented forcing function is followed by three conditions in discrete time extended from global sliding mode control (GSMC) in continuous time. Furthermore, we adopt a switching gain, which is auto‐tuned as a function of sliding surface s(k), such that chattering phenomena can be considerably alleviated during the steady‐state, significantly reducing switching control applied to the plant. The proposed GQSMC scheme can provide more advantages such as an even distribution of the control input throughout the entire response and an improvement in the accuracy and speed of the desired performance, guaranteeing a quasi‐sliding mode throughout the entire response. In addition, we also consider the input disturbance rejection according to the norm‐bounded exogenous signal. Results from both the simulation and the experiments are reported. The results further verify that we can use the global sliding surface to curtail reaching the phase stage.     

On Finite‐Time Stabilization of Active Disturbance Rejection Control for Uncertain Nonlinear Systems

This paper designs the active disturbance rejection control (ADRC) to achieve finite‐time stabilization for a class of uncertain nonlinear systems. The proposed control incorporates both an extended state observer (ESO) as well as an adaptive sliding mode controller. The ESO is utilized to estimate the full system states and the total uncertainties, and the adaptive strategy is incorporated to deal with the estimation errors. It is proved that, with the application of the proposed control law, semi‐global finite‐time stabilization can be achieved. Effectiveness of the proposed method is illustrated with a numerical example.     

An Active Disturbance Rejection Based Approach to Vibration Suppression in Two‐Inertia Systems

This study concerns the resonance problems found in motion control, typically described in a two‐inertia system model as compliance between the motor and the load. We reformulate the problem in the framework of active disturbance rejection control (ADRC), where the resonance is assumed to be unknown and treated as disturbance, estimated and mitigated. This allows the closed‐loop bandwidth to go well beyond the resonant frequency, which is quite difficult using existing methods. In addition, such level of performance is achieved with minimum complexity in the controller design and tuning: no parameter estimation or adaptive algorithm is needed, and the controller is tuned by adjusting one parameter, namely, the bandwidth of the control loop. It is also shown that the proposed solution applies to both the velocity and position control problems, and the fact that ADRC offers an effective and practical motion control solution, in the presence of unknown resonant frequency within the bandwidth of the control system. Finally, frequency response analysis is performed where stability margin is obtained before the simulation results are verified in the hardware experiments.     

一类具有非线性扰动的多重时滞不确定系统鲁棒预测控制

针对一类具有非线性扰动且同时存在多重状态和输入时滞的不确定系统, 提出 一种鲁棒预测控制器设计方法. 基于预测控制滚动优化原理, 运用Lyapunov稳定性 理论和线性矩阵不等式 (Linear matrix inequalities, LMIs)方法, 首先近似求解无限时域二次性能指标优化问题, 然后优化非 线性扰动项所应满足的最大上界, 定量地研究鲁棒预测控制在范数有界意义下的扰动抑制 问题, 并给出了鲁棒预测控制器存在的充分条件. 最后通过仿真验证了所提方法的有效性.     

Robust disturbance rejection for repetitive control systems with time‐varying nonlinearities

This paper presents a disturbance‐rejection method for a modified repetitive control system with a nonlinearity. Taking advantage of stable inversion, an improved equivalent‐input‐disturbance (EID) estimator that is more relaxed for system design is developed to estimate and cancel out the influence of the disturbance and nonlinearity in the low‐frequency domain. The high‐frequency influence is filtered owning to the low‐pass nature of the linear part of the closed‐loop system. To avoid the restrictive commutative condition and choose a Lyapunov function of a more general form, a new design algorithm, which takes into account the relation between the feedback control gains and the observer and improved EID estimator gains, is developed for the nonlinear system. Furthermore, comparisons with the generalized extended‐state observer (GESO) and conventional EID methods are conducted. A clear relation between the developed estimator and the GESO is also clarified. Finally, simulations show the effectiveness and the advantage of the developed method.     

Adaptive Observer‐Based Global Sliding Mode Control for Uncertain Discrete‐Time Nonlinear Systems with Time‐Delays and Input Nonlinearity

A new discrete‐time adaptive global sliding mode control (SMC) scheme combined with a state observer is proposed for the robust stabilization of uncertain nonlinear systems with mismatched time delays and input nonlinearity. A state observer is developed to estimate the unmeasured system states. By using Lyapunov stability theorem and linear matrix inequality (LMI), the condition for the existence of quasi‐sliding mode is derived and the stability of the overall closed‐loop system is guaranteed. Finally, simulation results are presented to demonstrate the validity of the proposed scheme.     

具有输入时滞和外部扰动的线性系统的过渡过程估计

给同了具有输入时滞和外部扰动的一类线性系统的过渡过程的估计,理论分析和仿真结果表明,文中的主要结论为时滞系统稳定性的定量分析提供了一种有效的分析方法。