Observer‐based compensation control of servo systems with backlash

For compensating backlash phenomenon in servo systems, the authors propose an observer method in this paper to estimate both system states and vibration torque before controller design. First, a systematic scheme is given to obtain plant parameters, which is very important in observing system states. This is a parameter estimation principle that gives a crude estimation and computes the differences between the crude and true values. As a result, the precise value of the parameters is obtained by adding together the crude value and the difference. Then, based on the precise estimated parameters, an extended state observer (ESO) is designed to obtain feedback and feedforward signals. Consequently, robust compensation control is achieved by designing an output feedback controller, consisting of a feedback term and a feedforward term. Finally, in order to validate the proposed approach, extensive experiments are performed on a practical servo system with backlash nonlinearity.     

An H∞non‐fragile observer‐based adaptive sliding mode controller design for uncertain fractional‐order nonlinear systems with time delay and input nonlinearity

In this paper the problem of non‐fragile adaptive sliding mode observer design is addressed for a class of nonlinear fractional‐order time‐delay systems with uncertainties, external disturbance, exogenous noise, and input nonlinearity. An H_∞ observer‐based adaptive sliding mode control considering the non‐fragility of the observer is proposed for this system. The sufficient asymptotic stability conditions are derived in the form of linear matrix inequalities. It is proven that the sliding surface is reachable in finite time. An illustrative example is provided which corroborates the effectiveness of the theoretical results.     

Probabilistic observation model correction using non-Gaussian belief fusion

This paper presents a framework for state estimation which tolerates uncertainty in observation model parameters by (1) incorporating this uncertainty in state observation, and (2) correcting model parameters to improve future state observations. The first objective is met by an uncertainty propagation approach, while the second is achieved by gradient-descent optimization. The novel framework allows state estimates to be represented by non-Gaussian probability distribution functions. By correcting observation model parameters, estimation performance is enhanced since the accuracy of observations is increased. Monte Carlo simulation experiments validate the efficacy of the proposed approach in comparison with conventional estimation techniques, showing that as model parameters converge to ground-truth over time, state estimation correspondingly improves when compared to a static model estimate. Because observation models cannot be known with perfect accuracy and existing approaches do not address parametric uncertainties in non-Gaussian estimation, this work has both novelty and usefulness in most state estimation contexts.     

球对称n维反应扩散方程的边界观测与输出反馈控制

许多实际系统可用n 维超球坐标系来描述, 并且系统有球对称的性质, 因而可通过研究半径方向的状态变化, 得到系统的全局动态过程. 通过将高维的对称系统转化为等价的径向一维方程, 本文采用边界Backstepping 方法设计了球对称反应扩散方程的输出反馈控制器. 使用容易测量的边界状态值, 设计了状态观测器来估计系统在空间域的所有状态, 从而实现输出反馈控制. 本文扩展了连续Backstepping 方法,提出了n维球坐标的Volterra 积分映射, 从而求出了显式表达的控制器和状态观测器. 论文用Lyapunov 函数法证明了输出反馈系统在H1范数下指数稳定, 表明状态对初值的连续依赖, 确保控制系统具有较好的性质, 不会在空间某点发散. 最后进行了数值仿真, 仿真结果表明系统在输出反馈控制律的作用下收敛到稳态值.     

Observer-based predictive controller design with network-enhanced time-delay compensation

State feedback control is very attractive due to the precise computation of the gain matrix, but the implementation of a state feedback controller is possible only when all state variables are directly measurable. This condition is almost impossible to accomplish due to the excess number of required sensors or unavailability of states for measurement in most of the practical situations. Hence, the need for an estimator or observer is obvious to estimate all the state variables by observing the input and the output of the controlled system. As such, the goal of this paper is to provide a control design methodology based on a Luenberger observer design that can assure the closed-loop performances of a vehicle drivetrain with backlash, while compensating the network-enhanced time-varying delays. This goal is achieved in a sequential manner: firstly, a piecewise linear model of two inertias drivetrain, which takes into consideration the backlash nonlinearity and the network-enhanced time-varying delay effects is derived; then, a Luenberger observer which estimates the state variables is synthesized and the robust full state-feedback predictive controller based on flexible control Lyapunov functions is designed to explicitly take into account the bounds of the disturbances caused by time-varying delays and to guarantee also the input-to-state stability of the system in a non-conservative way. The full state-feedback predictive control strategy based on the Luenberger observer design was experimentally tested on a vehicle drivetrain emulator controlled through controller area network, with the aim of minimizing the backlash effects while compensating the network-enhanced delays.     

输入饱和与姿态受限的四旋翼无人机反步姿态控制

本文针对四旋翼无人机研究了鲁棒反步姿态控制策略.由于四旋翼无人机结构复杂,其非线性数学模型难以精确建立,因此在控制器设计过程中需要综合考虑模型不确定性、未知外部干扰、输入饱和以及姿态受限等因素.针对模型中的不确定项,使用神经网络进行逼近;对于外部未知干扰,使用非线性干扰观测器进行补偿;使用双曲正切函数逼近饱和函数,解决输入饱和问题;同时使用界限Lyapunov函数设计控制器,确保姿态满足限制条件.最后,设计四旋翼无人机反步姿态控制器,并根据Lyapunov稳定性定理证明了闭环控制系统的有界稳定.仿真结果表明了所研究控制方法的有效性.     

A modified dynamic surface approach for control of nonlinear systems with unknown input dead zone

This paper focuses on the robust output precise tracking control problem of uncertain nonlinear systems in pure‐feedback form with unknown input dead zone. By designing an extended state observer, the states unmeasurable problem in traditional feedback control is solved, and the lumped uncertainty, which is caused by system unknown functions and input dead zone, is estimated. In order to apply separation principle, finite‐time extended state observer is designed to obtain system states and estimate the lumped uncertainty. Then, by introducing tracking differentiator, a modified dynamic surface control approach is developed to eliminate the ‘explosion of complexity’ problem and guarantee the tracking performance of system output. Because tracking differentiator is a fast precise signal filter, the closed‐loop control performance is significantly improved when it is used in dynamic surface control instead of first‐order filters. The L _∞ stability of the whole closed‐loop system, which guarantees both the transient and steady‐state performance, is shown by the Lyapunov method and initialization technique. Numerical and experiment examples are performed to illustrate our proposed control scheme with satisfactory results. Copyright © 2013 John Wiley & Sons, Ltd.     

Output feedback control of discrete‐time systems with self‐triggered controllers

This paper is concerned with the self‐triggered output feedback control for discrete‐time systems, where an updating instants scheduler is implemented to determine when the controller is updated. For both the full‐order and reduced‐order observer cases, the updating instants are determined, respectively, where only the information of the estimated state at the current updating instant is required to obtain the next updating instant. It is shown that, with the proposed self‐triggered control schemes, not only the updating frequency is significantly reduced, but also the uniform ultimate boundedness of the closed‐loop system is guaranteed. Finally, a numerical example is used to verify the effectiveness and the merits of the proposed approaches. Copyright © 2014 John Wiley & Sons, Ltd.     

On ADRC for non-minimum phase systems: canonical form selection and stability conditions

Active disturbance rejection control (ADRC), as proposed by Prof. Jingqing Han, reduces first the plant dynamics to its canonical form, normally in the form of cascade integrators, for which the standard controller can be employed to meet the design specifications. This paper concerns with the selection of the canonical form for non-minimum phase systems. In particular, it is shown that, by employing the well known controllable canonical form, the uncertainties of such systems can be divided into two terms in the state space model, one in the control channel and the other in the output channel. The necessary and sufficient condition is obtained for the stability of the closed-loop system with the proposed canonical form and ADRC. Also, by showing the necessity of the detectability of the extended system as well as certain information of the systemˉs “zeros”, we present the fundamental guidelines of design ADRC for non-minimum phase uncertain systems.     

Active disturbance rejection control: between the formulation in time and the understanding in frequency

With the rapid deployments of the active disturbance rejection control (ADRC) as a bonafide industrial technology in the background, this paper summarizes some recent results in the analysis of linear ADRC and offers explanations in the frequency response language with which practicing engineers are familiar. Critical to this endeavor is the concept of bandwidth, which has been used in a more general sense. It is this concept that can serve as the link between the otherwise opaque state space formulation of the ADRC and the command design considerations and concerns shared by practicing engineers. The remarkable characteristics of a simple linear ADRC was first shown in the frequency domain, followed by the corresponding analysis in time domain, where the relationship between the tracking error and the ADRC bandwidth is established. It is shown that such insight is only possible by using the method of solving linear differential equations, instead of the more traditional techniques such as the Lyapunov methods, which tend to be more conservative and difficult to grasp by engineers. The insight obtained from such analysis is further demonstrated in the simulation validation.