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.     

Second-order terminal sliding mode control for hypersonic vehicle in cruising flight with sliding mode disturbance observer

This paper focuses on the design of nonlinear robust controller and disturbance observer for the longitudinal dynamics of a hypersonic vehicle (HSV) in the presence of parameter uncertainties and external disturbances. First, by combining terminal sliding mode control (TSMC) and second-order sliding mode control (SOSMC) approach, the secondorder terminal sliding control (2TSMC) is proposed for the velocity and altitude tracking control of the HSV. The 2TSMC possesses the merits of both TSMC and SOSMC, which can provide fast convergence, continuous control law and hightracking precision. Then, in order to increase the robustness of the control system and improve the control performance, the sliding mode disturbance observer (SMDO) is presented. The closed-loop stability is analyzed using the Lyapunov technique. Finally, simulation results illustrate the effectiveness of the proposed method, as well as the improved overall performance over the conventional sliding mode control (SMC).     

Stabilization of One‐Dimensional Schrödinger Equation with Variable Coefficient under Delayed Boundary Output Feedback

This article considers stabilization of a one‐dimensional Schrödinger equation with variable coefficient and boundary observation which suffers from an arbitrary given time delay. We design an observer and predictor to stabilize the system. The state is estimated in the time span where the observation is available, and also predicted in the time interval where the observation is not available. It is shown that the estimated state feedback stabilizes the system exponentially. A numerical simulation is presented to illustrate the effect of the stabilizing controller.     

全维观测器问题的算法研究

全维观测器就是通过两个状态反馈矩阵F和G的选取,得到这两个矩阵就可以得到全维状态观测器。对于多输入线性时不变系统,状态反馈矩阵F和G不唯一。目前,常用设计方法都没有解决F和G的优化设计,本文将矩阵遗传算法引入基于Sylvester方程的算法中,优化反馈矩阵,仿真结果表明：该算法求出的反馈矩阵F和G优于其它各种方法,对于工程实现无疑是有意义的。     

Design and analysis of switching reduced-order observer and separation principle for T-S fuzzy system

This paper designs and analyzes switching fuzzy reduced-order observer and proves that the corresponding separation principle does hold. A numerical simulation and comparison with smooth fuzzy full-order observer are given to assess switching fuzzy reduced-order observer and the validity of the separation principles. Supported by the National Laboratory of Space Intelligent Control and Open Foundation (Grant No. SIC07010202), and the National Natural Science Foundation of China (Grant Nos. 60604010, 90716021, 60736023)     

广义时滞系统的降维观测器设计

讨论广义时滞系统的降维观测器的设计方法．通过引入矩阵的广义逆矩阵,给出在一定条件下降维观测器的具体形式,然后分别利用广义逆矩阵及Lyapunov函数方法给出这些条件成立的具体条件及验证方法。最后给出一个例子来说明方法的有效性。