基于模糊滑模控制器的伺服跟踪控制研究

为了有效地消除精密机床伺服进给系统的参数变化和外部扰动对其跟踪性能的影响,将滑模控制引入其伺服跟踪控制.文章将模糊逻辑与滑模控制相结合提出了一种简捷的模糊滑模控制器设计的方法以减小滑模控制器的颤抖.实验结果表明采用该方法设计的模糊滑模控制器与离散准滑模控制器相比具有较强的鲁棒性和跟踪性能.最后将该控制器用于超精密机床伺服跟踪控制取得了良好的控制效果.     

Target tracking using artificial potentials and sliding mode control

In this article we develop an algorithm for capturing/intercepting a moving target based on the sliding mode control method. First, we consider a ‘‘kinematic'' model (in a sense) for the capture/intercept problem and develop a method for that case. Then, we build on the developed method to include general fully actuated vehicle dynamics for the pursuer agent. The algorithm is robust with respect to the system uncertainties and additive disturbances. Finally, we also provide a numerical simulation in order to illustrate the procedure.     

On discrete-time variable structure sliding mode control

The purpose of this paper is to show the limitations of discrete-time variable structure sliding mode control and that the equivalent control must be used in order to have sliding in a neighborhood of the switching surface. Conflicting requirements for the sliding mode controller behavior in the continuous and discrete-time domains are revealed and analyzed. A linear control law for an uncertain discrete-time linear plant, with bounded uncertainties, is analyzed and its superiority over nonlinear controllers is demonstrated. The conclusion of the obtained results is that in the discrete-time variable structure sliding mode controller design, unlike in the continuous-time, the designer may have limited flexibility in selecting controller architectures.     

Robust discrete-time chattering free sliding mode control

A new control algorithm based on discrete-time variable structure systems theory is proposed. The basic feature of this algorithm is that trajectories reach the sliding manifold in finite time, without chattering. Apart from stability, the robustness of the algorithm with respect to parameter uncertainties, as well as external disturbances is considered. It is demonstrated that the robustness is improved by decreasing the sampling period. The theory is illustrated on a DC servo-position system.     

Robust discrete-time sliding mode control for tracking and model following of uncertain nonlinear systems

This paper proposes a discrete-time controller for robust tracking and model following of a class of nonlinear, multi-input multi-output, systems. For this purpose, a discrete-time sliding mode controller (DTSMC) is used to ensure the stability, robustness and an output tracking against the modelling uncertainties, even at relatively large sampling periods. In this way, Takagi–Sugeno (T–S) fuzzy modelling is used to decompose the nonlinear system to a set fuzzy-blended locally linearised subsystems. Implementation of the second Lyapunov theory for mismatched uncertain nonlinear T–S fuzzy models results in a set of linear matrix inequalities, which is used to design the sliding surface. A new method is then proposed to reach the quasi-sliding mode and stay thereafter. Simulation studies show that the proposed method guarantees the stability of closed-loop system and achieves small tracking error in the presence of parametric uncertainties at large sampling periods.     

A frequency-shaping methodology for discrete-time sliding mode control

This paper proposes a frequency shaping methodology for performance enhancement of discrete-time sliding mode control for systems with narrow band disturbances. This approach augments the sliding mode surface as a dynamic feedback system and designs an ‘optimal’ shaping filter in the feedback loop based on H-infinity synthesis, which assures both the stability and the desired frequency-response characteristics of the sliding mode surface. Furthermore, this frequency-shaping technique is advanced to be parameter-dependent to improve the efficiency and flexibility. The methodology enables the design of sliding mode control in frequency domain, which is critically important for high-precision systems that are subjected to high-frequency disturbances. The proposed frequency-shaped sliding mode control is applied onto a hard disk drive in the presence of vibrations with multiple peak frequencies; effective vibration suppression is demonstrated through comprehensive simulation study.     

无抖振离散滑模趋近律

针对离散滑模趋近律形式多样且容易产生高频抖振的问题,提出了离散滑模趋近律的一般形式,并给出了无抖振的到达条件及其理论证明,从一般意义上为离散滑模趋近律的设计提供了理论依据。针对满足匹配条件的不确定系统,给出了切换函数收敛域的推导方法,推导了无抖振的最小收敛域。以典型的高氏指数趋近律为例,利用无抖振的到达条件,对其一般形式进行了无抖振改进,验证了所提出方法的有效性。     

Robust tracking and model following of uncertain dynamic systems via discrete-time integral sliding mode control

A discrete-time integral sliding mode control scheme is proposed to realize the problem of robust tracking and modeling following for a class of uncertain linear systems. It will be shown that the proposed scheme guarantees the stability of closed-loop system and achieves zero-tracking error in the presence of parameter uncertainties and external disturbances. The selection of switching surface and the existence of sliding mode are two important issues, which have been addressed. This scheme assures robustness against system uncertainties and disturbances. Chattering phenomenon and reaching phase are eliminated. Moreover, the knowledge of upper bound of uncertainties is not required. Both the theoretical analysis and illustrative example demonstrate the validity of the proposed scheme. Recommended by Editorial Board member Ju Hyun Park under the direction of Editor Young IL Lee. Ming-Chang Pai received the M.S. and Ph.D. degrees in Mechanical Engineering in 1994 and 1998 from Pennsylvania State University, State College, P.A.. He is currently an Associate Professor in the Department of Automation Engineering at Nan-Kai University of Technology. His research interests are in mechatronics, robots, robust control and nonlinear control.     

High-speed and precision control of a piezoelectric positioner with hysteresis,resonance and disturbance compensation

A novel composite control strategy is developed in this paper to compensate hysteresis, resonance and disturbances in a piezo-actuated nanopositioner. The control objective of the piezoelectric positioner is to achieve high tracking performance in terms of accuracy and speed. For this purpose, a Bouc–Wen model based hysteresis compensator is first applied to mitigate the hysteresis nonlinearity without the complex inverse hysteresis calculation. And then, the linear dynamic of the hysteresis compensated system is identified and inverted to account for the resonance. A model-based inversion feed-forward controller is designed to achieve high speed tracking. Afterwards, a high-gain feedback controller is designed based on a notch filter to handle the modeling inaccuracy and all kinds of disturbances. So, the feed-forward controller can be augmented to the feedback controller to realize high speed and precision tracking. The enhancement of tracking performance is demonstrated through several comparative experiments. The performance of 70 Hz bandwidth and 0.281 μm precision can be achieved, which validated the effectiveness of the proposed composite control scheme.     

Adaptive sliding mode control for a class of uncertain discrete-time systems using multi-rate output measurement

This article is concerned with the design of an adaptive sliding mode control (SMC) for a class of uncertain discrete-time systems using the multi-rate output measurement. The states of the discrete-time systems are assumed to be taken in the multi-rate output measurement by the contamination with measurement noise. The uncertainties are assumed not to satisfy the matching condition, and are expressed in a parameterised form. A least squares estimator (LSE) to take the estimates for the un-measurable states and the uncertainties is designed in a batch form by using the noisy multi-rate output measurement. The proposed adaptive SMC is designed by using the sliding surface expressed as the linear state function and the estimates obtained from the LSE. It is proved that the estimation errors converge to zero as time tends to infinite, and the states of the system are bounded under the action of the proposed adaptive SMC. The effectiveness of the proposed method is indicated through the simulation experiment in a simple system.     

On the stability of discrete-time sliding mode control systems

The stability of discrete-time sliding mode control systems is investigated and a new sliding mode condition is suggested. It is shown that the control must have upper and lower bounds. A numerical example is discussed as an illustration.     

一类不确定离散时间系统的积分滑模控制

针对一类同时存在匹配和非匹配不确定性的离散时间系统,提出一种基于幂次函数的离散积分滑模控制方法.理论分析表明,所提出的方法可以消除离散积分滑模控制系统的抖振,而且能够保证对系统的匹配和非匹配不确定性具有强鲁棒性.在系统不确定性的界未知的情况下,通过引入一步延时干扰估计完成了控制器的设计,并给出了闭环系统稳定性证明.仿真结果验证了所提出方法的有效性.     

没有参数的系统辨识方法与模型估计方式

基于模型类/参数模式的传统系统辨识,虽然囊括了系统辨识几乎所有的成果,理论也趋于成熟,但不宜使用在空间中分布不均匀且数量相对少的数据.鉴于此,提出针对这类数据建模的无参数系统辨识研究方向,讨论基于代表点和加权距离的无参数系统辨识方法,给出基于分类一致性准则的模型估计方式.与传统系统辨识的区别是,＂没有参数＂并且从实质上改变估计模型的方式.用IRIS,Breast Cancer等典型数据检验了模型的有效性.     

Adaptive sliding mode control for discrete-time multi-input multi-output systems

In this paper, robust adaptive sliding mode tracking control for discrete-time multi-input multi-output systems with unknown parameters and disturbance is considered. The robust tracking controller is comprised of adaptive control and sliding mode control design. Bounded motion of the system around the sliding surface and stability of the global system in the sense that all signals remain bounded are guaranteed. If the disturbance and the reference signal are slowly varying with respect to the sampling frequency, the proposed sliding mode controller can reject the disturbance and output tracking can be approximately achieved. Simulation results are presented to illustrate the proposed approach.     

Finite-time attitude tracking control for a rigid spacecraft using time-varying terminal sliding mode techniques

This paper investigates the finite-time attitude tracking control for a rigid spacecraft in the presence of inertia uncertainties and external disturbances. Two novel time-varying terminal sliding mode control algorithms are derived for attitude tracking control system. The proposed two control algorithms not only eliminate the reaching phase of the conventional sliding mode control but also guarantee the tracking errors converge to zero in finite time. Moreover, the singularity problem can be avoided. Simulation results are provided to demonstrate the effectiveness of the proposed design methods.     

Adaptive backstepping sliding mode trajectory tracking control for a quad-rotor

A quad-rotor aircraft is an under-actuated,strongly coupled nonlinear system with parameter uncertainty and un-modeled disturbance.In order to make the aircraft track the desired trajectory,a nested double-loops control system is adopted in this paper.A position error proportional-derivative(PD) controller is designed as the outer-loop controller based on the coupling action between rotational and translational movement,and an adaptive backstepping sliding mode control algorithm is used to stabilize the attitude.Finally,both the numerical simulation and prototype experiment are utilized to demonstrate the effectiveness of the proposed control system.     

基于幂次函数的离散滑模控制算法

利用幂次函数构造一种新的趋近律离散滑模控制算法,并给出了无抖振的理论证明.对于标称系统,该算法可使切换函数无抖振、无正负交替地快速趋近于零;对于满足匹配条件的不确定性系统,可使切换函数无抖振、单调地收敛于与外干扰相关的某一数值.利用倒立摆模型进行了数值仿真,结果表明,控制器的输出、切换函数、被控系统的输出均不存在抖振现象,而且被控系统表现出了良好的动态品质.     

Improving velocity feedback for position control by using a discrete-time sliding mode filtering with adaptive windowing

In position control of mechatronic devices, velocity feedback is important for injecting additional damping to avoid low-frequency fluctuation around desired trajectories. In practice, velocity signal is often obtained by finite difference of position signal from an optical encoder. However, such a numerical differentiation produces high-frequency noise by magnifying quantization error contained in the position signal. As a result, the controller may produce high-frequency vibration. This paper presents a new noise-reduction discrete-time filter based on sliding mode and adaptive windowing. The presented filter is an improved version of a sliding mode filter by Jin et al. (2012), with including adaptive windowing of which the window size is determined in a similar way to that of a discrete-time adaptive windowing differentiator by Janabi-Sharifi et al. (2000). The presented filter is then applied to a position control of a mechatronic device for improving velocity feedback. Experimental results show that the presented filter provides better velocity feedback than its previous version, Janabi-Sharifi et al.’s differentiator, and combinations of these two filters.     

Trajectory tracking for an autonomous airship using fuzzy adaptive sliding mode control

We present a novel control approach for trajectory tracking of an autonomous airship.First,the dynamics model and the trajectory control problem of an airship are formulated.Second,the sliding mode control law is designed to track a time-varying reference trajectory.To achieve better control performance,fuzzy adaptive sliding mode control is proposed in which the control gains are tuned according to fuzzy rules,and an adaptation law is used to guarantee that the control gains can compensate for model uncertainties of the airship.The stability of the closed-loop control system is proven via the Lyapunov theorem.Finally,simulation results illustrate the effectiveness and robustness of the proposed control scheme.     

Stable,robust tracking by sliding mode control

Sliding mode control is examined from the perspective of obtaining stable and robust tracking of an arbitrary time-varying reference by a multi-input-output, linear, time-invariant system driven by a certain class of bounded errors, nonlinearities and disturbances. Most existing sliding mode schemes for such systems are subsumed by the one presented here. The results are developed via the use of inverse models, and make clear the constraints imposed by the finite and infinite zero structure of the system. In particular, stable and robust tracking is shown to be obtained by the scheme in this paper if and only if the system is minimum phase.