Functional observer-based sliding mode control for linear discrete-time-delayed stochastic systems

Functional observers are the primary solution to sundry estimation problems, wherein full- or reduced-order observer cannot be directly applied. This paper presents a functional observer-based sliding mode control method for the linear discrete-time delayed stochastic system. Stability analysis of sliding function is presented for the delayed stochastic system with a linear matrix inequality approach. The functional observer method for the linear discrete-time-delayed stochastic system is proposed based on the Kronecker product approach. Sliding mode controller is estimated using the functional observer method. Finally, to demonstrate the efficacy of the proposed design, comparison of its performance with some of the well-known existing state feedback controller is presented.     

Reduced-order Generalized Proportional Integral Observer Based Continuous Dynamic Sliding Mode Control for Magnetic Levitation System with Time-varying Disturbances

In order to reduce the influence of time-varying disturbances for magnetic levitation system, we propose a reduced-order generalized proportional integral observer (RGPIO) based continuous dynamic sliding mode control scheme for magnetic levitation system in this paper. Unlike the popular extended state observer (ESO), it could deal with constant or slowing varying disturbances from theoretical point of view, the reduced-order generalized proportional integral observer (RGPIO) is designed to estimate the time-varying disturbances and system states, then the dynamic sliding mode surface is developed and deduce a continuous sliding mode controller (CSMC) for magnetic levitation system. Compared with ESO based continuous sliding mode controller, the proposed method not only ensures the position tracking accuracy, but also obtain better time-varying disturbance reject ability. Simulation and experimental results are also given to verify the effectiveness.

     

Robust reduced-order sliding mode observer design

In this article, a triple state and output variable transformation-based method combined with linear matrix inequality (LMI) techniques to design a new robust reduced-order sliding mode observer for perturbed linear multiple-input and multiple-output systems is developed. The state and output variables of the original system are triple transformed into suitable canonical form coordinates to facilitate the design of a reduced-order observer. The existing transformations are summarised in this study and presented systematically. A new combined observer configuration is proposed and compared with another type of observers. Global asymptotical stability LMI and sliding mode existence conditions for the coupled observer error system are derived using Lyapunov full quadratic form. Reaching and sliding modes of motion of decoupled observer error system are discussed as well. Two numerical and simulation examples are given to illustrate the usefulness of the proposed design techniques.     

级联式滑模观测器的永磁同步电机鲁棒滑模控制

提出了一种基于无速度传感器运行的永磁同步电机非线性控制方法。针对电机速度和位置观测,设计了一种新颖的级联式滑模观测器,解决了传统滑模观测采用低通滤波器的相位延迟问题。前级电流滑模观测器得到反电动势,后级反电动势滑模观测器获取转速和位置信息,利用李亚普诺夫理论进行了稳定性分析。针对速度控制,提出了带扩张状态观测器的滑模速度控制器取代PI调节器,提高了系统的鲁棒性。在滑模观测和控制中均利用双曲正切函数取代符号函数,削弱了系统抖振。将上述方法应用到永磁同步电机矢量控制系统中,通过仿真验证方法的有效性。     

直流降压变换器的降阶扩张状态观测器与滑模控制设计与实现

本文针对直流降压变换器的负载电阻扰动和输入电压变化等系统不确定因素对输出电压的影响,提出了基于降阶扩张状态观测器的滑模控制方法(SMC+RESO).首先设计降阶扩张状态观测器对系统状态,负载电阻扰动和输入电压变化进行估计,然后基于估计值利用滑模控制技术设计控制器,实现对直流降压变换器系统给定电压跟踪的快速性和准确性.值得注意的是,不同于文[1]所提出的基于扩张状态观测器的滑模控制方法(SMC+ESO),本文所提出的方法采用降阶扩张状态观测器,实现简单,且无需电流传感器,减小了实际应用的成本.利用Lyapunov稳定性定理从理论上证明了所设计的控制器可以保证闭环系统的稳定性.仿真和实验结果表明,与已有的基于扩张状态观测器的滑模控制方法相比,所提出的控制方法更好地改善了系统的跟踪性能和对干扰和不确定性的鲁棒性能,且减少了成本,但是牺牲了系统稳态性能.     

Vertical manoeuvring and rotor speed robust control for mini-helicopter

A robust control approach is presented for vertical manoeuvring helicopters with aerodynamics acting on the main rotor. An induced inflow observer is applied which only requires the measured values of the vertical accelerator in the body frame. The controller consists of three parts: a feedback linearisation controller, a nominal controller and a robust compensator. Feedback linearisation is applied to decouple the vertical motion dynamics and the rotor speed dynamics; the nominal controller aims to achieve desired performances for the nominal system without external disturbances or uncertainties; and the robust compensator is designed to restrain the effect of the external disturbance and the uncertainties. It is proven that all the states involved are bounded and the tracking error of the actual system can converge into an arbitrary specified boundary in a finite time for any given initial state. The results of outdoor flight experiments show that the robust tracking performances are consistent with the theory analysis conclusions.     

Decentralised sliding mode control for nonminimum phase interconnected systems based on a reduced-order compensator

In this paper, a class of interconnected systems with mismatched uncertainties is considered. A sliding surface is proposed in an augmented space formed by the system output and the compensator state variables, and the stability of the corresponding sliding mode is analysed. A robust decentralised reduced-order output feedback sliding mode controller is then designed to drive the system to the composite sliding surface and maintain a sliding motion on it thereafter. The proposed approach allows both the isolated nominal subsystem and the nominal interconnected system to be nonminimum phase. The known interconnections and the bounds on the uncertain interconnections are fully used in the control design to reduce conservatism.     

基于观测器的滑模控制非线性中立型时滞系统

针对一类状态不可测的非线性不确定中立型时滞系统,基于滑模控制理论,采用线性矩阵不等式的处理方法,提出了滑动模态鲁棒渐近稳定时滞相关的充分条件,设计了一类滑模观测器,同时给出了该观测器存在的充分条件;然后应用滑模控制的趋近率方法和基于观测器所得到的系统估计状态,综合了一类滑模控制器,该控制器同时保证了估计状态下滑模面和估计误差状态下滑模面的渐近可达性;最后通过数值实例证明了该控制方案的可行性.     

High-order sliding mode observers and integral backstepping sensorless control of IPMS motor

This paper presents a robust high-order sliding mode interconnected observer and an integral backstepping controller for a sensorless interior permanent magnet synchronous motor. To limit the chattering phenomenon on the observed state, a super twisting algorithm is combined with an interconnected observer to design a new high-order sliding mode observer which will be used for multiple-input multiple-output systems. The proposed observer is used to estimate in finite time the rotor position, the speed and the stator resistance. Moreover, a robust nonlinear controller based on the backstepping algorithm is designed where integral actions are introduced step by step. This controller allows to track a desired reference which is computed by using a maximum-torque-per-ampere strategy. Simulation results are shown to illustrate the performance of the proposed scheme by using significant trajectories including the zero speed and under parametric uncertainties.     

DISCRETE-TIME VSS CONTROLLER DESIGN

In this paper, a sliding sector for discrete-time systems is defined based on a norm of the system state. Inside the sliding sector, the norm decreases. The discrete-time VSS control law is designed to move the system state from the outside to the inside of the sliding sector. A second order discrete-time system and a second order sampled data system are considered in the simulation. The results show the effectiveness of the proposed VSS controller in both cases. © 1997 by John Wiley & Sons, Ltd.     

Decentralized discrete-time quasi-sliding mode control of uncertain linear interconnected systems

In this paper, a new global decentralized discrete-time quasi-sliding mode control of linear interconnected systems is presented. The proposed controller is free of chattering problem and can be applied to a broader class of large-scale systems. Additionally, it is capable to deal with both known and unknown interconnections among the subsystems. Stability of the reduced-order interconnected systems is analyzed using Lyapunov approach. The proposed decentralized controller guarantees the reachability of the connective sliding manifold. The resultant dynamics are proved to be globally asymptotically stable. Furthermore, the controller is made robust to external disturbances by employing a disturbance estimation scheme. The simulations are performed on model of a two-area power generation system and the results show the efficacy of the proposed scheme.     

基于鲁棒滑模观测器的两关节柔性机械手控制

柔性机械手系统为非最小相位系统, 当控制有界时, 该特性阻碍其端点位移渐近跟踪期望轨迹. 本文首先重新定义柔性机械手系统的输出, 通过输入输出线性化, 将系统分解为输入输出子系统和零动态子系统; 然后提出一种用于观测柔性模态导数的鲁棒滑模观测器, 使状态估计达到预期的指标, 解决了柔性模态导数难以获得的问题; 设计积分滑模控制策略, 使输入输出子系统在有限时间收敛到零; 选择适当的控制器参数, 使零动态子系统在 平衡点附近渐近稳定, 从而保证整个系统的渐近稳定. 本文提出的方法设计过程简单, 易于实现. 仿真结果证明了设计的有效性.     

H∞ Control and Sliding Mode Control of Magnetic Levitation System

In this paper, H∞ disturbance attenuation control and sliding mode disturbance estimation and compensation control of a magnetic levitation system are studied. A magnetic levitation apparatus is established, and its model is measured. Then the system model is feedback linearized. A H∞ controller is then designed. For comparison, a sliding mode controller and a PID controller also were designed. Some experiments were performed to compare the performance of the H∞ controller, the sliding mode controller and the PID controller.     

Discrete-time extended state observer-based model-free adaptive constrained sliding mode control with modified prescribed performance via CFDL and PFDL

To tackle the trajectory tracking problem and achieve high control accuracy in many actual nonlinear systems with unknown dynamics and input saturation, a novel discrete-time extended state observer-based model-free adaptive constrained sliding mode control with modified prescribed performance is investigated via compact-form dynamic linearization (CFDL) and partial-form dynamic linearization (PFDL). Firstly, the original non-affine system is turned into an affine one comprising an unknown nonlinear term and a linearly parametric term affine to the input via both PFDL and CFDL. Then, a discrete-time extended state observer (DESO) is used to estimate the lumped disturbance containing the unknown nonlinear time-varying term and the term relevant to the estimation error of pseudo partial derivative (PPD) parameter. Furthermore, a modified prescribed performance function is introduced in the model-free adaptive sliding mode control scheme to keep the output tracking error in the prescribed bound without causing any asymmetric offset error in the steady-state. Meanwhile, to suppress the influence of input saturation on the control system, an anti-windup compensator is used. Finally, rigorous theoretical analyses show the robust convergence of the tracking error via the proposed CFDL and PFDL-based methods under external disturbances. Simulations verify the superiority of the modified prescribed performance function, DESO, and anti-windup compensator in the proposed method. Also, the effects of the PFDL-based method and the CFDL-based one are compared during the simulation.     

Second order sliding mode block control of single‐phase induction motors

The authors propose a robust nonlinear controller based on a block control linearization technique combined with a second order sliding mode super‐twisting algorithm for controlling the rotor speed of single‐phase induction motors. The block control approach is used to design a sliding manifold in terms of the stator current and its desired value. The super‐twisting sliding mode algorithm is applied then to render the designed manifold be attractive. A nonlinear observer is designed to estimate the unmeasured variables (rotor flux linkages and torque load). Copyright © 2012 John Wiley & Sons, Ltd.     

A Robust Backstepping Sensorless Control for Interior Permanent Magnet Synchronous Motor Using a Super‐Twisting Based Torque Observer

In order to achieve high‐performance speed regulation for sensorless interior permanent magnet synchronous motors (IPMSMS), a robust backstepping sensorless control is presented in this paper. Firstly, instead of a real mechanical sensor, a robust terminal sliding mode observer is used to provide the rotor position. Then, a new super‐twisting algorithm (STA) based observer is designed to obtain estimates of load torque and speed. The proposed observer ensures finite‐time convergence, maintains robust to uncertainties, and eliminates the common assumption of constant or piece‐wise constant load torque. Finally, a sensorless scheme is designed to realize speed control despite parameter uncertainties, by combining the robust backstepping control with sliding mode actions and the presented sliding mode observers. The stability of the observer and controller are verified by using Lyapunov's second method to determine the design gains. Simulation results show the effectiveness of the proposed approach.     

基于AFSMC算法的四旋翼飞行器控制策略研究

针对四旋翼飞行器在飞行过程中,控制系统存在非线性、强耦合、不确定性和鲁棒性差的问题,建立了关于四旋翼飞行器的动力学数学模型,将自适应控制、模糊控制和滑模控制相结合,提出基于自适应模糊滑模控制(AFSMC)的快速平稳控制策略。采用模糊系统推理方法实现理想控制律的逼近。在满足李雅普诺夫稳定性条件的前提下进行控制器的设计和稳定性分析,并结合四旋翼的数学模型和给定参数进行了MATLAB仿真。仿真结果表明,AFSMC控制器相比常规PID控制器具有良好的动态性能和抗干扰能力。     

Robust Stabilization of Uncertain Fuzzy Systems Using Variable Structure System Approach

Based on the variable structure system (VSS) theory, we develop a fuzzy control system design method for a class of uncertain nonlinear multivariable systems that can be represented by a Takagi-Sugeno fuzzy model. We make the first attempt to relax the restrictive assumption that each nominal local system model shares the same input channel, which is required in the traditional VSS-based fuzzy control design methods. As the local controller we use a sliding mode controller with a switching feedback control term. In terms of linear matrix inequalities (LMIs), we derive a sufficient condition for the existence of linear sliding surfaces guaranteeing asymptotic stability of the reduced-order equivalent sliding mode dynamics. We present an LMI characterization of such sliding surfaces. We also give an LMI-based algorithm to design the switching feedback control term so that a stable sliding motion is induced in finite time. Finally, we give a numerical design example.     

滑模控制一类非线性分布式时滞系统

针对一类状态不可测的非线性不确定分布式时滞系统, 给出了系统滑动模态鲁棒渐近稳定的充分条件. 设计了一类滑模观测器, 同时采用线性矩阵不等式的处理方法给出了该观测器存在的充分条件. 再应用滑模控制的趋近率方法和基于观测器所得到的估计状态, 综合了一类滑模控制器. 该控制器同时保证了估计状态下的滑模面和估计误差状态下的滑模面的渐近可达性.