Vibration control subjected to windup problem: An applied view on analysis and synthesis with convex formulation

In this paper, the windup problem in active vibration control (AVC) is studied systematically. Instead of evaluating the performance of several anti-windup compensators implemented on independent abstract simulation problems, a unified benchmark setup in active-damping control (ADC) is used. The investigated anti-windup schemes (analysis and synthesis) are adapted to the disturbance rejection control. Large attention is given to capture the similarities and differences of the methods in dealing with the windup event in a practical context. Therefore, instead of categorizing the methods into static and non-static methods or model recovery and direct linear anti-windup schemes, a logical route is followed to highlight the significance of each method. The mathematical interpretations of the methods are provided for the vibration engineer while delivering forthright implementation algorithms for AVC. The tackled methods are unified on a state space model obtained from the frequency-domain subspace system identification approach. Practical issues that may raise for each technique are mentioned, and detained guidelines are provided for tuning each algorithm. Finally, in order to compare the compensated system’s performance, comprehensive time-domain studies are carried out by separating the transient response of the compensated systems to three modes: linear mode, where the actuation nonlinearity is inactive; the nonlinear mode, where the windup event is in progress, and finally, the output mismatch rejection mode, where the windup incident is over, but performance degradation is still present.     

Design of multiple anti-windup loops for multiple activations

This paper considers anti-windup design for linear systems subject to actuator saturation.Three anti-windup gains are designed for activations immediately at the occurrence actuator saturation,after the saturation has reached a certain level and in anticipation of the occurrence of saturation,respectively.The design is based on the minimization of L 2 gain from the disturbance to the controlled output of the resulting closed-loop system.Traditional anti-windup scheme involves a single anti-windup loop for immediate activation.A recent innovation is to design a single anti-windup loop for delayed or anticipatory activation,as well as to design two anti-windup gains,one for immediate activation and one for delayed activation.Our design of three anti-windup gains for three different activations is shown through simulation to lead to significant further performance improvement over the previous activation schemes.     

ACTIVE VIBRATION ISOLATION FOR A LONG RANGE SCANNING TUNNELING MICROSCOPE

Vibration isolation or control is critical for the optimum operation of the Molecular Measuring Machine (M³), a high‐resolution, length‐metrology instrument at the National Institute of Standards and Technology. This paper describes the extension of the M3 Mallock isolation suspension from passive to six degrees‐of‐freedom (DOF) active vibration isolation. System modeling is presented, and experimental system identification is carried out for the purpose of model verification. The paper then compares the vibration isolation performance achieved using a classical proportional‐integral‐derivative (PID) controller versus that achieved using a modified, model‐based, Linear‐Quadratic‐Gaussian (LQG) controller. Attenuation of 3 dB to 15 dB is achieved within the active vibration isolation control bandwidth, and images taken with the M³ scanning tunneling microscope (STM) probe show improved performance.     

结构振动控制仿真分析软件TSHOW

介绍结构振动控制仿真分析软件TSHOW基于结构振动控制的算法和原理,建立了在无控、主动控制、隔振控制和半主动控制时结构运动的微分方程,并应用MATLAB控制系统工具箱（Control System Toolbox）中的函数,研制了仿真分析程序。对于实验结果,经TSHOW进行后处理,可以与仿真结果进行对比,从而分析控制实验的效果。仿真结果以图形方式显示,内容包括控制力时程、所选楼层的动力响应等,例如位移、速度、加速度时程。频域分析包括位移、速度、加速度的幅频响应曲线。所绘曲线的显示特性可以按照要求进行设置和调整。为了探求隔振层和控制装置的动力特性,利用图形技术,实现了层间恢复力-位移曲线的动态显示。     

Active vibration isolation using negative stiffness and displacement cancellation controls: Comparison based on vibration isolation performance

Two vibration control techniques, negative stiffness and displacement cancellation, are characterized and employed to achieve active vibration isolation. A horizontal vibration isolation system is developed and then used to investigate each of these techniques theoretically and experimentally. The respective responses of the developed system are measured separately while closed-loop poles of the system are kept unchanged; these measured responses are compared. The developed system is based on a series combination of two isolators and consists of two moving tables; one of the moving tables is mounted on the series-connected isolators and the other is placed between the isolators. Using the negative stiffness technique, the isolators are controlled so that one of them has a negative stiffness and the other has a positive stiffness of equal absolute magnitude; using the displacement cancellation technique, one isolator is set to cancel displacement while the other behaves as a positive-stiffness isolator. The active negative, positive, and displacement cancellation isolators are created using voice-coil motors guided by a negative stiffness controller, proportional derivative controller and integral-proportional derivative controller, respectively.     

Anti-windup design of uncertain discrete-time Markovian jump systems with partially known transition probabilities and saturating actuator

This paper carries out a study on the design of anti-windup gains for uncertain discrete-time Markovian jump systems subject to both actuator saturation and partially known transition probabilities. The parameter uncertainties appearing in both the state and input matrices are assumed to be time-varying and norm-bounded. Under the assumption that a set of linear dynamic output feedback controllers have been designed to stabilise the Markovian jump system in the absence of actuator saturation, anti-windup compensation gains are designed for maximising the domain of attraction of the closed-loop system with actuator saturation. Then, by solving a convex optimisation problem with constraints of a set of linear matrix inequalities, the anti-windup compensation gains are obtained. A simulation example is provided to illustrate the effectiveness of the proposed technique.     

Active vibration isolation in a “smart spring” mount using a repetitive control approach

In a variety of different engineering systems there is a requirement to isolate sensitive equipment from foundation vibration or alternatively, isolate the foundation from machinery vibration. Passive solutions to this problem provide some isolation but performance is significantly degraded in the presence of structural compliance. A recently proposed hybrid active/passive solution known as the “Smart Spring” mounting system specifically addresses this problem of compliance. The work reported here investigates the application of a repetitive control approach to deal with periodic vibration sources in such a mounting system. The industrial potential of the approach has been shown using an experimental facility where isolation results in the region of 50 dB have been achieved.     

DSP的VCM低频主动隔振控制系统设计

音圈电机(Voice Coil Motor,VCM)因其良好的线性驱动性能,在主动隔振系统中作为主动吸振器的驱动器日益受到人们的青睐.本文设计了一种应用于低频主动隔振系统中,基于DSP的VCM控制系统,给出了软、硬件设计方法,并介绍了一种基于时钟节拍和消息机制的软件系统的工作原理.     

Optimal anti-windup synthesis for repetitive controllers

Repetitive controllers use internal models that provide very high gain at a selected fundamental frequency and its harmonics, additionally, some of the internal models may result unstable, as in the high order repetitive control approach. These characteristics make the repetitive control system susceptible to exhibit wind-up when actuator saturation occurs. This paper proposes an anti-windup scheme for repetitive control based on the model recovery anti-windup strategy. The proposed scheme provides low order, low computational burden and also isolation of the controller from the saturation effects. The anti-windup compensator is constructed from the plant model and provides an additional linear feedback path aimed at enhancing system performance. This feedback path is designed to obtain a deadbeat behaviour, which makes the system recovery faster. Finally, internal stability and deadbeat features are designed in a compact procedure based on linear matrix inequalities and an optimal linear quadratic design. Experimental validation of the proposed anti-windup compensator is provided using a mechatronic plant.     

Dynamic anti-windup design for anticipatory activation：enlargement of the domain of attraction

Traditional anti-windup compensators are designed for activation immediately at the occurrence of actuator saturation.Recently,anti-windup compensators were designed for actuation either after the saturation has reached a certain level or in anticipation of its occurrence.In the case of static anti-windup compensators,it has been shown that an anti-windup compensator designed for activation in anticipation of actuator saturation would lead to better performance than those designed for immediate or delayed activation could,both in terms of transient performance and the size of the domain of attraction.More recently,it has been shown that a dynamic anti-windup compensator designed for anticipatory activation would also result in better transient performance than those designed for immediate or delayed activation could.In this paper,we design dynamic anti-windup compensators for the enlargement of the domain of attraction.These compensators are designed respectively for immediate,delayed and anticipatory activation.We will show by simulation that a dynamic anti-windup compensator designed for anticipatory activation would result in a larger domain of attraction than a dynamic anti-windup compensator designed for immediate or delayed activation could.     

Introducing concepts of passivity-based control in anti-windup algorithms

This work presents a reference conditioning anti-windup scheme based on passivity control theory. The main closed-loop is controlled by a proportional–integral–derivative (PID) control, and the injection and damping assignment technique ensures that PID variables are compatible with the process input. In the proposed algorithm, a fictitious actuator, modeled as a first-order filter, is incorporated to estimate the rate of change and the output of the actuator device. Amplitude and rate constraints are weight by coefficients that shape the energy function of the anti-windup scheme. Finally, to show how the algorithm can cope with the windup problem, simulation results are presented. Even when shown the results on a linear PID, the proposal can extend to any linear or nonlinear control in the main control loop.     

Anti-windup design with guaranteed regions of stability for discrete-time linear systems

The purpose of this paper is to study the determination of stability regions for discrete-time linear systems with saturating controls through anti-windup schemes. Considering that a linear dynamic output feedback has been designed to stabilize the linear discrete-time system (without saturation), a method is proposed for designing an anti-windup gain that maximizes an estimate of the basin of attraction of the closed-loop system in the presence of saturation. It is shown that the closed-loop system obtained from the controller plus the anti-windup gain can be locally modeled by a linear system with a deadzone nonlinearity. Then, based on the use of a new sector condition and quadratic Lyapunov functions, stability conditions in an LMI form are stated. These conditions are then considered in a convex optimization problem in order to compute an anti-windup gain that maximizes an estimate of the basin of attraction of the closed-loop system. Moreover, considering asymptotically stable open-loop systems, it is shown that the conditions can be slightly modified in order to determine an anti-windup gain that ensures global stability. An extension of the proposed results to the case of dynamic anti-windup synthesis is also presented in the paper.     

Linear LMI-based external anti-windup augmentation for stable linear systems

We study linear anti-windup augmentation for linear control systems with saturated linear plants in the special case when the anti-windup compensator can only modify the input and the output of the windup-prone linear controller. We also measure the arising performance in terms of the finite L₂ gain from exogenous inputs to selected performance outputs. Our main results are a system theoretic feasibility characterization for fixed order anti-windup design and a linear matrix inequality (LMI) formulation for optimal static and plant-order anti-windup design. Interpretations of lower bounds on the achievable performance are also given. The effectiveness of the design procedure is demonstrated on a simulation example.     

高阶非线性系统状态反馈抗饱和跟踪控制

针对参数未知的高阶非线性系统,提出了一种简单有效的反馈抗饱和控制方法,并进行了状态反馈抗饱和控制吸引域估计.利用反馈控制思想,借助于李亚普诺夫稳定性理论,设计出了相应的状态抗饱和反馈控制器,并借助于Matlab进一步求出了控制器的参数.将所设计的抗饱和控制应用于Duffing混沌系统,仿真结果验证了该控制方法的有效性.     

具有输入饱和的近空间飞行器鲁棒控制

针对近空间飞行器这一类存在外部扰动,输入饱和和参数不确定的多输入多输出线性系统,提出了一种基于干扰观测器的抗饱和鲁棒控制方案.将干扰观测器与抗饱和控制技术相结合,从而消除系统存在的未知外部扰动、输入饱和和不确定性对系统控制的影响.首先,设计干扰观测器对线性外部系统产生的未知扰动进行估计.然后根据干扰观测器输出,通过超前抗饱和方法设计抗饱和补偿器,并将其加入到鲁棒控制器的设计中,保证闭环系统存在输入饱和、未知外部扰动和参数不确定情况下的稳定性.为便于设计,干扰观测器、抗饱和补偿器和控制器设计矩阵均通过求解线性矩阵不等式得到.最后,将提出的鲁棒抗饱和控制方法应用于近空间飞行器,仿真结果验证了该控制方案的有效性.     

Six-degree-of-freedom active vibration isolation using a stewart platform mechanism

Intelligent Automation, Inc. has performed a study of a six-degree-of-freedom (dof) active vibration isolation system based on a Stewart platform mechanism to be used for precision control of a wide range of space-based structures as well as earth-based systems. This article presents part of the study results, which includes a new Terfenol-D actuator design and analysis, a design of a Stewart platform as a vibration isolation device, and robust adaptive filter algorithms for active vibration control. Prototype hardware of a six-dof active vibration isolation system has been implemented and tested. About 30 dB of vibration attenuation is achieved in real-time experiments.     

Anti-windup compensator for active queue management in TCP networks

In this paper, we apply a dynamic anti-windup scheme for improving the performance of a conventional proportional–integral (PI) controller for active queue management (AQM) supporting TCP flows. When a PI controller is used for AQM, the windup phenomenon of the integral action can cause performance degradation because the packet drop probability is limited between 0 and 1. Therefore we suggest a TCP/AQM model with a saturating actuator and apply a dynamic anti-windup method for improving the performance of the conventional PI AQM scheme. The proposed scheme not only provides graceful performance degradation, but also guarantees the stability of the overall system with the linearized TCP model. We verify the performance of the proposed scheme through ns-2 simulations. The simulation results show that our scheme outperforms the conventional PI controller when the traffic load is not stationary, which is always the case in real network environment.     

Anti-windup control design for exponentially unstable LTI systems with actuator saturation

In this paper, a new saturation control technique in the framework of anti-windup compensation is developed for exponentially unstable linear time-invariant systems subject to input nonlinearities. The proposed control algorithm guarantees regional stability in the existence of input saturation, and provides less conservative performance than most existing anti-windup schemes. Moreover, an explicit form of anti-windup controller with its order no more than the order of the plant is derived. An inverted pendulum example is used to demonstrate the advantages of the newly proposed anti-windup control technique.     

共轴八旋翼无人飞行器的偏航静态抗饱和补偿控制

设计了一种共轴八旋翼无人飞行器,与四旋翼飞行器相比,其具有更大的驱动能力、更强的带载能力和一定的冗余能力．首先,建立了飞行器的动力学模型．针对共轴八旋翼飞行器偏航运动能力比俯仰、滚转运动能力弱,偏航容易出现执行器饱和现象的问题,从实际工程出发提出了基于线性自抗扰控制器的静态抗饱和补偿器．线性自抗扰算法易于工程调节,能够实时估计与补偿外界扰动．静态抗饱和补偿器不增加系统阶次,有效抑制偏航执行器饱和．利用李亚普诺夫稳定理论证明了基于线性自抗扰控制器的静态抗饱和偏航控制系统的稳定性．最后,通过共轴八旋翼飞行器的仿真实验与原型机比较实验验证了算法的有效性与鲁棒性．原型机实验结果表明：在室内固定干扰下,执行器退出饱和的最长时间约为4 s,偏航角误差收敛到±0.085 rad;在室外变干扰下,执行器退出饱和的最长时间约为9 s,偏航角误差收敛到±0.127 rad．基于线性自抗扰控制器的静态抗饱和补偿器在外界干扰情况下能够有效地抑制执行器饱和,具有良好的偏航控制性能与强鲁棒性．     

模糊控制在ESA地面试验装置主隔振系统中的应用

将模糊控制应用于静电悬浮加速度计(ESA)地面试验装置主隔振系统,用M atlab/S imu link工具建立了控制系统仿真模型,并进行了仿真试验研究。结果表明:采用该控制技术的主动隔振系统有一定的可行性,在频率1~50Hz范围内,控后隔振平台振动幅值衰减51.91%~99.86%。