Semi-global output consensus of discrete-time multi-agent systems with input saturation and external disturbances

This paper investigates the problem of leader-following output consensus of a linear discrete-time multi-agent system with input saturation and external disturbances. Low-gain state feedback technique and output regulation theory are used to deal with the output consensus of multi-agent systems with input saturation and external disturbances. Both the cases with identical and non-identical disturbances are discussed in the multi-agent systems. For the case of identical external disturbance, the output consensus can be attained when the directed graph has no loop and there exists at least one directed path from the leader to every follower agent. For the case of non-identical external disturbances, the output consensus can be achieved if the directed graph is strongly connected and detailed balanced, and at least one follower can have access to the information of the leader. Numerical simulation results are presented to demonstrate the validation of the proposed design.     

A refined nonlinear vibration absorber

Presented here is a theoretical study on how to use saturation phenomena to design nonlinear vibration absorbers and how to improve their stability and effective frequency bandwidth. The so-called original saturation control method uses 2 : 1 internal resonances and saturation phenomena to suppress steady-state vibrations of a dynamical system by connecting it to a second-order controller using quadratic position coupling terms, which do not really suppress vibration to zero as a linear vibration absorber does. However, a linear vibration absorber uses direct position feedbacks and splits one natural frequency of the original system into two and hence spill-over effects exist when the system is subjected to broad-band and/or transient excitations. Although a saturation controller does not split one natural frequency into two, one large-amplitude nonlinear solution coexists with a small-amplitude linear solution outside of the resonance area. Hence, the existence of spillover effects depends on initial conditions. A refined nonlinear vibration absorber is designed by using a quadratic velocity coupling term in the controller and adding a negative velocity feedback to the system. It is shown that the quadratic velocity coupling term enables a saturation controller to suppress system vibrations to zero. Moreover, the linear velocity feedback enhances the capability of suppressing transient vibrations and prevents the system from having the large-amplitude nonlinear response. Two equations describing the first-mode vibration of a stainless-steel beam and a saturation controller from the authors’ previous experimental work are used in this theoretical study. Both perturbation and direct numerical integration solutions are presented. Guidelines for designing nonlinear vibration absorbers are derived.     

On-off nonlinear active control of floor vibrations

Human-induced floor vibrations can be mitigated by means of active control via an electromagnetic proof-mass actuator. Previous researchers have developed a system for floor vibration comprising linear velocity feedback control (LVFC) with a command limiter (saturation in the command signal to avoid actuator overloading). The performance of this control is highly dependent on the linear gain utilised, which has to be designed for a particular excitation and might not be optimum for other excitations. This work explores the use of on-off nonlinear velocity feedback control (NLVFC) as the natural evolution of LVFC when high gains and/or significant vibration level are present together with saturation in the control law. Firstly, the describing function tool is employed to analyse the stability properties of: (1) LVFC with saturation, (2) on-off NLVFC with a dead zone and (3) on-off NLVFC with a switching-off function. Particular emphasis is paid to the resulting limit cycle behaviour and the design of appropriate dead zone and switching-off levels to avoid it. Secondly, experimental trials using the three control laws are conducted on a laboratory test floor. The results corroborate the analytical stability predictions. The pros of on-off NLVFC are that no gain has to be chosen and maximum actuator energy is delivered to cancel the vibration. In contrast, the requirement to select a dead zone or switching-off function provides a drawback in its application.     

Observer-based reliable stabilization of uncertain linear systems subject to actuator faults,saturation, and bounded system disturbances

A matrix inequality approach is proposed to reliably stabilize a class of uncertain linear systems subject to actuator faults, saturation, and bounded system disturbances. The system states are assumed immeasurable, and a classical observer is incorporated for observation to enable state-based feedback control. Both the stability and stabilization of the closed-loop system are discussed and the closed-loop domain of attraction is estimated by an ellipsoidal invariant set. The resultant stabilization conditions in the form of matrix inequalities enable simultaneous optimization of both the observer gain and the feedback controller gain, which is realized by converting the non-convex optimization problem to an unconstrained nonlinear programming problem. The effectiveness of proposed design techniques is demonstrated through a linearized model of F-18 HARV around an operating point.     

Position control of a rodless cylinder in pneumatic servo with actuator saturation

In this paper, positioning control of a rodless cylinder in pneumatic servo systems with actuator saturation is investigated via an active disturbance rejection control. A linear extended state observer is designed to estimate and compensate strong friction force and other nonlinearities in the pneumatic rodless cylinder system. An actuator saturation linear feedback control law is developed to further improve the control performance. Furthermore, a linear matrix inequality-based optimization algorithm is employed to estimate a strictly invariance set for the closed-loop system. Experiment results with response time 0.5 s and accuracy 0.005 mm for a 200 mm step signal demonstrate the effectiveness of the proposed control strategy.     

Periodic and chaotic motions of a harmonically forced piecewise linear system

The dynamics of a harmonically excited single degree-of-freedom linear system with a feedback control, in which the actuator is subjected to dead zone and saturation constraints, is investigated in detail. The controlled system is mathematically modeled by a set of three piecewise linear equations. It is found that the system may exhibit nine types of symmetric and asymmetric period-one motions, which are characterized by a different number of crossing dead zone and saturation region per cycle. A solution for the symmetric period-one motion with a doubly crossing dead zone and saturation region is analytically constructed and its stability characteristics is examined. Other types of dynamic response such as sub-harmonic periodic motions and chaotic motions, found through numerical simulations, are also presented.     

Output feedback boundary control of an axially moving system with input saturation constraint

This paper is concerned with boundary control for an axially moving belt system with high acceleration/deceleration subject to the input saturation constraint. The dynamics of belt system is expressed by a nonhomogeneous hyperbolic partial differential equation coupled with an ordinary differential equation. First, state feedback boundary control is designed for the case that the boundary states of the belt system can be measured. Subsequently, output feedback boundary control is developed when some of the system states can not be accurately obtained. The well-posedness and the uniformly bounded stability of the closed-loop system are achieved through rigorous mathematical analysis. In addition, high-gain observers are utilized to estimate those unmeasurable states, the auxiliary system is introduced to eliminate the constraint effects of the input saturation, and the disturbance observer is adopted to cope with unknown boundary disturbance. Finally, the control performance of the belt system is illustrated by carrying out numerical simulations.     

五自由度纳米级定位工作台的设计研究

提出一种新型的五自由度精密定位平台的工作原理及其设计方法。工作台采用柔性导向机构实现平移及转动功能,采用压电陶瓷作为驱动元件,外置纳米级电容传感器作为位移量测量反馈元件,采用数字PID控制方法,可以实现纳米级精度的定位。给出了多种形式柔性导向机构刚度计算公式及设计实例。     

A dual-stage control system for high-speed, ultra-precise linear motion

Modern manufacturing equipment often requires high-speed and ultra-precise linear motion. For implementing such motion, a coarse–fine dual stage is effective because the coarse stage has a low bandwidth with a large workspace, and in contrast, the fine stage has a high bandwidth with a small stroke. This paper presents the implementation of an air-bearing, dual-stage system and its control strategy. A closed-loop feedback in an absolute space is used to realize coarse–fine control. The fine stage is driven by a voice coil motor that tracks the designed trajectory, while the coarse stage is driven by permanent-magnet linear synchronous motor that tracks the trajectory of the fine stage to prevent its motion saturation. Also analyzed are the coupled dynamics of the air-bearing dual stage driven by a direct-drive motor. Identification and robust control design for the fine stage are introduced in detail. Method tests for the single fine stage are performed, and the results demonstrate that ultra-precision control can be realized for the fine stage. Next, experiments are presented with the dual stage using different loads. Experimental results show that our control strategy can achieve high-speed, ultra-precision linear motion through the dual stage with a satisfactory performance.     

基于正切函数非线性反馈的"育鹏"轮自动舵控制算法

自动舵是重要的航海仪器, 对于船舶的安全航行有着重要作用. 为了进一步改善自动舵的性能, 本研究采用一阶闭环增益成形算法(PID)设计了具有鲁棒性的自动舵控制算法, 并用正切函数非线性反馈技术代替线性反馈以提升自动舵的节能效果. 以大连海事大学新交付使用的"育鹏"轮为例, 开展仿真研究. 结果表明模型参数改变25%控制效果良好, 说明设计的自动舵算法具有良好的鲁棒性, 与线性反馈相比, 非线性反馈能节能7.9%. 本文所提算法简单, 物理意义明显, 同时该控制算法也有助于船舶控制器设计的国产化.     

Simulation and Control of an Active Tilting-Pad Journal Bearing

This study developed an active tilting-pad journal bearing with a feedback control system to regulate the orbit of a rotating shaft. The control is implemented by means of linear actuators installed behind the pivot of each pad, which allow the radial motion of the pads in real time. The control design uses the linear feedback of the state variables of the bearing-rotor system, with the feedback gains determined by the optimization of a quadratic performance index. The optimization is based on a linear spring-mass model that incorporates the direct stiffness and damping elements associated with each of the bearing pads. This linear model is found by the simulation of the system under small perturbations using a nonlinear Reynolds equation model. The nonlinear model is capable of simulating the radial motions of the pads by the actuators and is used to verify the effectiveness of the feedback control. It is shown that certain design parameters in the quadratic performance index may be used to determine both the stiffness and the damping of the closed-loop bearing system and that the shaft orbit can be thereby suitably regulated.     

Finite-time consensus of Markov jumping multi-agent systems with time-varying actuator faults and input saturation

This paper gives attention to the issue of finite-time leader-following consensus of nonlinear discrete-time multi-agent systems with Markov jump parameters. A robust fault-tolerant control protocol that takes the effect of time-varying actuator faults and actuator saturation into account is considered for the addressed system. The main purpose of the paper is to design a fault-tolerant controller such that the leader-following consensus of the addressed system is achieved over a prescribed finite-time interval. By using the Lyapunov functional approach, Abel’s lemma and some properties of Kronecker product, a sufficient condition for the existence of fault-tolerant state feedback controller for the addressed system is presented and an explicit parameterization of such a controller is obtained. Eventually, a numerical example along with its simulation results is exploited to reflect the applicability of the proposed design method, wherein the robust performance of controller is exhibited despite the presence of actuator saturation and time-varying actuator faults.     

Large dynamic range nanopositioning using iterative learning control

This paper presents the control system design and tracking performance for a large range single-axis nanopositioning system that is based on a moving magnet actuator and a flexure bearing. While the physical system is designed to be free of friction and backlash, the nonlinearities in the electromagnetic actuator as well as the harmonic distortion in the drive amplifier degrade the tracking performance for dynamic commands. It is shown that linear feedback and feedforward proves to be inadequate to overcome these nonlinearities. This is due to the low open-loop bandwidth of the physical system, which limits the achievable closed-loop bandwidth given actuator saturation concerns. For periodic commands, like those used in scanning applications, the component of the tracking error due to the system nonlinearities exhibits a deterministic pattern and repeats every period. Therefore, a phase lead type iterative learning controller (ILC) is designed and implemented in conjunction with linear feedback and feedforward to reduce this periodic tracking error by more than two orders of magnitude. Experimental results demonstrate the effectiveness of ILC in achieving 10 nm RMS tracking error over 8 mm motion range in response to a 2 Hz band-limited triangular command. This corresponds to a dynamic range of more than 10⁵ for speeds up to 32 mm/s, one of the highest reported in the literature so far, for a cost-effective desktop-sized single-axis motion system.     

Feedback linearization control of the looper system in hot strip mills

This paper studies on the linearization of a looper system in hot strip mills, that plays an important role in regulating a strip tension or a strip width. Nonlinear dynamic equations of the looper system are analytically linearized by a static feedback linearization algorithm with a compensator. The proposed linear model of the looper is validated by a comparison with a linear model using Taylor’ s series. It is shown that the linear model by static feedback well describes nonlinearities of the looper system than one using Taylor’ s series. Furthermore, it is shown from the design of an ILQ controller that the linear model by static feedback is very useful in designing a linear controller of the looper system.     

Position tracking control of saturated LSRM

This paper deals with the tracking control design of a linear synchronous reluctance motor (LSRM) drive. An extended nonlinear dynamic LSRM model with magnetic saturation included is used in the control design and practical realization, in order to improve tracking performances at very low speeds of motion. Iron core saturation is included in the extended model with the experimentally determined flux linkages given as functions of the direct and quadrature axes currents. Experimental results show that the proposed input-output linearizing tracking control with included saturation behaves considerably better than the one without saturation, introducing smaller position and speed errors and better motor stiffness, on account of the increased computational complexity.     

Robust covariance control for discrete system by Takagi-Sugeno fuzzy controllers

Variances of the system states or outputs often play vital roles in the problem for performance requirements of many stochastic control systems. For linear stochastic systems, the covariance control technique has been applied to deal with the variance constrained design problem. This paper extends this technique to a class of discrete-time nonlinear perturbed stochastic systems, which are modeled by the Takagi-Sugeno (TS) fuzzy systems. By fuzzy IF-THEN rules, which represent local linear input-output relations, the nonlinear systems can be described by TS fuzzy models. According to the parallel distributed compensation (PDC) concept, the discrete-time nonlinear perturbed stochastic systems can be driven by the linear feedback gains. The purpose of this paper is to provide a method to design an output feedback fuzzy controller, which is based on the upper bound state covariance control technique and PDC concept, for the discrete-time perturbed stochastic systems using TS fuzzy models.     

双压力角非对称齿廓渐开线齿轮的振动分析

基于非对称渐开线圆柱齿轮传动时的啮合机理和齿轮系统动力学。同时考虑到齿轮系统时变啮合刚度和静态传递误差的影响，建立了齿轮动力学模型，利用数值积分和数值仿真方法对其进行了非线性振动研究。比较了标准齿轮与非对称齿轮的振动特性，分析了齿轮系统各参数对系统动态特性的影响。仿真结果对考虑动载荷情况下的油膜厚度计算提供了基础数据，为进一步研究非对称渐开线的各种特性提供了理论依据。     

Modeling and control of a pneumatically actuated inverted pendulum

This paper presents the results of modeling of an inverted pendulum system driven by a linear pneumatic motor and equipped with relatively low-cost potentiometer-based position measurement system. Based on the nonlinear model of the overall pendulum system, which also includes notable friction effects, a linearized model is derived. The linearized model is used as a basis for the design of state feedback controller based on LQ and LQG optimization procedures. The linear state feedback controllers are augmented by a compensator of nonlinear friction effects whose design is based on the results of experimental identification of an appropriate static friction model. The proposed pendulum controller structures have been verified by means of computer simulations and experimentally on the experimental setup of a pneumatically actuated inverted pendulum.     

密集模态响应饱和与线性模型失效研究

通过对一两自由度密频近线性系统主共振响应分析 ,揭示了由于密频内共振的存在 ,密集模态坐标的运动将产生复杂的非线性响应饱和现象 ,此时 ,线性模型失效 ,必须采用非线性模型 ;同时 ,讨论了线性模型失效与激励强度、系统初始条件的依赖关系。     

异常情况下转子系统的不平衡响应特性

用Riccati传递矩阵法计算分析了支撑系统异常情况下转子的不平衡响应特性。分析结果表明，支撑刚度不对称情况下，在转子上加对称不平衡量，不仅激发一阶分量，同时还激发出明显的二阶分量，同样，加反对称不平衡量，不仅激发二阶分量，同时还能激发出明显的一阶分量，转子不平衡响应特性发生了很大变化。该结论对于指导机组动平衡具有非常重要的工程应用价值。