Model study and active control of a rotating flexible cantilever beam

For a dynamic system of a rotating flexible cantilever beam, the traditional model assumes the small deformation in structural dynamics where axial and transverse displacements at any point in the beam are uncoupled. This traditional hybrid coordinate model is referred as the zero-order approximation coupling model in this paper, which may result in divergence to the dynamic problem of a flexible cantilever beam with a high rotational speed. In this paper, a first-order approximation coupling model is presented to analyze the dynamics of rotating flexible beam system, which is based on the Hamilton theory and the finite element discretization method. The proposed model for the system considers the second-order coupling quantity of the axial displacement caused by the transverse displacement of the beam. The dynamic characteristics of the rotating beam system when using the zero-order approximation coupling model are compared with those when using the first-order approximation coupling models through numerical simulations. In addition, the applicability of the two dynamic models for control design are studied by using the classical optimal control method. Simulation and comparison studies show that, for the case without control for the system, there exists big difference between the result using the zero-order approximation coupling model and that using the first-order approximation coupling model even for the case of small angular velocity of the system. The larger is the angular velocity, the bigger is the difference. Vibration frequency of the beam by using the first-order approximation coupling model is higher than that by using the zero-order approximation coupling model. When the angular velocity of the system is close to or is larger than the fundamental frequency of the beam without rotation motion, the zero-order approximation coupling results in a wrong result, while the first-order approximation coupling model is valid. For the case with control for the system, the applicability of the zero-order approximation coupling model can be much broadened. The critical angular velocity of the system for validity of the zero-order approximation coupling model is much larger than that without control for the system. The first-order approximation coupling model is available not only for the case of small angular velocity but also for the case of large angular velocity of the system, and is applicable to the cases with or without control for the system.     

考虑附加质量的中心刚体-柔性悬臂梁系统的动力特性研究

对考虑附加质量的中心刚体-柔性悬臂梁系统的动力特性进行研究.首先采用Hamilton原理和有限元离散化方法,在计入柔性梁由于横向变形而引起的轴向变形的二阶耦合量的条件下,给出该系统的刚柔耦合动力学方程(即一次近似耦合模型),以及相应的非惯性系下的动力学模型,然后通过数值仿真对系统的动力特性进行研究.仿真结果显示,即使是小的附加质量也会对系统动力特性产生重要影响,附加质量使得梁的响应幅值变大和响应频率降低,且会影响柔性梁和中心刚体的终点位置.附加质量的影响随系统大范围运动的角速度的增大而变大.当系统大范围运动为低速时,传统的混合坐标模型仍然会导致较大误差;当系统大范围运动为高速时,传统的混合坐标模型存在失效的可能.     

Active vibration control based on modal controller considering structure-actuator interaction

Active vibration control to suppress structural vibration of the flexible structure is investigated based on a new control strategy considering structure-actuator interaction. The experimental system consists of a clamped-free rectangular plate, a controller based on modal control switching, and a magnetostrictive actuator utilized for suppressing the vibrations induced by external excitation. For the flexible structure, its deformation caused by the external actuator will affect the active control effect. Thus interaction between structure and actuator is considered, and the interaction model based on magnetomechanical coupling is incorporated into the control system. Vibration reduction strategy has been performed resorting to the actuator in optimal position to suppress the specified modes using LQR (linear quadratic regulator) based on modal control switching. The experimental results demonstrate the effectiveness of the proposed methodology. Considering structure-actuator interaction (SAI) is a key procedure in controller design especially for flexible structures.     

柔性机械臂的位置主动控制

采用一次近似模型对柔性机械臂的运动跟踪主动控制问题进行研究,控制策略采用最优跟踪控制方法。仿真结果显示,一次近似模型能够较好地对柔性机械臂的动力学行为进行描述,最优跟踪控制方法能使机械臂到达期望的指定位置,并可使机械臂的残余振动得到抑制。     

Adaptive fuzzy sliding mode control for a robotic aircraft flexible tooling system

A robotic aircraft flexible tooling system is proposed in this paper, of which high-precision synchronous motion control of dual robots is a key part. In order to alleviate the effects of the mechanical coupling over synchronous and tracking errors of the two robots, a cross-coupling scheme based on an adaptive fuzzy sliding mode controller (AFSMC) is developed. First, the mechanical coupling model is established by dynamics analysis of the dual-robot driving system. Then, a novel cross-coupling error is proposed, which combines both the position and speed tracking and synchronous errors of dual robots. Moreover, the cross-coupling control scheme based on AFSMC is presented. For the proposed AFSMC, a fuzzy logic controller is adopted to generate the hitting control signal, and the output gain of the sliding mode control is tuned online by a supervisory fuzzy system. Finally, the preferable performance of the proposed AFSMC cross-coupling approach is verified by the simulation results compared with the conventional proportional-integral-derivative control and SMC cross-coupling controls.     

一类多缸液压机的分散滑模控制

通过对一类锻造液压机的分析,在考虑多缸耦合情况下为其建立了非线性系统数学模型.将该模型视为非线性关联大系统,且将其转化为可控正则型,提出采用分散滑模控制理论对其进行滑模变结构控制.针对模型转换后控制方程中状态量与控制量同时具有关联性的特点,提出通过模拟求解一个多元一次方程组的方法,得到了基于指数趋近律的分散滑模控制律,有效解决了多缸耦合情况下控制律难于求解的问题.仿真结果表明,所设计的控制器使系统实现了高精度的位置跟踪,获得了较强的抗扰性,控制效果良好,且所提方法思路清晰,为同类模型的控制方案提供了参考.     

Adaptive backstepping slide mode control of pneumatic position servo system

With the price decreasing of the pneumatic proportional valve and the high performance micro controller, the simple structure and high tracking performance pneumatic servo system demonstrates more application potential in many fields. However, most existing control methods with high tracking performance need to know the model information and to use pressure sensor. This limits the application of the pneumatic servo system. An adaptive backstepping slide mode control method is proposed for pneumatic position servo system. The proposed method designs adaptive slide mode controller using backstepping design technique. The controller parameter adaptive law is derived from Lyapunov analysis to guarantee the stability of the system. A theorem is testified to show that the state of closed-loop system is uniformly bounded, and the closed-loop system is stable. The advantages of the proposed method include that system dynamic model parameters are not required for the controller design, uncertain parameters bounds are not need, and the bulk and expensive pressure sensor is not needed as well. Experimental results show that the designed controller can achieve better tracking performance, as compared with some existing methods.     

An Integral Sliding Model Tracking Strategy for 3D Laser Beam Position Control

This paper discusses how to improve the tracking precision of a laser beam positioning system by using a new sliding model tracking strategy. A continuous strategy of integral sliding mode control is proposed in order to achieve high-accuracy and high robustness of position tracking control. Modelling deviation and unmeasurable external disturbance is compen-sated for by an integral action term. This scheme can solve the chattering problem without loss of robustness and controaccuracy. The simulation and experimental results show that a laser beam position control system with the integrated sliding mode control (ISMC) has higher robustness, higher global stability, higher tracking precision, and speed than a traditional controller.     

基于趋近律离散滑模控制的柔性梁振动抑制

研究了基于趋近律的离散滑模控制在智能柔性悬臂梁振动控制中的应用.以压电陶瓷为作动器,电阻应变片为传感器,采用有限元方法和模态截断技术建立结构动力学模型.由于柔性结构系统受到不确定外部扰动和量测噪声的影响以及参数的不确定性,滑模变结构控制可以实现滑动模态与系统的外干扰和参数摄动无关,即滑动模态的不变性.结构振动控制在系统状态由于外部干扰的影响偏离平衡状态,在控制器作用下能使系统趋于零状态.采用趋近律离散滑模控制方法设计状态调节器.由于状态量不能直接测量,故利用离散卡尔曼滤波技术构造状态估计器.采用试验模态测试方法得到结构的前4阶固有频率和阻尼比,与有限元方法的结果比较,说明该模型的正确性.使用dSPACE实时仿真系统和MATLAB/Simulink搭建控制系统,进行了振动主动控制试验.试验结果表明,所设计的控制器能有效抑制结构的振动响应.     

Adaptive backstepping sliding mode control of flexible ball screw drives with time-varying parametric uncertainties and disturbances

This paper presents a method to model and design servo controllers for flexible ball screw drives with dynamic variations. A mathematical model describing the structural flexibility of the ball screw drive containing time-varying uncertainties and disturbances with unknown bounds is proposed. A mode-compensating adaptive backstepping sliding mode controller is designed to suppress the vibration. The time-varying uncertainties and disturbances represented in finite-term Fourier series can be estimated by updating the Fourier coefficients through function approximation technique. Adaptive laws are obtained from Lyapunov approach to guarantee the convergence and stability of the closed loop system. The simulation results indicate that the tracking accuracy is improved considerably with the proposed scheme when the time-varying parametric uncertainties and disturbances exist.     

载体位置、姿态均不受控的飘浮基柔性空间机器人的Terminal滑模控制

讨论了载体位置、姿态均不受控的飘浮基柔性空间机器人的Terminal滑模控制问题。为讨论既有柔性关节又有柔性臂的欠驱动系统,以一个具有两个柔性关节和一个柔性臂的飘浮基空间机器人为例,首先利用拉格朗日方程并结合系统总质心定义,得到了系统的动力学方程,然后利用奇异摄动法,将柔性空间机器人系统分解为一个柔性空间机械臂子系统和一个柔性关节快变子系统。以此为基础,提出了一种包含柔性空间机械臂子控制项和柔性关节快变子控制项的组合控制器。其中,柔性空间机械臂Terminal滑模子控制项实现了机械臂关节铰期望轨迹的跟踪,柔性关节快变子控制项使得快变子系统稳定在由柔性空间机械臂子控制项产生的机械臂关节轨迹上。系统的数值仿真结果表明,该方法能在抑制柔性关节的柔性振动的同时跟踪上机械臂关节期望轨迹。该控制方案的显著优点为不需要测量、反馈载体的位置、移动速度、移动加速度,同时可保证机械臂关节铰跟踪误差在任意指定有限时间内收敛到零。     

Measurement and correlation of high frequency behaviors of a very flexible beam undergoing large deformation

A correlation method of high frequency behaviors of a very flexible beam undergoing large displacement is presented. The suggested method based on the experimental modal analysis leads to more accurate correlation results because it directly uses the modal parameters of each mode achieved from experiment. First, the modal testing and the parameter identification method are suggested for flexible multibody dynamics. Due to the flexibility of a very thin beam, traditional testing methods such as impact hammer or contact type accelerometer are not working well. The suggested measurement with high speed camera, even though the test beam is very flexible, is working well. Using measurements with a high speed camera, modal properties until the 5th mode are measured. And After measuring each damping ratio until the 5th mode, a generic damping model is constructed using inverse modal transformation technique. It’s very interesting that the modal transformation technique can be also applied even in the ANCF simulation which uses the global displacement and finite slope as the nodal coordinates. The results of experiment and simulation are compared until the 5th mode frequency, respectively, by using ANCF forced vibration analysis. Through comparison between numerical simulation and experiment, this study showed that the proposed generic damping matrix, modal testing and parameter identification method is very proper in flexible multibody dynamic problems undergoing large deformation.     

液压柔性机械臂等效模型的鲁棒控制

针对液压柔性机械臂的等效动力学模型——柔性负载电液位置伺服系统,提出了滑模控制和自适应反演控制相结合的鲁棒控制器设计方法。基于Lyapunov稳定性理论的系统稳定性分析,证明系统跟踪误差将收敛至零,同时控制了柔性负载的振动。仿真实例表明了设计方法的正确性。     

Model reduction of a multibody system including a very flexible beam element

An optimum method to reduce the system size of a multibody system including a very flexible beam element is presented. In this paper, the absolute nodal coordinate formulation (ANCF) is used to describe the motion of the flexible beam in this system. Based on continuum mechanics approach, the bending stiffness matrix of the system is assumed to be a constant matrix when the axial strain is small. Thus, free-interface method, in which modal coordinate vector is free from the boundary region, is used to reduce the degrees of freedom of a flexible beam with sliding joints. Finally, two numerical examples are presented to verify the efficiency and accuracy of this method. The results show that the present method can reduce the computing time with precision. Meanwhile, a deformation energy criterion of mode truncation is established.     

A study of “mode selecting stochastic controller” for a dynamic system under random vibration

This paper presents a new stochastic controller applied on the vibration control system under irregular disturbances based on the mode selection scheme. Measured displacement and frequency characteristics are simultaneously used in designing a mode selecting controller. This technique is validated by applying to the suppression problem of a flexible beam with randomly vibrated circumstances. The presented method, called Mode Selecting Stochastic Controller, uses the frequency measurement of the flexible system based on a Fast-Fourier transformation algorithm. This controller is constructed by combining mode selection method with previous known Stochastic Controller in real time. Numerical simulations and several experiments are conducted to validate the proposed method. The performance of the proposed method is compared with a stochastic controller developed recently. This method was improved compared with previous one.     

Adaptive robust motion trajectory tracking control of pneumatic cylinders with LuGre model-based friction compensation

Friction compensation is particularly important for motion trajectory tracking control of pneumatic cylinders at low speed movement. However, most of the existing model-based friction compensation schemes use simple classical models, which are not enough to address applications with high-accuracy position requirements. Furthermore, the friction force in the cylinder is time-varying, and there exist rather severe unmodelled dynamics and unknown disturbances in the pneumatic system. To deal with these problems effectively, an adaptive robust controller with LuGre model-based dynamic friction compensation is constructed. The proposed controller employs on-line recursive least squares estimation（RLSE） to reduce the extent of parametric uncertainties, and utilizes the sliding mode control method to attenuate the effects of parameter estimation errors, unmodelled dynamics and disturbances. In addition, in order to realize LuGre model-based friction compensation, the modified dual-observer structure for estimating immeasurable friction internal state is developed. Therefore, a prescribed motion tracking transient performance and final tracking accuracy can be guaranteed. Since the system model uncertainties are unmatched, the recursive backstepping design technology is applied. In order to solve the conflicts between the sliding mode control design and the adaptive control design, the projection mapping is used to condition the RLSE algorithm so that the parameter estimates are kept within a known bounded convex set. Finally, the proposed controller is tested for tracking sinusoidal trajectories and smooth square trajectory under different loads and sudden disturbance. The testing results demonstrate that the achievable performance of the proposed controller is excellent and is much better than most other studies in literature. Especially when a 0.5 Hz sinusoidal trajectory is tracked, the maximum tracking error is 0.96 mm and the average tracking error is 0.45 mm. This paper constructs an adaptive robust controller     

基于改进扩展状态观测器的四旋翼无人机轨迹鲁棒跟踪控制

针对四旋翼无人机在轨迹跟踪过程中会受到内外部扰动、模型误差等不确定性因素的影响,本文提出了一种基于改进型扩展状态观测器的积分滑模控制方案。具体来讲,首先,将四旋翼无人机系统存在的模型误差以及内外部扰动等不确定性因素视作集总干扰,通过借鉴的改进扩展状态观测器对其进行观测;进而,在此基础上,进一步考虑四旋翼无人机系统控制的连续性,基于四旋翼无人机轨迹误差、速度误差、姿态角误差和姿态角速度误差设计积分滑模控制器,分析了系统的稳定性并分别进行了数值仿真和实机实验。结果表明,采用本文算法时,在数值仿真中,各状态跟踪误差不超过1%,跟踪精度最高;在实机实验中,位置跟踪误差总体上能控制在20%以下。因此,本文方法具备有效性和可行性。     

Vibration control of a frame structure using electro-rheological fluid mounts

A squeeze-mode electro-rheological (ER) mount has been designed, manufactured, and applied to the vibration control of a frame structure subjected to external excitations. After verifying that the damping force of the ER mount can be controlled by controlling the applied voltage, a frame structure system supported by spring mounts and the proposed ER mounts has been assembled. The governing equation of the structural system is derived in the modal coordinate and is rewritten as a state-space control model. An optimal controller, which consists of the velocity feedback signal of the frame structure and the force feedback signal transmitted from the exciting point to the mount position, is formulated in order to attenuate the imposed excitations. The controller has been optimized experimentally and control responses such as the acceleration of the frame structure and the transmitted force at each mount position are presented in both time and frequency domains.     

Robust current control-based generalized predictive control with sliding mode disturbance compensation for PMSM drives

This paper addresses the current control of permanent magnet synchronous motor (PMSM) for electric drives with model uncertainties and disturbances. A generalized predictive current control method combined with sliding mode disturbance compensation is proposed to satisfy the requirement of fast response and strong robustness. Firstly, according to the generalized predictive control (GPC) theory based on the continuous time model, a predictive current control method is presented without considering the disturbance, which is convenient to be realized in the digital controller. In fact, it's difficult to derive the exact motor model and parameters in the practical system. Thus, a sliding mode disturbance compensation controller is studied to improve the adaptiveness and robustness of the control system. The designed controller attempts to combine the merits of both predictive control and sliding mode control, meanwhile, the controller parameters are easy to be adjusted. Lastly, the proposed controller is tested on an interior PMSM by simulation and experiment, and the results indicate that it has good performance in both current tracking and disturbance rejection.     

Precision tracking control of a horizontal arm coordinate measuring machine in the presence of dynamic flexibilities

One of the major sources that affect measurement accuracy and limit the use of high motion speeds in coordinate measuring machines (CMM) is the position error. In fact, static and dynamic probe errors are more direct factors in measuring machine accuracy, but are not the subject of this research. However the accuracy of acquisition of component position errors using a CMM in motion is also of importance, hence the dynamics of a CMM need to be considered. Therefore, this research aims to model the dynamics of a horizontal arm CMM by considering drive flexibility at joints and evaluates the characteristics of the system for fine motion control purposes. Design of a precision tracking controller (PTC) to perform superior tracking for enhancing the measurement accuracy and the probing speed in providing less inspection time at high motion speeds is carried out. A dynamic model for the CMM is developed including drive flexibilities represented with lumped springs at the joints. Due to the non-collocated nature of the control scheme in the flexible CMM dynamics, a non-minimum phase system is observed in the proposed CMM model. Using the derived CMM model with joint flexibilities, tracking motion control simulations are conducted at different probing speeds for the cases where a PI controller and a feedback PTC are employed. A comparison of the PI controller with the feedback PTC is also performed. Results demonstrate that the effects of joint flexibilities on the contour error and probing speeds are significant and the PI controller is not capable of providing good accuracy during challenging tasks such as corner tracking. However, the simulation results indicated that by using the proposed feedback precision tracking controller, contour errors in corner tracking that are caused by joint flexibilities can be reduced effectively .