Maximum principle for optimal control of vibrations of a dynamic Gao beam in contact with a rigid foundation

In our preceding paper, we studied an optimal control problem of vibrations of a dynamic Gao beam in contact with a reactive foundation and derived the Pontryagin maximum principle for the controlled system in fixed final horizon case. As a follow-up, in this paper, we focus on the investigation of the Gao beam that may come in contact with a rigid foundation underneath it. In this case, the nonlinear viscoelastic beam equation is equipped with the Signorini condition. By the Dubovitskii and Milyutin functional analytical approach, we investigate the new optimal control problem with multiple inequality constraints and present further original results of current interests.     

On the optimal design of elastic beams

In this paper we investigate the optimal dynamics of simply supported nonlinearly elastic beams with rectangular cross-sections. We consider the elastic beam under the assumption of time-dependent intensive transverse loading. The state of the beam is described by a system of partial differential equations of the fourth order. We deal with the problem of choosing the optimal shape for the beam. The optimal shape is determined in such a way that the deflection of the nonlinearly elastic beam for any given time is minimal. The problem of choosing the optimal shape is formulated as an optimal control problem. To solve the obtained problem effectively, we use the optimality principle of Bellman (Bellman and Dreyfus 1962; Bryson and Ho 1975) and the penalty function method (Polyak 1987). We present a constructive algorithm for the optimal design of nonlinearly elastic beams. Some simple examples of the implementation of the proposed numerical algorithm are given.     

Optimal tilt lifting of beams as a min-max problem

This paper considers the problem of finding the optimal pickup points for a beam that is to be tilt lifted by a system of slings attached to a crane. Under the assumptions of a rigid beam and inextensible cables, this task is formulated as a min-max optimization problem. As for its numerical solution, we propose an efficient and robust algorithm involving smoothing and an appropriate discretization of the objective function. A typical numerical example is provided to illustrate the approach.     

Boundary control of a circular curved beam using active disturbance rejection control

In this paper, boundary stabilisation of vibration of a circular curved beam in the presence of exogenous disturbances using active disturbance rejection control is addressed. Based on the Euler–Bernoulli beam theory, the vibration of the inextensible curved beam including a tip mass is governed by a sixth-order partial differential equation (PDE) with dynamic boundary conditions. Based on the considered PDE, linear boundary control is introduced that exponentially stabilises the beam without disturbance. Furthermore, to control the beam under exogenous disturbances, the established linear control is enhanced by adding the estimates of disturbances. This is achieved by first designing an extended state observer that estimates the external disturbances using the beam vibration at the controlled end. The stability of the closed-loop system in the sense of Lyapunov is analysed based on the PDE model. Using the Faedo–Galerkin method combined with the compactness argument, it is shown the closed-loop system is well-posed. The efficacy of the suggested method is illustrated using simulation results.     

多线程技术在LIA中两路束流测量的实现

强流脉冲电子束作为一种高亮度的光源,具有广阔的应用前景,而双轴束流测量的控制对于研究产生电子束的加速器技术具有重要意义;利用多线程技术在CVI环境下的实现方法,研究了双路束流参数特点、双路束流测量的时序同步控制方法,在此基础上采用线程池多线程技术实现基于TCP/IP的加速器束流测量的数据采集软件;结果表明采用多线程技术可以很好地实现多任务的同时工作,有助于提高束测量的响应速度和测量的执行效率。     

Optimal control of large space structures governed by a coupled system of ordinary and partial differential equations

In this paper we consider the problem of optimal regulation of large space structures in the presence of flexible appendages. For simplicity of presentation, we consider a spacecraft consisting of a rigid bus and a flexible beam. The complete dynamics of the system is given by a coupled set of ordinary and partial differential equations. We show that the solution of this hybrid system is defined in a product space of appropriate finite- and infinite-dimensional spaces. We develop necessary conditions for determining the control torque and forces for optimal regulation of attitude maneuvers of the satellite along with simultaneous suppression of elastic vibrations of the flexible beam.     

Optimal tracking control of a flexible hub–beam system with time delay

In this paper, a new technique of time-delay compensation is proposed for active control of a flexible hub–beam system. The first-order approximation coupling (FOAC) model proposed recently for dynamics of hub–beam systems is used to verify the applicability of this technique. The FOAC model is first linearized to obtain a linearized equation. The linearized equation with time delay is then transformed into a standard form with no time delay by a particular integral transformation. The time-delay controller is designed based on this standard equation using the classical optimal tracking control theory. Since the controller is a function of modal coordinates, a modal filter is presented to estimate the modal coordinates from physical sensor measurements. The effectiveness of the proposed technique for time delay is demonstrated by numerical simulations. Simulation results indicate that a very small time delay may result in instability of the control system if it is not compensated in control design. The proposed time-delay controller is effective in controlling the system even when the maximum time delay for stability without time-delay compensation is greatly exceeded. Moreover, for the system without time delay, the proposed time-delay controller may possibly obtain much better control effectiveness than the controller without time delay.     

Boundary control of a Timoshenko beam system with input dead-zone

In this paper, boundary control is designed for a Timoshenko beam system with the input dead-zone. By the Hamilton’s principle, the dynamics of the Timoshenko beam system is represented by a distributed parameter model with two partial differential equations and four ordinary differential equations. The bounded part is separated from the input dead-zone and then forms the disturbance-like term together with the boundary disturbance, which finally acts on the Timoshenko beam system. Boundary control, based on the Lyapunov’s direct method, is proposed to ensure the Timoshenko beam converge into a small neighbourhood of zero, where stability of the system is also analysed. Besides, the existence and uniqueness of the solution of the Timoshenko beam system are proved. Simulations are provided to reveal the applicability and effectiveness of the proposed control scheme.     

Optimal control of thermoelastic beam vibrations by piezoelectric actuation

This paper presents the vibrations suppression of a thermoelastic beam subject to sudden heat input by a single piezoelectric actuator. An optimization problem is formulated as the minimization of a quadratic functional in terms of displacement and velocity at a given time and with the least control effort. The solution method is based on a combination of modal expansion and variational approaches. The modal expansion approach is used to convert the optimal control of distributed parameter system into the optimal control of lumped parameter system. By utilizing the variational approach, an explicit optimal control law is derived and the determination of the corresponding displacement and velocity is reduced to solving a set of ordinary differential equations. Numerical results are presented to demonstrate the effectiveness and the applicability of the proposed method.     

Stabilization and shape control of a 1D piezoelectric Timoshenko beam

In this paper we show how to perform stabilization and shape control for a finite dimensional model that recasts the dynamics of an inflatable space reflector in port-Hamiltonian (pH) form. We show how to derive a decentralized passivity-based controller which can be used to stabilize a 1D piezoelectric Timoshenko beam around a desired shape. Furthermore, we present simulation results obtained for the proposed decentralized control approach.     

柔性臂振动系统角速度反馈控制的最优指数衰减率问题

讨论柔性臂的端点角速度反馈控制问题。通过对系统特征值和特征函数的渐近表示式的进一步研究,用特征扰动的Payley-Wiener稳定性理论,证明了该系统的最优指数衰减率可由系统的谱来确定。     

束搜索算法的精度优化研究

启发式爬山搜索算法能高效地实现搜索剪枝,求解实际问题时,能在庞大的假设空间中,找到最优或近似最优解,束搜索算法保持了爬山搜索算法的高效剪枝特性,同时能有效减小爬山搜索收敛到局部最优解的风险,人工智能领域广泛采用束搜索策略。对于宽度为k的束搜索,由于只维持有限的k条搜索路径,提高束搜索算法的搜索精度,重在这k条路径的选择上,但如何选取这k条路径,作者未见描述相关方法的资料,目前多数算法是在每一搜索步选取具有最大启发式性能量度值的k个候选作为进一步搜索的入口。论文简要讨论了束搜索算法,提出了几种合理的候选选取方法以及避免单亲填满的思想,并在UCI测试数据库上进行了对比实验,给出了实验结果。     

悬臂梁参数辨识及PD控制器的设计

首先介绍了用一种实验方法辨识悬臂梁的参数,建立其数学模型。然后基于此模型,利用控制理论并结合Matlab仿真设计了PD控制器。在Matlab中对基于PD控制器的控制系统进行仿真,获得了很好的仿真结果。用实时仿真系统dSPACE实现仿真模型与硬件装置的连接,利用压电陶瓷作为传感器和驱动器,建立了实验系统。实验结果表明,建立的数学模型比较接近实际的悬臂梁对象,设计的PD控制器能较好地抑制悬臂梁的振动。     

索-梁耦合结构的分岔反控制研究

斜拉索是斜拉桥主要的支撑单元,是斜拉桥的重要组成部分.本文研究了控制增益参数G对索-梁耦合结构的振动控制.利用文献已得到的索-梁耦合结构的面内非线性运动微分方程,根据离散法,对其进行分离变量法处理,进而得到索-梁耦合结构的单自由度和两自由度模态方程.不同于以往的研究,本文假设索(梁)的左支撑点即坐标原点处是可以沿纵向方向自由移动的,则索的动态应变会发生改变,进而改变其模态方程一次项系数,通过这一规律可以在理论上转换得到一套状态控制反馈准则,并根据Floquet稳定性理论,将上述方程转换为Hill方程形式.然后通过摄动法,得到运动微分方程的稳定解.最后对索-梁耦合结构的单自由度和两自由度系统进行了数值分析计算,通过改变反馈控制增益系数,可以实现系统的反控制.而设计者可以通过这些复杂现象的参数变化范围设计选择合适的参数,尽量使得系统能在工程师所能控制的安全范围内振动.这种控制策略保持了系统的平衡,并且可以应用于在期望位置处具有最优稳定性的退化倍周期分岔.研究表示,无论结构是单自由度还是两自由度系统,反馈控制增益系数的变化能明显有效地改变系统的共振情形下的幅值.通过适当调整控制参数,能在预先...     

大直径电子束束斑质心精确定位方法研究

强流脉冲电子束作为一种高亮度的光源,具有广阔的应用前景,而电子束的质心位置的控制对于研究产生电子束的加速器技术具有重要意义;针对短脉冲电子束位置的时间变化测量要求,研究了一种对数据本底、噪声相对不敏感的束斑质心位置的计算方法,该方法在结合传统的质心法的基础上,再利用不同数据区计算质心时得到的多条中心轨迹曲线的交点位置来判断质心位置,大大地降低了对数据质量的要求,最重要的是解决了从单次计算结果给出准确数据时存在较大误差以及易于受到各种不利因素如噪声、数据截断等影响的问题;对于扩展型电子束光斑的质心位置,即使存在较大噪声时,计算误差仍可小于0.5像素。     

Stability of a nonuniform Rayleigh beam with indefinite damping

This is a continuation of our earlier work [J.M. Wang, G.Q. Xu, S.P. Yung, Exponential stability for variable coefficients Rayleigh beams under boundary feedback control: a Riesz basis approach, Systems Control Lett. 51 (1) (2004) 33–50] on the study of a nonhomogeneous Rayleigh beam and this time the stabilization is achieved via an internal damping instead of the boundary feedbacks. We continue to address a conjecture of Guo [Basis property of a Rayleigh beam with boundary stabilization, J. Optim. Theory Appl. 112(3) (2002) 529–547] in this paper and demonstrate how the damping term can affect the decay rate asymptotically. By a detailed spectral analysis, we obtain a necessary condition for the stability and establish the Riesz basis property as well as the spectrum determined growth condition for the system. Furthermore, when the damping is indefinite, we provide a condition on how “negative” the damping can be without destroying the exponential stability.     

步进式加热炉炉温优化设定模型及软件开发

针对线材厂步进式加热炉实际工况，提出了基于经验规则的炉温优化设定模型和在线自学习获取知识的思想，并以炉温优化设定模型为核心，开发出加热炉计算机控制系统的优化运行软件。     

柔性悬臂梁非线性非平面运动的多脉冲轨道分析

首先建立了柔性悬臂梁非线性非平面运动的偏微分方程;然后运用Galerkin和多尺度方法得到平均方程．并利用规范形理论进一步将方程化简;最后用能量相位法求出多脉冲跳跃的能量函数序列．Dynamics软件数值计算表明：在系统中确实存在着由多脉冲跳跃而导致的Smale马蹄型混沌．     

Numerical simulations of cantilever beam response with saturation control and full modal coupling

Numerical simulations of the response of a uniform, cantilever beam subjected to a base excitation are performed. A saturation absorber is implemented to control the beam response. In previous investigations of similar configurations, the inertial and structural properties of the piezoelectric actuators have been neglected, resulting in an analytical model of a uniform beam. This investigation includes the nonuniformities in the beam properties that are introduced when piezoelectric actuators are bonded to the uniform beam. The resulting coupling between uniform, cantilever beam modes is fully included in the analytical model. It is shown that this modal coupling has a significant effect on the beam response, which is not present when modal coupling is neglected.     

Exponential stability of variable coefficients Rayleigh beams under boundary feedback controls: a Riesz basis approach

In this paper, we study the boundary stabilizing feedback control problem of Rayleigh beams that have non-homogeneous spatial parameters. We show that no matter how non-homogeneous the Rayleigh beam is, as long as it has positive mass density, stiffness and mass moment of inertia, it can always be exponentially stabilized when the control parameters are properly chosen. The main steps are a detail asymptotic analysis of the spectrum of the system and the proving of that the generalized eigenfunctions of the feedback control system form a Riesz basis in the state Hilbert space. As a by-product, a conjecture in Guo (J. Optim. Theory Appl. 112(3) (2002) 529) is answered.