Multiobjective design of actively controlled structures using a hybrid optimization method

A multiobjective approach to the combined structure and control optimization problem for flexible space structures is presented. The proposed formulation addresses robustness considerations for controller design, as well as a simultaneous determination of optimum actuator locations. The structural weight, controlled system energy, stability robustness index and damping augmentation provided by the active controller are considered as objective functions of the multiobjective problem which is solved using a cooperative game-theoretic approach. The actuator locations and the cross-sectional areas of structural members are treated as design variables. Since the actuator locations are spatially discrete, whereas the cross-sectional areas are continuous, the optimization problem has mixed discrete-continuous design variables. A solution approach to this problem based on a hybrid optimization scheme is presented. The hybrid optimizer is a synergetic blend of artificial genetic search and gradient-based search techniques. The computational procedure is demonstrated through the design of an ACOSS-FOUR space structure. The optimum solutions obtained using the hybrid optimizer are shown to outperform the optimum results obtained using gradient-based search techniques.     

Simultaneous optimal design of structural topology, actuator locations and control parameters for a plate structure

 Simultaneous optimization with respect to the structural topology, actuator locations and control parameters of an actively controlled plate structure is investigated in this paper. The system consists of a clamped-free plate, a H ₂ controller and four surface-bonded piezoelectric actuators utilized for suppressing the bending and torsional vibrations induced by external disturbances. The plate is represented by a rectangular design domain which is discretized by a regular finite element mesh and for each element the parameter indicating the presence or absence of material is used as a topology design variable. Due to the unavailability of large-scale 0–1 optimization algorithms, the binary variables of the original topology design problem are relaxed so that they can take all values between 0 and 1. The popular techniques in the topology optimization area including penalization, filtering and perimeter restriction are also used to suppress numerical problems such as intermediate thickness, checkerboards, and mesh dependence. Moreover, since it is not efficient to treat the structural and control design variables equally within the same framework, a nested solving approach is adopted in which the controller syntheses are considered as sub processes included in the main optimization process dealing with the structural topology and actuator locations. The structural and actuator variables are solved in the main optimization by the method of moving asymptotes, while the control parameters are designed in the sub optimization processes by solving the Ricatti equations. Numerical examples show that the approach used in this paper can produce systems with clear structural topology and high control performance. Received 16 November 2001 / Accepted 26 February 2002     

A simultaneous approach for compliance minimization and piezoelectric actuator design considering the polarization profile

This article addresses the compliance problem along with the piezoelectric actuator design for active vibration control. The topology structural design is obtained by solving a compliance minimization problem with volume constraint, whereas the actuator design is carried out by the maximization of a control performance index written in terms of the controllability Gramian. This measure describes the ability of the actuator to move the structure from an initial condition to a desired final state, at rest for instance, in a finite time interval. The actuator design is also characterized by the polarization profile, which is defined according to the distribution of an additional design variable. Therefore, the actuators can yield both tensile and compressing fields at different points of the structure using the same applied control voltage. To achieve this goal, a material interpolation scheme based on the solid isotropic material with penalization and the piezoelectric material with penalization and polarization (PEMAP-P) models is employed, and both the optimum structure/actuator layout and polarization profile are obtained simultaneously. The sensitivities with respect to the polarization and design variables are calculated analytically. Numerical examples are presented considering the design and vibration control for a cantilever beam, a beam fixed at both ends, and an L-bracket structure to show the efficiency of the proposed formulation. The control performance of the designed structures are analyzed employing a linear-quadratic regulator simulation, and these results are compared to verify the influence of the optimized polarization profiles.     

Application of a Genetic Algorithm on the Assessment of the Capabilities of Cctuator Systems for Laser Mircro Adjustment

Laser forming with actuator systems is a very attractive process to meet the rising demand for accuracy in micro system technology. However, the actuator systems have to be designed specifically for the given adjustment task. A computer assisted design system for actuator systems for laser based micro adjustment has been developed which supports the designer by creating a number of optimized design choices from a starting design. A multiobjective genetic algorithm has been successfully applied to this task. The algorithm for evaluation of adjustment capability of the actuator system uses another single objective genetic algorithm to determine the forming capability of the actuator system. The approach is similar to the inverse kinematics algorithm used in robotics but also considers elastic forming. The irradiated components of the actuator system are treated as robotic links for which the amount of laser based forming are the link parameter. An elastic structural mechanic simulation of the actuator system with beam elements calculates the resulting adjustment movement of the actuator system. The research performed to develop a configuration of this algorithm specifically to the needs of actuator system design evaluation is presented in this paper.     

DESIGN OF STRUCTURE CONTROL SYSTEM USING BOUNDED LQG

An approach for designing a structure and its control system for vibration suppression is presented. The control system is based on the Linear Quadratic Gaussian (LQG) and is modified to allow bounds on the actuators forces to simulate real actuators. The simultaneous design of the structure and control problem is formulated as a nonlinear optimization problem. The system is designed for minimum weight where the weight includes both the weight of the structure and the weight of the actuators. The weight of an actuator is assumed to be proportional to the bound on the maximum force that it can supply. The design variables include the cross-sectional areas of the structural members and the bounds on the actuator forces. The constraints are imposed on the closed loop frequency distribution and the time to reduce the energy of vibration to a small portion of the initial vibrational energy of the system. The structure is analyzed using a finite element approach. For illustration of the design approach, a truss structure idealized with rod elements is used.     

A computational method for optimal structural design II: Continuous problems

A method for solving structural design problems that allows a continuous distribution of material along structural elements is presented. The method is an extension of the generalized steepest descent method presented in Reference 1. Inequality constraints on design variables, displacement, natural frequency, and buckling are explicitly treated and a minimum weight cost function is employed. A steepest descent method for boundary-value state equations is developed and a computational algorithm is given. Several example problems in minimum weight structural design are solved and compared with results obtained by discretization techniques.     

Optimal shapes of PZT actuators for laminated structures subjected to displacement or eigenfrequency constraints

In this paper, dynamics, electromechanical couplings, and control of piezoelectric laminated cylindrical shells and rectangular plates are investigated. It is assumed that the piezoelectric layers are distributed on the top and bottom surfaces of the structures. First of all the governing equations and boundary conditions including elastic and piezoelectric couplings are formulated and solutions are derived. Then control of the plate/shells deflections and natural frequencies using high control voltages are studied in order to optimize the structural response. The present formulation of optimal design introduces boundaries of piezoelectric patches as new class of design variables. In addition, classical design variables in the form of ply orientation angles of orthotropic layers are also taken into account. For the actuator/actuator configuration, it was shown that the piezoelectric actuators can significantly reduce deformations/eigenfrequencies of the composite plate. Those effects were dependent on the value of the applied voltage. It was demonstrated that the proper choice of the actuator area is more efficient in reducing deflections/eigenfrequencies. The accuracy of optimal design are verified both with the aid of the FE package ABAQUS and using the standard Rayleigh-Ritz method. The results concerning active vibration control for axisymmetric cylindrical shells are also discussed.     

Experimental study on control fins of a small flying vehicle using piezo-composite actuators

A camber morphing control fin design and an all-moving control fin design using piezo-composite unimorph actuators are presented in this paper. The control fin of a small flying object is usually actuated using a servo motor system with an electromagnetic motor. Much research has been conducted to solve the structural complexity of servo actuation systems to convert the rotation of a servo motor to a linear actuation motion. To simplify this structural complexity, several types of smart actuators have been developed, such as bimorph or unimorph actuators with piezoelectric material layers and shape memory alloy actuators. In this study, a camber morphing type control fin and an all-moving type control fin actuated using piezo-composite actuators are designed to evaluate their ability to simplify the structural complexity of the gear transmission and electromagnetic servo motor system or hydraulic actuator system. Within the skin of the control fin, a piezo-composite actuator is mounted and the other end inserted in a slot of the control fin. As the piezo-composite actuator is excited by an electric field, the pitch angle of the control fin is changed. Experimental testing for the pitch rotation angle of a control fin in a 450 V electric field showed the deflection angle of the camber morphing control fin was 1.4° and the rotational angle of the all-moving control fin was 5.4°, which is obtained from the rotation angle magnification linkage structural system.     

Shape morphing of laminated composite structures with photostrictive actuators via topology optimization

In this paper, a new design method is presented for achieving remote wireless shape morphing of laminated composite structures using topology optimization methods. A recently emerging family of smart materials, photostrictive materials, is introduced as the actuation discipline to implement the active control of optical structures by utilizing the photostriction mechanism, which arises from the superposition of photovoltaic effect and converse piezoelectric effect when exposed to the illumination of near ultraviolet light. In terms of the Mindlin plate theory of first-order shear deformation, a finite element formulation including multiphysics effects of photovoltaic, pyroelectric and thermal expansion is developed to model composite structures of ferroelectric materials polarized in 0–1 and 0–3 directions, respectively. The design is formulated as a multi-constrained optimization problem with a least square objective function to minimize structural shape errors. The topology optimization method is used as a systematic design approach to seek the optimal topologies of material layouts for both the photostrictive and host layers as well as the actuator light distribution. In terms of design sensitivity analysis, many gradient-based optimization algorithms can be applied to solve the problem effectively. Numerical examples are presented to demonstrate the effectiveness of this method in the field of active photonic control of laminated composite structures.     

Integrated optimization of structure and control for piezoelectric intelligent trusses with uncertain placement of actuators and sensors

The finite element modeling of truss structures with piezoelectric members is presented. Based on the approach of independent modal space control, the controllability and observability indices of the system related to the positions of actuators/sensors are demonstrated. Consequently, the effective damping response time is evaluated. The object of the optimization model is to minimize a specified performance index of the intelligent truss subjected to constraints on the natural frequency and the amplitude of displacement response as well as the applied voltages under a given disturbance. Structural sizing variables, control parameters and actuator/sensor placements are treated as the independent design variables. Coding, the calculation of fitness and the optimization procedure of Genetic Algorithms are discussed so as to solve the integrated optimization with two different types of design variable space: discrete and continuous. Numerical examples are presented to show the effectiveness and usefulness of integrated optimization of structure and control for piezoelectric intelligent trusses.The authors would like to thank for the support by Natural Science Foundation of China under grant 10072050 and the Doctorate Creation Foundation of Northwestern Polytechnical University under grant 200236.     

Simultaneous optimization of controlled structures

A formulation is presented for finding the combined optimal design of a structural system and its control by defining a composite objective function as a linear combination of two components; a structural objective and a control objective. When the structural objective is a function of the structural design variables only, and when the control objective is represented by the quadratic functional of the response and control energy, it is possible to analytically express the optimal control in terms of any set of admissible structural design variables. Such expression for the optimal control is used recursively in an iterative Newton-Raphson search scheme, the goal of which is to determine the corresponding optimal set of structural design variables that minimize the combined objective function. A numerical example is given to illustrate the computational procedure. The results indicate that significant improvement of the combined optimal design can be achieved over the traditional separate optimization.The research described in this paper was performed by the Jet Propulsion Laboratory, California Institute of Technology, and was sponsored by the Air Force Wright Aeronautical Laboratories, Wright-Patterson Air Force Base, Ohio, through an agreement with the National Aeronautics and Space Administration     

振动控制传感器／作动器的数目和位置优化设计

提出一种确定传感器、作动器的数目和优化设计传感器、作动器位置的方法。以独立模态最优控制方法为基础,将模态控制力、作动器作动力和传感器测量的信号处理为随机变量,分别建立了模态控制力能量、作动器作动力能量的自相关矩阵的测量信号的能量自相关矩阵。进一步通过作动力能量的自相关矩阵的和测量信号的能量自相关矩阵包含的能量分别确定了作动器和传感器的数目。在此基础上,建立了基于控制系统作动力消耗能量最小和传感器测量信号能量最大,分别设计了控制系统的作动器和传感器的最优位置。通过数值算例证明了该方法的有效性。     

考虑作动器联接方式的结构形状控制优化

以压电材料梁式作动器控制复合材料层合板形状的设计问题为对象,研究有限个独立控制参数条件下的形状最优控制问题。研究了作动器与信号发生器(独立控制参数)联接关系的参数化描述方式,建立了作动器联接方式与控制参数协同设计的问题提法;针对优化问题中离散变量(联接方式描述参数)和连续变量(控制参数)共存的特点,建立了遗传算法和线性最小二乘(Linear Least Square,LLS)方法相结合的求解策略和方法;在响应分析所采用的有限元模型中,采用粘结层单元描述本体结构与作动器之间的连接。复合材料层合板形状控制设计的实例,验证了该文中建立的问题提法、优化模型和求解策略的有效性。     

Design sensitivity analysis of non-linear structural systems part I: Theory

A unified approach is presented for design sensitivity analysis of non-linear structural systems that include truss, beam, plane elastic solid and plate components. Both geometric and material non-linearities are treated. Sizing design variables, such as thickness and cross-sectional areas of components of individual members and built-up structures, are considered. A distributed parameter structural design sensitivity analysis approach is used that retains the continuum elasticity formulation throughout the derivation of design sensitivity analysis results. Using this approach and an adjoint variable method, expressions for design sensitivity in terms of design variations are derived in the continuous setting which can be evaluated numerically using analysis results of finite element analysis. Both total Lagrangian and updated Lagrangian formulations in non-linear analysis of solid mechanics are used for design sensitivity analysis. Numerical implementation of design sensitivity analysis results using existing finite element code will be presented in Part II of this paper.     

基于0-3方向极化的PLZT作动器的开口圆柱壳的主动振动控制

基于理论分析及实验研究建立了沿0-3方向极化的PLZT光致伸缩作动器产生的光致应变随光照时间动态响应的本构方程,研究了光照强度、PLZT作动器的厚度与作动器产生的饱和光致应变及时间常数的关系。在此基础上研究了能产生非均匀控制力/力矩的新型四区域光致伸缩作动器对开口圆柱壳的主动振动控制。针对光致伸缩作动器产生驱动应变的特点,设计了速度反馈定光强半周期控制的控制策略,仿真结果表明,所提出的主动控制策略可以有效地抑制圆柱壳的振动。通过与沿0-1方向极化的PLZT作动器对比表明,由于沿0-3方向极化的PLZT作动器响应速度快,在相同光强下对圆柱壳的控制效果更好,且光照强度赿大控制效果越好。     

Shape optimization using the boundary element method with substructuring

Applications of the boundary element method for two- and three-dimensional structural shape optimization are presented. The displacements and stresses are computed using the boundary element method. Sub-structuring is used to isolate the portion of the structure undergoing geometric change. The corresponding non-linear programming problem for the optimization is solved by the generalized reduced gradient method. B-spline curves and surfaces are introduced to describe the shape of the design. The control points on these curves or surfaces are selected as design variables. The design objective may be either to minimize the weight or a peak stress of the component by determining the optimum shape subject to geometrical and stress constraints. The use of substructuring allows for problem solution without requiring traditional simplifications such as linearization of the constraints. The method has been successfully applied to the structural shape optimization of plane stress, plane strain and three-dimensional elasticity problems.     

A proximate-time-optimal-control design and its application to a hard disk drive dual-stage actuator system

We propose a compensator-based strategy for design of a track-seeking and track-following control system for a dual-stage servo actuator in hard disk drives. A well-known decoupling structure is employed to disconnect the control of the primary voice coil motor (VCM) actuator from the loop for a secondary high-bandwidth actuator. The compensator is placed in the secondary loop and suitably combined with a saturation nonlinearity in order to obtain actuator signal boundedness. The design procedure consists of four steps: 1) design of an established nonlinear seek-settle-track following controller for the VCM; 2) design of a linear track following controller for the secondary actuator; 3) observer design; and 4) design of a compensator to retain global stability and to improve performance. The proposed control system improves performance of both long-span seeking (proximate-time-optimal controller) and short-span seeking. In addition, it achieves high-bandwidth track following performance. The experimental results show good track-following performance, and short-span/long-span-seeking performance with fast settling time. The overshoot during track seeking can be made negligible for a suitably tuned VCM-actuator control loop.     

压电智能结构的一种模态控制新方法

提出了一个用于压电智能结构振动控制的模态控制方法。就智能梁给出了压电模态传感器与压电模态致动器的新设计方法以及相应的模态控制方法，并对相应的观测溢出与控制溢出问题进行了分析，给出了抑制这些溢出的措施。     

结构主动控制的一体化多目标优化研究

基于Pareto多目标遗传算法提出了结构主动控制系统的一体化多目标优化设计方法,对作动器位置与主动控制器进行同步优化设计.外界激励采用平稳过滤白噪声来模拟,在状态空间下通过求解Lyapunov方程,得到结构响应和主动控制力的均方值.主动控制器采用LQG控制算法来进行设计.以结构位移和加速度均方值最大值与相应无控响应均方值的最大值之比,以及所需控制力均方值之和作为多目标同步优化的目标函数.优化过程还考虑了结构与激励参数对优化结果的影响.最后以某6层平面框架有限元模型为例进行了计算机仿真分析,结果表明所提出的主动控制系统多目标一体化优化方法简单,高效,实用,具有较好的普适性.     

微振动主动隔振平台的超磁致伸缩驱动器设计

对三自由度微振动主动隔振平台的基础器件--超磁致伸缩驱动器（GMA）和放大机构进行结构参数的优化设计。基于对GMA系统从能量输入到输出整个过程的电-磁-机械耦合特性分析,提出了结构的能量损耗率最小的优化方法。结构参数优化后的GMA能量损耗率仅为优化前的0.34倍。将优化结果带入驱动系统动力学模型,优化后的位移响应幅值增大为优化前的2.28倍,初始时刻的冲击加速度响应减小为优化前的0.11倍。仿真结果表明基于能量损耗率最小的超磁致伸缩驱动系统的优化设计方法有效,设计结果满足微振动隔振平台对GMA及放大机构的驱动稳定性、驱动效率、驱动幅值的设计要求。