Topology optimization of frame structures with flexible joints

A method for structural topology optimization of frame structures with flexible joints is presented. A typical frame structure is a set of beams and joints assembled to carry an applied load. The problem considered in this paper is to find the stiffest frame for a given mass. By introducing design variables for beams and joints, a mass distribution for optimal structural stiffness can be found. Each beam can have several design variables connected to its cross section. One of these is an area-type design variable which is used to represent the global size of the beam. The other design variables are of length ratio type, controlling the cross section of the beam. Joints are flexible elements connecting the beams in the structure. Each joint has stiffness properties and a mass. A framework for modelling these stiffnesses is presented and design variables for joints are introduced. We prove a theorem which can be interpreted as the fact that the removal of structural elements, e.g. joints or beams, can be modelled by a small strictly positive material amount assigned to the element. This is needed for the computations of sensitivities used in the applied gradient based iterative method. Both two and three dimensional problems, as well as multiple load cases and multiple mass constraints, are treated.     

Active vibration control of flexible structures using delayed position feedback

The paper discusses the use of a simple position control system approach to improve the performance of lightly damped dynamic systems. This approach uses a delayed position feedback signal to actively control the vibrations of flexible structures. A complete analysis of the stability of a single-link flexible manipulator under time delay control is presented and critical values of time delay for a given controller gain have been determined. The paper also presents a short comparison between the delayed feedback signal control and the linear quadratic regulator.     

Intelligent fault-tolerant system of vibration control for flexible structures

This paper describes an intelligent fault-tolerant control method for vibration control of flexible structures. We consider a case where the fault phenomena of the control system for flexible structures can be treated as a change of system parameters. Therefore, the adaptive control method can be applied to a vibration control system for flexible structures with a fault. In this paper, a neural network (NN) adaptive control system is used to compensate for the change in the parameters of a plant with a fault. When the characteristics of the plant and of a nominal model have been agreed by a NN adaptive control system, the control method designed for the nominal model, such as decoupling feedback control or linearizing feedback control, can be used even if the change in the system parameters has been caused by a fault. To confirm the effectiveness of the proposed fault-tolerant control method, the simulational results from a 5-link robotic arm are shown at the end of the paper. This work was presented, in part, at the Fourth International Symposium on Artificial Life and Robotics, Oita, Japan, January 19–22, 1999     

Dynamic modelling, simulation and control of a manipulator with flexible links and joints

The paper presents a dynamic modelling technique for a manipulator with multiple flexible links and flexible joints, based on a combined Euler–Lagrange formulation and assumed modes method. The resulting generalised model is validated through computer simulations by considering a simplified case study of a two-link flexible manipulator with joint elasticity. Controlling such a manipulator is more complex than controlling one with rigid joints because only a single actuation signal can be applied at each joint and this has to control the flexure of both the joint itself and the link attached to it. To resolve the control complexities associated with such an under-actuated flexible link/flexible joint manipulator, a singularly perturbed model has been formulated and used to design a reduced-order controller. This is shown to stabilise the link and joint vibrations effectively while maintaining good tracking performance.     

Lyapunov analysis of the approximate motion equations of flexible structures

In this paper, the effectiveness of the approximate motion equations of a flexible structure, obtained by the RitzKantorovich method, is analysed by using Lyapunov functions. The analysis, which is restricted to the case of a single flexible beam for the sake of simplicity, is carried out under the assumption that a partial dissipation is present, affecting only the first degrees of freedom of the system. By means of suitable Lyapunov functions, an overbounding estimate of the quadratic approximation error is determined as a decreasing function of the approximation order. The analysis is completed by considering the two ‘extreme’ cases: the theoretical absence of dissipation and the presence of structural dissipation, affecting all the infinite degrees of freedom.     

A self-organizing fuzzy logic controller for the active control of flexible structures using piezoelectric actuators

This paper proposes an on-line self-organizing fuzzy logic controller (FLC) design applied to the control of vibrations in flexible structures containing distributed piezoelectric actuator patches. In this methodology, the fuzzy rules are generated using the history of input/output (I/O) pairs without using any plant model. The generated rules are stored in the fuzzy rule space and updated on-line by a self-organizing procedure. The validity of the proposed fuzzy logic control has been demonstrated experimentally in a steel cantilever test beam and a set of experimental tests are made in the system to verify the efficiency of the on-line self-organizing fuzzy controller.     

Metamorphic development: a new topology optimization method for continuum structures

An effective optimization procedure for finding structural shapes and topologies that minimize structural compliance and weight subject to stress and deflection constraints is presented. This new approach, called “Metamorphic Development” (MD), can allow a structure to grow and degenerate towards an optimum topological layout. In this method, the optimization can start from the simplest possible geometry (layout) or any degree of development of the structure rather than from a complex ground mesh. The structure is then developed metamorphically using rectangular and triangular elements that can be of any specified sizes. Examples demonstrate the potential of the MD optimization procedure to generate innovative solutions to structural design problems. Results are given and the growth and degeneration histories during optimization are illustrated. Received August 20, 1999     

Robust control of flexible structures with stable bandpass controllers

In this paper, a control law for the active vibration control of mechanical flexible systems is considered. The proposed strategy minimizes an index and results in a stable stabilizing controller with bandpass frequency shape, due to the presence of zeros at the origin. The control authority is thus effective in a chosen band of frequency, resulting in a selective broadband control action, as opposed to narrow-band (tonal) vibration reduction. Moreover, the explicit closed-form solution of the controller is also obtained, thus avoiding numerical calculation of the solution of the Riccati equations, which can be ill-conditioned in the case of very high-order, poorly damped flexible systems. The parametrization of all the controllers is also given and a family of controllers with the above properties is deduced. The case is also obtained as a byproduct. The controller is based on a colocated actuators/sensors pair strategy and numerical simulations are presented, showing the robustness of the proposed approach even for systems with zero damping. Finally, experimental results on a skin panel of a Boeing 717 aircraft also prove the effectiveness of the proposed approach in practical complex applications, with global vibration reduction performances.     

考虑间隙运动副的桁架单胞等效建模与分析

本文主要研究了含间隙运动副桁架单胞的等效建模方法.主要考虑了桁架单胞的等效刚度问题以及阻尼问题.首先从间隙铰链开始研究,提出全面的铰链模型;其次提出用位移法将桁架单胞等效成板,即把桁架单胞看成是由梁元组成的钢架结构,运用平面钢架位移法得出桁架单胞的等效刚度矩阵,进而得出结构的整体固有频率和等效后的板的刚度矩阵.最后用有限元软件ANSYS对单胞结构在不同边界条件下进行了模态分析,将在自由边界条件下的固有频率和解析得出的频率做了对比,发现二者有很好的吻合度.结果表明由于间隙运动副的存在,使得桁架单胞结构的刚度降低,柔性增强.     

Automatic routing of flexible 1D components with functional and manufacturing constraints

This article presents a novel and unifying method for routing of flexible one-dimensional components such as cables, hoses and pipes with geometric design constraints. A deterministic and resolution complete grid search is used to find a nominal configuration of the component that is collision-free and satisfies functional and manufacturing constraints. Local refinement is done in tandem with a computationally efficient and physically accurate simulation model based on Cosserat rod theory to ensure that the deformed configuration still satisfies functional constraints when influenced by gravity. Test results show that the method is able to solve industrial scenarios involving complex geometries and real constraints with different objectives in mere seconds.     

Vibration control of a flexible aerial refuelling hose with input saturation

In this study, we consider a boundary control problem of a flexible aerial refuelling hose in the presence of input saturation. To provide an accurate and concise representation of the hose's behaviour, the flexible hose is modelled as a distributed parameter system described by partial differential equations (PDEs). By using the backstepping method, a boundary control scheme is proposed based on the original PDEs to regulate the hose's vibration. An auxiliary system based on a smooth hyperbolic function and a Nussbaum function is designed to handle the effect of the input saturation. Then based on Lyapunov's direct method, the state of the system is proven to converge to a small neighbourhood of zero by appropriately choosing design parameters. Finally, the results are illustrated using numerical simulations for control performance verification.     

Optimization of a complex flexible multibody systems with composite materials

The paper presents a general optimization methodology for flexible multibody systems which is demonstrated to find optimal layouts of fiber composite structures components. The goal of the optimization process is to minimize the structural deformation and, simultaneously, to fulfill a set of multidisciplinary constraints, by finding the optimal values for the fiber orientation of composite structures. In this work, a general formulation for the computation of the first order analytical sensitivities based on the use of automatic differentiation tools is applied. A critical overview on the use of the sensitivities obtained by automatic differentiation against analytical sensitivities derived and implemented by hand is made with the purpose of identifying shortcomings and proposing solutions. The equations of motion and sensitivities of the flexible multibody system are solved simultaneously being the accelerations and velocities of the system and the sensitivities of the accelerations and of the velocities integrated in time using a multi-step multi-order integration algorithm. Then, the optimal design of the flexible multibody system is formulated to minimize the deformation energy of the system subjected to a set of technological and functional constraints. The methodologies proposed are first discussed for a simple demonstrative example and applied after to the optimization of a complex flexible multibody system, represented by a satellite antenna that is unfolded from its launching configuration to its functional state.     

Boundary feedback stabilisation of a flexible robotic manipulator with constraint

In this paper, the flexible robotic manipulator is modelled as a distributed parameter system, represented by a group of partial differential equations and ordinary differential equations. Control is designed at the boundary of the robotic manipulator based on integral-barrier Lyapunov function to suppress the vibration of the elastic deflection and track the desired angular position. With the proposed boundary control, the manipulator can be driven to the desired set-point with angular position and elastic deflection stay under the former setting constraint. Uniformed boundedness of the closed-loop system under the unknown time-varying disturbance is achieved. Stability analysis of the closed-loop system is given by employing the Lyapunov stability theory. Simulation results illustrate the effectiveness of the proposed boundary controller for ensuring output constraint and suppressing vibrations.     

Buckling design optimization of complex built-up structures with shape and size variables

The design optimization of buckling behaviour is studied for complex built-up structures composed of various kinds of elements and implemented within JIFEX95, a general-purpose software for finite element analysis and design optimization. The direct and adjoint methods of sensitivity analysis for critical buckling loads are presented with detailed computational procedures. Particularly, the variations of prebuckling stresses and external loads have been accounted for. The design model and solution methods presented in this paper are available for both shape and size optimization, and buckling optimization can also be combined with static, frequency and dynamic response optimization. The numerical examples show the applications of the buckling optimization method and the effectiveness of the methods and the program of this paper. Received February 23, 1999     

Structural optimization of modular product families with application to car space frame structures

This paper extends classical structural optimization from single-product optimization to optimization of a whole family of products that have common modules. It integrates the family commonality problem with the finite element models of the structures. A general mathematical frame where optimization is seen as a balance between cost and performance is given. The most obvious cost function is mass, while performance is taken to be a weighted sum of compliances. As a case study, a car product family consisting of three products is presented. These three products are a base model, a seven-seat version, and a pickup version. The study shows how optimal results are effected by requiring modules to be shared between products. Loads emanating from prescribed acceleration fields that simulate crash situations are used. This is a proof-of-concept paper which is a first step toward including more general manufacturing costs than mass and performance measures other than compliance.     

Design and analysis of a flexible robotic hand with soft fingers and a changeable palm

This study describes the design of a novel flexible robotic hand that can adapt its configurations to different grasping demands. Firstly, a mathematical model, based on the Yeoh strain energy function and virtual work principle, is established to investigate deformation properties of the designed soft finger. To achieve a flexible grasping capability, a changeable palm is presented with its variable configurations in terms of target objects with different sizes and shapes. A kinematic model of the flexible robotic hand is established, and then the numerical simulations based on the Monte-Carlo method and Matlab is applied to analyse the workspace of the hand and address the parameter optimisation problem of the rigid-flexible coupled system. Furthermore, an optimised grasping strategy on the basis of the principle of optimal efficiency is proposed to obtain an optimal grasping pose for the target object. Finally, a prototype is developed and tested in a laboratory to demonstrate the feasibility and effectiveness of our proposed hand. The results of practical experiments show that the robotic hand cannot only stably grasp objects with different sizes and shapes but also flexibly manipulate soft and fragile ones.     

Distributed control of a class of flexible mechanical systems with global constraint

In this paper, the constrained problem is investigated for both flexible string model and Euler–Bernoulli beam model with the tip payload, based on an infinite dimensional generalisation of a distributed control method. The control objectives are to develop the control law so that the motion of flexible mechanical systems can track a desired reference signal, and ensure that the string or beam remain in a constrained space. We prove that, with the proposed control, the tracking error is exponentially stable without violation of the constraint. The proof of convergence is based on an Integral-Barrier Lyapunov Function (IBLF), and extensive simulations are provided to illustrate the performance of the control system.     

Proportional derivative and strain (PDS) boundary feedback control of a flexible space structure with a closed-loop chain mechanism

A simple space truss structure, a rigid connection of two flexible beams, is modeled as a distributed parameter system subject to holonomic constraints. Boundary feedback control synthesis is developed for this structure. The synthesis is carried out in the infinite-dimensional setting, mathematical features of which give rise to a stabilizing PDS control algorithm. Due to simplicity of the implementation, the algorithm becomes extremely attractive under limitations on the computer power in the space. The effectiveness of the control strategy proposed is supported by experimental tests.     

Robust adaptive boundary control of a flexible marine riser with vessel dynamics

In this paper, robust adaptive boundary control for a flexible marine riser with vessel dynamics is developed to suppress the riser’s vibration. To provide an accurate and concise representation of the riser’s dynamic behavior, the flexible marine riser with vessel dynamics is described by a distributed parameter system with a partial differential equation (PDE) and four ordinary differential equations (ODEs). Boundary control is proposed at the top boundary of the riser based on Lyapunov’s direct method to regulate the riser’s vibration. Adaptive control is designed when the system parametric uncertainty exists. With the proposed robust adaptive boundary control, uniform boundedness under the ocean current disturbance can be achieved. The proposed control is implementable with actual instrumentation since all the required signals in the control can be measured by sensors or calculated by a backward difference algorithm. The state of the system is proven to converge to a small neighborhood of zero by appropriately choosing design parameters. Simulations are provided to illustrate the applicability and effectiveness of the proposed control.