Thomas E. Alberts

Multivariable Transfer Functions for a Slewing Piezoelectric Laminate Beam

In this paper a distributed parameter model of a slewing beam system with piezoelectric actuators and sensors is considered. The system has a torque motor at a pinned (proximal) end, an endpoint motion sensor at the distal end, and patches of thin piezoelectric laminates attached to its surface. The partial differential equation of motion for this system is transformed to Laplace domain transfer functions after application of the appropriate boundary conditions. Transfer functions relating the various actuator/sensor pairs are developed. The results are shown to reduce to previously known results which are special cases of the system under consideration. Examples and experimental results are presented using a beam experiment at the US Air Force, Frank J. Seiler Research Laboratory.

Force control of a multi-arm robot system

Kinematic resolved-rate control is extended to the coordinated control of multiple robot arms cooperatively manipulating a single object. To provide the capability to control the forces applied to the jointly manipulated body and to the external environment, a force feedback loop is closed around the system. This results in a multiarm realization of the damping control method. The problem of redundancy in determining the distribution of loads among the manipulators is handled by minimizing a quadratic cost function in task-space force and torque. A coordinate system structure is described that permits manipulator control relative to a control reference frame which may be independent of the base coordinate systems of the respective manipulators and of the world reference system.<<ETX>>

Observations on the Nature of Transfer Functions for Control of Piezoelectric Laminates

In this paper, some fundamental relationships for beams incorporating piezoelectric film actuators and sensors are examined. The differential equation of motion for a beam with piezoelectric film bonded to both sides is used to develop Laplace domain transfer function models of the system. These transfer functions are exact Laplace domain representations of the system equations of motion. The transfer functions are cast into a closed rational form using Maclaurin series expansions representing a specific number of modes. In this form, the transfer functions lend themselves to classical control analysis. It is shown that the transfer function relating a voltage applied to a full coverage actuating layer, to the voltage induced in a full coverage sensing layer on the opposite beam face, be haves like a classic colocated system with alternating poles and zeros and accordingly the system is easy to stabilize with low order compensation. In contrast to this result, it is shown that in spite of the effective colocation of actuator and sensor in the case of the transfer function from actuating voltage to tip position, the desirable alternating pole/zero pattern is not exbibited due to incompatibility of actuating and sensing signals. This result is verified experimentally.

Dynamic analysis to evaluate viscoelastic passive damping augmentation for the Space Shuttle Remote Manipulator System

This paper presents a NASTRAN finite element analysis for evaluation of the effectiveness of viscoelastic damping treatments as passive controls for large flexible space manipulators. The passive damping could be used alone or as an augmentation to active control. Perhaps the best existing example of a practical flexible manipulator is the space shuttle Remote Manipulator System (RMS). The authors use the RMS as an example for this investigation, subjecting it to a detailed dynamic analysis which can be used to evaluate the critical modes for control and to distinguish the modes which are good candidates for active control from those which are well suited for passive control. Modal potential energy analysis (MPE) is used to examine the modal energy distribution in each structural member of the complex flexible chained system. The results indicate that the most dominant contributors to end-point oscillations fall into two categories. These include very low frequency modes due to joint flexibility and higher frequency modes due to bending in the booms. Significant end-point motions result from each category, but the most significant motions are associated with joint flexibility. Finally, a finite element analysis is performed to evaluate the effectiveness of constrained viscoelastic layer damping treatments for passive vibration control. Passive damping augmentation is introduced through the use of a constrained viscoelastic layer damping treatment applied to the surface of the manipulator’s flexible booms. It is shown that even the joint compliance dominated modes can be damped to some degree through appropriate design of the treatment.

Experimental verification of transfer functions for a slewing piezoelectric laminate beam

Abstract This paper presents the development and experimental verification of a distributed parameter model for a slewing beam system with piezoelectric actuators and sensors. The beam is pinned at the proximal end, an endpoint motion sensor is attached at the distal end, and patches of thin piezoelectric laminates attached to its surface. The differential equation of motion for this system is transformed to Laplace domain transfer functions after application of the appropriate boundary conditions. Transfer functions relating the various actuator/sensor pairs are presented. Experimental results, which verify the model, are presented using a beam experiment at the US Air Force Academy, Frank J. Seiler Research Laboratory.

Dissipative Controllers for Nonlinear Multibody Flexible Space Systems

The problem of controlling a class of nonlinear multibody flexible space systems is considered. The system configuration consists of a flexible central body to which a number of flexible articulated appendages are attached, resulting in highly nonlinear dynamics. Assuming collocated actuators and sensors, global asymptotic stability of such systems is established using a nonlinear passivity-based control law. In addition, a special case where the central-body motion is small while the appendages can undergo unlimited motion, it is shown that the system, although highly nonlinear, can be stabilized by linear static and dynamic dissipative control laws. Furthermore, the static dissipative control law preserves stability despite actuator and sensor nonlinearities of certain types. In all cases, the stability does not depend on the knowledge of the model and hence is robust to modeling errors and uncertainties. The results are applicable to a broad class of systems, such as flexible multilink manipulators and multipayload space platforms. The stability proofs use the Lyapunov approach and exploit the inherent passivity of such systems.

Design and Analysis of Fiber Enhanced Viscoelastic Damping Polymers

A new composite damping material is investigated, which consists of a viscoelastic matrix and high elastic modulus fiber inclusions. This fiber enhanced viscoelastic damping polymer is intended to be applied to lightweight flexible structures as a surface treatment for passive vibration control. A desirable packing geometry for the composite material is proposed, which is expected to produce maximum shear strain in the viscoelastic damping matrix. Subsequently, a micromechanical model is established in which the effect of fiber segment length and relative motion between neighboring fibers are taken into account. Based on this model, closed form expressions for the effective storage and loss properties of the damping material are developed, and an optimal relation between design parameters, such as the length, diameter spacing, and Youngs modulus of fibers and the shear modulus of viscoelastic matrix, is derived for achieving maximum damping performance. To address the verification of the development, the theoretical results are compared with NASTRANfinite element results. Upon comparison of an enhanced viscoelastic damping treatment with a conventionally constrained layer damping treatment, it is found that the enhanced polymer provides a significant improvement in damping performance.

Stable levitation control of magnetically suspended vehicles with structural flexibility

This paper presents a simple analysis evaluating the stability threshold for magnetically levitated flexible structures using dissipative collocated controllers. It is shown that with such a control structure, the controller that stabilizes a rigid levitated mass can also stabilize a flexible structure with the same overall mass and electrodynamics. This principle has been experimentally demonstrated on flexible single and multi- magnet levitation systems.

Vibration analysis using symbolic computation software

This paper presents a general approach to modelling and learning vibration analysis for simple beams using symbolic computation software. The emphasis here is on the fact that a complete solution of the beam vibrations problem, for different boundary conditions and arbitrary forcing functions, is made very simple by using symbolic computation software. The heart of the procedure is to convert the beam vibration problem into a system of simultaneous algebraic linear equations and then use symbolic computation software to solve it. The analysis also shows how to obtain models suitable to design controllers for flexible systems.

Broadband dynamic modification using feedforward control

Recently published results arising from the acoustic noise control research community, demonstrate that system dynamics can be modified using feedforward control. Initial investigations applied to known disturbances in the form of steady-state harmonic excitation. This paper further explores feedforward dynamic modification, provides a proof of the nature of the modification, extends the method to allow for broadband excitation, and introduces a design technique for arbitrary assignment of transfer function poles. The results apply to any structure representable using modal expansion, and are applicable to systems with nonminimum phase zeros.