Robert E. Scheid

Combined control-structural optimization

ConclusionsAn approach for combined control-structure optimization keyed to enhancing early design trade-offs has been outlined and illustrated by numerical examples. The approach employs a homotopic strategy and appears to be effective for generating families of designs that can be used in these early trade studies.Analytical results were obtained for classes of structure/control objectives with LQG and LQR costs. For these, we have demonstrated that global optima can be computed for small values of the homotopy parameter. Conditions for local optima along the homotopy path were also given. Details of three numerical examples employing the LQR control cost were given showing variations of the optimal design variables along the homotopy path. The results of the second example suggest that introducing a second homotopy parameter relating the two parts of the control index in the LQG/LQR formulation might serve to enlarge the family of Pareto optima, but its effect on modifying the optimal structural shapes may be analogous to the original parameter λ.

Frequency Domain Identification for Robust Large Space Structure Control Design

A methodology is demonstrated for synthesizing robust H¿ controllers directly from raw experimental data. The method is applicable to on-orbit identification and control of large flexible structures in space.

Fast parallel Preconditioned Conjugate Gradient algorithms for robot manipulator dynamics simulation

In this paper fast parallel Preconditioned Conjugate Gradient (PCG) algorithms for robot manipulator forward dynamics, or dynamic simulation, problem are presented. By exploiting the inherent structure of the forward dynamics problem, suitable preconditioners are devised to accelerate the iterations. Also, based on the choice of preconditioners, a modified dynamic formulation is used to speedup both serial and parallel computation of each iteration. The implementation of the parallel algorithms on two interconnected processor arrays is discussed and their computation and communication complexities are analyzed. The simulation results for a Puma Arm are presented to illustrate the effectiveness of the proposed preconditioners. With a faster convergence due to preconditioning and a faster computation of iterations due to parallelization, the developed parallel PCG algorithms represent the fastest alternative for parallel computation of the problem withO(n) processors.

A Hankel singular value approach for identification of low level dynamics in flexible structures

The intensity of dynamics in a flexible structure is characterized by its Hankel singular values. Low level dynamics may be caused by generic properties of a structure or by its actuator and sensor configurations. In the latter case, it is shown that the dynamics can significantly be amplified by small perturbations of actuator and/or sensor configurations. In the presented examples, the variations of sensor configuration of 0.05 or less caused an increase of Hankel singular values of order 1000. This approach is useful for model reduction and model order determination in the presence of noise.<<ETX>>

Factorization and the synthesis of optimal feedback kernels for differential-delay systems

In this paper a combination of ideas from the theories of operator Riccati equations and Volterra factorizations leads to the derivation of a new and relatively simple set of hyperbolic equations which characterize the optimal feedback kernel for the finite-time regulator problem for autonomous differential-delay systems. Analysis of these equations elucidates the underlying structure of the feedback kernel and leads to the development of fast and accurate numerical methods for its computation. Unlike traditional formulations based on the operator Riccati equation, the gain is characterized by means of classical solutions of the derived set of equations. This leads to the development of approximation schemes which are analagous to what has been accomplished for systems of ordinary differential equations with given initial conditions.