Unified control/structure design and modeling research

To demonstrate the applicability of the control theory for distributed systems to large flexible space structures, research was focused on a model of a space antenna which consists of a rigid hub, flexible ribs, and a mesh reflecting surface. The space antenna model used is discussed along with the finite element approximation of the distributed model. The basic control problem is to design an optimal or near-optimal compensator to suppress the linear vibrations and rigid-body displacements of the structure. The application of an infinite dimensional Linear Quadratic Gaussian (LQG) control theory to flexible structure is discussed. Two basic approaches for robustness enhancement were investigated: loop transfer recovery and sensitivity optimization. A third approach synthesized from elements of these two basic approaches is currently under development. The control driven finite element approximation of flexible structures is discussed. Three sets of finite element basic vectors for computing functional control gains are compared. The possibility of constructing a finite element scheme to approximate the infinite dimensional Hamiltonian system directly, instead of indirectly is discussed

An analytical sensitivity method for use in integrated aeroservoelastic aircraft design

Interdisciplinary analysis capabilities have been developed for aeroservoelastic aircraft and large flexible spacecraft, but the requisite integrated design methods are only beginning to be developed. One integrated design method which has received attention is based on hierarchal problem decompositions, optimization, and design sensitivity analyses. This paper highlights a design sensitivity analysis method for Linear Quadratic Gaussian (LQG) optimal control laws, enabling the use of LQG techniques in the hierarchal design methodology. The LQG sensitivity analysis method calculates the change in the optimal control law and resulting controlled system responses due to changes in fixed design integration parameters using analytical sensitivity equations. Numerical results of a LQG design sensitivity analysis for a realistic aeroservoelastic aircraft example are presented. In this example, the sensitivity of the optimal control law and aircraft response for various parameters such as wing bending natural frequency is determined. The sensitivity results computed from the analytical expressions are used to estimate changes in response resulting from changes in the parameters. Comparisons of the estimates with exact calculated responses show they are reasonably accurate for + or - 15 percent changes in the parameters. Evaluation of the analytical expressions is computationally faster than equivalent finite difference calculations

Sensitivity method for integrated structure/active control law design

The development is described of an integrated structure/active control law design methodology for aeroelastic aircraft applications. A short motivating introduction to aeroservoelasticity is given along with the need for integrated structures/controls design algorithms. Three alternative approaches to development of an integrated design method are briefly discussed with regards to complexity, coordination and tradeoff strategies, and the nature of the resulting solutions. This leads to the formulation of the proposed approach which is based on the concepts of sensitivity of optimum solutions and multi-level decompositions. The concept of sensitivity of optimum is explained in more detail and compared with traditional sensitivity concepts of classical control theory. The analytical sensitivity expressions for the solution of the linear, quadratic cost, Gaussian (LQG) control problem are summarized in terms of the linear regulator solution and the Kalman Filter solution. Numerical results for a state space aeroelastic model of the DAST ARW-II vehicle are given, showing the changes in aircraft responses to variations of a structural parameter, in this case first wing bending natural frequency

Space shuttle active-pogo-suppressor control design using linear quadratic regulator techniques

Two methods of active pogo suppression (stabilization) for the space shuttle vehicle were studied analytically. The basis for both approaches was the linear quadratic regulator, state space technique. The first approach minimized root-mean-square pump inlet pressure by using either fullstate feedback, partial-state feedback, or output feedback with a Kalman filter. The second approach increased the modal damping associated with the critical structural modes by using either full-state feedback or reconstructed state feedback. A number of implementable controls were found by both approaches. The designs were analyzed with respect to sensitivity, complexity, and controller energy requirements, as well as controller performance. Practical controllers resulting from the two design approaches tended to use pressure and flow as feedback variables for the minimum-rms method and structural accelerations or velocities for the modal control method. Both approaches are suitable for the design of active pogo-suppression controllers

Results of an integrated structure/control law design sensitivity analysis

A design sensitivity analysis method for Linear Quadratic Cost, Gaussian (LQG) optimal control laws, which predicts change in the optimal control law due to changes in fixed problem parameters using analytical sensitivity equations is discussed. Numerical results of a design sensitivity analysis for a realistic aeroservoelastic aircraft example are presented. In this example, the sensitivity of the optimally controlled aircraft's response to various problem formulation and physical aircraft parameters is determined. These results are used to predict the aircraft's new optimally controlled response if the parameter was to have some other nominal value during the control law design process. The sensitivity results are validated by recomputing the optimal control law for discrete variations in parameters, computing the new actual aircraft response, and comparing with the predicted response. These results show an improvement in sensitivity accuracy for integrated design purposes over methods which do not include changes in the optimal control law. Use of the analytical LQG sensitivity expressions is also shown to be more efficient than finite difference methods for the computation of the equivalent sensitivity information

Maximum Entropy/Optimal Projection (MEOP) control design synthesis: Optimal quantification of the major design tradeoffs

The underlying philosophy and motivation of the optimal projection/maximum entropy (OP/ME) stochastic modeling and reduced control design methodology for high order systems with parameter uncertainties are discussed. The OP/ME design equations for reduced-order dynamic compensation including the effect of parameter uncertainties are reviewed. The application of the methodology to several Large Space Structures (LSS) problems of representative complexity is illustrated