The performance requirements of spacecraft missions are usually specified in terms of root-mean-squared (rms) values on both the input and output variables. The rms contribution of each input or output in the overall system performance metric is called the "input" or "output" cost. A technique is derived that allows a linear controller to assign each of the multi-input or output costs. The procedure is illustrated by the design and shape control for NASA's 64-m Hoop-Column Antenna subject to power-limited actuators. By assigning only the output costs rather than the input costs, the procedure serves to determine the power required of the actuators (required input costs) to achieve the mission requirements (specified output costs). This determination of actuator sizing (and location) for the control of flexible structures is an important feature of the method.

Space structure control design by variance assignment

Procedures are discussed for selecting closed loop eigenvalues and eigenvectors to achieve desired transient response behavior. The admissible eigenvector subspace is defined with basis vectors calculated using a singular value decomposition. These vectors are optimally combined to 1) minimize the vector element errors between desired and achievable eigenvectors, or 2) blend the control effort to exactly place desired eigenvectors, or 3) a combined optimization. Appropriate transmission zeros reveal tradeoffs between eigenvalue and eigenvector placement. Modal control ls used to realize the eigenspace placement goals using output feedback and user supplied compensation. Two aerospace examples demonstrate techniques for achieving desired response characteristics consistent with conventional design specifications.

Eigenspace selection procedures for closed loop response shaping with modal control

Fast and accurate tracking control of a flexible one-link robot based on real-time link deflection measurements

A multivariable synthesis procedure based on eigenvalue/eigenvector assignment is reviewed and is employed to develop a systematic design procedure to meet the lateral handling qualities design objectives of a fighter aircraft over a wide range of flight conditions. The closed loop modal characterization developed provides significant insight into the design process and plays a pivotal role in the synthesis of robust feedback systems. The simplicity of the synthesis algorithm yields an efficient computer aided interactive design tool for flight control system synthesis.

/pdf/modal-control-theory-and-application-to-aircraft-lateral-zr00lolgtq.pdf

Modal control theory and application to aircraft lateral handling qualities design

Chapter C4 - Tools indices for dynamic I/O-controllability assessment control structure selection

: This is the final report on a multi-year research program to bridge the gap between modern control theory and practical control system design. The results of the total program are summarized and the last year's results are described in detail. Characterizations of optimal linear controls have been derived, from which guides for selecting the structure of the control system and the weights in the performance index were developed, so that optimal controls meeting conventional design specifications can be designed for single-input systems. For multi-input systems a method of selecting weights for the performance index on the basis of desired closed-loop modal properties and system bandwidth was developed. For such systems it was also found that optimal controls which use state estimators have no guaranteed stability margins, and a method was developed for adjusting the state estimator design so that good margins could be obtained. It was also found that single-loop stability margins in multi-input systems were inadequate measures of robustness, the quality of stability being preserved for a class of perturbations of system characteristics. A new measure of robustness expressed in terms of singular values was developed which is a valid generalization of the concept of stability margins for single-input systems. A method for estimating bounds on system perturbations in terms of singular values associated with parameter uncertainties and unmodeled dynamics, including some forms of nonlinearities, is described in detail in this report. Illustrative examples have been treated in each phase of the program. In this report such an example is presented, demonstrating the se of singular value analysis in design.

Optimal Linear Control.

: This report presents results on characterizations of optimal multi-input systems. The major results are: (1) equivalence of quadratic state weighting to quadratic weighting of m responses where m is the dimension of the input, (2) characterization of quadratic performance indexes in terms of asymptotic eigenvalues and eigenvectors, (3) characterization of the effects of compensators on high frequency attenuation, and (4) development of a procedure for constructing quadratic performance indexes based on modal design specifications. (Author)

G. Stein

Papers

Optimal Linear Control.

Optimal Linear Control (Characterization of Multi-Input Systems).