Development and experimental validation of direct controller tuning for spaceborne telescopes

Abstract

Strict requirements in the performance of future space-based observatories such as the Space Interferometry Mission (SIM) and the Next Generation Space Telescope (NGST), will extend the state-of-the-art of critical mission spaceflight-proven active control design. A control design strategy, which combines the high performance and stability robustness guarantees of modem, robust-control design with the spaceflight heritage of conventional control design, is proposed which will meet the strict requirements and maintain traceability to the successful controllers from predecessor spacecraft. Two principal tools are developed: an analysis algorithm that quantifies each sensor/actuator combination's effectiveness for control, and a design engine which tunes a baseline controller to improve performance and/or stability robustness. The sensor/actuator effectiveness indexing tool requires a reduced-order state-space model of the plant. A modification of the balanced reduction method is introduced which improves numerical conditioning so that the order of large models of flexible spacecraft may be decreased. For each sensor and actuator an index is computed using the modal controllability from an actuator weighted by the modal cost in the performance, and the model observability of a sensor weighted by the modal cost of the disturbance. The special case of actuators that are used for active output isolation is handled separately. The designer makes use of the sensor/actuator indexing tool to select which control channels to emphasize in the tuning. The tuning tool is based on forming an augmented cost from weighting performance, stability robustness, deviation from the baseline controller, and controller gain. The tuning algorithm can operate with the plant's state-space design model or directly with the plant's measured frequency-response data. Two differentiable multivariable stability robustness metrics are formed, one based on the maximum singular value of the Sensitivity transfer matrix and one based on the multivariable Nyquist locus. The controller is parameterized with a general tridiagonal parameterization based on the real-modal state-space form. The augmented cost is chosen to be differentiable and a closed-loop stability-preserving unconstrained nonlinear descent program is used to directly compute controller parameters that decrease the augmented cost. To automate the closed-loop stability determination in the measured-data-based designs, a rule-based algorithm is created to invoke the multivariable Nyquist stability criteria. The use of the tuning technique is placed in context with a high-level control design methodology. The tuning technique is evaluated on a sample problem and then experimentally demonstrated on a laboratory test article with dynamics, sensor suite, and actuator suite all similar to future spaceborne observatories. The developed test article is the first spacetelescope- like experimental facility to combine large-angle slewing with nanometer optical phasing and sub-arcsecond pointing in the presence of spacecraft-like disturbances. The technique is applied to generate an improved controller for a model of the SIM spacecraft.