Explicit and Iterative LQG Controller Design

This dissertation presents two new LQG controller designs, namely, explicit and iterative designs. For the explicit design, the explicit solutions to the corresponding Riccati equations of controller design for large structures with collocated rate sensors and actuators are derived. Numerically solving the Riccati equations for state feedback and state estimation is no longer required. Since the number of design parameters for either state feedback or state estimation equals the number of controlled modes, the performance of each mode can be easily adjusted. NASA\u27s Spacecraft COntrol Laboratory Experiment (SCOLE) configuration is used to demonstrate the effectiveness of the explicit design. For the iterative design, a closed-loop identification method is developed for identifying an open-loop system and Kalman filter gain when the system is under closed-loop operation. The iterative controller design basically consists of the closed-loop identification and state-feedback redesign cycle. In each cycle, the identification is used to identify the open-loop model and Kalman filter. The identified Kalman filter can be directly used for state estimation so that the noise statistics are no longer needed to be detected. The identified model is then used to redesign the state feedback. The state feedback and the identified Kalman filter are used to form an updated LQG controller for next cycle. This iterative process continues until the updated controller converges. Since the updated model is identified under the previous controller, the effect of the controller on noise statistics is automatically taken into account. NASA\u27s Large-Angle Magnetic Suspension Test Facility (LAMSTF) is used to validate the iterative design