Min-Hung Hsiao

INDIRECT IDENTIFICATION OF LINEAR STOCHASTIC SYSTEMS WITH KNOWN FEEDBACK DYNAMICS

An algorithm is presented for identifying a state-space model of linear stochastic systems operating under known feedback controller. In this algorithm, only the reference input and output of closed-loop data are required. No feedback signal needs to be recorded. The overall dosed-loop system dynamics is first identified. Then a recursive formulation is derived to compute the open.loop plant dynamics from the identified rinsed-loop system dynamics and known feedback controller dynamics. The controller can be a dynamic or constant-gain full-state feedback controller. Numerical simulations and test data of a highly unstable large-gap magnetic suspension system are presented to demonstrate the feasibility of this indirect identification method.

Iterative LQG Controller Design Through Closed-Loop Identification

This paper presents an iterative Linear Quadratic Gaussian (LQG) controller design approach for a linear stochastic system with an uncertain open-loop model and unknown noise statistics. This approach consists of closed-loop identification and controller redesign cycles. In each cycle, the closed-loop identification method is used to identify an open-loop model and a steady-state Kalman filter gain from closed-loop input/output test data obtained by using a feedback LQG controller designed from the previous cycle. Then the identified open-loop model is used to redesign the state feedback. The state feedback and the identified Kalman filter gain are used to form an updated LQC controller for the next cycle. This iterative process continues until the updated controller converges. The proposed controller design is demonstrated by numerical simulations and experiments on a highly unstable large-gap magnetic suspension system.

Identification of Stochastic System and Controller via Projection Filters

A method based on projection filters is presented for identifying an open-loop stochastic system with an existing feedback controller. The projection filters are derived from the relationship between the state-space model and the AutoRegressive with eXogeneous input (ARX) model including the system, Kalman filter and controller. Two ARX models are identified from the control input, closed-loop system response and feedback signal using least-squares method. Markov parameters of the open-loop system, Kalman filter and controller are then calculated from the coefficients of the identified ARX models. Finally, the state-space model of the open-loop stochastic system and the gain matrices for the Kalman filter and controller are realized. The method is validated by simulations and test data from an unstable large-angle magnetic suspension test facility.

Identification of linear stochastic systems from closed-loop data with known feedback dynamics

A method is presented for identifying a linear statespace model of an open-loop stochastic system from closed-loop excitation and output data with a known feedback controller. For unstable systems, feedback control is required for identification to ensure overall system stability. For stable systems, feedback control may also be used to enhance the damping and thus shorten the input/output data required for identification. If a known dynamic output feedback controller is used, the closed-loop system and Kalman filter Markov parameters (i.e. pulse response samples) are first obtained from closed-loop input/output data Then the open-loop system and Kalman filter Markov parameters can be calculated through a recursive formulation derived by using z-transform. If a known constant-gain full-state feedback controller is used, the identification procedure is simpler. The closed-loop system matrices are identified and then used to compute the open-loop system matrices after removing the control gain. An experimental example is provided to demonstrate the proposed closed-loop system identification method.

Identification of stochastic system and controller via projection filters

A method based on projection filters is presented for identifying an open-loop stochastic system with an existing feedback controller. The projection filters are derived from the relationship between the state-space model and the autoregressive with exogeneous input (ARX) model including the system, Kalman filter and controller. Two ARX models are identified from the control input, closed-loop system response and feedback signal using least-squares method. Markov parameters of the open-loop system, Kalman filter and controller are then calculated from the coefficients of the identified ARX models. Finally, the state-space model of the open-loop stochastic system and the gain matrices for the Kalman filter and controller are realized. The method is validated by simulations and test data from an unstable large-angle magnetic suspension test facility.

An optimal modal-space controller for structural damping enhancements

A stochastic optimum-based compensator is developed to enhance structural damping with collocated rate sensors/actuators. This controller is based on explicit solutions for the Riccati equations from a modal-space model. The performance of each controlled mode can be easily adjusted by the corresponding design parameters in the controller. NASAs Spacecraft Control Laboratory Experiment (SCOLE) facility is used to demonstrate the effectiveness of this control design. A distributed parameter model is first obtained by using the Holzers transfer matrix method and the corresponding modal parameters are identified. Then the distributed parameter model is reduced to a finite-dimensional modal-space model for the controller design. Three torque actuators and three collocated rate sensors are used to suppress the vibration of the first five modes. Analytical and experimental results show that the proposed controller is effective in damping enhancements for large flexible structures.