Time-Varying Deadbeat Controller Design

Abstract

A time-varying generalization of the classical deadbeat controller is derived directly from input-output data in the present paper. The natural extension of the time invariant deadbeat condition to the time-varying case is presented by using the key developments of the observer/Kalman filter time-varying system identification theory reported recently by the authors. In stark contrast to the time invariant deadbeat controller design, it is shown that the timevarying deadbeat controller parameters do not follow the recursive relationship that was developed in the past. In the special case of periodic systems, where repeated experimental data are available naturally, it seems that such a controller can be designed to set the output of the closed-loop system to rest after a few time steps. Numerical simulation example demonstrates the efficacy of the deadbeat controller design method proposed in this paper. A deadbeat controller, realized from the departure motion dynamics of a spacecraft, is then shown to enhance the performance of an attitude control system by minimizing the deviations from a reference trajectory.

A method to construct reduced‐order parameter‐varying models

“…This indicates that the additional state information used with the input/output data for the IOROM approach can help identify a low‐dimensional model for the actuator disk example. Lastly, it should be noted that ERA has been extended to a time‐varying framework in . A comparison between this IOROM approach and other time‐varying approaches will be explored in future work.…”

“…For example, eigensystem realization algorithm (ERA) is a popular method in the system identification literature that uses impulse response data to construct a linear model of the system . This method has been extended to generic input signals and time‐varying systems . In the fluid dynamics literature, proper orthogonal decomposition (POD) is a standard method where the state is projected onto a low‐dimensional subspace of POD modes constructed using data from the high‐order system .…”

“…The key technical issue in this second step is to ensure the reduced-order linear parameter-varying system approximates the nonlinear system even when the operating point changes in time.REDUCED-ORDER PARAMETER-VARYING MODELS 583 impulse response data to construct a linear model of the system [11]. This method has been extended to generic input signals and time-varying systems [12][13][14][15]. In the fluid dynamics literature, proper orthogonal decomposition (POD) is a standard method where the state is projected onto a lowdimensional subspace of POD modes constructed using data from the high-order system [16][17][18].…”