New Algorithms for Robust Parameter Identification and Time-Variant Parameter Identification
Date Issued
2012
Date
2012
Author(s)
Li, Jyun-Sian
Abstract
Two subjects of continuous-time parameter identification problems expressed in linear regression form are discussed in this thesis. One is the time-invariant parameter identification while subject to non-stochastic disturbances termed as the robust identification. The other is the time-variant parameter identification.
In addition to the measurement stochastic noise, the output signal of a system is usually contaminated with the non-stochastic disturbances which are usually resulted from errors of measure devices, system unmodled dynamics or the process disturbances acting on the system. Most identifications considering the disturbance as a white noise will have biased estimates while subject to these kinds of disturbances. In the parameterization, one can lump all the disturbances into one disturbance term at the output expressed in linear regression form. We proposes one off-line approach and two on-line approaches to deal with this problem.
In the off-line approach, the unknown disturbance will be approximately expanded by a finite Fourier cosine series with unknown coefficients. The unknown coefficients and the known basis functions will be augmented to the original parameter vector and the regressor respectively. With the expanded regressor, one can obtain the estimates of the expanded parameter vector by adopting the least-squares batch calculation. A necessary condition on persistent excitation of the expanded regressor is proposed too.
In the first of the two on-line approaches, the estimation scheme is built under the structure of gradient algorithm. A compensation is made to reject the effect of the disturbance in the estimation error dynamics by designing a stabilized controller. In the design procedure, the averaging method is used for system approximation and the $H_{infty}$ frequency shaping methodology is utilized to synthesize the controller. The control signal will be able to track the disturbance signal and cancel it in the estimation error dynamics and that guarantees the convergence of the parameter estimation.
In the second of the on-line approaches, an state-observer based estimator is constructed. To include the estimation of the disturbance into the estimation scheme, the system plant is augmented with the model of the proposed disturbance generating filter also termed as dynamics extension filter. The Kalman filter is adopted to perform the states estimation. Compared with the conventional internal model approach, the proposed method could be applied to a more general disturbance class. The three proposed approaches can identify both parameters and the disturbance simultaneously.
The design procedures of the above two on-line approaches can be grafted to the time-variant parameter identification problem with some modifications. Special consideration will be addressed in the context.
Keywords: Robust identification, Time-variant parameter identification, Disturbance
identification, Kalman filter.
Subjects
robust identification
time-variant parameter identification
disturbance identification
Kalman filter
Type
thesis
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