| Summary: | 博士 === 大同大學 === 電機工程學系(所) === 92 === This dissertation is devoted to developing systematic methods for analyzing the stability of the discrete-time closed-loop system by some stabilizing digital controller implementations subject to finite word length (FWL) effects.
First, mathematical models of the respective floating-point and fixed-point arithmetic for digital controller implementations are proposed.
Next, to establish the stability criteria in terms of word length, we use Bellman-Grownwall Lemma and small gain theorem to derive conditions that can preserve the stability of linear closed-loop systems using fixed-point or floating-point controller implementations, respectively.
%In addition, for a class of unknown discrete-time nonlinear dynamical systems, stability criterion in terms of mantissa length of the parameters for the digital neural adaptive tracking controller implementation is developed in the sense of Lyapunov stability, where the digital dynamical neural networks are used for model reference learning and controller design.
Secondary, it is well known that the eigenvalues of a closed-loop system are identical with similar controller realizations using infinite precision representation.
However, for FWL digital controller implementations, this property will no longer exist.
This implies that different controller realization will cause different stability margin of the closed-loop system.
Recently, sensitivity minimization approach subject to the FWL effects has been proposed in a number of literatures to overcome such a problem.
This approach used in control systems has the following two merits: (1) mathematically and computationally tractable, (2) direct connection between controller implementation and closed-loop stability.
In this dissertation, we propose two novel approaches for eigenvalue sensitivity minimization.
For the first, the scheme of the orthogonal Hermitian transform is used to play an important role for similarity transformation.
It has advantage that any given original controller realization may transfer to the one that with minimal eigenvalue sensitivity measure.
Contrast to the methods using numerical searching algorithm in the literatures, this approach can provide an algebraic closed-form solution to prevent computational time consumptions and avoid being trapped to a local minimum.
Moreover, since the eigenvalues of a closed-loop system may be with complex values, this implies that not only the magnitude deviations of all eigenvalues but their phase deviations should be considered for obtaining better robustness of the closed-loop system.
Hence, the second approach simultaneously considers both magnitude and phase sensitivities of eigenvalues.
We propose a new measure which compromises the magnitude and phase sensitivities of the closed-loop system eigenvalues such that it can be minimized subject to FWL effects.
As well as the first approach, this one can also provide an algebraic closed-form solution.By using this approach and based on orthogonal Hermitian transform, any original given controller realization can be transferred to the one with minimal sensitivity that contains both magnitude and phase-supplement of eigenvalues.
A serious of numerical examples, which demonstrate the effectiveness of our proposed scheme, are also included in this dissertation.
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