Optimal Digital Controller Implementations with Fixed-Point Computation: Eigenvalue Sensitivity Minimization Approach

• Main Authors: Hsuan wei,Liu, 劉宣緯
• Other Authors: Hsien Ju,Ko
• Format: Others
• Language: zh-TW
• Published: 2012
• Online Access: http://ndltd.ncl.edu.tw/handle/78732815136048549585

碩士 === 亞洲大學 === 光電與通訊學系 === 100 === This note presents an approach to analyze the stability of the closed-loop system for digital controller implementations by minimizing a measure synthesized by the magnitude and phase sensitivities of eigenvalues. First, uncertainties of the controller parameters using fixed-point arithmetic caused by roundoff and computational errors are expressed as a function of word length. Then, a stability criterion of the closed-loop system based on fixed-point statistical model is derived by means of small gain theorem and Bellman-Grownwall Lemma. Thus, a measure that combines the magnitude and phase sensitivities of the closed-loop system eigenvalues with respect to controller parameters is constructed and is minimized in the sense of mixed matrix-2/Frobenius norms. Then an optimal similarity transformation is obtained from an analytically algebraic method based on this minimum measure. Using this transformation as well as the stability criterion, a least word length can be obtained. Finally, an example is performed to illustrate the effectiveness of the proposed scheme.