Model Conversion and Robust Digital Redesign of Uncertain Linear Systems

• Main Authors: Shieh, Cheng-Shion, 謝正雄
• Other Authors: Jason Sheng-Hong Tsai, York-Yih Sun
• Format: Others
• Language: zh-TW
• Published: 1998
• Online Access: http://ndltd.ncl.edu.tw/handle/63965336056354928430

博士 === 國立成功大學 === 電機工程學系 === 86 === In this dissertaion , some new method together with interval operation arithmetic and genetic algorithms(GAs) are proposed to solve the problems:1) model conversion of uncertain linear systems, 2) robust digital redesign of sampled-data uncertain systems with input time delay and 3) non-conservativeindividual bound and controller bound of linear quadratic (LQ) regulator of uncertain linear systems. Based on the bilinear approximation method, we induct one parameter for tuning the error bound between the exact and approximate uncertain system matrices. The bounds of the interval system matrices via the proposed intervaltuning bilinear approximation method are narrower than those of the existing interval bilinear and the interval pade approximation methods. The resulting interval models (the enclosing interval models) are able to tightly enclose the exact uncertain models. Also the approcximate discrete-time interval solution is able to tightly enclose the exact interval solution of the continuous-time uncertain state-space equation. Based on the law of mean, the tuning bilinear method and the interval arithmetic operation, we propose two methods for determining the robust digital control law from the continuous-time uncertain system with input time delay so that the resulting dynamic states of the digitally controlledsampled-data uncertain system are able to closely match those of the originalcontinuous-time well-designed uncertain system. Whereas, due to the nature of the interval arithmetic and the inherent conservativeness of interval arithmetic operations, we present a new method together with genetic algorithmsto solve the conservativeness problem. Meanwhile, when the system state is notavailable, a discrete- time observer is built based on the original continuous-time observer with input time delay and predictor such that the estimated states of the redesigned discrete-time observer match those of the originalcontinuous-time observer with input time delay at the sampling instants. We also use the property of global search of genetic algorithm to calculate theindividual eigenvalue bound and controller bound of the LQ regulator for uncertain linear systems. The proposed methods will be helpful for 1)analysis and synthesis of uncertain systems, 2)implememtation of hybrid control of sampled-data uncertain systems with input time delay and 3) improving the direct digitalcontroller design which only considers the system behavior at sampling instants(not inter-sampling behavior). Some illustrative examples are included to demonstate the effectiveness of the proposed methods