A Study On Design And Realizations Of Finite Word Length Digital Controllers

Digital control system has been considered as one of the most important and active fields in engineering for many years, and the infinite precision design theory and application have been well studied for a long time. An ideal system can be implemented in different but equivlent realizations theoretically, however, due to the finite word length (FWL) effects resulting from actual devices, modules or subsystems, the system performance will always deviate from the ideal performance in practice. The system performance is closely related with the implementation of the system. Thus, the FWL effects need to be considered when a digital controller is designed and implememted.One approach of FWL controller study is to obtain the optimal realizations of a given FWL controller to minimize the FWL effects. An alternative approach is to design the FWL controller directly according to some given performance index.The backgrounds and a historical view of FWL problems and non-fragile controller design are presented at the beginning of the dissertation. In the body of the dissertation, different performance indexes are defined and analyzed based on the analysis of different types of FWL errors in digital controller, and different FWL digital controller design and realization problems are considered and solved. The major contributions of this dissertation are as follows:Considering the FWL errors of controller coefficients, define and analyze the closed-loop transfer function sensitivity measure with respect to the controller coefficients, obtain the optimal controller realizations via minimizing the transfer function sensitivity measure. Both z -operator and δ -operator parameterized systems are considered.Considering the FWL errors of controller coefficients, define and analyze the closed-loop pole place sensitivity measure with respect to the controller coefficients, obtain the optimal controller realizations via minimizing the pole sensitivity measure. Both z -operator and δ -operator parameterized systems are considered.Considering the FWL errors of internal signals in digital controller, based on stochastic control theory, define and analyze the closed-loop roundoff noise gain in both z -operator and 5 -operator parameterized FWL systems, and obtian the optimal controller realizations via minimizing the roundoff noise gain.Considering the FWL errors of internal signals in digital controller, define and analyze the roundoff noise gain based on l1 -norm and H∞ -norm respectively,and obtain the optimal controller realization via minimize the newly defined roundoff noise gains. The H∞ roundoff noise gain minimizing problem isreduced to an linear matrix inequalities problem which can be solved using MATLAB conveniently.Considering the FWL errors of internal signals in digtial controllers, direct approach is adopted to design FWL controller. A FWL covariant upper bound control problem and a FWL H∞ control problem are reduced to a unified matrix inequalities problem.Finally, more problems to be studied and investigated are pointed out on the basis of summarization of this dissertation.