Performance of digital linear regulators which use logarithmic arithmetic

This paper analyzes the performance of digital linear regulators which use finite-precision logarithmic arithmetic. A linear equation is derived which describes the steady-state covariance matrix of such a closed-loop regulator system. The utility of this covariance matrix in designing regulators which use logarithmic arithmetic is illustrated through several numerical examples and the presentation of a regulator design methodology.

[1]  Earl E. Swartzlander,et al.  The Sign/Logarithm Number System , 1975, IEEE Transactions on Computers.

[2]  B. Widrow.  Statistical analysis of amplitude-quantized sampled-data systems , 1961, Transactions of the American Institute of Electrical Engineers, Part II: Applications and Industry.

[3]  T. Kurokawa,et al.  Error analysis of recursive digital filters implemented with logarithmic number systems , 1980 .

[4]  Samuel C. Lee,et al.  FOCUS microcomputer number system , 1979, CACM.

[5]  N. Kingsbury,et al.  Digital filtering using logarithmic arithmetic , 1971 .

[6]  R. Rink,et al.  Performance of state regulator systems with floating-point computation , 1979 .

[7]  J. Lang.  On the design of a special-purpose digital control processor , 1984 .

[8]  Samuel C. Lee,et al.  The Focus Number System , 1977, IEEE Transactions on Computers.

[9]  R. Rink,et al.  Covariance equation for a floating-point regulator system , 1979 .

[10]  W. Koning,et al.  The influence of finite word length on digital optimal control , 1984 .

[11]  Paul Moroney,et al.  The digital implementation of control compensators: The coefficient wordlength issue , 1979, 1979 18th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.

[12]  Jeffrey H. Lang,et al.  Integrated-Circuit Logarithmic Arithmetic Units , 1985, IEEE Transactions on Computers.