Optimal low-sensitivity linear feedback systems

✍ Scribed by H. Kwakernaak

• Publisher: Elsevier Science
• Year: 1969
• Tongue: English
• Weight: 564 KB
• Volume: 5
• Category: Article
• ISSN: 0005-1098
• DOI: 10.1016/0005-1098(69)90070-3

✦ Synopsis

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By choosing in the stochastic linear regulator problem the matrix which weights the input as the zero matrix, feedback filters may be obtained which make the closed-loop system insensitive in the sense of Cruz-Perkins.

Summary--The paper considers the stochastic linear regulator and tracking problem for multivariable timeinvariant systems. It is shown that in the limiting case, where the matrix weighting the input in the quadratic criterion is the zero matrix, the closed-loop system is insensitive to parameter variations in the sense of Cruz-Perkins, provided that the system to be controlled is minimum-phase. The weighting matrix in the Cruz-Perkins sensitivity criterion turns out to be the inverse of the covariance matrix of the measurement noise. A simple example illustrates the decrease of sensitivity obtained for a system with two inputs and two outputs.