# On Self-Tuning Regulators

Research output: Chapter in Book/Report/Conference proceeding › Book chapter

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**On Self-Tuning Regulators.** / Åström, Karl Johan; Wittenmark, Björn.

Research output: Chapter in Book/Report/Conference proceeding › Book chapter

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*Control Theory: Twenty-Five Seminal Papers (1932-1981).*John Wiley and Sons.

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*Control Theory: Twenty-Five Seminal Papers (1932-1981)*John Wiley and Sons.

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### MLA

*Control Theory: Twenty-Five Seminal Papers (1932-1981).*John Wiley and Sons. 2001.

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### RIS

TY - CHAP

T1 - On Self-Tuning Regulators

AU - Åström, Karl Johan

AU - Wittenmark, Björn

N1 - Reprint of paper from Automatica vol 9, pages 185--199..

PY - 2001

Y1 - 2001

N2 - The problem of controlling a system with constant but unknown parameters is considered. The analysis is restricted to discrete time single-input single-output systems. An algorithm obtained by combining a least squares estimator with a minimum variance regulator computed from the estimated model is analyzed. The main results are two theorems which characterize the closed loop system obtained under the assumption that the parameter estimates converge. The first theorem states that certain covariances of the output and cross-covariances of the control variable and the output will vanish under weak assumptions on the system to be controlled. In the second theorem it is assumed that the system to be controlled is a general linear nth order system. It is shown that if the parameter estimates converge the control law obtained is in fact the minimum variance control law that could be computed if the parameters of the system were known. This is somewhat surprising since the least squares estimate is biased. Some practical implications of the results are discussed. In particular it is shown that the algorithm can be feasibly implemented on a small process computer. . Reprint of paper from Automatica vol 9, pages 185-199 available at http:dx.doi.org/10.1016/0005-1098(73)90073-3 (restricted access)

AB - The problem of controlling a system with constant but unknown parameters is considered. The analysis is restricted to discrete time single-input single-output systems. An algorithm obtained by combining a least squares estimator with a minimum variance regulator computed from the estimated model is analyzed. The main results are two theorems which characterize the closed loop system obtained under the assumption that the parameter estimates converge. The first theorem states that certain covariances of the output and cross-covariances of the control variable and the output will vanish under weak assumptions on the system to be controlled. In the second theorem it is assumed that the system to be controlled is a general linear nth order system. It is shown that if the parameter estimates converge the control law obtained is in fact the minimum variance control law that could be computed if the parameters of the system were known. This is somewhat surprising since the least squares estimate is biased. Some practical implications of the results are discussed. In particular it is shown that the algorithm can be feasibly implemented on a small process computer. . Reprint of paper from Automatica vol 9, pages 185-199 available at http:dx.doi.org/10.1016/0005-1098(73)90073-3 (restricted access)

M3 - Book chapter

SN - 0-7803-6021-4

BT - Control Theory: Twenty-Five Seminal Papers (1932-1981)

A2 - Basar, Tamer

PB - John Wiley and Sons

ER -