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Model Uncertainty and Robust Control K. J. Åström Department of Automatic Control Lund University, Lund, Sweden Email: [email protected], Fax: +46 46 13 81 18 1 In tr od uc tio n A key reason for using feedback is to reduce the effects of uncertainty which may appear in different forms as disturbances or as other imperfections in the models used to desi gn the fee dba cklaw. Mod el unc erta inty and rob ust nes s ha ve bee n a centr al the me in the deve lopmen t of the field of automatic contr ol. This paper give s an eleme ntary presentation of the key results. A central problem in the early development of automatic control was to construct feedback amplifiers whose properties remain constant in spite of variations in supply voltage and component variations. This problem was the key for the telephone industry that emerged in the 1920s. The problem was solved by [9]. We quote from his paper: “ .. by building an amplifier whose gain is deliberately made say 40 deci- bels higher than necessary (10 000 fold exce ss on energ y basis) and then feeding the output back on the input in such a way as to throw away excess gain, it has been found possible to effect extraordinarily improvement in constancy of amplification and freedom from nonlinearity. ” Blacks invention had a tremendous impact and it inspired much theoretical work. This was required both for understanding and for development of design method. A novel approach to stability was developed in [36], fundamental limitations were explored by [10] who also develope d methods for designing feedback amplifiers, see [11]. A systematic approach to design controllers that were robust to gain variations were also developed by Bode. The work on feedback amplifiers became a central part of the theory of servomech- anisms that appear ed in the 1940s, see [22], [27]. Syste ms were then described using 63

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