Criterion to assess stability of a ‘lowest wins’ control strategy

Abstract

A problem frequently arising in control engineering is how to manipulate a single control input to ensure that several outputs remain within specified ranges under all conditions. A common solution is to employ strategy to feedback the lowest of two competing signals. Even though each feedback loop, when considered separately, may be stable, this is insufficient to guarantee stability of the complete system. Limit cycling or unstable oscillations may occur. These configurations have been analysed by transforming them into a single-input/single-output nonlinear system. Stability was assessed by applying describing-function and passivity criteria. It was found that, by plotting a composite transfer function, a substantial amount of information on the dynamic behaviour could be obtained. This was verified by simulating a typical gas turbine controller using fuel to regulate shaft speed and temperature. In accordance with theory it was shown that, by altering coefficients in the temperature controller, a system could be obtained which limit-cycled when the ‘lowest wins’ strategy was activated. In addition, the three passivity criteria for monotonic nonlinearities used in this analysis – Popov, off-axis circle and Dewey – have been been shown to be special cases of a more general result.