Improved Relay Feedback

Abstract

Luyben (1987) pioneers the use of relay feedback tests for system identification. The ultimate gain and ultimate frequency from the relay feedback test are used to fit a typical transfer function (e.g., first-, second- or third-order plus time delay system). As mentioned in Chapter 2, it can lead to significant errors in the ultimate gain and ultimate frequency approximation (e.g., 5 ~ 20% error in K _u ) for typical transfer functions in a control system. The errors come from the linear approximation (describing function analysis) to a nonlinear element. The square type of output from the relay is approximated with the principal harmonic from the Fourier transform (Antherton, 1982; Chang et al., 1992) and the ultimate gain is computed accordingly. Several attempts have been proposed to overcome this inaccuracy. Li et al. (1991) use two relay tests to improve the estimation of K _u and ω _u . Chang et al. (1992) employ the concept of a discrete time system to give a better estimation of ω _u . Notice that, in these attempts, an ideal relay is employed in the experiments and modifications are made afterward. Since, the source of the error comes from sine-wave approximation of a square type of oscillation, a straightforward approach to overcome the inaccuracy is to re-design the experiment (instead of taking remedial action afterward). That is, to produce a more sine-wave like output using a different type of relay.