Use of Relay Transient Responses

Abstract

In the preceding chapter, relay feedback has been employed to identify the process frequency response. It is, however, noted that the frequency response is obtained only at a few discrete frequency points. Essentially, only one point, the critical point on the process frequency response, is estimated from a symmetric relay test, and a few other points can also be estimated at the expense of possibly a longer testing time and a more complicated relay, such as biased, parasite or cascade relay. Fundamentally, this is because only the steady-state response, i.e., the limit cycle, is exploited for identification and this contains spectral information on the oscillation frequency and its higher harmonics only, and harmonics at high frequencies are practically not identifiable due to the low-pass nature of most process dynamics. Note that the transient responses of the process input and output are ignored although they are also available from a relay test and contain rich spectral information of the process. As a result, one can expect that use of the relay transient response in identification will produce more process information than an approach based solely on the steady-state response. To do so, time domain based least squares techniques may be utilized and good books on this topic are readily available (Ljung and Söderström, 1983), which is thus not pursued here. Instead, the goal of the present chapter is to show how to estimate the process frequency response from the system transient responses to a single and simple relay test.