Towards a New Generation of Relay Autotuners

Abstract

The relay autotuner for PID control is based on the simple idea of investigating process dynamics by the oscillation obtained when the PID controller is replaced by a relay function. In this paper an asymmetric relay function is used, which provides an equation for the static gain of the process. A method to find the normalized time delay is proposed and the benefits of this is discussed. Ways to find low-order models from the experiment are described. Considerations of how to choose the relay parameters are made and some examples are given.

Identification for control of biomedical systems using a very short experiment

“…The relay method has seen several modifications: In [6] an integrator was connected in series with a second relay, to change the phase shift of the plant at which the limit cycle occurs. In [9,3] an asymmetric relay was proposed. Unlike the symmetric relay, the output levels are −u off = u on for the asymmetric relay.…”

“…Once a stable limit cycle has been reached, this yields the possibility to identify parameters of a first order time delay (FOTD) model by only looking at switch durations and amplitudes. Formulas, based on describing function analysis, are presented in [9] and their practical application is demonstrated in [3].…”

Improved relay autotuning using normalized time delay

“…When the process is lag dominated, i.e., if τ is small, the half-period ratio instead reflects the asymmetry of the amplitudes. This was shown for FOTD processes under asymmetric relay feedback with no hysteresis in [7]. Results which are only valid for FOTD processes and a relay without hysteresis are of limited practical use.…”

“…The model parameters are estimated from a system identification method based on Newton's method, as in [7]. To assure convergence in the iterative method, appropriate initial parameter values are needed.…”

“…A version of the asymmetric relay function was used in [4], and later on investigated in e.g. [5], [6] [7]. For a more thorough review of the advances in modeling from relay feedback experiments, see [8].…”