A Robust Relay Feedback Structure for Processes Under Disturbances: Analysis and Applications

Abstract

In this paper, a robust relay feedback structure is used to provide a stable oscillation under large static disturbances or drift. This relay structure is composed of a block to remove static disturbance or drift followed by a relay. The robust relay structure is analyzed using the describing function method. Furthermore, based on Poincaré map, the conditions for the existence and local stability of the limit cycle are obtained. In order to estimate multiple frequency points of the process, a step change and periodic square waves with frequencies lower than the ultimate frequency are applied at the process input. Thus, these frequencies information are used to identification of first-order plus time delay models over a wider frequency region. For these models, a phase adjustment is proposed from the frequencies information of the additional signal. From simulated and experimental studies, it is verified that the robust relay structure provides a symmetrical oscillation at the process output, independent of the disturbance in the process input and iterations between the loops.

Improving the identification from relay feedback experiments

“…According to equation (7), as more harmonics are considered, the restrictions between τ k increase. Then, the task of obtaining τ k , even if it is straightforward, becomes more tedious.…”

“…For example, considering 2 harmonics, the restrictions between τ k are: It is worth noticing that the solutions of equation ( 7) result in a finite number of combinations of |τ m − τ n |, covering the maximum and minimum possible differences between τ m and τ n . However, taking into account that τ i ∈ [0, 1], there are infinite combinations of τ i that fulfill the restrictions imposed by equation (7). In order to facilitate the selection of τ i , the following corollary states a simple and useful criterion based on the number of harmonics considered for the estimation.…”

“…Very popular methods, such as Ziegler-Nichols and others use the results provided by this kind of test, [1], [2]. Furthermore, many auto-tuning methods also consider variations of relay based experiments in the identification phase of the algorithms, [3], [4], [5], [6], [7], [8].…”

“…These works and most of the successive publications use the Describing Function (DF) method as the analysis tool, [13]. Some other investigations improve the initial idea trying to satisfy the filtering hypothesis required by DF method introducing modifications in the relay experiment, i.e., using a pre-load relay [14] or a saturation non-linearity [15], introducing more levels in the output of the relay [16], adding a mapping function to the relay output [17], proposing new multi-relays schemes [7], or changing the relay by a symmetric-send-on-delta (SSOD) non-linearity which allows to obtain a more sinusoidal-like signal [18].…”

Simultaneous tuning of cascade controllers based on nonlinear optimization

“…In Tan et al (2000), a single relay experiment was applied to the outer-loop reference. The tuning of the two PID controllers was computed directly based on the sustained oscillation obtained from the relay test (Da Silva and Barros, 2019). In addition, robustness analyses were used to verify and guarantee robust tuning of the cascade system.…”