Relay Feedback Systems — Established Approaches and New Perspectives for Application

Abstract

Relay feedback systems belong, since long, to the rather classical topics of control theory and engineering. While they were first used as robust and simple switching elements in automatic control systems, over time, they have experienced different periods of renewed interest with regards to both theoretical analysis and applications. Examples include the automatic tuning of simple feedback controllers, delta-sigma modulators for analog-digital converters, robust relay-based controls, nonlinear systems analysis and identification, among others. One of the remarkable features of using relays in feedback is the appearance of stable limit cycles. The structural and parametric conditions for the stable limit cycles, their prediction, and controllability of magnitude and frequency have already been solved, to a large part, in previous researches, driven by both theoretical curiosity and application requirements. This brief tutorial paper summarizes the basic principles of relay feedback systems, discusses several characteristics that are interesting from an application perspective, and addresses some issues related to its further use for system identification. A casespecific study for estimating the unknown backlash, hidden within two-mass systems, is demonstrated along with an experimental example, based on provoking the controllable drifting limit cycles by the non-ideal relay in the velocity feedback loop.

Self-Tuning Controller Using Shifting Method

“…22], etc. A more detailed list and description of methods using relay feedback identification can be found in review publications, e.g., [23][24][25][26][27].…”

“…To estimate more model parameters, the use of a biased relay was proposed, e.g., [13]; the insertion of an integrator, as demonstrated in [14,15]; a time delay into the loop, e.g., [16]; the modification of a relay hysteresis, e.g., [17]; the utilization of the describing function method, e.g., [18,19]; the use of the so-called shifting method, e.g., [20][21][22], etc. A more detailed list and description of methods using relay feedback identification can be found in review publications, e.g., [23][24][25][26][27].…”

Relay Identification Using Shifting Method for PID Controller Tuning

“…At present, more publications exist that are devoted to relay-based parametric estimation techniques for control purposes. A summary of the obtained results can be found in survey publications, for example, [9][10][11][12][13][14].…”

Determination of Self-Oscillations in Relay Control Systems

“…Because of this propriety, they have gained a new interest since they have been successfully used as auto-tuners in control applications to tune PID controllers [5,6]. In fact, they have also been used in various applications such as delta-sigma modulators for analog-digital converters [7], in robust relay-based controls, in optimal control, in nonlinear systems analysis and identification, and others [8,9]. From the viewpoint of practical applications, relays and other on-off switching devices were used at the beginning as electromechanical devices in power amplifiers [2,3].…”