TABLE OF CONTENTS Relay control systems [1, 2, 3] (also referred to as relay feedback systems [4, 5, 6]) constitute an important class of non-linear regulation systems and are widely used in many fields of engineering and applied science [3, 4, 7, 8, 9, 10, 11, 12]. Examples are power converters, AC and DC electric drives [13, 14, 15, 16, 17, 18, 19], adaptive control systems [20, 21, 22, 23] and a variety of other mechanical and electromechanical systems [1, 2]. Johansson et al. [24, 25, 26] provide examples of applications in variable-structure systems [8], supervisory switch-control systems [27], hybrid systems [28, 29], and delta-sigma modulators for signal processing [30, 31].
Typically, systems of this type are free running which means that the oscillations are determined by the properties of the system itself [1] and not sustained by an external periodic action.
The advantages of using relay control systems rather than systems with continuous control are that the relay element serves as an amplifier that converts the continuous control signal into a well-defined switching sequence. Relay systems have a broad variety of applications in engineering due to the large power gains of the relay element and because of their simplicity. Oscillatory relay systems exploit self-oscillations as a main operating mode. Such systems include, for example, systems for automatic regulation of the voltage (current) for power converters and control systems for AC and DC electric drives with semiconductor converters. Relay systems can provide arbitrarily small ripple...
