Parallel Compensator for Continuous and Relay Control Systems with Difficult Plants

New method of design of the transfer function (TF) of the replacement plant (RP), being a part of the parallel compensator proposed in [3] is presented in the paper. The RPTF with relative degree equal to one is chosen such that the system is stable for high gain of the regulator and the numerator polynomial of the RPTF determines the characteristic equation of the closed loop system. The choice of some fast modes of this polynomial give fast transient response. The control saturations are also accounted. It is shown that the system with parallel compensator and relay implementation of the control, with hysteresis of the relay tending to zero, has the same output response as the continuous system with high gain of the regulator and control saturation values equal to those of the relay switched outputs.