BANG‐BANG CONTROL OF A SECOND‐ORDER NON‐LINEAR STABLE PLANT WITH THIRD‐ORDER NONLINEARITY Available to Purchase

In this paper the design of a controller for a relay‐controlled second‐order non‐linear stable plant with third‐order nonlinearity is considered. The task of the controller is the simultaneous reduction of output and output derivative to zero with the input being at zero. It will be shown that for all initial values of output and output derivative it would be possible to bring them to zero, simultaneously and with at most one switching reversal of the relay. It will also be shown that, through simple transformation of error and error derivative, the equation of the switching curve can be made independent of any constant gain of the plant and also of the coefficient of the non‐linear term.