The Determination of Periodic Modes in Relay Systems Using the State Space Approach†

Abstract

A method for determining the exact mode of oscillation of a time-invariant feedback system containing relays is presented. This method is based on tho state space approach in the real time domain, and results in a set of transcendental algebraic equations which can easily be solved by digital computation. General state transition and control matrices for plants with n poles and m zeros are derived. For complicated plant characteristics, the switching equations can be obtained easily by simple superposition of the switching equations of ‘elementary plants’. The general expression is given in discrete form, and may be reduced to a continuous form when no impulse control is present, otherwise a combined form is used. Switching equations for elementary plants up to third order are listed for reference, and illustrative examples are given with results compared by analogue simulation.