INVESTIGATION OF THIRD-ORDER CONTACTOR CONTROL SYSTEMS WITH TWO COMPLEX POLES WITHOUT ZEROS

摘要

The present paper reports an investigation of third-order systems lander contactor control. The transfer function of the uncontrolled system has one real and two conjugate complex poles and may have zeros. In general, it is assumed that all, poles have negative real parts;how-ever, cases with positive real parts of the complex poles are included. The switching function depends on error and error derivatives, the error being the difference between the input and output of the system. The major portion of this report, is devoted to systems without zeros in the transfer function;however, systems with zeros in the transfer function are discussed briefly.nIt is shown that for an initial error (or a step input) the coef¬ficients of a linear switching function F = e + k1e' + k2e" (where k1 and K2 are coefficients and e, e', and e" are the error and error derivatives, respectively) can be chosen in such a way that the ' system trajectory becomes optimum, that is, the origin (or the step height) can be reached in minimum time without chatter. Obviously, this statement is valid only for an ideal system with perfect relays and no transport delays.nThe dependence of the coefficients of the error derivatives k1 and K2 on initial error or step height for fixed system parameters has been studied theoretically (behavior of the system trajectory in the phase space) and with the help of an analog computer. Results from both methods agree well.