The optimum response of second-order, velocity-controlled systems with contactor control

This paper is concerned with the optimum control problem for plants described by second-order differential equations with constant coefficients and with velocity control. Emphasis is placed on the case where the characteristic equation of the system has one zero root and two complex conjugate roots. The problem is studied in terms of the motion of the pliase point in a three-dimensional phase space. An iteration method is developed to obtain the optimum trajectory, which in turn gives the optimum response. © 1961 by ASME.