Nonlinear compensator for a piecewise linear second-order feedback system

The nonlinear computer for a second-order system preceded by a saturating amplifier, with significant linear zone, was designed through the transformation of the zero-force curve and the geometry of the phase plane into the topology of the nonlinear computer. A finite-gain system was thus designed for the requirement of minimum settling time for step input functions. The method of design was based upon the division of the phase plane into three regions of operation: a saturated one, and two linear ones. The equation of the zero-force curve was that of a parabola. The nonlinear compensator had as its output the sum of the error signal and a nonlinear function of the error rate. Different systems were compared in order to determine the fastest one. One of them proved to be superior to all the others for a spectrum of different input step magnitudes.