ANALYSIS OF TWO NONLINEAR FLIGHT CONTROL SYSTEMS. PART I. LIAPOUNOV-LURJE APPROACH TO A SIMPLIFIED PITCH RATE AUTOPILOT. PART II. ANALYSIS OF A HIGH-GAIN ADAPTIVE PITCH RATE AUTOPILOT.

This report covers the analytical treatment of two non-linear control configurations of immediate interest to the flight control designer. In Part I stability borders and their properties are derived by the Liapounov-Lurje approach for third and fifth order versions of a simplified Pitch Rate Autopilot. For each system version pertinent Liapounov functions are set up and processed, then Lurjes stability equations separated and the latter processed as far as reasonable to yield sufficient stability conditions defined by discriminants in closed algebraic form. The treatment of each system version is paralleled by analyses based on the method of harmonic balance. In Part II simple mathematical expressions for estimating the oscillation or limit cycle paaarameters of a High Gain Adaptive Pitch Rate Autopilot involving an 8-th order system with 2 non-linearities are derived. For the cl4seer sstudy of the system response to gain perturbations an equivalent third order model operating at the stability border is derived and investigated for thhhhh he poskibility of parametric excitations. Ultimately, by introducing a sampling concept, a method for approximate computation of the system response to gaai inn 3c3cccccccchanges is derived. Incorporated into the report are 4 Appendices, dealing with the mathematical background of the methods employed in the main body of the report. Author