A UNIFIED APPROACH TO THE OPTIMAL DESIGN OF ADAPTIVE AND GAIN SCHEDULED CONTROLLERS TO ACHIEVE MINIMUM HELICOPTER ROTOR VIBRATION

An analytic approach is presented for the systematic design of active controllers to reduce helicopter vibration through higher harmonic control. Six basic control concepts are designed, ranging in sophistication from a full active adaptive controller to a gain scheduled linear quadratic gaussian (LQG) design. The six control concepts are obtained from the general minimization of a quadratic function of the vibration, and each control law obtained is a result of making suitable simplifying assumptions. The three properties of adaptive control - (1) caution, (2) probing, and (3) deterministic control - are quantified in the adaptive designs. These properties, which arise from stochastic control theory, are important to adaptive controllers because they provide further reductions in vibration than controllers without them. Gain scheduled controllers presented include LQG, proportional-integral, and a perturbation controller---all based on linear optimal control. Four of the designed controllers have been implemented and tested using aeroelastically scaled wind tunnel model rotors. The experience gained in testing these controllers is discussed. "Caution" was found to be of particular importance to the performance of the adaptive controllers. Test results are presented which quantify the variation of the transfer matrix with advance ratio. The analytic control designs presented and the results of the test program provide a useful data base to further understand the properties important to higher harmonic control for vibration reduction.