| An adaptive blade control algorithm for helicopter vibration reduction is developed as an application of an impulse response control method. The method is based on an impulse response formulation which is applicable to any linear system with periodic dynamics. For such systems, a matrix of discretized impulse responses defines the relationship between sequences of inputs and outputs sampled throughout a period. Under a nearly constant control vector assumption, the impulse response matrix is shown to be full, and for constant dynamics plants, belong to a class of matrices diagonalizable by Fast Fourier transforms, the circulant matrices. For systems with periodic input coefficients, a circulant/diagonal structure results. Such structures are shown to act as a theoretical link between impulse response control methods and frequency domain techniques.;The filters derived are examined in open loop simulations to determine their identification capabilities independent of the control feedback. Two levels of open loop control variation are used to evaluate estimation performance with constant and time-varying plants. The Kalman filters are found to produce lower estimate errors than the WLS filters.;Closed loop simulations of the regulators are then conducted with the filters retuned. The global Kalman filter certainty-equivalent regulator produced the best overall vibration reduction, typically better than 90%. In some tests, invariable regulators yielded promising results. Cautious regulators are found to be of no benefit.;In the investigation of adaptive helicopter vibration control presented, a vertical-axis-only plant is simulated by a model composed of an impulse response matrix and an uncontrolled vibration vector. The adaptive control is implemented by a regulator composed of an estimator and a controller. The model parameters are identified by either Kalman or batch weighted least squares (WLS) filtering in either global or local form. The resulting estimates are used in an optimal control law obtained by the minimization of a constrained, single-step, quadratic performance function. Four control laws are derived: global certainty-equivalent, local certainty equivalent, global cautious, and local cautious. |
