Active control of vibrations in helicopters by periodic optimal control

A Survey of Repetitive Control for Nonlinear Systems

“…However, for nonlinear systems, it is often required to derive error dynamics to convert a tracking problem to a disturbance rejection problem as (3). This in fact follows the idea of general tracking controller design, whereas the special feature of periodic signals is under-exploited.…”

“…In aerospace engineering, many control tasks are often of a periodic nature as well. For example: magnetic spacecraft attitude control [1], [2], active control of vibrations in helicopters [3], [4], autonomous vertical landing on an oscillating platform [5], [6] and harmonics elimination in aircraft power supplies [7]. Besides these, in industrial manipulators executing operations of picking, placing or painting, machine tools and magnetic disk or CD drives, the control systems are often required to track or reject periodic exogenous signals.…”

Periodic control of helicopter rotors for attenuation of vibrations in forward flight

“…In conclusion, considering that usually , , and , in the direct approach one encounters a big Riccati equation (of dimension ranging from 17-27), whereas in the indirect approach the biggest Riccati equation one has to deal with has dimension (i.e., [6][7][8][9][10] only. Note that the Riccati equation to be solved for the computation of the controller has dimension both in the direct and indirect approach.…”

“…Thus, the spectral content of covers a much wider range of frequencies than that of . By making reference to system (3), the problem of designing a control system so as to attenuate the effect of oscillations can be easily cast into an optimal control framework by considering the performance index (4) where (5) In conclusion, thanks to the introduction of the fictitious input signal , we come to a standard periodic linear quadratic Gaussian (LQG) control problem, characterized by the performance index (4) over the system (6) Clearly, with respect to conventional LQG control, where the required state estimates are obtained by means of a Kalman filter, the additional issue of estimating the IED arises. The control system will be therefore composed of three elements:…”

“…I N THE last few years, a considerable effort has been devoted to the development of active control systems for the attenuation of vibrations in helicopters (see, e.g., [1]- [6]). Besides improving the comfort of the crew and passengers, such an attenuation would be profitable to reduce fatigue in the rotor and structure of the aircraft and to protect on-board equipment from damage.…”