# ESA GNC Conference Papers Repository

**Title:**

##### Time Variant Notch Filter for Bending Modes Active Supression in Aerospace Systems

**Authors:**

**Presented at:**

**Abstract:**

Aerospace systems such as launchers and missiles are subjected to bending dynamics from structural origin, which could be excited by thrust commands, aerodynamics and other exogenous forces. Special care should be devoted to the vehicle flexion in the control system design phase, since this phenomenon plays an important role in the vehicle stability. Some techniques are adopted to reduce the bending influence over the attitude control loop. Notch filtering is a conventional way of suppressing an undesirable oscillatory signal in the control loop, resulting in gain stabilization of a particular flexible mode. The use of notch filtering ensures that the specific mode is not destabilized by feedback control; however, it does not introduce any active damping, which often results in too much ringing that may not be acceptable in certain cases. In general, roll-off of the control loop gain at frequencies above the control bandwidth is always needed to avoid destabilizing non-modeled high-frequency modes and to attenuate high-frequency noise, and it is often simply achieved by using a double-pole low-pass filter. Another important fact is that the influence of the bending modes is much more weighted in the angular velocity measure than in the attitude signal, therefore, in this the particular case, a notch filter only in the velocity feedback loop can become a natural choice. Although, the bending signal can also flow through the attitude control channel, becoming the filters location choice a more complicated task. Other important vehicle characteristic is that their structural properties change continually due to the mass loss during the flight, and the bending mode frequency increases proportionally to the mass variation. Then, a fixed-tuned notch filter, designed such that its central frequency is chosen according to the bending behavior at that time, can not be efficient for a suitable flexion rejection. In this case, a varying-time notch filter should be used. Despite of this varying-time notch filter should be designed in an off-line procedure based on early structural studies, so many adaptive on-line techniques have been proposed in the literature. The first tentative is to consider a tracking filter that tunes itself according to a feedback law [3], [7], but this methodology assumes slowly variation on structural characteristics that is not ever true in some cases. Furthermore, the tracking filters can present difficulties for noisy bending signals. Better results can be achieved by frequency estimation approaches based on bending mode recursive identification. The more traditional strategy is to use a Recursive Least Squares Estimator to obtain the bending frequency and then to proceed the notch filter tuning [1], [2], [4], [8]. However, other recursive techniques are also available like the lattice-based IIR filtering [6], the modified notch filter structure [5], and robust filtering [9]. In this paper is presented a deeper discussion about the application of the bending active suppression in aerospace vehicles. The bending behavior for a small launcher is studied, where the fixed-tuned notch filtering is applied to provide sufficient bending rejection. After, an off-line variable-tuned filtering approach is discussed since that they can maximize the rejection performance. Some difficulties related to the varying-time filtering are also presented, such as the uncertainty over the finite-element estimation. Afterwards, some on-line adaptive approaches to active bending are also discussed in this paper, following ideas yet available in the literature. The objective is to discuss the problems that an active methodology can suffer in a real application and possible remedies for them. All results are based upon the Brazilian Launcher VLS.