Digital Filters for Gain Stabilization of Flexible Vehicle Dynamics

The necessity of having low-cost aerospace vehicles with short development times means that control designers need to work with simplified and approximate dynamic models. Aerospace vehicles typically being light and slender, exhibit body bending and flexibility effects at relatively lower frequencies. It may not be possible or practical in every case to carry out detailed test and analyses exercises to determine the structural dynamic characteristics of a vehicle. So, body bending shapes and slopes may not be precisely known; the mode frequencies can however be roughly estimated through simplified analysis. Here it will be assumed that the flexible mode frequencies are approximately known, and are sufficiently high so that gain stabilization is possible. This paper discusses different digital filters for gain stabilization of flexible vehicles, and elaborates their advantages and drawbacks. Various filters are compared; Butterworth, Bessel, Chebychev, Elliptical and simple quadratic filters of various orders are discussed. The filter selection is based on having desirable magnitude attenuation characteristics while at the same time leading to minimum phase lag near the closed-loop bandwidth. The filter design and selection process is illustrated by an example of a sounding rocket stabilization problem. Two flights of the vehicle have been conducted, the first with no consideration of the body-bending dynamics and hence no filters. Serious problems were observed, hence Elliptic filters were used to provide gain stabilization in the second flight. Flight test results are presented and discussed.