Conceptual Study of Gondola Stabilization in a Balloon System

Abstract

Pointing stabilization of a gondola carried by a stratospheric balloon is a challenging problem due to upper atmospheric winds and due to the multibody nature of the balloon system. The gondola provides a platform for a scientific experiment that requires point stabilization. The experiment apparatus is inside a capsule attached to the gondola base. The proposed actuator is a displacement mechanism that moves the capsule along the gondola base. The current paper presents a feasibility study of this concept. The flight dynamic model of the balloon system is formulated and analyzed, and a preliminary investigation of feasible control logic is presented and tested. Nomenclature A = system matrix B = control matrix b = length Cba = rotation matrix (a !b) CD = drag coefficient D = drag d = length F = force g = gravity acceleration I = moment of inertia I� = controller input K = kinetic energy K = stiffness matrix L� = length M = mass matrix m� = mass n = surface normal direction p = roll rate q = pitch rate R = control weight matrix R� = vectrix r = yaw rate S = state weight matrix T = torque t = time U = potential energy u = control vector V = velocity W = wind velocity X = state vector XI = balloon inertial coordinate YI = balloon inertial coordinate ZI = balloon inertial coordinate � = control displacement � = pitch angle � a = air density � � = length � = roll angle = yaw angle ! = angular velocity ! � = angular velocity matrix Subscripts B = balloon C = capsule G = gondola P = payload T = tether � = wild card Superscripts A=B = subscriptA relative to subscriptB � = time derivative in the inertial frame � = time derivative in the local frame