Canadian researchers have proposed a design for a new radio telescope consisting of an array of very large re ectors. A large multitethered aerostat will be used to support each re ector's receiver. The length of each tether can be adjusted by ground-based winches, and active control is used to overcome the effects of wind turbulence on the aerostat. To aid in the system's mechanical and controller design, a computer model has been developed, including models of the tethers and the aerostat. Two types of aerostat have been considered: spherical and streamlined. A wind turbulence model is incorporated to provide disturbance to the system. Controllers are used to adjust the tether lengths based on feedback of the receiver's position. The model is used to optimize the control gains. We nd that, with 50 kW available at each winch, it is possible to maintain the receiver's position within 85 cm of its desired location, even in the worst-case con guration.
NomenclatureA = cross-sectional area of cable element, or n aspect ratio A f = n planform area a = constant in von Kármán turbulence model C D , C D0 = n drag coef cient, n parasitic drag coef cient C d = normal drag coef cient of cable element, spherical aerostat, or receiver C L = n lift coef cient C v = cable damping coef cient (Cd h / 0 , (Cd c / h = hull zero-angle axial and cross ow drag coef cients D h = drag force acting on hull D s = aerodynamic drag force on receiver or spherical aerostat D i = aerodynamic drag force on cable element, [D i p1 , D i p2; D i q ] T d c = diameter of cable element d s = aerostat or receiver diameter E = effective Young's modulus of cable element E max = maximum error in receiver position e = n ef ciency factor e j = error in distance between winch and receiver f p , f q = aerodynamic loading functions g = gravitational acceleration h, h g = height and gradient height in the planetary boundary layer I 1 , I 3 = hull-related geometric quantities J 1 , J 3 = hull-related geometric quantities k P , k D , k I = proportional, derivative, and integral controller gains 3055. Student Member AIAA.k 1 , k 3 = axial and lateral added-mass coef cients L, L 0 , 1L = tether length, initial length, and change in length L u , L v , L w = turbulence scale lengths in longitudinal, lateral, and vertical directions l i , l i u = stretched and unstretched length cable element M nose = moment about the nose acting on hull m c = mass of cable element N= number of discrete spectral bands considered in turbulence spectrum N h = transverse force acting on hull n t ; n l = number of elements in each tether and in the leash P max = maximum winch power required P i q = tension due to internal damping in cable element p 1 , p 2 , q = axes of the element-xed reference frame p, p d = actual and desired position of receiver p W j = winch position q 0 = steady-state dynamic pressure, ½ V 2hull reference area, (hull volume) 2=3 T i = tether tension at winch i T i q = tension due to structural stiffness in cable element t , T = number of tethers or time, and total...