This paper discusses an algorithm lo compute the Markov parameters of an observer or Kalman filter from experimental input and output data. The Markov parameters can then be used for identificatinn of a state-space representation, with associated Kalman or observer gain, for the purpose of controller design. The algorithm is a nonrecursive matrix version of two recursive algorithms developed in previous works for different purposes, and the relationship between these other algorithms is developed. The new matrix formulation here gives insight into the existence and uniqueness of solutions of certain equations and offers bounds on the proper choice of observer order. It is shown that if one uses data containing noise and seeks the fastest possible deterministic observer, the deadbeat observer, one instead obtains the Kalman filter, which is the fastest possible observer in the stochastic environment. The results of the paper are demonstrated in numerical studies and experiments on the Huhhle space telescope.

This paper discusses an algorithm lo compute the Markov parameters of an observer or Kalman filter from experimental input and output data. The Markov parameters can then be used for identificatinn of a state-space representation, with associated Kalman or observer gain, for the purpose of controller design. The algorithm is a nonrecursive matrix version of two recursive algorithms developed in previous works for different purposes, and the relationship between these other algorithms is developed. The new matrix formulation here gives insight into the existence and uniqueness of solutions of certain equations and offers bounds on the proper choice of observer order. It is shown that if one uses data containing noise and seeks the fastest possible deterministic observer, the deadbeat observer, one instead obtains the Kalman filter, which is the fastest possible observer in the stochastic environment. The results of the paper are demonstrated in numerical studies and experiments on the Huhhle space telescope.

No abstract

The NASA Morphing Project seeks to develop and assess advanced technologies and integrated component concepts to enable efficient, multi-point adaptability in air and space vehicles. In the context of the project, the word "morphing" is defined as "efficient, multi-point adaptability" and may include macro, micro, structural and/or fluidic approaches.The project includes research on smart materials, adaptive structures, micro flow control, biomimetic concepts, optimization and controls. This paper presents an updated overview of the content of the Morphing Project including highlights of recent research results.

PROBLEM FORMULATIONThe governing equations of motion for a general multi-story shear frame structure with a passivevibration isolator arewhere M, C, and K are mass, damping, and stiffness matrices, respectively, and x is the vector containing the floor displacement relative to the base. As shown in Figure 1, xb is the relative displacement between the base of the structure and the ground, _g is the horizontal ground acceleration, and {1} is a column vector whose elements are all unity. For a fixed-base structure (without a passive isolator), _b --0. In this study, a three-story building is the structural model. Olb mbThe natural frequency of the laminated rubber bearing wb, and its effective damping ratio _b are defined as 2¢'bWbCb kbwhere mt is the total mass of the structure, and cb and kb are the damping and the horizontal stiffness of the bearing, respectively. The parameter ab is the ratio of base mass to the total mass of the structure, i.e.,where mi is the ith floor mass , and rnb is the effective base mass of the structure.In this study, a commonly suggested natural frequency of 0. where B is a n x p actuator force distribution matrix for the p x 1 control vector u, y is the m x 1 measurement vector, and Ha is the m x n acceleration influence matrix.The second-order AVA controller, is governed by the system equations where, G_ is a gain matrix defined asSince the sensors/actuators are collocated,Let, B_ be defined asthen the closed-loop mass matrix becomeswhich is symmetric. To assure positive definiteness In this study, the second-order controller is assumed to be attached to the third floor as shown in Figure 1. The AVA control law is u = +The xc is computed from from first to third floor. With the active AVA controller as shown in Figure 3b, the absolute accelerationlevel at all floors is reducedin comparisonto Figure 3a, however,the amplification of the transmitted accelerationat higher floors is noticeable.A structure with passiveand hybrid controllersshowssignificant accelerationreduction at all floor levels as shown in Figures3c and 3d. Furthermore,the passiveand hybrid systemsfilter the high frequencycontentsof the ground acceleration. Figures 3c and 3d also showthat the accelerationtime histories of different floors areroughly the same.This implies that when passiveand/or hybrid control systemsareused,the super-structurevibrates more like a rigid body and doesnot amplify the ground excitation.Fourier decompositionsof the accelerationresponses at eachfloor for variousvibration control systemsare shown in Figure 4. This figure showsthe frequency content of the accelerationat different floors for structure with and without vibration control devices. The Fourier spectrum of the ground shown in Figure 4a is that of the accelerogramof the N00W componentof the E1 Centro 1940earthquake. It is observedthat the ground accelerationhas a broad spectrum in the frequency rangeof 1 to 5 Hz. During an earthquake, the unprotected building filters the broad-band excitation into narrow-band vibration at its fun...