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.

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IDENTIFICATION AND CONTROL OF MECHANICAL SYSTEMS Vibration is a significant issue in the design of many structures including aircraft, spacecraft, bridges, and high-rise buildings. This book discusses the control of vibrating systems, integrating structural dynamics, vibration analysis, modern control, and system identification. Integrating these subjects is an important feature in that engineers will need only one book, rather than several texts or courses, to solve vibration/control problems. The book begins with a review of the fundamentals in mathematics, dynamics, and control that are needed for understanding subsequent materials. Chapters then cover recent developments in aerospace control and identification theory, including virtual passive control, observer and state-space system identification, and data-based controller synthesis. Many practical issues and applications are addressed, with examples showing how various methods are applied to real systems. Some methods show the close integration of system identification and control theory from the statespace perspective, rather than from the traditional input-output model perspective of adaptive control. This text will be useful for advanced undergraduate and beginning graduate students in aerospace, mechanical, and civil engineering, as well as for practicing engineers.