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Academic Commons Search Resultsen-usLinear State Representations for Identification of Bilinear Discrete-Time Models by Interaction Matrices
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Vicario, Francesco; Phan, Minh Q.; Betti, Raimondo; Longman, Richard W.http://dx.doi.org/10.7916/D84X571TThu, 13 Aug 2015 00:00:00 +0000Bilinear systems can be viewed as a bridge between linear and nonlinear systems, providing a promising approach to handle various nonlinear identification and control problems. This paper provides a formal justification for the extension of interaction matrices to bilinear systems and uses them to express the bilinear state as a linear function of input-output data. Multiple representations of this kind are derived, making it possible to develop an intersection subspace algorithm for the identification of discrete-time bilinear models. The technique first recovers the bilinear state by intersecting two vector spaces that are defined solely in terms of input-output data. The new input-output-to-state relationships are also used to extend the Equivalent Linear Model method for bilinear system identification. Among the benefits of the proposed approach, it does not require data from multiple experiments, and it does not impose specific restrictions on the form of input excitation.Mechanical engineering, Aerospace engineeringfv2157, rb68, rwl4Civil Engineering and Engineering Mechanics, Mechanical EngineeringArticlesAddressing Stability Robustness, Period Uncertainties, and Startup of Multiple-Period Repetitive Control for Spacecraft Jitter Mitigation
http://academiccommons.columbia.edu/catalog/ac:165159
Ahn, Edwin S.http://hdl.handle.net/10022/AC:P:21614Fri, 13 Sep 2013 00:00:00 +0000Repetitive Control (RC) is a relatively new form of control that seeks to converge to zero tracking error when executing a periodic command, or when executing a constant command in the presence of a periodic disturbance. The design makes use of knowledge of the period of the disturbance or command, and makes use of the error observed in the previous period to update the command in the present period. The usual RC approaches address one period, and this means that potentially they can simultaneously address DC or constant error, the fundamental frequency for that period, and all harmonics up to Nyquist frequency. Spacecraft often have multiple sources of periodic excitation. Slight imbalance in reaction wheels used for attitude control creates three disturbance periods. A special RC structure was developed to allow one to address multiple unrelated periods which is referred to as Multiple-Period Repetitive Control (MPRC). MPRC in practice faces three main challenges for hardware implementation. One is instability due to model errors or parasitic high frequency modes, the second is degradation of the final error level due to period uncertainties or fluctuations, and the third is bad transients due to issues in startup. Regarding these three challenges, the thesis develops a series of methods to enhance the performance of MPRC or to assist in analyzing its performance for mitigating optical jitter induced by mechanical vibration within the structure of a spacecraft testbed. Experimental analysis of MPRC shows contrasting advantages over existing adaptive control algorithms, such as Filtered-X LMS, Adaptive Model Predictive Control, and Adaptive Basis Method, for mitigating jitter within the transmitting beam of Laser Communication (LaserCom) satellites.Mechanical engineering, Electrical engineering, Aerospace engineeringesa2121Mechanical EngineeringDissertationsMulti-Input Multi-Output Repetitive Control Theory And Taylor Series Based Repetitive Control Design
http://academiccommons.columbia.edu/catalog/ac:144391
Xu, Kevinhttp://hdl.handle.net/10022/AC:P:12492Tue, 07 Feb 2012 00:00:00 +0000Repetitive control (RC) systems aim to achieve zero tracking error when tracking a periodic command, or when tracking a constant command in the presence of a periodic disturbance, or both a periodic command and periodic disturbance. This dissertation presents a new approach using Taylor Series Expansion of the inverse system z-transfer function model to design Finite Impulse Response (FIR) repetitive controllers for single-input single-output (SISO) systems, and compares the designs obtained to those generated by optimization in the frequency domain. This approach is very simple, straightforward, and easy to use. It also supplies considerable insight, and gives understanding of the cause of the patterns for zero locations in the optimization based design. The approach forms a different and effective time domain design method, and it can also be used to guide the choice of parameters in performing in the frequency domain optimization design. Next, this dissertation presents the theoretical foundation for frequency based optimization design of repetitive control design for multi-input multi-output (MIMO) systems. A comprehensive stability theory for MIMO repetitive control is developed. A necessary and sufficient condition for asymptotic stability in MIMO RC is derived, and four sufficient conditions are created. One of these is the MIMO version of the approximate monotonic decay condition in SISO RC, and one is a necessary and sufficient condition for stability for all possible disturbance periods. An appropriate optimization criterion for direct MIMO is presented based on minimizing a Frobenius norm summed over frequencies from zero to Nyquist. This design process is very tractable, requiring only solution of a linear algebraic equation. An alternative approach reduces the problem to a set of SISO design problems, one for each input-output pair. The performances of the resulting designs are studied by extensive examples. Both approaches are seen to be able to create RC designs with fast monotonic decay of the tracking error. Finally, this dissertation presents an analysis of using an experiment design sequence for parameter identification based on the theory of iterative learning control (ILC), a sister field to repetitive control. This is suggested as an alternative to the results in optimal experiment design. Modified ILC laws that are intentionally non-robust to model errors are developed, as a way to fine tune the use of ILC for identification purposes. The non-robustness with respect to its ability to improve identification of system parameters when the model error is correct is studied. It is demonstrated that in many cases the approach makes the learning particularly sensitive to relatively small parameter errors in the model, but sensitivity is sometimes limited to parameter errors of a specific sign.Electrical engineering, Mechanical engineering, Aerospace engineeringkx2101Electrical EngineeringDissertations