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Academic Commons Search Resultsen-usSuperspace and Subspace Identification of Bilinear Models by Discrete-Level Inputs
https://academiccommons.columbia.edu/catalog/ac:192778
Phan, Minh Q.; Vicario, Francesco; Longman, Richard W.; Betti, Raimondohttp://dx.doi.org/10.7916/D8XS5V4CTue, 05 Jan 2016 18:01:48 +0000When excited by an input consisting of a number of discrete levels, a bilinear system becomes a linear time-varying system whose dynamics switches from one linear subsystem to another depending on the input level. This paper describes an identification method that uses the concept of a superstate of a linear switching system as a superstate of the bilinear system. In a superspace method, these superstates are used directly to identify a bilinear system model. In a subspace method, two or more superstate representations are intersected to find a reduced dimension subspace prior to identification of a bilinear model.Mechanical engineering, Mathematics, Aerospace engineering, Space flight--Mathematical models, State-space methods, Bilinear formsfv2157, rwl4, rb68Mechanical Engineering, Civil Engineering and Engineering MechanicsConferencesOKID as a Unified Approach to System Identification
https://academiccommons.columbia.edu/catalog/ac:192629
Vicario, Francesco; Phan, Minh Q.; Betti, Raimondo; Longman, Richard W.http://dx.doi.org/10.7916/D869739XTue, 05 Jan 2016 17:38:15 +0000This paper presents a unified approach for the identification of linear state-space models from input-output measurements in the presence of noise. It is based on the established Observer/Kalman filter IDentification (OKID) method of which it proposes a new formulation capable of transforming a stochastic identification problem into a (simpler) deterministic problem, where the Kalman filter corresponding to the unknown system and the unknown noise covariances is identified. The system matrices are then recovered from the identified Kalman filter. The Kalman filter can be identified with any deterministic identification method for linear state-space models, giving rise to numerous new algorithms and establishing the Kalman filter as the unifying bridge from stochastic to deterministic problems in system identification.Mechanical engineering, Mathematics, Aerospace engineering, System identification, Space flight--Mathematical models, Kalman filtering, State-space methodsfv2157, rb68, rwl4Mechanical Engineering, Civil Engineering and Engineering MechanicsConferencesBilinear Observer/Kalman Filter Identification
https://academiccommons.columbia.edu/catalog/ac:192626
Vicario, Francesco; Phan, Minh Q.; Betti, Raimondo; Longman, Richard W.http://dx.doi.org/10.7916/D8FQ9WCDTue, 05 Jan 2016 17:15:05 +0000Bilinear systems are important per se since several phenomena in engineering and other fields are inherently bilinear. Even more interestingly, bilinear systems can approximate more general nonlinear systems, providing a promising approach to handle various nonlinear identification and control problems, such as satellite attitude control. This paper develops and demonstrates via numerical examples a method for discrete-time state-space model identification for bilinear systems in the presence of noise in the process and in the measurements. The formulation relies on a bilinear observer which is proven to have properties similar to the linear Kalman filter under the sole additional assumption of stationary white excitation input, and on a novel approach to system identification based on the estimation of the observer residuals. The latter are used to construct a new, noise-free identification problem, in which the observer is identified and the matrices of the system state-space model are recovered. The resulting method represents the bilinear counterpart of the Observer/Kalman filter Identification (OKID) approach for linear systems, originally developed for the identification of lightly-damped structures and distributed by NASA.Mechanical engineering, Mathematics, Aerospace engineering, Bilinear forms, Discrete-time systems--Mathematical models, Kalman filtering, Space flight--Mathematical modelsfv2157, rb68, rwl4Mechanical Engineering, Civil Engineering and Engineering MechanicsConferencesBilinear System Identification by Minimal-Order State Observers
https://academiccommons.columbia.edu/catalog/ac:192617
Vicario, Francesco; Phan, Minh Q.; Longman, Richard W.; Betti, Raimondohttp://dx.doi.org/10.7916/D87944DVTue, 05 Jan 2016 15:44:01 +0000Bilinear systems offer a promising approach for nonlinear control because a broad class of nonlinear problems can be reformulated and approximated in bilinear form. System identification is a technique to obtain such a bilinear approximation for a nonlinear system from input-output data. Recent discrete-time bilinear model identification methods rely on Input-Output-to-State Representations (IOSRs) derived via the interaction matrix technique. A new formulation of these methods is given by establishing a correspondence between interaction matrices and the gains of full-order bilinear state observers. The new interpretation of the identification methods highlights the possibility of utilizing minimal-order bilinear state observers to derive new IOSRs. The existence of such observers is discussed and shown to be guaranteed for special classes of bilinear systems. New bilinear system identification algorithms are developed and the corresponding computational advantages are illustrated via numerical examples.Mechanical engineering, Mathematics, Aerospace engineering, Orbital mechanics, Space flight--Mathematical models, Bilinear forms, Observers (Control theory)fv2157, rwl4, rb68Mechanical Engineering, Civil Engineering and Engineering MechanicsConferencesLinear State Representations for Identification of Bilinear Discrete-Time Models by Interaction Matrices
https://academiccommons.columbia.edu/catalog/ac:187836
Vicario, Francesco; Phan, Minh Q.; Betti, Raimondo; Longman, Richard W.http://dx.doi.org/10.7916/D84X571TThu, 13 Aug 2015 15:00:36 +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, rwl4Mechanical Engineering, Civil Engineering and Engineering MechanicsArticlesAddressing Stability Robustness, Period Uncertainties, and Startup of Multiple-Period Repetitive Control for Spacecraft Jitter Mitigation
https://academiccommons.columbia.edu/catalog/ac:165159
Ahn, Edwin S.http://hdl.handle.net/10022/AC:P:21614Fri, 13 Sep 2013 15:03:33 +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
https://academiccommons.columbia.edu/catalog/ac:144391
Xu, Kevinhttp://hdl.handle.net/10022/AC:P:12492Tue, 07 Feb 2012 14:53:09 +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