Identification of linear multivariable systems from a single set of data by identification of observers with assigned real eigenvalues

A formulation is presented for identification of linear multivariable from a single set of input-output data. The identification method is formulated with the mathematical framework of learning identifications, by extension of the repetition domain concept to include shifting time intervals. This method contrasts with existing learning approaches that require data from multiple experiments. In this method, the system input-output relationship is expressed in terms of an observer, which is made asymptotically stable by an embedded real eigenvalue assignment procedure. Through this relationship, the Markov parameters of the observer are identified. The Markov parameters of the actual system are recovered from those of the observer, and then used to obtain a state space model of the system by standard realization techniques. The basic mathematical formulation is derived, and numerical examples presented to illustrate

On Markov parameters in system identification

A detailed discussion of Markov parameters in system identification is given. Different forms of input-output representation of linear discrete-time systems are reviewed and discussed. Interpretation of sampled response data as Markov parameters is presented. Relations between the state-space model and particular linear difference models via the Markov parameters are formulated. A generalization of Markov parameters to observer and Kalman filter Markov parameters for system identification is explained. These extended Markov parameters play an important role in providing not only a state-space realization, but also an observer/Kalman filter for the system of interest

Comparison of several system identification methods for flexible structures

In the last few years various methods of identifying structural dynamics models from modal testing data have appeared. A comparison is presented of four of these algorithms: the Eigensystem Realization Algorithm (ERA), the modified version ERA/DC where DC indicated that it makes use of data correlation, the Q-Markov Cover algorithm, and an algorithm due to Moonen, DeMoor, Vandenberghe, and Vandewalle. The comparison is made using a five mode computer module of the 20 meter Mini-Mast truss structure at NASA Langley Research Center, and various noise levels are superimposed to produced simulated data. The results show that for the example considered ERA/DC generally gives the best results; that ERA/DC is always at least as good as ERA which is shown to be a special case of ERA/DC; that Q-Markov requires the use of significantly more data than ERA/DC to produce comparable results; and that is some situations Q-Markov cannot produce comparable results

Rules and Mutation - A Theory of How Efficiency and Rawlsian Egalitarianism/Symmetry May Emerge

For any game, we provide a justification for why in the long-run outcomes are mostly both efficient and egalitarian/symmetric in the Rawlsian sense. We do this by constructing an adaptive dynamic framework with four features. First, agents select rules to implement actions. Second, rule selection satisfies some minimal payoff monotonicity: rules that do best are chosen with a positive probability. Third, in choosing rules agents are subject to "small" random mutation. Fourth mutation is payoff-dependent with agents mutating more when they do badly than when they do well. Our main result is: if the set of feasible rules R is sufficiently rich then outcomes that survive maximise the payoff of the player that does least well. We also show that if R is restricted to those that do best-reply on uniform histories then outcomes that survive are efficient and egalitarian amongst the set of minimum weak CURB sets. Finally, we consider long-run outcomes assuming mutation is payoff-independent; in contrast to our strong selection result above, in this case we show indeterminacy: any outcome can survive if R is sufficiently rich

System identification from closed-loop data with known output feedback dynamics

This paper presents a procedure to identify the open loop systems when it is operating under closed loop conditions. First, closed loop excitation data are used to compute the system open loop and closed loop Markov parameters. The Markov parameters, which are the pulse response samples, are then used to compute a state space representation of the open loop system. Two closed loop configurations are considered in this paper. The closed loop system can have either a linear output feedback controller or a dynamic output feedback controller. Numerical examples are provided to illustrate the proposed closed loop identification method

Passive dynamic controllers for nonlinear mechanical systems

A methodology for model-independant controller design for controlling large angular motion of multi-body dynamic systems is outlined. The controlled system may consist of rigid and flexible components that undergo large rigid body motion and small elastic deformations. Control forces/torques are applied to drive the system and at the same time suppress the vibration due to flexibility of the components. The proposed controller consists of passive second-order systems which may be designed with little knowledge of the system parameter, even if the controlled system is nonlinear. Under rather general assumptions, the passive design assures that the closed loop system has guaranteed stability properties. Unlike positive real controller design, stabilization can be accomplished without direct velocity feedback. In addition, the second-order passive design allows dynamic feedback controllers with considerable freedom to tune for desired system response, and to avoid actuator saturation. After developing the basic mathematical formulation of the design methodology, simulation results are presented to illustrate the proposed approach to a flexible six-degree-of-freedom manipulator

Identification of linear systems by an asymptotically stable observer

A formulation is presented for the identification of a linear multivariable system from single or multiple sets of input-output data. The system input-output relationship is expressed in terms of an observer, which is made asymptotically stable by an embedded eigenvalue assignment procedure. The prescribed eigenvalues for the observer may be real, complex, mixed real and complex, or zero. In this formulation, the Markov parameters of the observer are identified from input-output data. The Markov parameters of the actual system are then recovered from those of the observer and used to obtain a state space model of the system by standard realization techniques. The basic mathematical formulation is derived, and extensive numerical examples using simulated noise-free data are presented to illustrate the proposed method

An application of the Observer/Kalman Filter Identification (OKID) technique to Hubble flight data

The objective of the current research is to identify vibration parameters, including frequencies, damping ratio and uncertainty characteristics, of the Hubble Space Telescope from flight data using an advanced system identification technique. The Observer/Kalman Filter Identification (OKID) technique is used to identify the vibration parameters. The OKID was recently developed by the researchers in the Spacecraft Dynamics Branch at NASA Langley Research Center

Broadband Noise Control Using Predictive Techniques

Predictive controllers have found applications in a wide range of industrial processes. Two types of such controllers are generalized predictive control and deadbeat control. Recently, deadbeat control has been augmented to include an extended horizon. This modification, named deadbeat predictive control, retains the advantage of guaranteed stability and offers a novel way of control weighting. This paper presents an application of both predictive control techniques to vibration suppression of plate modes. Several system identification routines are presented. Both algorithms are outlined and shown to be useful in the suppression of plate vibrations. Experimental results are given and the algorithms are shown to be applicable to non- minimal phase systems

Reduced order models for control of fluids using the Eigensystem Realization Algorithm

In feedback flow control, one of the challenges is to develop mathematical models that describe the fluid physics relevant to the task at hand, while neglecting irrelevant details of the flow in order to remain computationally tractable. A number of techniques are presently used to develop such reduced-order models, such as proper orthogonal decomposition (POD), and approximate snapshot-based balanced truncation, also known as balanced POD. Each method has its strengths and weaknesses: for instance, POD models can behave unpredictably and perform poorly, but they can be computed directly from experimental data; approximate balanced truncation often produces vastly superior models to POD, but requires data from adjoint simulations, and thus cannot be applied to experimental data. In this paper, we show that using the Eigensystem Realization Algorithm (ERA) \citep{JuPa-85}, one can theoretically obtain exactly the same reduced order models as by balanced POD. Moreover, the models can be obtained directly from experimental data, without the use of adjoint information. The algorithm can also substantially improve computational efficiency when forming reduced-order models from simulation data. If adjoint information is available, then balanced POD has some advantages over ERA: for instance, it produces modes that are useful for multiple purposes, and the method has been generalized to unstable systems. We also present a modified ERA procedure that produces modes without adjoint information, but for this procedure, the resulting models are not balanced, and do not perform as well in examples. We present a detailed comparison of the methods, and illustrate them on an example of the flow past an inclined flat plate at a low Reynolds number.Comment: 22 pages, 7 figure