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Research Papers

Real-Time Estimation of Endogenous and Exogenous Inputs

[+] Author and Article Information
William Kirchner

Flight Control and Navigation,
Rockwell Collins Control Technologies,
Warrenton, VA 20187
e-mail: william.kirchner@gmail.com

Steve Southward

Associate Professor
Performance Engineering Research Lab,
Department of Mechanical Engineering,
Virginia Tech,
Blacksburg, VA 24061
e-mail: scsouth@vt.edu

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received March 31, 2013; final manuscript received January 4, 2014; published online March 13, 2014. Assoc. Editor: Srinivasa M. Salapaka.

J. Dyn. Sys., Meas., Control 136(4), 041005 (Mar 13, 2014) (10 pages) Paper No: DS-13-1140; doi: 10.1115/1.4026473 History: Received March 31, 2013; Revised January 04, 2014

Nearly all dynamic systems have input excitations that are either unmeasurable or unknown due to practical constraints such as feasibility or cost. Estimation of these excitations can be useful both in control applications as well as system modeling applications. The objective of this work is to expand upon an observer based approach to estimate unmeasurable or unknown inputs to a dynamic system using linear systems theory in an efficient manner that is suitable for real-time implementation. In this work, we explicitly explore two fundamental questions. How should the structure, dimensionality, and parameterization of an internal model or waveform generator model be selected for a given dynamic system? How do we determine, based on the structure of the dynamic system, whether estimation of exogenous and endogenous inputs is possible? A series of numerical simulations is performed, providing insight into these issues.

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Figures

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Fig. 1

Generalized nonlinear dynamic system model with exogenous and endogenous inputs

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Fig. 2

Simple second-order oscillator with exogenous forcing input

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Fig. 3

The 1-DOF bouncing ball model used for simulation

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Fig. 4

Free body diagram of bouncing ball approximated as spring mass damper system

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Fig. 5

Bicycle model used to include lateral dynamics

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Fig. 6

Longitudinal dynamics of the planar bicycle model

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Fig. 7

Proposed architecture for estimating exogenous and endogenous inputs

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Fig. 8

Simulation results for the second-order forced oscillator; (a) position and (b) disturbance error

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Fig. 9

Simulation results for the bouncing ball dynamics; (a) position and (b) disturbance error

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Fig. 10

Disturbance estimation results for the bouncing ball dynamics at the second point of impact with the ground plane

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Fig. 11

Disturbance estimation error results for Duffings' equation

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Fig. 12

Vehicle position results from a simulation of a vehicle performing a circular driving maneuver at a fixed steering angle δf = 60 deg on a flat uniform surface

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Fig. 13

Disturbance error in v∧' between the Kalman filter and the true values using data from a simulation of a vehicle performing a circular driving maneuver at a fixed steering angle δf = 60 deg on a flat uniform surface

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