Parameter estimation for towed cable systems using moving horizon estimation

This paper presents a strategy for optimal estimation of parameters for towed cable systems using moving horizon estimation (MHE). The main contributions of the work include a novel formulation of MHE using a dead-band that explicitly rejects measurement noise, real-time implementation results, and the investigation of time-varying stochastic disturbances as well as unknown yet constant disturbances. Further analysis is conducted on the observability and sensitivity of key parameters to determine which parameters can be estimated by the proposed approach using real-time streaming data from experiments. In addition to the real-time results, an offline multiobjective optimization is conducted to reveal the tradeoff between the computational burden and estimation variation. A Pareto frontier is used to demonstrate a series of optimal experimental configurations obtained by adjusting the model complexity (number of cable links and horizon steps). Finally, a multivariate parameter estimation is performed to explore the applicability of the proposed approach in simultaneously estimating multiple parameters.

[1]  Louis V. Schmidt,et al.  Dynamic modeling of a trailing wire towed by an orbiting aircraft , 1995 .

[2]  James B. Rawlings,et al.  Critical Evaluation of Extended Kalman Filtering and Moving-Horizon Estimation , 2005 .

[3]  Randal W. Beard,et al.  Optimal Trajectory Generation Using Model Predictive Control for Aerially Towed Cable Systems , 2014 .

[4]  L. Biegler,et al.  Large‐scale DAE optimization using a simultaneous NLP formulation , 1998 .

[5]  O. Egeland,et al.  Active depth control of towed cables in 2D , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[6]  Liang Sun,et al.  Motion planning and control for mothership-cable-drogue systems in aerial recovery of micro air vehicles , 2010, Proceedings of the 2010 American Control Conference.

[7]  Gerasimos G. Rigatos,et al.  Nonlinear Kalman Filters and Particle Filters for integrated navigation of unmanned aerial vehicles , 2012, Robotics Auton. Syst..

[8]  J.D. Hedengren,et al.  Moving Horizon Estimation and Control for an Industrial Gas Phase Polymerization Reactor , 2007, 2007 American Control Conference.

[9]  F. S. Hover Experiments in dynamic positioning of a towed pipe , 1993, Proceedings of OCEANS '93.

[10]  John D. Hedengren,et al.  Advanced Process Monitoring , 2011 .

[11]  Stephen P. Boyd,et al.  Embedded estimation of fault parameters in an unmanned aerial vehicle , 2006, 2006 IEEE Conference on Computer Aided Control System Design, 2006 IEEE International Conference on Control Applications, 2006 IEEE International Symposium on Intelligent Control.

[12]  Mario Innocenti,et al.  Dynamics and Control of Maneuverable Towed Flight Vehicles , 1992 .

[13]  P. Trivailo,et al.  Optimal control of aerial tethers for payload rendezvous , 2004, 2004 5th Asian Control Conference (IEEE Cat. No.04EX904).

[14]  P. Williams,et al.  Optimal Cross-Wind Towing and Power Generation with Tethered Kites , 2007 .

[15]  Bernard Etkin Stability of a Towed Body , 1998 .

[16]  Randal W. Beard,et al.  Towed body altitude stabilization and states estimation in aerial recovery of micro air vehicles , 2010 .

[17]  Meyer Nahon,et al.  Stability Analysis of a Tethered Aerostat , 2002 .

[18]  L. Biegler An overview of simultaneous strategies for dynamic optimization , 2007 .

[19]  Randal W. Beard,et al.  Multi-vehicle dynamics and control for aerial recovery of micro air vehicles , 2011 .

[20]  R. Skop,et al.  The configuration of a cable towed in a circular path. , 1971 .

[21]  Richard M. Murray,et al.  Trajectory Generation for a Towed Cable System Using Differential Flatness , 1996 .

[22]  Efstratios N. Pistikopoulos,et al.  Disturbance Estimation via Moving Horizon Estimation for In-flight Model-based Wind Estimation , 2011 .

[23]  Johnny E. Quisenberry,et al.  Dynamic Simulation of Low Altitude Aerial Tow Systems , 2004 .

[24]  Pavel Trivailo,et al.  Dynamics of Circularly Towed Aerial Cable Systems, Part I: Optimal Configurations and Their Stability , 2007 .

[25]  Paul Williams,et al.  Dynamics of Towed Payload System Using Multiple Fixed-Wing Aircraft , 2009 .

[26]  Gabriele Pannocchia,et al.  Disturbance models for offset‐free model‐predictive control , 2003 .

[27]  Eric C. Kerrigan,et al.  Offset-free control of constrained linear discrete-time systems subject to persistent unmeasured disturbances , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[28]  I. Kolodner,et al.  Heavy rotating string—a nonlinear eigenvalue problem , 1955 .

[29]  Akira Obata,et al.  Longitudinal stability analysis of aerial-towed systems , 1992 .

[30]  Timothy W. McLain,et al.  Aerial rendezvous of small unmanned aircraft using a passive towed cable system , 2014 .

[31]  P. Trivailo,et al.  Circularly-Towed Lumped Mass Cable Model Validation from Experimental Data , 2006 .

[32]  Joseph Genin,et al.  Coupling of Longitudinal and Transverse Motions of a Flexible Cable in a Uniform Flow Field , 1972 .

[33]  Robin Tucker,et al.  A NON-LINEAR EIGENVALUE PROBLEM ASSOCIATED WITH INEXTENSIBLE WHIRLING STRINGS , 2001 .

[34]  Paul Williams Optimal terrain-following for towed-aerial-cable sensors , 2006 .

[35]  Kody M. Powell,et al.  Nonlinear modeling, estimation and predictive control in APMonitor , 2014, Comput. Chem. Eng..

[36]  Ronald L. Huston,et al.  Modeling of Variable Length Towed and Tethered Cable Systems , 1999 .

[37]  F. Campillo,et al.  Convolution Particle Filter for Parameter Estimation in General State-Space Models , 2009, IEEE Transactions on Aerospace and Electronic Systems.

[38]  Timothy W. McLain,et al.  Dynamics and control of cable-drogue system in aerial recovery of Micro Air Vehicles based on Gauss's Principle , 2009, 2009 American Control Conference.

[39]  Kenneth R. Muske,et al.  Disturbance modeling for offset-free linear model predictive control , 2002 .

[40]  James W. Kamman,et al.  Modeling and Simulation of Hose-Paradrogue Aerial Refueling Systems , 2010 .

[41]  J F Henderson,et al.  The dynamics of an airborne towed target system with active control , 1999 .

[42]  Paul Williams Periodic Optimal Control of a Towed Aerial-Cable System in Presence of Cross-Wind , 2006 .

[43]  Shrabani Ghosh,et al.  Tracking Reentry Ballistic Targets using Acceleration and Jerk Models , 2011, IEEE Transactions on Aerospace and Electronic Systems.

[44]  S. Jones,et al.  Nonlinear Dynamic Simulation of a Tethered Aerostat , 1981 .

[45]  Lorenz T. Biegler,et al.  On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming , 2006, Math. Program..

[46]  Randal W. Beard,et al.  Towed-body trajectory tracking in aerial recovery of micro air vehicle in the presence of wind , 2011, Proceedings of the 2011 American Control Conference.

[47]  Halil Ersin Soken,et al.  UKF-Based Reconfigurable Attitude Parameters Estimation and Magnetometer Calibration , 2012, IEEE Transactions on Aerospace and Electronic Systems.