A Nonlinear State-Space Model of a Resonating Single Fiber Scanner for Tracking Control: Theory and Experiment

2004 ◽  
Vol 126 (1) ◽  
pp. 88-101 ◽  
Author(s):  
Quinn Y. J. Smithwick ◽  
Per G. Reinhall ◽  
Juris Vagners ◽  
Eric J. Seibel
Keyword(s):  
State Space ◽  
State Space Model ◽  
Single Fiber ◽  
Model Parameters ◽  
Experimental Frequency ◽  
Centripetal Acceleration ◽  
Frequency Responses ◽  
Continuum Dynamics ◽  
Nonlinear Continuum ◽  
Nonlinear State

A nonlinear state-space dynamic model of a resonating single fiber scanner is developed to understand scan distortion—jump, whirl, amplitude dependent amplitude and phase shifts—and as the basis for controllers to remove those distortions. The non-planar nonlinear continuum dynamics of a resonating base excited cantilever are reduced to a set of state-space coupled Duffing equations with centripetal acceleration. Methods for experimentally determining the model parameters are developed. The analytic frequency responses for raster, spiral and propeller scans are derived, and match experimental frequency responses for all three scan patterns, for various amplitudes, and using the same model parameters.

scholarly journals Bayesian Analysis of Interleaved Learning and Response Bias in Behavioral Experiments

2007 ◽  
Vol 97 (3) ◽  
pp. 2516-2524 ◽  
Author(s):  
Anne C. Smith ◽  
Sylvia Wirth ◽  
Wendy A. Suzuki ◽  
Emery N. Brown
Keyword(s):  
Bayesian Analysis ◽  
State Space ◽  
State Space Model ◽  
Estimation Procedure ◽  
Ideal Observer ◽  
Model Parameters ◽  
Behavioral Experiments ◽  
Actual Object ◽  
Space Model ◽  
Multiple Tasks

Accurate characterizations of behavior during learning experiments are essential for understanding the neural bases of learning. Whereas learning experiments often give subjects multiple tasks to learn simultaneously, most analyze subject performance separately on each individual task. This analysis strategy ignores the true interleaved presentation order of the tasks and cannot distinguish learning behavior from response preferences that may represent a subject's biases or strategies. We present a Bayesian analysis of a state-space model for characterizing simultaneous learning of multiple tasks and for assessing behavioral biases in learning experiments with interleaved task presentations. Under the Bayesian analysis the posterior probability densities of the model parameters and the learning state are computed using Monte Carlo Markov Chain methods. Measures of learning, including the learning curve, the ideal observer curve, and the learning trial translate directly from our previous likelihood-based state-space model analyses. We compare the Bayesian and current likelihood–based approaches in the analysis of a simulated conditioned T-maze task and of an actual object–place association task. Modeling the interleaved learning feature of the experiments along with the animal's response sequences allows us to disambiguate actual learning from response biases. The implementation of the Bayesian analysis using the WinBUGS software provides an efficient way to test different models without developing a new algorithm for each model. The new state-space model and the Bayesian estimation procedure suggest an improved, computationally efficient approach for accurately characterizing learning in behavioral experiments.

scholarly journals Adaptive Model Predictive Vibration Control of a Cantilever Beam with Real-Time Parameter Estimation

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
Gergely Takács ◽  
Tomáš Polóni ◽  
Boris Rohal’-Ilkiv
Keyword(s):  
Control System ◽  
Vibration Control ◽  
State Space ◽  
Real Time ◽  
Cantilever Beam ◽  
State Space Model ◽  
Model Parameters ◽  
Extended Kalman Filtering ◽  
Space Model ◽  
Continuous State

This paper presents an adaptive-predictive vibration control system using extended Kalman filtering for the joint estimation of system states and model parameters. A fixed-free cantilever beam equipped with piezoceramic actuators serves as a test platform to validate the proposed control strategy. Deflection readings taken at the end of the beam have been used to reconstruct the position and velocity information for a second-order state-space model. In addition to the states, the dynamic system has been augmented by the unknown model parameters: stiffness, damping constant, and a voltage/force conversion constant, characterizing the actuating effect of the piezoceramic transducers. The states and parameters of this augmented system have been estimated in real time, using the hybrid extended Kalman filter. The estimated model parameters have been applied to define the continuous state-space model of the vibrating system, which in turn is discretized for the predictive controller. The model predictive control algorithm generates state predictions and dual-mode quadratic cost prediction matrices based on the updated discrete state-space models. The resulting cost function is then minimized using quadratic programming to find the sequence of optimal but constrained control inputs. The proposed active vibration control system is implemented and evaluated experimentally to investigate the viability of the control method.

The nonlinear state space model

2012 ◽  
pp. 146-168
Author(s):  
Sean Meyn ◽  
Richard L. Tweedie ◽  
Peter W. Glynn
Keyword(s):  
State Space ◽  
State Space Model ◽  
Space Model ◽  
Nonlinear State

scholarly journals Multiple-Input Single-Output Polynomial Nonlinear State-Space Model of the Li-ion Battery’s Short-term Dynamics

2018 ◽  
Vol 51 (15) ◽  
pp. 497-502
Author(s):  
Rishi Relan ◽  
Koen Tiels ◽  
Jean-Marc Timmermans ◽  
Johan Schoukens
Keyword(s):  
State Space ◽  
State Space Model ◽  
Short Term ◽  
Space Model ◽  
Single Output ◽  
Multiple Input ◽  
Li Ion ◽  
Nonlinear State

scholarly journals Specification of initial Kalman recursions of symmetric nonlinear state-space model

Heliyon ◽  
2020 ◽  
Vol 6 (10) ◽  
pp. e05152
Author(s):  
M. Tasi'u ◽  
H.G. Dikko ◽  
O.I. Shittu ◽  
I.A. Fulatan
Keyword(s):  
State Space ◽  
State Space Model ◽  
Space Model ◽  
Nonlinear State
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