Exogenous Force Estimation Using Disturbance Modeling for Optical Trap Experiments

Author(s):  
Jason G. Pickel ◽  
Daniel G. Cole

In many optical trapping experiments, exogenous forces are estimated by assuming the exogenous force is balanced with the optical force. These optical forces are measured using Hooke’s law, and the displacement of the particle is low-pass filtered to minimize the effects of Brownian noise. This paper explores a different approach that uses a disturbance model approach for estimating exogenous forces using a Kalman filter. The state estimate is then used in a LQG structure to manipulate the relative position of a dielectric particle within an optical trap. The exogenous force estimate using a Kalman filter has been shown to have a higher SNR than the force estimation using Hooke’s Law. In addition to force estimation, the control structure can also manipulate the relative displacement of the particle to satisfy experimental conditions. A simulation is presented to demonstrate the performance of the LQG control structure.

Author(s):  
D. G. Cole ◽  
J. G. Pickel

This article explores nonlinear proportional plus integral (PI) feedback for controlling the position of an object held in an optical trap. In general, nonlinearities in the spatial dependence of the optical force complicate feedback control for optical traps. Nonlinear PI control has been shown to provide all of the benefits of integral control: disturbance rejection, servo tracking, and force estimation. The controller also linearizes the closed-loop system. More importantly, the nonlinear controller is shown to be equivalent to an estimator of the exogenous force. The ability of nonlinear PI control to lower the measurement SNR is evaluated and compared to the variational open-loop case. A simulation demonstrating the performance of the nonlinear PI control is presented.


Author(s):  
Daniel G. Cole

This article explores nonlinear position plus integral (PI) feedback for controlling an optical trap used in single-molecule experiments. In general, nonlinearities in the spatial dependence of the optical force complicate feedback control for optical traps. Furthermore, the extension of a molecule creates an additional feedback path that puts constraints on the PI control gains. The nonlinear PI control presented here is shown to provide all of the benefits of integral control: disturbance rejection, servo tracking, and force estimation. The ability of nonlinear PI control to lower the measurement SNR is evaluated. Finally, constraints on the pulling rate are given to ensure the system trajectory remains in a quasi-static condition, stable, and the bead remains held in the trap.


2013 ◽  
Vol 62 (2) ◽  
pp. 251-265 ◽  
Author(s):  
Piotr J. Serkies ◽  
Krzysztof Szabat

Abstract In the paper issues related to the design of a robust adaptive fuzzy estimator for a drive system with a flexible joint is presented. The proposed estimator ensures variable Kalman gain (based on the Mahalanobis distance) as well as the estimation of the system parameters (based on the fuzzy system). The obtained value of the time constant of the load machine is used to change the values in the system state matrix and to retune the parameters of the state controller. The proposed control structure (fuzzy Kalman filter and adaptive state controller) is investigated in simulation and experimental tests.


1963 ◽  
Vol 3 (01) ◽  
pp. 1-8 ◽  
Author(s):  
N.T. Burdine

BURDINE, N.T., SOCONY MOBIL OIL CO., INC., DALLAS, TEX Abstract The present investigation is concerned with the cumulative damage to rock samples when exposed to cyclic stresses under various loading conditions. Information on the response of rocks to repetitive deformational forces is an essential prerequisite to an understanding of the fundamentals of drilling. Using a laboratory designed and constructed dynamic-stress apparatus, preliminary data were obtained on cylindrical rock samples. The experiments consist of measuring the number of cycles to failure for a given axial load ( static plus dynamic). Data were obtained for various confining and pore pressures, pore fluids (air and water), frequencies of stress application and loading procedures. The results are related to failure theories and dynamic fatigue properties of other materials. Introduction In most conventional and new drilling processes, repetitive forces are applied to the bottom of the borehole. Furthermore, in hard-rock drilling the number of applications of the forces to a particular section of rock may become excessively large. The present investigation is concerned with the cumulative damage to rocks when exposed to cyclic stresses under various loading conditions. It is believed that the experiments will lead to a better understanding of the mechanical response of rocks to particular deformational forces and to a more efficient drillingprocedure.Thepresent investigation is the initial part of a general study of the behavior of inelastic materials under static and dynamic conditions, including both theoretical and experimental studies. SURVEY OF FAILURE THEORIES OF MATERIALS Few, even phenomenological, theories on rock deformation have been established because the state of knowledge of flow, fracture and strength of rocks is largely empirical. Most of the theories that do exist were originally formulated for other materials. HOOKE'S LAW The state of stress in continuous media is completely determined by the stress tensor and the state of deformation by the strain tensor . In the linear theory of elasticity the generalized Hooke's law is ..........................(1) where the coefficients are the components of the elasticity tensor. For homogeneous and isotropic conditions the number of independent coefficients reduce to two, and Eq. 1 becomes ..................(2) in which and are Lame's constants; is the kronecker delta; and is the dilation. This simplified version of Hooke's law has been used quite extensively in geophysical research where most of the information about the mechanical properties of the earth have been obtained. However, it has only limited application in rock fatigue studies. MATERIAL BEHAVIOR Many solids obey Hooke's law at small stresses, but for higher stresses a hysteretic effect occurs due to temporary or permanent residual deformation of the solid (inelastic deformation). Such deviations in mechanical behavior exist in varying degrees in different classes of materials. Most elastic materials have a microscopic heterogeneity due either to random distribution of anisotropic particles, or due to some preferred particle orientation, or both. Other materials are quite grossly heterogeneous. And the method of formation, particularly in rocks, oftentimes creates residual stress concentrations which have complicated states of imperfect equilibrium. Also, the thermal effects resulting from structural behavior give rise to nonuniform temperature distributions and the degradation of mechanical energy. When such bodies are exposed to certain large loading conditions, the inelastic behavior is intensified so strongly that the deformation, normally brittle, becomes ductile. SPEJ P. 1^


Author(s):  
Michael D. Paskett ◽  
Mark R. Brinton ◽  
Taylor C. Hansen ◽  
Jacob A. George ◽  
Tyler S. Davis ◽  
...  

Abstract Background Advanced prostheses can restore function and improve quality of life for individuals with amputations. Unfortunately, most commercial control strategies do not fully utilize the rich control information from residual nerves and musculature. Continuous decoders can provide more intuitive prosthesis control using multi-channel neural or electromyographic recordings. Three components influence continuous decoder performance: the data used to train the algorithm, the algorithm, and smoothing filters on the algorithm’s output. Individual groups often focus on a single decoder, so very few studies compare different decoders using otherwise similar experimental conditions. Methods We completed a two-phase, head-to-head comparison of 12 continuous decoders using activities of daily living. In phase one, we compared two training types and a smoothing filter with three algorithms (modified Kalman filter, multi-layer perceptron, and convolutional neural network) in a clothespin relocation task. We compared training types that included only individual digit and wrist movements vs. combination movements (e.g., simultaneous grasp and wrist flexion). We also compared raw vs. nonlinearly smoothed algorithm outputs. In phase two, we compared the three algorithms in fragile egg, zipping, pouring, and folding tasks using the combination training and smoothing found beneficial in phase one. In both phases, we collected objective, performance-based (e.g., success rate), and subjective, user-focused (e.g., preference) measures. Results Phase one showed that combination training improved prosthesis control accuracy and speed, and that the nonlinear smoothing improved accuracy but generally reduced speed. Phase one importantly showed simultaneous movements were used in the task, and that the modified Kalman filter and multi-layer perceptron predicted more simultaneous movements than the convolutional neural network. In phase two, user-focused metrics favored the convolutional neural network and modified Kalman filter, whereas performance-based metrics were generally similar among all algorithms. Conclusions These results confirm that state-of-the-art algorithms, whether linear or nonlinear in nature, functionally benefit from training on more complex data and from output smoothing. These studies will be used to select a decoder for a long-term take-home trial with implanted neuromyoelectric devices. Overall, clinical considerations may favor the mKF as it is similar in performance, faster to train, and computationally less expensive than neural networks.


1939 ◽  
Vol 7 (2) ◽  
pp. 134-134
Author(s):  
Zigmond Wilchinsky

2015 ◽  
Vol 5 (1) ◽  
Author(s):  
Hao Hu ◽  
Hepeng Ding ◽  
Feng Liu

1990 ◽  
Vol 207 ◽  
Author(s):  
Stephen C. Cowin

AbstractThis paper addresses the question of representing the dependence of the elastic coefficients in the anisotropic form of Hooke's law upon the microstructure of a material. The concern is with textured material symmetries, that is to say materials such as natural and man-made composites whose material symmetry is determined by microstructural organization. The approach is to relate the anisotropic elastic coefficients to local geometric or stereological measures of the microstructure. The predictions of micromechanical models and continuum mechanical models are compared and are found to be consistent with each other.


2000 ◽  
Vol 159 ◽  
pp. 1-24 ◽  
Author(s):  
Masayuki Henmi ◽  
Ryoichi Kobayashi

The concept of the canonical divergence is defined for dually flat statistical manifolds in terms of the Legendre transform between dual affine coordinates. In this article, we introduce a new two point function defined for any triple (g,∇, ∇*) of a Riemannian metric g and two affine connections ∇ and ∇*. We show that this interprets the canonical divergence without refering to the existence of special coordinates (dual affine coordinates) but in terms of only classical mechanics concerning ∇- and ∇*-geodesics. We also discuss the properties of the two point function and show that this shares some important properties with the canonical divergence defined on dually flat statistical manifolds.


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