Nonlinear Proportional Plus Integral Control of Optical Traps for Exogenous Force Estimation

2011 ◽  
Vol 134 (1) ◽  
Author(s):  
D. G. Cole ◽  
J. G. Pickel
Keyword(s):  
Optical Trap ◽  
Open Loop ◽  
Optical Force ◽  
Optical Traps ◽  
Pi Control ◽  
Force Estimation ◽  
Nonlinear Controller ◽  
Closed Loop System ◽  
Integral Control ◽  
Servo Tracking

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.

On Nonlinear Control of Optical Traps Using Pulling Trajectory Tracking for Single-Molecule Experiments

2011 ◽  
Author(s):  
Daniel G. Cole
Keyword(s):  
Single Molecule ◽  
Optical Trap ◽  
Static Condition ◽  
Optical Force ◽  
Optical Traps ◽  
Pi Control ◽  
Force Estimation ◽  
Integral Control ◽  
Servo Tracking ◽  
Additional Feedback

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.

Exogenous Force Estimation Using Disturbance Modeling for Optical Trap Experiments

2011 ◽  
Author(s):  
Jason G. Pickel ◽  
Daniel G. Cole
Keyword(s):  
Kalman Filter ◽  
Control Structure ◽  
Optical Trap ◽  
Relative Displacement ◽  
Optical Force ◽  
Force Estimation ◽  
Experimental Conditions ◽  
Hooke’S Law ◽  
Hooke's Law ◽  
Disturbance Model

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.

scholarly journals Numerical Analysis of Optical Trapping Force Affected by Lens Misalignments

Photonics ◽  
2021 ◽  
Vol 8 (12) ◽  
pp. 548
Author(s):  
Hanlin Zhang ◽  
Wenqiang Li ◽  
Nan Li ◽  
Huizhu Hu
Keyword(s):  
Numerical Calculation ◽  
Numerical Analysis ◽  
Optical Trapping ◽  
Optical Trap ◽  
Geometrical Optics ◽  
Optical Force ◽  
Optical Traps ◽  
Trapping Force ◽  
Calculation Results ◽  
The Asymmetry

Geometrical optics approximation is a classic method for calculating the optical trapping force on particles whose sizes are larger than the wavelength of the trapping light. In this study, the effect of the lens misalignment on optical force was analyzed in the geometrical optics regime. We used geometrical optics to analyze the influence of off-axis placement and the tilt of the lens on the trapping position and stiffness in an optical trap. Numerical calculation results showed that lens tilting has a greater impact on the optical trap force than the off-axis misalignments, and both misalignments will couple with each other and cause a shift of the equilibrium point and the asymmetry of the optical trap stiffness in different ways. Our research revealed the asymmetry in optical traps caused by lens misalignment and can provide guidance for optimize lens placement in future experiments.

Feedback Control and Exogenous Force Estimation for Improved Single-Molecule Experiments

2010 ◽  
Author(s):  
Daniel G. Cole
Keyword(s):  
Feedback Control ◽  
Single Molecule ◽  
Force Feedback ◽  
Open Loop ◽  
Optical Traps ◽  
Measured Signal ◽  
Force Estimation ◽  
Position Feedback ◽  
Integral Feedback

This article explores two types of feedback used to control optical traps: position feedback, which was shown to be equivalent to force feedback, and integral feedback. The ability of each of these types of feedback to lower the measurement SNR in single molecule experiments is evaluated and compared to the open-loop case. While position feedback did not result in any improvement in the SNR, the case of integral feedback results in an improvement. Integral feedback is shown to improve the SNR of the measured signal of interest, and is relatively robust and easy to implement. It is also shown that integral feedback acts as an exogenous force estimator.

PI Control of HSFDs for Active Control of Rotor-Bearing Systems

1997 ◽  
Vol 119 (3) ◽  
pp. 658-667 ◽  
Author(s):  
J. P. Hathout ◽  
A. El-Shafei
Keyword(s):  
Vibration Control ◽  
Active Control ◽  
Closed Loop ◽  
Rotating Machinery ◽  
Loop System ◽  
Pi Control ◽  
Closed Loop System ◽  
Transient Vibration ◽  
Critical Speeds ◽  
Rotor Bearing

This paper describes the proportional integral (PI) control of hybrid squeeze film dampers (HSFDS) for active control of rotor vibrations. Recently it was shown that the automatically controlled HSFD based on feedback of rotor speed can be a very efficient device for active control of rotor vibration when passing through critical speeds. Although considerable effort has been put into the study of steady-state vibration control, there are few methods in the literature applicable to transient vibration control of rotor-bearing systems. Rotating machinery may experience dangerously high dynamic loading due to the sudden mass unbalance that could be associated with blade loss. Transient run-up and coast down through critical speeds when starting up or shutting down rotating machinery induces excessive bearing loads at criticals. In this paper, PI control is proposed as a regulator for the HSFD system to attenuate transient vibration for both sudden unbalance and transient runup through critical speeds. A complete mathematical model of this closed-loop system is simulated on a digital computer. Results show an overall enhanced behavior for the closed-loop rotor system. Gain scheduling of both the integral gain and the reference input is incorporated into the closed-loop system with the PI regulator and results in an enhanced behavior of the controlled system.

DETERMINING ROBUST PARAMETERS IN STABILIZING SET OF BACKSTEPPING BASED NONLINEAR CONTROLLER FOR SHIP COURSE KEEPING

2021 ◽  
Vol 158 (A3) ◽  
Author(s):  
X K Zhang ◽  
G Q Zhang
Keyword(s):  
Closed Loop ◽  
Simulation Experiment ◽  
Empirical Knowledge ◽  
Backstepping Method ◽  
Nonlinear Controller ◽  
Closed Loop System ◽  
Robust Performance ◽  
System A ◽  
Uniformly Asymptotic Stability ◽  
Novel Method

In order to solve the problem that backstepping method cannot effectively guarantee the robust performance of the closed-loop system, a novel method of determining parameter is developed in this note. Based on the ship manoeuvring empirical knowledge and the closed-loop shaping theory, the derived parameters belong to a reduced robust group in the original stabilizing set. The uniformly asymptotic stability is achieved theoretically. The training vessel “Yulong” and the tanker “Daqing232” are selected as the plants in the simulation experiment. And the simulation results are presented to demonstrate the effectiveness of the proposed algorithm.

Optimal trap velocity in a dynamic holographic optical trap using a nematic liquid crystal spatial light modulator

2022 ◽  
Author(s):  
Karuna Sindhu Malik ◽  
Bosanta Ranjan Boruah
Keyword(s):  
Liquid Crystal ◽  
Nematic Liquid Crystal ◽  
Spatial Light Modulator ◽  
Optical Trap ◽  
Optical Element ◽  
Optical Traps ◽  
Light Modulator ◽  
Step Size ◽  
Microscopic Object ◽  
Optimal Velocity

Abstract A dynamic holographic optical trap uses a dynamic diffractive optical element such as a liquid crystal spatial light modulator to realize one or more optical traps with independent controls. Such holographic optical traps provide a number of flexibilities and conveniences useful in various applications. One key requirement for such a trap is the ability to move the trapped microscopic object from one point to the other with the optimal velocity. In this paper we develop a nematic liquid crystal spatial light modulator based holographic optical trap and experimentally investigate the optimal velocity feasible for trapped beads of different sizes, in such a trap. Our results show that the achievable velocity of the trapped bead is a function of size of the bead, step size, interval between two steps and power carried by the laser beam. We observe that the refresh rate of a nematic liquid crystal spatial light modulator is sufficient to achieve an optimal velocity approaching the theoretical limit in the respective holographic trap for beads with radius larger than the wavelength of light.

Robust Adaptive Nonlinear Controller for Robotic Systems: Linear Matrix Inequality Approach

2008 ◽  
Author(s):  
Itzhack Levy ◽  
Nadav Berman ◽  
Amit Ailon
Keyword(s):  
Linear Matrix Inequalities ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Nonlinear Controller ◽  
Closed Loop System ◽  
Storage Function ◽  
Linear Matrix Inequality Approach ◽  
Case Simulation ◽  
Robust Adaptive ◽  
Two Degree Of Freedom

In this paper the tracking problem of a robotic system with model uncertainty is considered via an application of the H∞ control theory for nonlinear systems. In particular, we develop a state feedback controller which yields a global exponential stability of the underlying system and provides the closed loop system with relatively low gains. The main ingredient which facilitates our development is the choice of a particular storage function (which serves as a Lyaponov function). This particular storage function leads to certain linear matrix inequalities, the solution of which yields the desired controller. Moreover, the resulting LMIs (Linear Matrix Inequalities) turn out to be of the same form of the LMIs achieved in the analogous linear case. Simulation results and implementation of the control algorithm in a two-degree of freedom robot illustrate the controller efficiency.

Simultaneous Manipulator/Controller Design Optimization Using Multi-Objective Evolutionary Algorithms

2003 ◽  
Author(s):  
T. Ravichandran ◽  
G. R. Heppler ◽  
D. W. L. Wang
Keyword(s):  
Optimal Design ◽  
Controller Design ◽  
Dynamic Performance ◽  
Algorithm Optimization ◽  
Nonlinear Controller ◽  
Closed Loop System ◽  
Multi Objective ◽  
Quintic Polynomial ◽  
Point Motion ◽  
Point To Point

A multi-objective design methodology that uses an evolutionary algorithm optimization process is presented and is applied to the simultaneous optimal design of a robotic manipulator/controller for performing point-to-point motion tasks. Dynamic performance measures, for the closed-loop system, are optimized by considering a nonlinear PD controller and quintic polynomial trajectories for point-to-point motions. Results of the simultaneous optimal design of a planar manipulator, a nonlinear controller, and some sample trajectories are presented to illustrate the efficacy of this methodology.

Sign in / Sign up

Export Citation Format

Share Document