Minimizing Residual Vibrations in High-Speed Cam-Follower Systems Over a Range of Speeds

1995 ◽  
Vol 117 (1) ◽  
pp. 166-172 ◽  
Author(s):  
M. Chew ◽  
C. H. Chuang
Keyword(s):  
Boundary Conditions ◽  
Lagrange Multiplier ◽  
High Speed ◽  
Displacement Function ◽  
Lagrange Multiplier Method ◽  
Multiplier Method ◽  
Rules Of Thumb ◽  
Cam Follower

A direct procedure, based on the generalized Lagrange multiplier method, will be presented for designing high-speed cam-follower systems over a range of cam speeds. With this method residual vibrations at the end of the rise of a Dwell-Rise-Dwell (DRD) cam motion are minimized for any specified range of rise times. A minimum of boundary conditions on the cam displacement function will be specified to reduce unnecessary constraints on the cam displacement function. The applicability of rules of thumb generally accepted in designing for minimum vibrations will be discussed and compared to the results from this approach.

scholarly journals Controllability, not chaos, key criterion for ocean state estimation

2017 ◽  
Vol 24 (3) ◽  
pp. 351-366 ◽  
Author(s):  
Geoffrey Gebbie ◽  
Tsung-Lin Hsieh
Keyword(s):  
Boundary Conditions ◽  
State Estimation ◽  
Lagrange Multiplier ◽  
Weather Prediction ◽  
Lagrange Multiplier Method ◽  
Multiplier Method ◽  
Estimation Methods ◽  
Surface Boundary ◽  
Highly Nonlinear ◽  
Ocean State Estimation

Abstract. The Lagrange multiplier method for combining observations and models (i.e., the adjoint method or 4D-VAR) has been avoided or approximated when the numerical model is highly nonlinear or chaotic. This approach has been adopted primarily due to difficulties in the initialization of low-dimensional chaotic models, where the search for optimal initial conditions by gradient-descent algorithms is hampered by multiple local minima. Although initialization is an important task for numerical weather prediction, ocean state estimation usually demands an additional task – a solution of the time-dependent surface boundary conditions that result from atmosphere–ocean interaction. Here, we apply the Lagrange multiplier method to an analogous boundary control problem, tracking the trajectory of the forced chaotic pendulum. Contrary to previous assertions, it is demonstrated that the Lagrange multiplier method can track multiple chaotic transitions through time, so long as the boundary conditions render the system controllable. Thus, the nonlinear timescale poses no limit to the time interval for successful Lagrange multiplier-based estimation. That the key criterion is controllability, not a pure measure of dynamical stability or chaos, illustrates the similarities between the Lagrange multiplier method and other state estimation methods. The results with the chaotic pendulum suggest that nonlinearity should not be a fundamental obstacle to ocean state estimation with eddy-resolving models, especially when using an improved first-guess trajectory.

scholarly journals Controllability, not chaos, key criterion for ocean state estimation

2016 ◽  
Author(s):  
Geoffrey Gebbie ◽  
Tsung-Lin Hsieh
Keyword(s):  
Boundary Conditions ◽  
State Estimation ◽  
Lagrange Multiplier ◽  
Weather Prediction ◽  
Lagrange Multiplier Method ◽  
Multiplier Method ◽  
Estimation Methods ◽  
Surface Boundary ◽  
Highly Nonlinear ◽  
Ocean State Estimation

Abstract. The Lagrange multiplier method for combining observations and models (i.e., the adjoint method or "4D-VAR") has been avoided or approximated when the numerical model is highly nonlinear or chaotic. This approach has been adopted primarily due to difficulties in the initialization of low-dimensional chaotic models, where the search for optimal initial conditions by gradient descent algorithm is hampered by multiple local minima. Although initialization is an important task for numerical weather prediction, ocean state estimation usually demands an additional task – solution of the time-dependent surface boundary conditions that result from atmosphere–ocean interaction. Here, we apply the Lagrange multiplier method to an analogous boundary control problem, tracking the trajectory of the forced chaotic pendulum. Contrary to previous assertions, it is demonstrated that the Lagrange multiplier method can track multiple chaotic transitions through time, so long as the boundary conditions render the system controllable. Thus, the nonlinear timescale poses no limit to the time interval for successful Lagrange multiplier-based estimation. That the key criterion is controllability, not a pure measure of dynamical stability or chaos, illustrates the similarities between the Lagrange multiplier method and other state estimation methods. The results with the chaotic pendulum suggest that there is no fundamental obstacle to ocean state estimation with eddy-resolving, highly-nonlinear models, especially when using an improved first-guess trajectory.

scholarly journals Lagrange Multiplier Method for Drilling Oil Reservoir

2017 ◽  
Vol 06 (03) ◽  
Author(s):  
Vasant P ◽  
Maung MT ◽  
Min YW ◽  
Tun HM ◽  
Thant KZ
Keyword(s):  
Lagrange Multiplier ◽  
Lagrange Multiplier Method ◽  
Multiplier Method ◽  
Oil Reservoir
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