Complementary Condensing for the Direct Multiple Shooting Method

The application of multiple shooting method in stability analysis of non-prismatic multi-segment columns with pinned ends loaded with a concentrated force applied to the upper node has been presented. Numerical analyses were carried out for an exemplary three-segment column by solving the system of differential equations with variable coefficients and parameter. The results were compared with the solution obtained by using SOFiSTiK software based on the finite element method. The analyses show that considering the stiffness changes along the length can have a significant influence on the values of critical loads and thus change the resistance of the column. The advantage of the proposed method is its high efficiency and easy description of stiffness changes.

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Nonlinear Analysis of Rotor Systems Including a Bearing Clearance by the Multiple Shooting Method

Volume 6C: 18th Biennial Conference on Mechanical Vibration and Noise ◽

10.1115/detc2001/vib-21770 ◽

2001 ◽

Author(s):

David Demailly ◽

Fabrice Thouverez ◽

Louis Jézéquel ◽

Jérôme Bonini

Keyword(s):

Contact Zone ◽

Response Curve ◽

Shooting Method ◽

Simplified Model ◽

Multiple Shooting ◽

Frequency Response Curve ◽

Rotor Systems ◽

Transition Zones ◽

Full Contact ◽

Multiple Shooting Method

Abstract In this paper the Multiple Shooting Method is briefly exposed. This method is then applied to a simplified model of a rotor/stator system including a bearing with clearance under static and unbalance forces. With bearing having a small amount of clearance, it is pointed out that the orbits are no longer circular at certain frequencies as for linear systems. If the clearance is large, the frequency response curve can be divided into three zones: a non-contact zone, a zone with one or several gains and looses of contact per period and a full contact zone. For both cases we emphasize on the evolution of the orbits while passing through transition zones.

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Direct multiple shooting method for solving approximate shortest path problems

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2012.11.001 ◽

2013 ◽

Vol 244 ◽

pp. 67-76 ◽

Cited By ~ 7

Author(s):

P.T. An ◽

N.N. Hai ◽

T.V. Hoai

Keyword(s):

Shortest Path ◽

Shooting Method ◽

Multiple Shooting ◽

Shortest Path Problems ◽

Multiple Shooting Method ◽

Approximate Shortest Path

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A direct multiple shooting method to improve vehicle handling and stability for four hub-wheel-drive electric vehicle during regenerative braking

Proceedings of the Institution of Mechanical Engineers Part D Journal of Automobile Engineering ◽

10.1177/0954407019867510 ◽

2019 ◽

Vol 234 (4) ◽

pp. 1047-1056

Author(s):

Nenglian Feng ◽

Jiawang Yong ◽

Ziqi Zhan

Keyword(s):

Electric Vehicle ◽

Control Strategy ◽

Shooting Method ◽

Single Point ◽

Function Optimization ◽

Driver Model ◽

Regenerative Braking ◽

Multiple Shooting ◽

Multiple Shooting Method ◽

Wheel Drive

Regenerative braking is an important technology to improve fuel economy for electric vehicles. Apart from improving energy recovery efficiency and vehicle stability, the arithmetic speed of the algorithm is also essential for an automotive-qualified micro control units. This paper presents a direct multiple shooting method–based algorithm to achieve multiple objectives for four hub-wheel-drive electric vehicle during mild braking situations. Mathematical models of the system are generated for numerical simulations in MATLAB, including a vehicle dynamics model, a modified tire model, a single-point preview driver model, and a regenerative braking motor efficiency map. With the limitation of hard constraint and minimization of adjustment rate in cost function, optimization tends to be accomplished by distribution of braking torque in front and rear wheels. Furthermore, the control strategy has been realized using a direct multiple shooting method to convert the nonlinear optimal control problem to a nonlinear programming problem, which will be settled by adopting a sequential quadratic programming method in each subintervals. The effectiveness and adaptation of the control strategy for four hub-wheel-drive electric vehicle has been evaluated by conducting many simulations during mild braking situations, and the simulation results also demonstrated that the direct multiple shooting–based strategy exhibits a better performance than that of proportional-integral-based or nonlinear model predictive control–based controller.

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