Direct single shooting for dynamic optimization of differential-algebraic equation systems with optimization criteria embedded

2021 ◽  
pp. 107643
Author(s):  
Tobias Ploch ◽  
Jens Deussen ◽  
Uwe Naumann ◽  
Alexander Mitsos ◽  
Ralf Hannemann-Tamás
Keyword(s):  
Algebraic Equation ◽  
Dynamic Optimization ◽  
Differential Algebraic Equation ◽  
Optimization Criteria

Simulation of differential-algebraic equation systems with optimization criteria embedded in Modelica

2020 ◽  
Vol 140 ◽  
pp. 106920 ◽  
Author(s):  
Tobias Ploch ◽  
Eric von Lieres ◽  
Wolfgang Wiechert ◽  
Alexander Mitsos ◽  
Ralf Hannemann-Tamás
Keyword(s):  
Algebraic Equation ◽  
Differential Algebraic Equation ◽  
Optimization Criteria

scholarly journals Testing a differential-algebraic equation solver in long-term voltage stability simulation

2006 ◽  
Vol 2006 ◽  
pp. 1-13
Author(s):  
José E. O. Pessanha ◽  
Alex A. Paz
Keyword(s):  
Power System ◽  
Algebraic Equation ◽  
Time Domain ◽  
Voltage Stability ◽  
Power System Stability ◽  
System Stability ◽  
Variable Order ◽  
Differential Algebraic Equation ◽  
Short Period

This work evaluates the performance of a particular differential-algebraic equation solver, referred to as DASSL, in power system voltage stability computer applications. The solver is tested for a time domain long-term voltage stability scenario, including transient disturbances, using a real power system model. Important insights into the mechanisms of the DASSL solver are obtained through the use of this real model, including control devices relevant to the simulated phenomena. The results indicate that if properly used, the solver can be a powerful numerical tool in time domain assessment of long-term power system stability since it comprises, among several important features, suitable and very efficient variable order and variable step-size numerical techniques. These characteristics are very important when CPU time is a great concern, which is the case when the power system operator needs reliable results in a short period of time. Prior to the present work, this solver has never been applied in power system stability computer analysis in time domain considering slow and fast phenomena.

On the Determination of Joint Reactions in Multibody Mechanisms

2004 ◽  
Vol 126 (2) ◽  
pp. 341-350 ◽  
Author(s):  
Wojciech Blajer
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Algebraic Equation ◽  
Matrix Inversion ◽  
Differential Algebraic Equation ◽  
Joint Coordinates ◽  
Reduced Dimension ◽  
Absolute Coordinates ◽  
Coordinate Partitioning

In this paper some existing codes for the determination of joint reactions in multibody mechanisms are first reviewed. The codes relate to the DAE (differential-algebraic equation) dynamics formulations in absolute coordinates and in relative joint coordinates, and to the ODE (ordinary differential equation) formulations obtained by applying the coordinate partitioning method to these both coordinate types. On this background a novel efficient approach to the determination of joint reactions is presented, naturally associated with the reduced-dimension formulations of mechanism dynamics. By introducing open-constraint coordinates to specify the prohibited relative motions in the joints, pseudoinverse matrices to the constraint Jacobian matrices are derived in an automatic way. The involvement of the pseudo-inverses leads to schemes in which the joint reactions are obtained directly in resolved forms—no matrix inversion is needed as it is required in the classical codes. This makes the developed schemes especially well suited for both symbolic manipulators and computer implementations. Illustrative examples are provided.

Prediction of Antagonistic Muscle Forces Using Inverse Dynamic Optimization During Flexion/Extension of the Knee

1999 ◽  
Vol 121 (3) ◽  
pp. 316-322 ◽  
Author(s):  
G. Li ◽  
K. R. Kaufman ◽  
E. Y. S. Chao ◽  
H. E. Rubash
Keyword(s):  
Dynamic Optimization ◽  
Optimization Procedure ◽  
Muscle Forces ◽  
Inverse Dynamic ◽  
Optimization Criteria ◽  
Flexion Extension ◽  
Antagonistic Muscle ◽  
Joint Reaction Forces ◽  
Reaction Forces ◽  
Joint Reaction

This paper examined the feasibility of using different optimization criteria in inverse dynamic optimization to predict antagonistic muscle forces and joint reaction forces during isokinetic flexion/extension and isometric extension exercises of the knee. Both quadriceps and hamstrings muscle groups were included in this study. The knee joint motion included flexion/extension, varus/valgus, and internal/external rotations. Four linear, nonlinear, and physiological optimization criteria were utilized in the optimization procedure. All optimization criteria adopted in this paper were shown to be able to predict antagonistic muscle contraction during flexion and extension of the knee. The predicted muscle forces were compared in temporal patterns with EMG activities (averaged data measured from five subjects). Joint reaction forces were predicted to be similar using all optimization criteria. In comparison with previous studies, these results suggested that the kinematic information involved in the inverse dynamic optimization plays an important role in prediction of the recruitment of antagonistic muscles rather than the selection of a particular optimization criterion. Therefore, it might be concluded that a properly formulated inverse dynamic optimization procedure should describe the knee joint rotation in three orthogonal planes.

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