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128 results on '"Bajodah, Abdulrahman H."'

31. Corrigendum: New Form of Kane's Equations of Motion for Constrained Systems

Author

Roithmayr, Carlos M, Bajodah, Abdulrahman H, Hodges, Dewey H, and Chen, Ye-Hwa

Subjects
Physics (General)
Abstract

A correction to the previously published article "New Form of Kane's Equations of Motion for Constrained Systems" is presented. Misuse of the transformation matrix between time rates of change of the generalized coordinates and generalized speeds (sometimes called motion variables) resulted in a false conclusion concerning the symmetry of the generalized inertia matrix. The generalized inertia matrix (sometimes referred to as the mass matrix) is in fact symmetric and usually positive definite when one forms nonminimal Kane's equations for holonomic or simple nonholonomic systems, systems subject to nonlinear nonholonomic constraints, and holonomic or simple nonholonomic systems subject to impulsive constraints according to Refs. 1, 2, and 3, respectively. The mass matrix is of course symmetric when one forms minimal equations for holonomic or simple nonholonomic systems using Kane s method as set forth in Ref. 4.

Published
2007

32. Canonical Generalized Inversion Form of Kane’s Equations of Motion for Constrained Mechanical Systems

Author

Bajodah, Abdulrahman H.

Subjects
Mathematics / Differential Equations
Abstract

The canonical generalized inversion dynamical equations of motion for ideally constrained discrete mechanical systems are introduced in the framework of Kane’s method. The canonical equations of motion employ the acceleration form of constraints and the Moore-Penrose generalized inversion-based Greville formula for general solutions of linear systems of algebraic equations. Moreover, the canonical equations of motion are explicit and nonminimal (full order) in the acceleration variables, and their derivation is made without appealing to the principle of virtual work or to Lagrange multipliers. The geometry of constrained motion is revealed by the canonical equations of motion in a clear and intuitive manner by partitioning the canonical accelerations’ column matrix into two portions: a portion that drives the mechanical system to abide by the constraints and a portion that generates the momentum balance dynamics of the mechanical system. Some geometrical perspectives of the canonical equations of motion are illustrated via vectorial geometric visualization, which leads to verifying the Gauss’ principle of least constraints and its Udwadia-Kalaba interpretation.

Published
2018

40. Positional control of rotary servo cart system using generalized dynamic inversion

Author

Ansari, Uzair, Mehedi, Ibrahim Mustafa, Bajodah, Abdulrahman H., Al Saggaf, Ubaid M., Ansari, Uzair, Mehedi, Ibrahim Mustafa, Bajodah, Abdulrahman H., and Al Saggaf, Ubaid M.

Abstract

This paper presents the design approach of Generalized Dynamic Inversion (GDI) for angular position control of SRV02 rotary servo base system. In GDI, linear first order constraint differential equations are formulated based on the deviation function of angular position and its rate, and its inverse is calculated using Moore-Penrose Generalized Inverse to realize the control law. The singularity problem related to generalized inversion is solved by the inclusion of dynamic scaling factor that will guarantee the boundedness of the elements of the inverted matrix and stable tracking performance. Numerical simulations and real-time experiment are performed to evaluate the tracking performance and robustness capabilities of the proposed control law considering nominal and perturbed model dynamics. For comparative analysis, the results of GDI is compared with conventional PID control. Simulation and experimental results demonstrate better angular position tracking for the square-wave and sinusoidal waveforms, which reveals the superiority, and agility of GDI control over conventional PID.

Published
2018

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