Tracking Controllers for Uncertain Systems: Application to a Manutec R3 Robot

1989 ◽  
Vol 111 (4) ◽  
pp. 609-618 ◽  
Author(s):  
Martin Corless
Keyword(s):  
Dynamical Systems ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
General Class ◽  
Uncertain Systems ◽  
Mechanical Systems ◽  
Degree Of Freedom ◽  
Tracking Controllers ◽  
Asymptotic Tracking ◽  
Three Degree Of Freedom

We consider a class of uncertain dynamical systems described by ordinary differential equations and characterized by certain structural conditions and known bounding functions. For a feasible class of desired state motions we present a class of controllers which assure asymptotic tracking to within any desired degree of accuracy. The results are applied to a general class of mechanical systems and are illustrated by a simple example and by application to a three degree-of-freedom model of a Manutec r3 robot.

scholarly journals On attracting sets in artificial networks: cross activation

2018 ◽  
Vol 16 ◽  
pp. 01005
Author(s):  
Felix Sadyrbaev
Keyword(s):  
Dynamical Systems ◽  
Differential Equations ◽  
Mathematical Models ◽  
Ordinary Differential Equations ◽  
Critical Points ◽  
Regulatory Networks ◽  
Main Diagonal ◽  
Sigmoidal Function ◽  
Genomic Regulatory Networks ◽  
Over Time

Mathematical models of artificial networks can be formulated in terms of dynamical systems describing the behaviour of a network over time. The interrelation between nodes (elements) of a network is encoded in the regulatory matrix. We consider a system of ordinary differential equations that describes in particular also genomic regulatory networks (GRN) and contains a sigmoidal function. The results are presented on attractors of such systems for a particular case of cross activation. The regulatory matrix is then of particular form consisting of unit entries everywhere except the main diagonal. We show that such a system can have not more than three critical points. At least n–1 eigenvalues corresponding to any of the critical points are negative. An example for a particular choice of sigmoidal function is considered.

On the Motion of Lineal Bodies Subject to Linear Damping

1997 ◽  
Vol 64 (1) ◽  
pp. 227-229 ◽  
Author(s):  
M. F. Beatty
Keyword(s):  
Differential Equation ◽  
Dynamical Systems ◽  
Rigid Body ◽  
General Class ◽  
Plane Motion ◽  
Rigid Bodies ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Linear Damping

Wilms (1995) has considered the plane motion of three lineal rigid bodies subject to linear damping over their length. He shows that these plane single-degree-of-freedom systems are governed by precisely the same fundamental differential equation. It is not unusual that several dynamical systems may be formally characterized by the same differential equation, but the universal differential equation for these systems is unusual because it is exactly the same equation for the three very different systems. It is shown here that these problems belong to a more general class of problems for which the differential equation is exactly the same for every lineal rigid body regardless of its geometry.

Dynamic Modelling of a Three Degree-of-Freedom Planar Platform-Type Manipulator

1997 ◽  
Author(s):  
Hazem A. Attia ◽  
Maher G. Mohamed
Keyword(s):  
Differential Equations ◽  
Efficient Solution ◽  
Equations Of Motion ◽  
Translational Motion ◽  
Dynamic Modelling ◽  
Degree Of Freedom ◽  
Constraint Forces ◽  
Dynamic Formulation ◽  
System Of Particles ◽  
Three Degree Of Freedom

Abstract In this paper, the dynamic modelling of a planar three degree-of-freedom platform-type manipulator is presented. A kinematic analysis is carried out initially to evaluate the initial coordinates and velocities. The dynamic model of the manipulator is formulated using a two-step transformation. Initially, the dynamic formulation is written in terms of the Cartesian coordinates of a dynamically equivalent system of particles. Since there is no rotational motion associated with a particle, then the differential equations of motion are derived by applying Newton’s second law to study the translational motion of the particles. The constraint forces between the particles are expressed in terms of Lagrange multipliers. Then, the differential equations of motion are written in terms of the relative joint variables. This leads to an efficient solution and integration of the equations of motion. A numerical example is presented and a computer program is developed.

AUTOMATIC PARALLELIZATION OF ELECTRO-MECHANICAL SYSTEMS GOVERNED BY ODEs

2002 ◽  
Vol 26 (3) ◽  
pp. 347-365
Author(s):  
C.A. Rabbath ◽  
A. Ait El Cadi ◽  
M. Abdonne ◽  
N. Lechevin ◽  
S. Lapierre ◽  
...  
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Block Diagram ◽  
Time Integration ◽  
Mechanical Systems ◽  
Automatic Parallelization ◽  
Iteration Step ◽  
Control Laws ◽  
Loop Control ◽  
Novel Method

The paper proposes an effective approach for the automatic parallelization of models of electro-mechanical systems governed by ordinary differential equations. The novel method takes a nominal mathematical model, expressed in block diagram language, and portions in parallel the code to be executed on a set of standard microprocessors. The integrity of the simulations is preserved, the computing resources available are efficiently used, and the simulations are compliant with real-time constraints; that is, the time integration of the ordinary differential equations is performed within restricted time limits at each iteration step. The proposed method is applied to a two-degree-of-freedom revolute joint robotic system that includes an induction motor and two inner-outer loop control laws. Numerical simulations validate the proposed approach.

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