Vibraciones Mecanicas

Modelamiento de Sistemas Dinamicos Dr. Jorge A. Olórtegui Yume, Ph.D.

MODELAMIENTO DE SISTEMAS FISICOS
Dr. Jorge A. Olortegui Yume, Ph.D.

Escuela Académico Profesional de Ingeniería Mecánica Universidad Privada Cesar Vallejo 1

MODELADO Y SIMULACION DE SISTEMAS FISICOS Differential Equations Solutions

MOD. SIST. FISICOS

Dr. Jorge A. Olortegui Yume, Ph.D.

MODELADO Y SIMULACIONDE SISTEMAS FISICOS Laplace Transforms

MOD. SIST. FISICOS

Dr. Jorge A. Olortegui Yume, Ph.D.

MODELADO Y SIMULACION DE SISTEMAS FISICOS Laplace Transforms

MOD. SIST. FISICOS

Dr. Jorge A. Olortegui Yume, Ph.D.

MODELADO Y SIMULACION DE SISTEMAS FISICOS Laplace Transforms

MOD. SIST. FISICOS

Dr. Jorge A. Olortegui Yume, Ph.D.

MODELADO Y SIMULACION DE SISTEMAS FISICOSProperties of the Laplace Transforms

MOD. SIST. FISICOS

Dr. Jorge A. Olortegui Yume, Ph.D.

MODELADO Y SIMULACION DE SISTEMAS FISICOS
For ease in writing linear lumped-parameter differential equations, the D operator (S operator) is introduced

The Laplace transform is used to represent a continuous time domain system, f(t), using a continuous sum of complex exponential functions of theform where s is a complex variable defined as . The complex domain (or s plane as it’s often called) is just a plane with a rectangular x–y coordinate system where is the real part and is the imaginary part
MOD. SIST. FISICOS

Dr. Jorge A. Olortegui Yume, Ph.D.

MODELADO Y SIMULACION DE SISTEMAS FISICOS
The cause–effect relationship for many systems can be approximated by a linear ordinarydifferential equation. For example, consider the following second-order dynamic system with one input, , and one output The transfer function is the ratio of the output variable over the input variable represented as the ratio of two polynomials in the D or s operator 3 step procedure to convert linear ordinary differ. equation to transfer function

MOD. SIST. FISICOS

Dr. Jorge A. OlorteguiYume, Ph.D.

MODELADO Y SIMULACION DE SISTEMAS FISICOS

3 step procedure to convert linear ordinary differ. equation to transfer function

GAIN
MOD. SIST. FISICOS

Dr. Jorge A. Olortegui Yume, Ph.D.

MODELADO Y SIMULACION DE SISTEMAS FISICOS
Simulation is the process of solving a block diagram model on a computer

Block diagram models have 2 fundamental objects: signal wires andblocks Fundamental set of 3 basic blocks that all block diagram languages possess

MOD. SIST. FISICOS

Dr. Jorge A. Olortegui Yume, Ph.D.

MODELADO Y SIMULACION DE SISTEMAS FISICOS

MOD. SIST. FISICOS

Dr. Jorge A. Olortegui Yume, Ph.D.

PROCESO DE DESARROLLO DEL SISTEMA MECATRONICO DE UN MOTOR DC DE POSICIONAMIENTO

Block diagrams are rarely constructed in a standard form, and it isoften necessary to reduce them to more efficient or understandable forms

MOD. SIST. FISICOS

Dr. Jorge A. Olortegui Yume, Ph.D.

MODELADO Y SIMULACION DE SISTEMAS FISICOS

Block diagrams are rarely constructed in a standard form, and it is often necessary to reduce them to more efficient or understandable forms

MOD. SIST. FISICOS

Dr. Jorge A. Olortegui Yume, Ph.D.

PROCESO DEDESARROLLO DEL SISTEMA MECATRONICO DE UN MOTOR DC DE POSICIONAMIENTO

MOD. SIST. FISICOS

Dr. Jorge A. Olortegui Yume, Ph.D.

PROCESO DE DESARROLLO DEL SISTEMA MECATRONICO DE UN MOTOR DC DE POSICIONAMIENTO

MOD. SIST. FISICOS

Dr. Jorge A. Olortegui Yume, Ph.D.

MODELADO Y SIMULACION DE SISTEMAS FISICOS

MOD. SIST. FISICOS

Dr. Jorge A. Olortegui Yume, Ph.D.

MODELADO YSIMULACION DE SISTEMAS FISICOS

• R is the input to the BFS • E is the control or error variable • Y is the output Determination of closed-loop transfer function for the BFS

MOD. SIST. FISICOS

Dr. Jorge A. Olortegui Yume, Ph.D.

MODELADO Y SIMULACION DE SISTEMAS FISICOS

• R is the input to the BFS • E is the control or error variable • Y is the output

MOD. SIST. FISICOS

Dr. Jorge A....