Consider the following hydraulic / mechanical system, where pj and P2 are the inputs to the system, and the piston is driving a pendulum. Assuming small angles 0 and a concentrated mass ma distance L1 from the pivot. P2 R2 P3 P4 Pa L2 Li m a. Develop the dynamic equation to model of the piston displacement, 0, as a function of the inputs, p1 and p2 in standard form.

Consider the following hydraulic / mechanical system, where pj and P2 are the inputs to the system, and the piston is driving a pendulum. Assuming small angles 0 and a concentrated mass ma distance L1 from the pivot. P2 R2 P3 P4 Pa L2 Li m a. Develop the dynamic equation to model of the piston displacement, 0, as a function of the inputs, p1 and p2 in standard form.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

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Stability Analysis

Stability analysis is a part of the system and control theory, and it is used to understand or expect the stability of a system with the help of a mathematical model. It indicates how a model reacts to changes and perturbations.

Question

Consider the following hydraulic / mechanical system, where pi and P2 are the inputs to the system,
and the piston is driving a pendulum. Assuming small angles 0 and a concentrated mass ma
distance L1 from the pivot.
Pell
(P2
R2
P1
Pa
¡P3
R1
P4
L2
Li
Develop the dynamic equation to model of the piston displacement, 0, as a function of the
inputs, p1 and p2 in standard form.
b. If you were to consider the input to the system to be the difference between the pressure on
0(s)
either side of the piston, write the transfer function for the displacement of the piston:
AP(s)
Xj = 0
c. Develop the state equations for this system if the state variables are:

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