Modelling of systems, Exercises of Systems Design

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Modelling of Systems

1) Mass Spring Damper System

• (^) Apply Newton’s Law (∑F = m.a)

F(t) – k.x(t) – c.v(t) = m.a(t)

F(t) – k.x(t) – c.ẋ(t) = m.ẍ(t)

• (^) To get the equation of motion

Equation of motion describe the motion of the

system

+ ) X(s)

• (^) Transfer function -->
• Number of parameters in the system k,c,m,Fc System state variable: x Input: Force(F) D.O.F: 1 DOF Dynamic Model “Neglect the mass of the k f c” k --> N/m c --> N.s/ v = = a = = =

2- Single Pendulum

• (^) Resolve the forces in the Y and Z direction
• (^) mÿ = -T sinθ  1
• (^) m z̈ = T cosθ – mg = T cosθ – mg  2
• (^) y and z are related (dependent) -> 1 DOF system
• (^) Non-Linear system due to (sinθ and cosθ)
• (^) Only 1 equation of motion
• θ θ T cosθ mg mg cosθ mg sinθ

T

T sinθ m

2- Single Pendulum

• (^) substitute in equation 1 and 2
• (^)  3
• (^)  4
• (^) Multiply equation 3 by cos and equation 4 by sin , then combine them by adding
• θ θ T cosθ mg mg cosθ mg sinθ

T

T sinθ m

3- RLC Circuit

• (^) )
• R LS 1/CS

Problem #1 : Simscape Foundation

solution

• Problem #
• Problem #
• Problem #
• Problem #
• Problem #
• Problem #

Problem #2 : Simulink Solution

Problem #2 : Simulink Solution

Problem #2 : Simulink Solution

Problem #2 : Simulink Solution