Second Order Systems

Second Order Systems

Second Order Equations

Standard Form

G(s

)

=

2

s

2

K + 2s

+1

K = Gain = Natural Period of Oscillation = Damping Factor (zeta)

Note: this has to be 1.0!!!

Corresponding Differential Equation

2

d2 y dt 2

+

2

dy dt

+

y

=

Kf

(t)

1

Origins of Second Order Equations

1. Multiple Capacity Systems in Series

K1 1s + 1

K2 2s +1

become

K1 K 2

(1s +1)( 2s + 1)

or

2. Controlled Systems (to be discussed later)

3. Inherently Second Order Systems

? Mechanical systems and some sensors ? Not that common in chemical process control

K 2s2 + 2s + 1

Examination of the Characteristic Equation

2s2 + 2s + 1 = 0

> 1 = 1 0 ................
................

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