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7Second order non-integrating system

7.1Differential equation

Image (7.1.1)

7.2Continuous-time transfer function

Image (7.2.1)

7.3Unit Step response

7.3.1ξ=0

Image

7.3.20<ξ<1

Image

7.3.3ξ=1

Image

7.3.4ξ>1

Image

7.4Continuous-time state-space representation

Image (7.4.1)
Image (7.4.2)

7.5Discrete-time state-space representation

See the References about discretisation methods.

7.5.1Zero Order Hold

Image (7.5.1.1)
Image (7.5.1.2)

7.5.2First Order Hold

Image (7.5.2.1)
Image (7.5.2.2)