Question

in the figure, obtain the state-space representation of the syster thè 1. Consider the mechanical system shown ssume y() is the output. (25 marks) ce representation of systel. ki lu k2

Answer 1

The given system can be expressed in another form too for the sake of simplicity.

The whole system is under the Force of 'u(t)

The displacement 'y' is varying with time hence represented as y(t).

The simplified space model is given below
The given state space model can be represented as below ki since springs are in parallel we an write as(ki K (t) is displacement the springs undergo while yct) is deridative of displacement for per And mass m undergoes ict) l second derva tive of-displacement The output yCt) gets involved becausel of So, The required state space model as below

wher e y(t)こ Acceleration Varying withti me 0 ct) di's placemeut
hope this helps.

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