Harman Patil (Editor)

Double integrator

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In systems and control theory, the double integrator is a canonical example of a second-order control system. It models the dynamics of a simple mass in one-dimensional space under the effect of a time-varying force input u .

Contents

State space representation

The normalized state space model of a double integrator takes the form

x ˙ ( t ) = [ 0 1 0 0 ] x ( t ) + [ 0 1 ] u ( t ) y ( t ) = [ 1 0 ] x ( t ) .

According to this model, the input u is the second derivative of the output y , hence the name double integrator.

Transfer function representation

Taking the Laplace transform of the state space input-output equation, we see that the transfer function of the double integrator is given by

Y ( s ) U ( s ) = 1 s 2 .

References

Double integrator Wikipedia
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