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DONOT ATTEMPT QUESTION 1 ) 8 . 2 Exercises Linearize, x ( t ) = ( x , u ) = - x 2 (
DONOT ATTEMPT QUESTION Exercises
Linearize,
Equilibrium conditions are and
Linearize about
Linearize about
Left blank
Consider the nonlinear equation
Linearize about and and form into a statespace equation.
Given the nonlinear equation of a pendulum, linearize this about the operating point,
Linearize and form into a statespace equation where is the input and is the output.
Ignore units for simplicity.
give that at operating point
and
In a paint mixing plant, two tanks supply fluids to a mixing cistern. the height of the fluid in the
cistern is dependent upon the difference between the input mass flow rate, and the output flow
rate, A nonlinear differential equation describing this dependency is given by
where crosssectional area of the cistern, crosssectional area of the exit pipe,
acceleration due to gravity, and liquid density.
Linearize the nonlinear equation about the equilibrium point D
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