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DONOT ATTEMPT QUESTION 1 ) 8 . 2 Exercises Linearize, x ( t ) = ( x , u ) = - x 2 (

DONOT ATTEMPT QUESTION 1)8.2 Exercises
Linearize,
x(t)=(x,u)=-x2(l)+9u(l)
Equilibrium conditions are x(t)=0 and up=1.
Linearize (x)=5cosx about x=2
Linearize 8.12 about x=4
d2xdt2+2dxdt+cosx=0
Left blank
Consider the nonlinear equation
y+y+yy=u
Linearize about yo=[10]T and uo=1 and form into a state-space equation.
Given the nonlinear equation of a pendulum, linearize this about the operating point, o=0.
Lgd2(t)dt2=-sin(t)
Linearize 8.15 and form into a state-space equation where i(l) is the input and h(t) is the output.
(Ignore units for simplicity.)
mbar(h)(t)=mg-i2(l)h2(t)-h(t)
give that at operating point i(t)=ip=0.12,
and m=0.1,=0.9,=0.95.
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, q, and the output flow
rate, qe. A nonlinear differential equation describing this dependency is given by
dhdt+Ac2gh2=q
where A= cross-sectional area of the cistern, Ae= cross-sectional area of the exit pipe, g=
acceleration due to gravity, and = liquid density.
Linearize the nonlinear equation about the equilibrium point (h,qo).D
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