6) (20 pts) Consider the triple integrator system (d^3y)/(dt^3) = u where y and u are the output

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Question

6) (20 pts) Consider the triple integrator system $\frac{d^3y}{dt^3} = u$ where y and u are the output and input of the system, respectively. a) (5 pts) Obtain a state-space representation for the system. b) (5 pts) Can you construct a state observer which can yield asymptotically true estimates of the system states? If yes, why? c) (5 pts) Write down 'state' and 'output' equations of a Luenberger observer and draw a block diagram for the observer. d) (5 pts) Determine the observer gain (L) so that the eigenvalues of the observer error dynamics are located at $\mu_1 = -3 + j4$, $\mu_2 = -3 - j4$, $\mu_3 = -7$.

          6) (20 pts) Consider the triple integrator system $\frac{d^3y}{dt^3} = u$ where y and u are the output and input of the system, respectively.
a) (5 pts) Obtain a state-space representation for the system.
b) (5 pts) Can you construct a state observer which can yield asymptotically true estimates of the system states? If yes, why?
c) (5 pts) Write down 'state' and 'output' equations of a Luenberger observer and draw a block diagram for the observer.
d) (5 pts) Determine the observer gain (L) so that the eigenvalues of the observer error dynamics are located at
$\mu_1 = -3 + j4$, $\mu_2 = -3 - j4$, $\mu_3 = -7$.

6) (20 pts) Consider the triple integrator system (d^3y)/(dt^3) = u where y and u are the output and input of the system, respectively.
a) (5 pts) Obtain a state-space representation for the system.
b) (5 pts) Can you construct a state observer which can yield asymptotically true estimates of the system states? If yes, why?
c) (5 pts) Write down 'state' and 'output' equations of a Luenberger observer and draw a block diagram for the observer.
d) (5 pts) Determine the observer gain (L) so that the eigenvalues of the observer error dynamics are located at
μ1 = -3 + j4, μ2 = -3 - j4, μ3 = -7.

Added by Kristen S.

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