Reference no: EM133296124

High Voltage Direct Current Transmission

Question 1: Consider the following system:

 

a) Design a state-feedback control in the form of u(t) = -k^Tx(t) + Fr(t) to place the eigenvalues of the closed-loop system at λ_1,2 = -0.5 ± j and λ3 = -0.7 and track a given constant reference and use MATLAB to plot the response of the system to see whether y(t) asymptotically tracks the reference signal. (This is a repeat from Mini-project 1)

b) Design an observer to estimate the state of the system.

c) For part (a), imagine you only have access to the output y(t). Usc the observer that you designed in part (b), to feedback the estimated state and control the system. Find the state space representation of the closed loop system, which includes both the controller and the observer.

d) In part (c), use MATLAB to plot the response of the system to see whether y(t) asymptotically tracks the reference signal r(t).

e) Compare the results in part (d) and (a).

Question 2: Consider the following system:

 

a) Use MATLAB to find the changes in Iystem's states in response to a step input and plot the states of the system. (It is similar to finding the step response. Instead of y=ex you just need to find x. one solution is to put C=I).
b) Design an observer to estimate the state of the system.
c) Imagine you only have access to the output y(t). Use the observer that you designed in part (b), to the changes in states of the system in response to a step input, and plot the estimated states.
d) Compare the states of the system in (a) with the estimated states in (c).