Let x(t), x2(t), x3 (t) and x(t) be the four state variables of the system, where 10:33 PM | 0.0KB/s x (t) = f(t) x2(t) = Xg(t) x3(t) = P(t) x(t) = P(t). Let the input vector, u(t), be defined as follows u(t) = Also, let the output of the system be defined as y(t) = f(t). Derive a state-space model of the power system in the form: x(t) = Ax(t) + Bu(t) y(t) = Cx(t) + Du(t). 4G+ 28% QUESTION 5 (9 marks) Q5(a) (3 marks): Consider a system described by the following differential equation: + 2 = - 5 + 6u [SEE701] [Advanced Control Systems Engineering] [Assessment task 1] Derive a state-space representation of the system in canonical form. Trimester 1, 2023 Q5(b) (3 marks): Consider a system with an open-loop transfer function given by: Y(s) s + 6s+ 1 G(s) = U(s) s - 2s +7 Derive a state-space representation of the system. Q5(c) (3 marks): Consider a system described by the following transfer function: Y(s) U(s) = (0.05s +1) (s+5s+25)(10s+1)(0.01s+1) Derive a state-space representation of the system. QUESTION 6 (5 marks) Do Problem 7 in chapter 2 (week 2), page 22. QUESTION 7 (6 marks) Time response of a dynamical system x(t) = Ax(t) + Bu(t) can be obtained by evaluating its solution x(t) = etx(0) + f e(tt) Bu(t)dt, where x(0) is the initial condition and e^t = {(sI A)}. Obtain time response for the following system by finding its solution: where u(t) = 1, and x(0) = [] 0 [8]=[]+Hu(t), -3] Use MATLAB to simulate the response of the system to a unit step input with the above initial condition. Comment on the analytical solution and the simulation generated from MATLAB. Determine whether that the system is controllable or not.