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QUESTION 1 (a) Given a block diagram for space satellite system as shown in Figure Q2(a). To get the desired angle of orientation, a single transfer function of the system Y(s) = (s) is - R(S) obtained. R(s) + H₂(s) H₂(s) G₁(s) S. G₂ (s) H₂ (s) H4(s) G3(s) Hg(s) Figure Q2(a): Space satellite block diagram (1) Construct a signal flow graph for the system in Figure Q2(a). -C(s) C2 [SP1] [4 marks] (ii) Identify the forward path, loop gain, combination of non-touching loop and loop gain that do not touch any respective forward path. C3 [SP2] [6 marks] (iii) By using Mason's rule, find the single transfer function Y(s) for the system if G₁(s) = G₂ (s) = G3 (S) = 2s and H₁ (s) = H₂(s) = H₂(s) = H₂(s) = H₂(s) = C3 [SP1] [6 marks]
(b) A translational mechanical control system is as shown in Figure Q2(b). f(0) X₂ (1) k₁ = 2N/ fu, 2N-s/m M₁ - Akg (t) f₂ = 1N-8/m 0000 K₂ - 3N/m f-IN-s/m M₂ - 2kg Figure Q2(b): Translational mechanical control system. [6 marks Construct a free-body diagram or electrical analogy diagram of the system. Properly indicate and label all forces that exist in the system. C2 [SP1] [4 marks] (ii) Write the equation of motion for the system based on the free body diagram or electrical analogy diagram obtained in Q2(b)(i). C2 [SP1] [3 marks] (iii) Perform the Laplace transform to the equation of motion and obtain state space equation for the system where the output is x₂ (t). C3 [SP2] [7 marks]