COMPRESSOR PROPELLER COMBUSTION (a) TURBINE R(s) E(s) Y(s) G(s) H(s) (b) Question 4 (12 marks) Apply the gain formula to the signal flow graph (SGF) below to determine the expressions for the following transfer functions:and G₁ G₁ G₂ -H₂ G₁ H₁ Y₁ -H₁ End of Questions---- 3 Assessment 3 Question 1 (10 marks) [40 marks] (i) Without using the Routh-Hurwitz criterion, determine if M(s) asymptotically stable, marginally stable, or unstable. 100(S-1) (s+5)(s²+25+2) is (ii) Using the Routh-Hurwitz criterion, determine the stability of the closed-loop system that has the following characteristic equations. Determine the number of roots of each equation that are in the right-half s-plane and on the jw-axis. (a) s3 + 25s² + 250s + 10 = 0 (b) s +2s5 +8s + 15s3 + 20s² + 16s+16=0 Question 2 (8 marks) Reduce the block diagram in Figure below and find the transfer function 35 (3) (5) H₂ G₁ G₂ G3 Y H₁ H3 Question 3 (10 marks) The aircraft turboprop engine shown in Figure (a) is controlled by a closed-loop system with block diagram in Figure (b). The engine is modelled as a multivariable system with input vector E(s), which contains the fuel rate and propeller blade angle, and output vector Y(s), consisting of the engine speed and turbine-inlet temperature. The transfer function matrices are given as 2 10 2(s+2) G(s) = 5 1 H(S) = [] s+1- Find the closed-loop transfer function matrix [I+ G(s)H(s)]-¹G(s) (10)