Prepare the root locus sketch (a) Write the characteristic equation so that the

Question

Prepare the root locus sketch (a) Write the characteristic equation so that the parameter of interest. K. appears as a multiplier. 1 + KP(s) = 0. (b) Factor P(t) m terms of n poles and M zeros. 1|+ K Product^_1 times 1 (s + z)/Product^n _1 = 1 (s + p_i) = 0. (c) Locate the open-loop poles and zeros of P(s) in the s-plane with selected symbols. (d) Determine the number of separate loci SL. (c) The root loci are symmetrical with respect to the horizontal real axis. X = poles O = zeros Locus begins at a pole and ends at a zero SL = n when n M; n = number of finite poles. M = number of finite zeros. 2. Locale the segments of the real axis that are root loci. The tod proceed to the zero at infinity along asymptotes centered at sigma_A and with angles Phi A. Determine the angle of locus departure from complex polo and the angle of locus arrival at complex zero using the phase criterion. Complete the root locus sketch. Locus lies to the left of an odd number of poles

Explanation / Answer

v1 = 0.00101 m3/kg, v2 = 0.001004 m3/kg,

P1 = 25 kPa, P2 = 20 MPa

b. Wp = v1*(P2-P1)= 0.00101*(20000-25)=20.17

c. Wp = vavg*(P2-P1) = (0.00101+0.001004)/2 =0.001007*(20000-25) = 20.11

error = (20.17-20.11)/20.11 = 0.3%

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