In Problem 47, Chapter 9, a steam-driven turbine governor system was implemented by a unity feedback system with a forward-path transfer function (Khodabakhshian, 2005)

a. Use a sampling period of T = 0.5 s and find a discrete equivalent for this system.

b. Use MATLAB to draw the root locus.

c. Find the value of K that will result in a stable system with a damping factor of ζ = 0.7.

d. Use the root locus found in Part a to predict the step-response settling time, T_s, and peak time, T_p.

e. Calculate the final value of the closed-loop system unit step response.

f. Obtain the step response of the system using Simulink. Verify the predictions you made in Parts c and d.

Data from Problem 47 Chapter 9:

Steam-driven power generators rotate at a constant speed via a governor that maintains constant steam pressure in the turbine. In addition, automatic generation control (AGC) or load frequency control (LFC) is added to ensure reliability and consistency despite load variations or other disturbances that can affect the distribution line frequency output. A specific turbine-governor system can be described only using the block diagram of Figure P9.1 in which G(s) = G_c(s)G_g(s)G_t(s)G_m(s), where (Khodabakhshian, 2005)

K G(s) = (s +0.08)(s+ 2)(s+5)