(Solved): 6. Steam-driven power generators rotate at a constant speed via a governor that maintains constant ...

6. 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 $$(\mathrm{AGC})$$ 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 turbinegovernor 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) $$G_g(s)=\frac{1}{0.2s+1}$$ is the governor's transfer function $$G_t(s)=\frac{1}{0.5s+1}$$ is the turbine transfer function $$G_m(s)=\frac{1}{10s+0.8}$$ represents the machine and load $$G_c(s)$$ is the LFC compensation to be designed a. Assuming $$G_c(s)=K$$, find the value of $$K$$ that will result in a dominant pole with $$?=0.7$$. Obtain the corresponding $$T_s$$. b. Design a PID controller to obtain the same damping factor as in Part a, but with a settling time of 2 seconds and zero steady-state error to step input commands. c. Verify your results using a MATLAB MATLAB simuation. FIGURE P9.1