Fruit flies flight dynamics are interesting to study

Chapter 10, Problem 47

(choose chapter or problem)

The block diagram of a cascade system used to control water level in a steam generator of a nuclear power plant (Wang, 2009) was presentedinFigureP6.14.Inthatsystem, the level controller, \(G_{LC}\)(s), is the master controller and the feed-water flow controller, \(G_{FC}\)(s), is the slave controller. Consider that the inner feedback loop is replaced by its equivalent transfer function, \(G_{WX}\)(s).

Using numerical values in (Wang, 2009) and (Bhambhani, 2008) the transfer functions with a 1 second pure delay are:

\(G_{f_w}(s)\) = \(\frac{2 \cdot e^{-\tau s}}{s\left(T_1 s+1\right)}\) = \(\frac{2 \cdot e^{-s}}{s(25 s+1)}\)

\(G_{W X}(s)\) = \(\frac{(4 s+1)}{3(3.333 s+1)}\)

\(G_{L C}(s)\) = \(K_{P_{L C}}+K_{D_{L C}} s\) = 1.5(10 s+1)

Use MATLAB or any other program to:

a. Obtain Bode magnitude and phase plots for this system using a fifth-order Padé approximation (available in MATLAB). Note on these plots, if applicable, the gain and phase margins.

b. Plot the response of the system, c(t), to a unit step input, r(t) = u(t). Note on the c(t) curve the rise time, Tr, the settling time, Ts, the final value of the output, and, if applicable, the percent overshoot, %OS, and mid peak time, Tp.

c. Repeat the above two steps for a pure delay of 1.5 seconds.