A rooms temperature can be controlled by varying the

Chapter 10, Problem 34

(choose chapter or problem)

An overhead crane consists of a horizontally moving trolley of mass \(m_T\) dragging a load of mass \(m_L\), which dangles from its bottom surface at the end of a rope of fixed length, L. The position of the trolley is controlled in the feedback configuration shown in Figure 10.20. Here, G(s) = KP(s), H = 1, and

P(s) = \(\frac{X_T(s)}{F_T(s)}=\frac{1}{m_T} \frac{s^2+\omega_0^2}{s^2\left(s^2+a \omega_0^2\right)}\)

The input is \(f_T(t)\), the input force applied to the trolley. The output is \(x_T(t)\), the trolley displacement. Also, \(\omega_0\) = \(\sqrt{\frac{g}{L}}\) and a = \(\left(m_L+m_T\right) / m_T\) (Marttinen, 1990) Make a qualitative Bode plot of the system assuming a > 1.