(Solved): A servo motor system is shown in Figure 3.1. Suppose the system involves velocity feedback with ga ...

A servo motor system is shown in Figure 3.1. Suppose the system involves velocity feedback with gain \( K \) varying from zero to infinity. The whole control system is shown in Figure \( 3.2 \). Figure 3.1: A servo motor system. Figure 3.2: Schematic of the velocity feedback control system. a) Find the characteristic equation of the system. (8 marks) b) Determine the value of \( K \) such that the system has the damping ratio of \( 0.7 \). (4 marks) c) Compare the system response speed under a step input when \( K=1 \) and \( K=3 \). Explain the reasons. (8 marks)