Transfer function, characteristic equation, state diagram, controllability, observability J 5-30. The block diagram of a linear spacecraft-control system is shown in Fig. 5P-30. (a) Determine the transfer function Y(s)/R(s). (b) Find the characteristic equation and its roots of the system. Show that the roots of the charac teristic equation are not dependent on K. (c) When K = 1. draw a state diagram for the system by decomposing Y(s)/R(s), using a mini- mum number of integrators. SIGNAL FLOW GRAPH (d) Repeat part (c) when K = 4. (e) Determine the values of K that must be avoided if the system is to be both state controllable and observable. Figure 5P-30 R(s) 1+58 K + 2(s+1) S Y(s)