Q4: Consider a closed-loop control system with the following transfer function for the open-loop transfer function: -≤W< G (s) = K (s+2) (s³ +5s² +7s+3) Determine the range of values of the gain K for which the closed-loop system is stable. Also, identify the number of poles that move as K varies within this range and the locations of these poles on the complex plane.

Consider the control system shown in Figure 1. Copy it into your answer book, labelling the actual output, control signal, desired output, plant, proportional action and derivative action. Also write down the control algorithm. Q1 (a) + s+1 kas I+ s+ 5 kp Figure 1 Determine the open-loop transfer function for the system shown in Figure 1 and hence obtain an expression for the closed-loop transfer function. (b) Find the state-space representation in phase-variable form for the above closed- loop system. Assume kp = 2 and ka = 1. (c) (d) Draw a signal flow diagram for the above system, assuming phase-variable form.

Q3: Draw the root locus for a control system of open loop transfer function below with unity feedback: G(S) K(2S+5) S(S²+45 + 3) (5² +45 +20)