Figure Q.5 shows the block diagram of a control system. a) Using block diagram reduction techniques determine the closed loop transfer function of the system shown in Figure Q5. b) Given the individual transfer functions listed below, using Rouths criteria determine the range of values of K which for the system to remain stable. G|(s) = K G2(s) = s+ 4 1 G3(s) = Hj(s) = s² H2(s) = 2s H3(s) = 1 H(s) R(s) C(s) G|(s) G2(s) G3(s) H½(s) + H3(s)

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.

3. In this problem, use the two closed loop systems given in the figure to answer the questions below. 4 R(s) K₁ 0.0099 In thin K₂ Y(s) R(s) K₁ 4 S(s) = 0.09 K₂ 0.09 (a) Show that these two systems have the same transfer function for K₁ = K₂ = 100 (b) Using the definition of sensitivity, S(s), for each system calculate the sensitivity to the parameter K₁ with K₁ and K₂ as variables. Recall: Y(s) OG G OG Gal (c) Substitute K₁ = K₂ = 100 into each S(s) and compare the sensitivities to parameter K₁.

a) Using a NTC thermistor with "B=4000K, resistance: 5k2 at 25°C" we want to measure the temperature of an environment in the range 50°C - 100°C. Design a suitable circuit for this purpose with "zero" output signal |v) value at 25ºC. Express the output and its temperature-sensitivity in terms of temperature (y=f(T°C) and dy/dT= f(TºC)). Roughly draw y and dy/dT for the given temperature range. (Note: For NTC: RNTC=Roexp(B(1/T-1/To))