QUESTION 1 (20 marks) The transfer function of an open loop system is: 5Ks Go(s) = s + 2s +4 The open loop system consists of a controller, a differentiator and a plant whose transfer functions are G(S), Ga(s) and Gp(s) respectively. All three components are connected in a series. a) If G(s) = K and Ga(s) = s, determine Gp(s). (1 mark) b) Determine the differential equation that describes the plant in the time domain with F(t) as the input and x(t) as the output. (1 mark) c) If the plant is a spring-mass-damper system (Figure 1), determine the values of the mass M, viscous coefficient C and spring stiffness k d) What is the order of the open loop system Go(s)? What is its type? (3 marks) (1 mark) e) Determine the steady state error of the closed loop system if the input is (i) a unit step function, or (ii) a unit ramp function of magnitude 10. Assume H(s)=1. (2 marks) f) Sketch the root locus of the dosed loop system for O