Question

Question 1 a) Define the term transfer function in relation to a linear control system. [5 marks] Figure Q1 shows a block diagram of a feedback control system, with a plant with transfer function G(s) , a controller with transfer function C(s) , and a sensor with transfer function H(s) . b) Derive from first principles the closed loop transfer function G (s) cl from the reference signal r(t) , to the output signal y(t) . [5 marks] c) Give expressions for the forward path and open loop transfer fuctions in terms of G(s), C(s) and H(s) as appropriate. [5 marks]

[5 marks] c) Give expressions for the forward path and open loop transfer fuctions in terms of G(s). C(s) and H(s) as appropriate. [5 marks] 11 C(5) G(s) H(8) Figure Q1 d) Obtain the transfer function G(s) of the linear system described by the following differential equation 4d y +8 dy + 7y=4u + 2u di [5 marks] The transfer function of a second linear system is given by G,($). Write down the overall transfer function when Gs) and G, (s) are connected in series and () parallel [5 marks] A