Q1) A first order system is modeled by the following differential equation y(t)+10y(t)=10x(t) Do the following a- Derive the transfer function of the system. b. If the input x(t) is changed by a unit impulse determiney (t). c- If a P-controller is used to control this system, Gv(s)=Gm(s)=1, do the following 1. Derive the closed loop transfer function for the load control case. ii. Calculate the value of kc that gives under damped response with (=0.25). iii- Calculate the offset and sketch both output responses of open loop (b) and closed loop (c-ii) on a single diagram. Q2) A first order process is modeled by the following transfer function G(s)=2.5s+11 If a Pl-controller is used to control this process, do the following a- Derive the closed loop transfer function for the load control case, Gv(s)=Gm(s)=1. b. If a value of Kc=9 is used, find the value of i that should be used to give the following values of damping factor (=2.,=1.,=0.5). C. If the input to the process is changed by a unit step function, sketch the output response for each value of on a single diagram. 23) A second order system has the following transfer function G(s)=s2+s+11 a. Derive the closed loop TF for the servo control case. Gv(s)=Gm(s)=1. b. If a P-control is used to control the system, calculate the value of Kc which gives (=0.25). c. If the set point is changed by a step function with size 2 , determine the offsct and sketch the output response