Answer all the above questions correctly providing necessary formulae, equations, expressions, diagrams, charts, graphs, plots and tables.

a) Consider a second order system with the following transfer function? G(s)=f(s)Y(s)=s2+s+11 Introduce a step change of magnitude one into the system and find (i) % overshoot, (ii) decay ratio, (iii) rise time, (iv) ultimate value of Y(t). (12 marks) b) Establish the time response for unit step change in input for a first order process described by the transfer function G(s)=ps+11 (8marks) Or a) Derive the transfer function of two interacting liquid level tanks connected inseries. (10 marks) b) Solve the Laplace transform dt2d2x+3dtdx+6x=0;x(0)=0andx(0)=3 (10 marks) 2. CO2 Draw the bode diagram for 1st order system and PID controller. 3. CO3 Derive the offset value for Proportional - integral control for set point change and load change. (20 marks) Or Compote the transfer function of the depicted block diagram by reduction