Determine the values of all parameters needed to characterise the transfer function

Find the dynamic response of tank 2 to a step input change of size A to inlet 𝐹𝐹𝑓𝑓(𝑑𝑑). Comment on the order of the dynamic response of the process and determine the values of the natural period of oscillation of the process, of the damping factor, and of the gain of the process. (Answers:𝐾𝐾𝑝𝑝=100π‘ π‘ π‘šπ‘š2, 𝜏𝜏=100𝑠𝑠, 𝜁𝜁=1. 5) ii)Find the dynamic response of tank 1 to a step input change of size A to inlet 𝐹𝐹𝑓𝑓(𝑑𝑑). Comment on the order of the dynamic response of the process and determine the values of all parameters needed to characterise the transfer function e.g. natural period of oscillation of the process, damping factor, etc. (Answers:𝐾𝐾𝑝𝑝=200π‘ π‘ π‘šπ‘š2, 𝜏𝜏=100𝑠𝑠, 𝜁𝜁=1. 5, πœπœπ‘™π‘™π‘™π‘™=50𝑠𝑠) iii)For a step change of size Ξ‘ in 𝐹𝐹𝑓𝑓(𝑑𝑑) at time t=0 and using inverse Laplace transforms and/or existing solutions of generic forms of transfer functions, determine which value (as % of the final value) will have been reached by the liquid level in tank 1 and by the liquid level in tank 2 after 300 s. Compare the two values and discuss. (Answers: Tank 1β‰ˆ70%, Tank 2β‰ˆ63%). c) Simulate biii) in Simulink using a step change of 0.01 m3/s in the feed flow rate of tank 1, plot the output responses of the two tanks height and verify your results from the previous question.Numerical valuesπ‘Žπ‘Ž1=0. 01 m2/s, π‘Žπ‘Ž2=0. 01 m2/s, 𝐴𝐴1=𝐴𝐴2=1 m2 (cross sectional areas of the tanks

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