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1. In a process a step change from 120 kPa to 250 kPa in actual pressure results in the measured recorder response shown in the sketch below with the vertical axis simply in units of millimetres of deflection (note that this sketch is not drawn to scale). 21.7 19.1 Recorder deflection R (mm) 11.8 -1.68(s) 0.0 Time (s) (a) (50%) Assuming second-order dynamics, calculate all important parameters and write an approximate system transfer function in the form R K = G(s) = P t's? +25ts +1 where R is the Laplace transform of the deflection response signal in mm units and P is the Laplace transform on the input (step) pressure deviation signal in kPa units. (b) (25%) If the time constant is held fixed but the system is tuned to ensure the damping factor is 0.5, estimate the decay ratio and the settling time for the response signal to come within 2% of the final value. (c) (25%) If instead of a simple step pressure change (step response) but a sinusoidal input pressure signal (frequency response) is forced on the system show that for a damping ratio 5 < 0.707, the Magnitude Ratio (MR = G(jo)|/G(0)) has a maximum value at a forcing frequency of V1-252 0 = max T