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4. Simplified model of a hydraulic cylinder: an integrator model. A hydraulic cylinder is often used in position control systems. The system input is fluid flow rate (expressed in m'/s), and output is piston displacement. The piston will move as long as there is fluid flow, and even when the input (flow) is constant, the output (displacement) will continue to increase. a. Write the D.E. model of the simplified system neglecting all other effects such as friction, fluid compressibility, inertia, etc. b. Find the transfer function of the simplified model. c. Find and plot the unit-step response of the integrator system, assuming gain is K. 5. Replacing s=jo, draw the frequency response of the standard first-order and the integrator models. That is, plot the magnitude and phase of the system transfer function G(jo). Use a semi-log scale to plot the frequency response