Many industrial applications require an accurate control of liquid level, either in order to generate a constant flow of the liquid or a constant pressure. In this assignment the liquid used will be water and a linearised model of the water tank system will be assumed (Figure 1). Figure 1 The dimensions of the tanks are the horizontal cross section area A and height hmax. The resistance of the outflow valve is R. The values of these three parameters are unknown at this stage, but we do know they are constant positive real numbers. Volumetric flows qi and qo are flows into and out of the tank respectively, while h is water level. Pre-tasks 1. Determine the transfer function G(s) of the one-tank system where qi is the input and h is the output variable. Identify the values (in terms of A and R) if the time constant and the steady state gain of the system. (1 mark) 2. Derive the response of the system to a step change to the input flow of magnitude B. Sketch h(t). (1 mark)