A digital controller is used to control the liquid level of the storage tank shown in Fig. The control valve has negligible dynamics and a steady-state gain, k_v = 0.1 ft³/(min)(mA). The level transmitter has a time constant of 30 s and a steady-state gain of 4 mA/ft. The tank is 4 ft in diameter. The exit flow rate is not directly influenced by the liquid level; that is, if the control valve stem position is kept constant, q₃ ? f(h). Suppose that a proportional digital controller and a digital-to-analog converter with 4 to 20 mA output are used. If the sampling period for the analog-b-digital converter is ?t =1 min, for what values of controller gain K_c is the closed-loop system stable? Use Simulink and trial values for K_c of ?10, ?50, and ?90. Will offset occur for the proportional controller after a change in set point?

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