Question

please answer all of part i really need them ASAP ...

The level ho of liquid in a vertical cylindrical tank as shown in Figure 4 is related to the inflow of liquid qi by the time domain equation d h dt where τ RLGL, the steady state gain of the system is G RL/pg and the tank capacitance, inlet ine ho outlet vave Tank Figure 4: Tank Level Process (a) You carry out some measurements on the tank and find that that the diameter of the tank is 2.1 m. You also find that when you apply a step change to the inlet flow that it takes about 3 minutes and 25 s for the tank level to reach a new steady state level. You also know that the liquid in the tank is mineral oil with a density of 850 kg/m2. From this information determine: The tank capacitance i) The time constant for this tank level process ii) The resistance of the outlet valve (6 marks) (b) Determine the steady state gain for the tank and use this to determine the inflow (and (4 marks) outflow) rates of the mineral oil if the steady state level in the tank is 1.4 m. With the level steady at 1.4 m, the system is now subjected to an input disturbance: (c) If the disturbance is such that the inflow of mineral oil is now suddenly decreased by S01/s, determine The level in the tank after 65 s The new steady state level (6 marks) i) Draw a neat scaled graph of the system response (ie output) to the given change in inflow in part (i) above. Show clearly the time constant, original steady state level, new steady state level, and level at 65 s. (4 marks) (d) With the level steady, back at 1.4 m, the system is now subjected to a ramp input disturbance State the general output response equation of the system with respect to time for a ramp input disturbance i) Find the response (level of mineral oil) in the tank 15 s after the inflow of mineral oil is ramped up by+10 1/s per second. (4 marks)

Answer 1

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