Exercise A liquid-level process control system is shown in Figure 1 below. The system parameters are:...

 

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Exercise A liquid-level process control system is shown in Figure 1 below. The system parameters are: A=2m², RF = 15 s/m², H₁ = 1 V/m (unity gain), Kv=0.1 m³/sV, K₁ = 1 (controller gain). Rf 1+ ARfs a) Model the system and obtain the transfer function b) What are the values of T, and when the undamped natural frequency wn is 0.1 rad/s? (Hint: Use the block diagram to obtain the forward path transfer function G(S), then use G(s) to obtain the closed loop transfer function for the system [Ha(s)/Hd(s)]). c) Find an expression for the time response of the system when there is a step change of ha(t) from 0 to 4m. Assume zero initial conditions. d) Use MATLAB to plot the time response for the system. h₂0 he(0) He(s) PI Controller H_(s) 동 E(s) LI(1) Control Valve K₂ Pressure transducer H₁ Ha -(s) U(s) /HIN Tank Area A Figure 1: Liquid level control system. Note: V₁(t) is the inflow to the tank, K, is the valve gain, v₂(t) is the tank outflow, R, is the outlet valve resistance, Ha(t) is the height of liquid in the tank. PI Controller H₁ Control valve K₂ VI(1) Pressure tranducer Outlet valve Resistance R V₁(s) /1\ V₂ (1) Tank and valve Figure 2: System block diagram h₂(1) R₁ 1+ARS H₂(s) Exercise A liquid-level process control system is shown in Figure 1 below. The system parameters are: A=2m², RF = 15 s/m², H₁ = 1 V/m (unity gain), Kv=0.1 m³/sV, K₁ = 1 (controller gain). Rf 1+ ARfs a) Model the system and obtain the transfer function b) What are the values of T, and when the undamped natural frequency wn is 0.1 rad/s? (Hint: Use the block diagram to obtain the forward path transfer function G(S), then use G(s) to obtain the closed loop transfer function for the system [Ha(s)/Hd(s)]). c) Find an expression for the time response of the system when there is a step change of ha(t) from 0 to 4m. Assume zero initial conditions. d) Use MATLAB to plot the time response for the system. h₂0 he(0) He(s) PI Controller H_(s) 동 E(s) LI(1) Control Valve K₂ Pressure transducer H₁ Ha -(s) U(s) /HIN Tank Area A Figure 1: Liquid level control system. Note: V₁(t) is the inflow to the tank, K, is the valve gain, v₂(t) is the tank outflow, R, is the outlet valve resistance, Ha(t) is the height of liquid in the tank. PI Controller H₁ Control valve K₂ VI(1) Pressure tranducer Outlet valve Resistance R V₁(s) /1\ V₂ (1) Tank and valve Figure 2: System block diagram h₂(1) R₁ 1+ARS H₂(s)

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