(Solved): 1. Consider the level control loop in Figure 1. Variable h is the water level in the tank as measu ...

1. Consider the level control loop in Figure 1. Variable h is the water level in the tank as measured from the floor to the top of the water column (see Figure 3). PT is mounted in the tank a distance \( h_{P T} \) from the floor. According to its spec sheet, the PT will output an RSE analog voltage \( V_{P T} \) that ranges from \( 0.5 \) to \( 4.5 \mathrm{~V} \) as sensed gauge pressure \( P \) ranges from 0 psig to 1 psig (and pressure head \( =P / \gamma \) ranges from 0 to \( 27.68 \mathrm{in} \). of water). The spec sheet also asserts that \( V_{P T} \) and sensed pressure \( P \) are linear. Since \( P \) maps linearly to \( V_{P T} \), and \( d \) (PT depth = pressure head) maps linearly to \( P \), and \( h \) maps linearly to \( d \), then \( h \) maps linearly to \( V_{P T} \) : \[ V_{P T}=K h+V_{P T o} \] Determine the gain \( K \) and offset \( V_{P T o} \) for this linear Transfer Function. Assume \( h_{P T}=10 \) in. Hint: how does \( d \) map to \( h \) and what is \( V_{P T} \) equal to when \( h=h_{P T} \) ? Figure 3. The Pressure Transmitter (PT) is factory calibrated to transmit a \( 0.5 \mathrm{~V} \) to \( 4.5 \mathrm{~V} \) signal \( \left(V_{P T}\right) \) that is linear with respect to a sensed gauge pressure that ranges from 0 psig to 1 psig. In lab, water level \( h \) will range from \( \mathrm{h}_{\text {lrv }} \) to \( h_{\text {urv }} \) as measured from the lab floor (the reference level). \( \mathrm{h}_{\mathrm{PT}} \) is the height of the PT above the lab floor. You will measure \( \mathrm{h}_{\text {lrv }}, \mathrm{h}_{\mathrm{urv}} \), and \( \mathrm{h}_{\mathrm{PT}} \) in lab. Figure 1. PFD of the water level control loop. You will measure the range values for \( h \) and \( V_{P T} \) in Lab. AMP is also an Offset/Gain Instrumentation Amplifier with additional hardware for powering the \( \mathrm{PT} \).