Consider the ratio control scheme shown in Fig. 15.6. Each flow rate is measured using an orifice plate and a differential pressure (D/P) transmitter. The pneumatic output signals from the D/P transmitters are related to the flow rates by the expressions 

d_m = d_m0 + K₁d² 

u_m = u_m0 + K₂u²

Each transmitter output signal has a range of 3€“15 psi. The transmitter spans are denoted by S_d and S_u for the disturbance and manipulated flow rates, respectively. Derive an expression for the gain of the ratio station K_R in terms of S_d, S_u, and the desired ratio R_d. 

Disturbance stream, d FT dm RS ) Ratio station Set point usp FC I FT Manipulated stream u Figure 15.6 Ratio control, Method II.