Calculate the optimal controller parameters for a composition control loop controlling the concentration in a cascade of three CSTR described in the Examples 3.2 and 6.5 (Fig. 12.17). The pumping flow...

Calculate the optimal controller parameters for a composition control loop controlling the concentration in a cascade of three CSTR described in the Examples 3.2 and 6.5 (Fig. 12.17).

The pumping flow of the mixing impeller is F_a
= 80 l/min, each reactor volume is V = V₁
= V₂
= V₃
= 200 l. The residence time in each reactor is 10 min. The correction of concentration is done adding reactant A (concentrate) with the concentration C_Ac
= 5 kmol/m³, with the flow rate nominal value of 5 l/min, the nominal input concentration being CAi = 0.8 kmol/m³. The transducer is a densimeter with the measuring range 0–2.5 kmol/m3 and an output signal 2–10 mA having 0 time lag. The gain of the final control element is K_AD
= 4.66 l/min/mA and the time constant of the control valve is considered 0.