Figure P12.6 shows a continuous stirred tank reactor in which an aqueous solution of sodium acetate (CH₃COONa) is neutralized in the mixing tank with hydrochloric acid (HCl) to maintain a particular pH in the mixing tank.
The amount of acid in the mix is controlled by varying the rotational speed of a feeding peristaltic pump. A nominal linearized transfer function from HCl flowrate to pH has been shown to be (Tadeo, 2000)

a. Write the system in state-space phase-variable form.

b. Use state-feedback methods to design a matrix K that will yield an overdamped output pH response with a settling time of T_s ≈5 min for a step input change in pH.

c. Simulate the step response of the resulting closed-loop system using MATLAB.

Transcribed Image Text:

-0.9580 x 10-s- 0.01197 x 10-4 G(s) = s3 + 0.5250s2 +0.01265s +0.000078