Process Control Tutoring

Process control is where chemical engineering turns into applied dynamics. The models are differential equations, the main tool is the Laplace transform, and the questions are how a plant responds to a disturbance and how a controller should react. Students find it abstract because nothing before it looked like this. STEM Tutor 360 ties each idea to a tank, heat exchanger, or column you can picture, so a time constant becomes how fast a vessel warms up, and a pole becomes a prediction you can check.

Sessions cover first and second order processes, dead time, transfer functions and block diagrams, P, PI, and PID control, tuning rules, stability by the Routh array and root locus, frequency response, and cascade, feedforward, and ratio control. We also practice reading P&IDs. Your text may be Seborg, Edgar, Mellichamp, and Doyle, or Marlin, and we follow it. The mechanical engineering version of the course has its own page.

A typical process dynamics problem, worked

A well-mixed tank holds $2\ \text{m}^{3}$ of liquid, with $0.5\ \text{m}^{3}\text{/min}$ flowing through. The inlet temperature steps from 20°C to 30°C. Find the outlet temperature over time.

An energy balance with constant density and heat capacity gives $$V\, \dfrac{dT}{dt} = q\,(T_{in} - T)$$ Divide by $q$ and the model becomes $\tau\, \dfrac{dT}{dt} + T = T_{in}$, where the time constant is $\tau = V/q = 2/0.5 = 4\ \text{min}$. In deviation variables the transfer function is $\dfrac{T'(s)}{T_{in}'(s)} = \dfrac{1}{4s + 1}$, with a gain of 1.

A 10°C step in the inlet gives $T'(s) = \dfrac{10}{s(4s + 1)}$, and the inverse transform is $T'(t) = 10\left(1 - e^{-t/4}\right)$. So $T(t) = 20 + 10\left(1 - e^{-t/4}\right)$.

At $t = 4\ \text{min}$ the outlet has covered 63.2% of the change, which is 26.3°C. At 8 min it is 28.6°C, and at 12 min it is 29.5°C. It takes $4 \ln 10 = 9.2\ \text{min}$ to get within 10% of the final value, and about 20 min (five time constants) to reach 99%.

Where students usually get stuck

• Forgetting deviation variables. Transfer functions assume the starting point is the steady state, so inputs and outputs are changes from it.
• Thinking a first order response is half done at one time constant. It is 63.2% done.
• Mixing up the process gain, the controller gain, and the loop gain.
• Getting the controller action wrong, direct against reverse acting, which can turn negative feedback into positive feedback.
• Applying a tuning rule to the wrong model form, such as first order plus dead time rules on a second order process.