Control Notes

Conventional pH Control
The control of pH is at best very difficult with a conventional PID control loop (Figure 1). The challenge results from variable product flow rates and the highly nonlinear pH titration curve.

Figure 1. Conventional pH control – not recommended.

The pH of a liquid stream (let’s call it the product) is controlled by adding a flow of acid or base (called the reactant). To achieve the required product pH, a certain (but often unknown) ratio of reactant is needed. And here is the first key to pH control: we need to manipulate the ratio of reactant flow to product flow.

Ratio pH Control
We should not simply manipulate the reactant flow independently of the product flow (as in Figure 1), because every time the product flow rate changes, the pH will first go off spec and then the pH controller will change the reactant flow to return the pH to its set point. With ratio control (as in Figure 2), if the product flow rate changes, the reactant flow rate is changed immediately to maintain a constant ratio between it and the product flow rate. The pH controller then manipulates this ratio to control the pH.

Figure 2. Ratio pH control – much better.

Advanced pH Control
As you probably know, pH control is a very nonlinear process – the gain of the process changes with pH. The process gain is very high around the equivalence point, and much lower elsewhere (Figure 3).

Figure 3. pH titration curve.

Because the process gain changes so significantly, we should dynamically adjust the controller gain to compensate. This is done by implementing gain scheduling to adjust the controller gain based on pH.

To design the gain scheduler we should determine the process gain at a few points along the titration curve by changing the ratio at different levels of pH and determining the process gain. Process gain = (change in pH in % of full scale) / (change in Ratio in % of full scale). We should also measure the process dynamics (dead time and time constant) at each point (although these will likely be quite constant throughout).

Then we calculate the controller gain settings that the controller should use at various pH levels, and implement these in a controller gain scheduler (Figure 4). Obviously we should also calculate the integral setting, and if used, the derivative setting but these will remain constant and can be set directly in the controller.

Figure 4. Advanced pH control.

The gain scheduler can be implemented with a standard f(x) curve or characterizer block provided in modern control systems. The gain scheduler’s input should come from the measured pH and its output should set the controller’s gain accordingly.  And voila! We have good pH control.

Stay tuned!
Jacques Smuts – Author of the book Process Control for Practitioners