Cascade, feedforward and split range

In short. In a cascade the controller of a slow variable (temperature) sets the set point of a controller of a fast one (flow): disturbances in the fast part are removed before they reach the temperature. Feedforward adds a correction from a measured disturbance to the output without waiting for an error. Split range distributes one output over two actuators (heating and cooling). In all three the controller must know the actual output — otherwise the integrator winds up.

Cascade

When it is needed: there is an intermediate measured variable that responds faster than the main one, and disturbances come through it (steam pressure, pump supply pressure).

Tuning order:

1. Master in manual. Tune the slave (flow) — a step test on its output, SIMC.
2. Slave in auto. Run a test for the master: a step of the slave set point → temperature. The model already includes the closed inner loop.
3. Tune the master clearly slower than the slave — in practice 4–10 times by the closed-loop time constant. Otherwise the loops interfere.

Saturation: if the slave is at a limit or in manual, the master must stop integrating and track the actual slave set point (anti-windup, bumpless transfer).

Feedforward

If the disturbance d is measured and its effect on PV is known, it can be compensated at once. Let Kd be the disturbance gain on PV and K the process gain from the output. Static feedforward:

u = u_PID − (Kd / K) · (d − d0)

Example: a product flow increase of 1 m³/h lowers the temperature by 0.6 °C (Kd = −0.6 °C/(m³/h)), K = 1.8 °C/%:

u_ff = −(−0.6 / 1.8) · Δd = +0.333 % per m³/h

Feedforward does not replace feedback: the PID removes the remainder caused by errors in Kd and K. If the disturbance and the control act at different speeds, a dynamic correction (lead-lag) is needed — beyond this article.

Split range

One controller output of 0–100 % is shared between actuators. The example in the figure: 0–50 % — cooling (valve from 100 to 0 %), 50–100 % — heating (from 0 to 100 %).

Specifics:

• Different K for heating and cooling: the loop gain changes when passing 50 %. Solutions — different Kc per range, or rescaling the output so that K per percent of output is the same.
• A dead zone or an overlap around the split point: a dead zone causes slow oscillation, an overlap — heating and cooling working at once.
• Saturation: the 0 and 100 % limits are common for the controller; set anti-windup on them.

Skogestad (2023) discusses split range together with alternatives — several controllers with different set points and selectors (min/max); they are easier to tune when K differs a lot.

Typical mistakes

• Master faster than the slave or at a similar speed — cascade oscillation.
• Slave tuned in cascade from the master test — the model is wrong.
• Feedforward with the wrong sign — the disturbance doubles instead of being compensated. Check with a small gain first.
• Split range ignoring different K — oscillation on only one of the ranges.

Limits

The diagrams show the principle. Dynamic feedforward, selectors, override control and multivariable systems are outside this section — see Skogestad's primary source (2023).