*4.1. Data Acquisition*

The on-site collection situation of an aluminum plant is shown in Figure 6. The actual working area of modern aluminum electrolysis is shown in Figure 6a. The data collected in the field include a feeding interval, distributed alumina concentration and distributed current. In Figure 6b, the data of the feeding interval were obtained using a stopwatch recording each feeding time. In Figure 6c, the distributed alumina concentration is scooped out by the field workers, cooled, bagged, and sent to the laboratory for analysis. The distributed current was obtained by a data collector installed on the anode guide rod, as shown in Figure 6d. Using the data collected in the field, 1000 sets of data for simulation mentioned in Section 2 can be obtained. The simulation parameters are: the input constraints of the six subsystems *U* = [0 0.1], and the error accuracy *ε* = 0.05, and each subsystem expects an output setpoint *r*(*k*) of 2.5.

### *4.2. Control Effect without Any Interference*

Under the premise that there is no model mismatch and external interference in the aluminum reduction cell, as shown in Figure 7, the first 1000 s is the control effect of the traditional control strategy, and the control effect of the control strategy in this paper is after 1000 s. The traditional control strategy is based on the relationship between the cell resistance and the concentration to drive the six feeding devices' group timing feeding: FD1, FD3, FD5 are a group of simultaneous feeding, FD2, FD4, and FD6 are a group of simultaneous feeding, and each group of feeding is staggered by half the feeding cycle.

(**c**) (**d**)

(**a**) (**b**)

**Figure 6.** Field collection diagram: (**a**) actual working area of modern aluminum electrolysis; (**b**) data acquisition diagram of feeding interval; (**c**) scoop out the electrolyte diagram; and (**d**) distributed current acquisition diagram.

**Figure 7.** Variation of alumina concentration: (**a**) subsystems 1–3; and (**b**) subsystems 4–6.

In the first 1000 s of Figure 7, the concentration of the six subsystems is distributed very unevenly, although it is roughly in the appropriate range after feeding for a period using the traditional control strategy. After 1000 s, the distributed subspace predictive control method proposed in this paper is used to control the aluminum reduction cell. Each feeder is distributed as needed under the influence of other feeders, so that the variation of the alumina concentration is greatly reduced in space and time, and the concentration of the six areas is well controlled near the set value, the alumina concentration distribution in the entire cell is more uniform. The continuous feeding amount of each feeder in Figure 8. Since alumina is dumped in discrete 1.8 kg batches each time during the actual operation on site, the actual feeding interval is calculated according to the theoretical consumption rate of alumina in Figure 9. It can be seen from Figure 9 that the control method proposed in this paper can make the six feeders of the aluminum electrolysis cell distribute according to the demand, considering the influence of other feeders. The distribution of alumina concentration throughout the cell is more uniform and can be effectively controlled within the set value.

**Figure 8.** Distributed feeding quantity control: (**a**) subsystems 1–3; (**b**) subsystems 4–6.

**Figure 9.** Distributed feeding interval control: (**a**) subsystems 1–3; (**b**) subsystems 4–6.

### *4.3. The Control Effect when the Feeding Amount of the Feeder Is Inconsistent with the Actual Set Value*

In practice, the feeder may be blocked or overloaded. Therefore, the disturbance of inaccurate feed quantity is introduced to test the stability of the proposed control method. As shown in Figure 10, after the second 500 s, the inaccurate feeding amount was simulated for the feeding ports of subsystem 2 and subsystem 6, and the control effects were increased by 15% and decreased by 15%, respectively.

**Figure 10.** Variation of the alumina concentration: (**a**) subsystems 1–3; and (**b**) subsystems 4–6.

As can be seen from Figure 10, after the simulation of a 15% increase and 15% decrease in feeding port 2 and feeding port 6, the concentration of subsystem 2 will increase for a short time, and the alumina concentration of subsystem 6 will decrease for a short time. Due to the flow of electrolyte in the reduction cell, the alumina concentration of other subsystems will also be affected, but the controller can quickly stabilize the alumina concentration of each subsystem, indicating that the controller designed in this paper has a good stability. The continuous feeding amount of each feeder is shown in Figure 11. Since 1.8 kg alumina is discretely dumped each time during the actual operation on site, the actual feeding interval is calculated according to the theoretical consumption rate of alumina in Figure 12.

**Figure 11.** Distributed feeding quantity control: (**a**) subsystems 1–3; (**b**) subsystems 4–6.

**Figure 12.** Distributed feeding interval control: (**a**) subsystems 1–3; (**b**) subsystems 4–6.

It can be seen from Table 1 that the control method in this paper can still maintain a small error in the presence of interference. The main reason is that the method proposed in this paper considers the influence of adjacent subsystems on itself so that each feeder can act independently to control the local alumina concentration to maintain the setpoint while making the concentration of the entire cell uniformly distributed, which is conducive to the stable operation of the cell.

**Table 1.** Mean squared error (MSE) of the actual concentration and set concentration when disturbance occurs.

