Control StationWorkshop #10

Cascade Control of the Jacketed Reactor02/24/14Devin Roy & Ethan Stewart

Introduction:In traditional feedback control, disturbance rejection occurs after the systems sensor has registered an upset. Only at that point, does the controller respond to a change and adjust accordingly. Cascade control was designed with the ability to handle disturbances more effectively by taking preventive actions before the disturbance was allowed to significantly affect the process. Thus, cascade control was able to reduce deviations from the set point and settling time when disturbances occurred. In this experiment the advantages of cascade control were examined using a jacketed reactor (See Figure 1 below). A secondary or inner loop controlled the jacketed reactor. The inner loop could sense a sudden change in temperature and increase or decrease control to compensate for the disturbance locally. Meanwhile, that disturbance could not spread to the primary or outer loop. This protected the exit reactor temperature, the primary process variable, from possible high frequency disturbances such as changes in cooling water jacket temperature. In this simulation, the system was designed to keep the exit temperature at a constant set point of 92oC. Performance of both a traditional PI controller and that of the cascade described above were compared.

Figure 1: Cascade Jacketed Reactor Process Flow Diagram

Step One: As mentioned above, the cascade jacketed reactor design involved two control loops including two sensors, two controllers, and one final control element (valve). The reactor exit temperature was the primary process variable, since the temperature within the reactor indicated the conversion achieved by the process. The cooling water entering the jacket was expected to enter at 50oC, however spikes of the variable occurred that could increase it to as high as 60oC. Therefore, the cascade design to be implemented was designed to reject this common disturbance. Offset in the primary process variable could result in poor product quality; therefore a PI controller was necessary for the outer loop to ensure offset did not occur. However, in terms of the inner loop, offset was not a major concern. Instead, success for the cascade loop required the settling time of the secondary loop to be significantly faster than that of the primary, and a P-Only controller was used. The design information for the two loops was recorded before any simulations took place.

Secondary (inner) P-Only Controller: Tsetpoint = 75.6oCbias = 42%

Primary (outer) PI Controller:Tsetpoint = 92.0oC

Step Two:Dynamic testing had to be performed on both loops for the cascade design. Testing began with the inner loop. This controller was designed as a P-Only controller that would track set point changes given from the primary controller and minimize disturbances. Process and tuning parameters were found in the exact same way as previous experiments, by fitting data to FOPDT models (See Figure 2 of Step 3). Data was found by implementing a doublet pulse from 42% 37% 47% 42%.

Step Three:Data was collected for both inner and outer loops of the control process. Therefore, before correct fitting could be achieved, it was necessary to ensure the correct process and manipulated variables were labeled in the data files. For the first test, the second column had to hold the secondary controller values (percentage of controller output, e.g. 42%) while the third column held the secondary measured process variable (outlet temperature of the jacket, e.g. 75.6oC). After all columns were labeled correctly, the data was fit to an FOPDT model (See Figure 2). The fit was deemed acceptable with an R2 value of 0.9972 and the process parameters were found to be:

Kp = -0.4072 p = 2.15 p = 0.1669

Figure 2: Open Loop Testing and FOPDT Fitting for Secondary Loop

Conservative tuning parameters were given by Control Station using IMC correlations (See Table 1). This gave the controller gain for the P-Only secondary loop.

Secondary controller P-Only controller gain, Kc = -11.17

Table 1: Conservative PID Tuning Values for Secondary Loop

Step Four:To implement P-Only control, the controller gain, set point and controller bias were designated for the secondary controller. After ensuring that controller tracked set point changes quickly and with minimal settling time, the controller was left in automatic well a second dynamic test was performed on the outer loop.

Step Five:Open loop testing was always done by doublet pulses, which involved stepping the controller output. In this case, the doublet test had to be completed by stepping the set point of the secondary controller, which ultimately sets the controller output for the primary loop. The doublet pulse of 75.6oC 72.6oC 78.6oC 75.6oC was preformed (See Figure 3 of Step 6).

Step Six:Data collected from the open loop test was fitted to another FOPDT model (See Figure 3). In this case, the default columns were improperly labeled and had to be corrected. The manipulated process variable was the set point for the secondary controller (e.g. 75.6oC) and the measured process variable was the reactor exit temperature (e.g. 92.0oC). The model was deemed reliable with an R2 value of 0.9968 and the following process parameters were obtained:

Kp = 0.722p = 0.4357p = 0.6777

Figure 3: Open Loop Testing and FOPDT Fitting for Primary Loop

Standard tuning parameters for a PI-controller were given by Control Station using IMC correlations (See Table 2).

Primary Controller PI Tuning Parameters: Kc = 0.495I = 0.436

Table 2: Standard PID Tuning Values for Primary Loop

Step Seven:The purpose of step seven was to compare the disturbance rejection performance of a cascade controller scheme with that of a single loop controller scheme. The cascade controller was tested and then compared to a diagram of the single loop controller response (see Figure 5). A disturbance from 50C up to 60C and back to 50C was implemented on the cooling jacket inlet temperature. The disturbance rejection results of the cascade controller scheme can be seen in Figure 4.

Figure 4: Cascade Controller Response to a Disturbance

Set Point TrackingDisturbance Rejection

Figure 5: Single Loop Response to a Disturbance

When comparing Figure 4 with Figure 5, it could be seen that the cascade controller minimized the large deviations in the reactor exit temperature that was caused by the disturbance much better than the single loop controller. The range of reactor exit temperature was reduced from a range of 88C - 95C with the single loop controller to a range of 90.5C - 93C with the cascade controller. Not only was the disturbance rejection improved with the cascade controller, the settling time was also significantly reduced.

Step Eight:In this step the set point tracking performance of a cascade controller was compared to a single loop controller. A step change from 92C up to 95C and back again was implemented and the results were compared (see Figure 5 and Figure 6).

Figure 6: Set Point Tracking Performance of a Cascade Controller Scheme

When comparing Figure 5 with Figure 6, it was observed that both responses were almost identical. The similarity in the two controller responses indicates that there was no benefit in using the cascade controller to improve the set point tracking performance.

Step Nine:This step was divided into four sections, Part A D. Each section dealt with the disturbance rejection performance of a controller when a disturbance from 50C up to 60C and back to 50C was implemented. In Part A, the purpose was to explore the tuning of a P-only controller and the affects of tuning on disturbance rejection. The P-Only controller was the inner loop, secondary controller, in the cascade controller scheme. The controller gain of the secondary controller was increased and then decreased and the results were compared (see Figure 7). In Part B, the inner loop was changed from a P-Only controller to a PI controller and the disturbance rejection performance of the two controllers was evaluated. The values for the tuning parameters of the PI controller were obtained from Table 1. The results comparing the two controllers can be found in Figure 8. Part C involved restoring the P-Only controller gain to the design value (see Table 1), and exploring the disturbance rejection performance of the primary PI controller (the outer loop). The PI tuning parameters for the outer loop were obtained from Table 2. Similar to Part A, the controller gain and the integral action parameters were both doubled and halved one at a time, and the results were observed (see Figure 9). In Part D, the primary controller was changed from a PI controller to a PID controller and the disturbance rejection performance was observed (see Figure 10).

Part A:

KC = -15.0KC = -7.0KC = -11.17

Figure 7: Controller Gain Effects on the Disturbance Rejection in the Secondary Loop

The following Kc values for the secondary P-only controller were compared: Kc = -11.17 Kc = -15 Kc = -7.0 It appeared a larger value for Kc increased the aggressiveness of the controller, providing a faster disturbance response. A much larger deviation occurred with the smaller value of Kc.

Part B:

P-Only ControllerPI Controller

Figure 8: Secondary PI Controller Effects on Disturbance Rejection Performance

When the PI controller was implemented for the secondary loop, the dynamic response of the process deteriorated. Integral action is used to minimize offset, however offset was not an issue for the secondary process variable. The desired response of the inner loop was to provide immediate response and settling time, therefore the aggressive P-only control was sufficient. Using the PI-controller in this instance just increased settling time, which was the opposite response than what was desired.

Part C:

KC = 0.248KC = 0.99KC = 0.495

Figure 10: Controller Gain Effects on Disturbance Rejection Performance in a PI Controller of a Primary Loop

For the PI controller of the outer loop, the following values of Kc were adjusted to look at different responses: Kc = 0.495 Kc = 0.99 Kc = 0.248 Doubling Kc provided a more aggressive response but with more oscillations and therefore a longer overall settling time. Meanwhile, halving Kc increased the settling time substantially.

I= 0.436I= 0.872I= 0.218

Figure 11: Integral Action Effects on Disturbance Rejection Performance in a PI Controller of a Primary Loop

For the PI-controller of the outer loop the values of I were adjusted also: I = 0.436 I = 0.872 I = 0.218Changes in integral action showed similar responses to changes in controller gain. It appeared that the optimal tuning values for PI-control that were given were sufficient and provided an excellent desired response.

Part D:

Figure 12: Comparing the PI Controller Disturbance Rejection to the PID controller on the Primary Loop

In terms of the primary process variable, derivative action did lead to improved control response. However, the noise level for the secondary process variable and for controller valve output was significantly increased. The increase in noise measurement, and just a small improvement in control performance, would be the main reason why a PI-controller for the outer loop would be the controller of choice.

References:

Control Station (Loop-PRO 4.2) Workshop Series, Douglas J. Cooper (2005)"Chemical & Bio-Process Control," 3rd ed., by J. B. Riggs & M. N. Karim, FerretPublishing, Lubbock, TX (2006). ISBN 0-9669601-4-9