Inferential Composition Control of a Distillation Column Using Active Disturbance Rejection Control with Soft Sensors
Abstract
:1. Introduction
2. An Overview of Active Disturbance Rejection Control and Inferential Control
2.1. Active Disturbance Rejection Control
2.2. Overview of Inferential Control
- They provide more insight into the process through catching the information hidden in data;
- They provide enhanced monitoring and control of industrial processes with the consequences of reducing environmental impact, enhancing productivity and energy efficiency, and improving business profitability through decreasing the production cost related to off-specification products;
- They can be simply implemented on existing hardware. Moreover, on-line model identification algorithms can be utilized to adapt the model when plant characteristics change; and
- They entail little or no capital costs such as installation cost, commissioning and management of the required infrastructure.
3. A Binary Distillation Column for Methanol-Water Separation
4. Inferential ADRC Scheme
5. PCR Model-Based Software Sensors
5.1. Static PCR Models
5.2. Dynamic PCR Models
6. Inferential ADRC Scheme Based on PCR Models
7. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Appendix A
t | t − 1 | t − 2 | t − 3 | t − 4 | t − 5 | |
---|---|---|---|---|---|---|
T1 | −0.037 | 0.006 | 0.077 | 0.091 | 0.039 | −0.151 |
T2 | 0.012 | −0.039 | −0.030 | −0.061 | 0.031 | −0.001 |
T3 | 0.115 | 0.059 | 0.031 | −0.021 | −0.002 | −0.030 |
T4 | 0.051 | 0.014 | −0.003 | −0.035 | −0.009 | −0.020 |
T5 | 0.046 | −0.022 | −0.021 | −0.044 | −0.052 | −0.016 |
T6 | −0.083 | −0.045 | 0.056 | 0.068 | 0.065 | 0.016 |
T7 | −0.138 | −0.069 | 0.020 | 0.044 | 0.071 | 0.055 |
T8 | −0.171 | −0.110 | −0.042 | −0.023 | 0.004 | 0.007 |
T9 | −0.175 | −0.103 | −0.015 | 0.013 | 0.068 | 0.100 |
T10 | −0.219 | −0.146 | −0.088 | −0.071 | −0.047 | −0.017 |
t | t − 1 | t − 2 | t − 3 | t − 4 | t − 5 | |
---|---|---|---|---|---|---|
T1 | −0.569 | −0.453 | −0.307 | −0.140 | 0.032 | 0.191 |
T2 | −0.122 | −0.084 | −0.037 | 0.042 | 0.154 | 0.261 |
T3 | 0.056 | 0.052 | 0.047 | 0.060 | 0.100 | 0.142 |
T4 | 0.019 | −0.004 | −0.041 | −0.076 | −0.093 | −0.097 |
T5 | 0.083 | 0.059 | 0.020 | −0.033 | −0.084 | −0.122 |
T6 | 0.113 | 0.065 | 0.016 | −0.028 | −0.005 | −0.062 |
T7 | 0.002 | −0.027 | −0.047 | −0.053 | −0.041 | −0.015 |
T8 | 0.032 | 0.014 | 0.004 | 0.007 | 0.026 | 0.055 |
T9 | −0.008 | −0.033 | −0.048 | −0.048 | −0.027 | 0.008 |
T10 | 0.017 | 0.001 | −0.004 | 0.003 | 0.028 | 0.067 |
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Variables | Nominal Values |
---|---|
Top composition (y1) | 93% (wt) methanol |
Bottom composition (y2) | 7% (wt) methanol |
Reflux flow rate (u1) | 10.108 g/s |
Steam flow rate (u2) | 13.814 g/s |
Feed composition (d1) | 50.12% (wt) methanol |
Feed flow rate (d2) | 18.23 g/s |
No. of PCs | Top Composition | Bottom Composition | ||
---|---|---|---|---|
Training Data | Testing Data | Training Data | Testing Data | |
1 | 410.00 | 230.00 | 1400 | 280.30 |
2 | 32.00 | 10.00 | 679.90 | 82.27 |
3 | 31.00 | 10.00 | 89.39 | 19.71 |
4 | 4.00 | 0.78 | 68.10 | 8.50 |
5 | 3.50 | 0.48 | 49.35 | 6.71 |
6 | 3.15 | 0.32 | 40.86 | 5.45 |
7 | 3.14 | 0.32 | 35.64 | 6.43 |
8 | 3.07 | 0.36 | 27.82 | 3.36 |
9 | 2.93 | 0.38 | 20.21 | 2.66 |
10 | 2.85 | 0.34 | 17.86 | 1.94 |
Model Orders | Model Output | SSE | No. of Principal Components |
---|---|---|---|
1 | Top composition | 0.662 | 11 |
Bot composition | 13.04 | 11 | |
2 | Top composition | 0.361 | 14 |
Bot composition | 9.958 | 7 | |
3 | Top composition | 0.045 | 32 |
Bot composition | 2.970 | 7 | |
4 | Top composition | 0.140 | 50 |
Bot composition | 2.542 | 7 | |
5 | Top composition | 0.122 | 17 |
Bot composition | 1.323 | 7 | |
6 | Top composition | 0.145 | 42 |
Bot composition | 4.722 | 8 | |
7 | Top composition | 0.141 | 54 |
Bot composition | 3.958 | 8 |
Control Schemes | Top Comp. | Bottom Comp. | |
---|---|---|---|
Inferential ADRC with static PCR model | Without mean updating | 54,542 | 6946.9 |
With mean updating | 1.6889 | 1.8309 | |
Inferential ADRC with 5th order dynamic PCR model | Without mean updating | 165.52 | 219.59 |
With mean updating | 0.1856 | 0.1551 |
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Al Kalbani, F.; Zhang, J. Inferential Composition Control of a Distillation Column Using Active Disturbance Rejection Control with Soft Sensors. Sensors 2023, 23, 1019. https://doi.org/10.3390/s23021019
Al Kalbani F, Zhang J. Inferential Composition Control of a Distillation Column Using Active Disturbance Rejection Control with Soft Sensors. Sensors. 2023; 23(2):1019. https://doi.org/10.3390/s23021019
Chicago/Turabian StyleAl Kalbani, Fahad, and Jie Zhang. 2023. "Inferential Composition Control of a Distillation Column Using Active Disturbance Rejection Control with Soft Sensors" Sensors 23, no. 2: 1019. https://doi.org/10.3390/s23021019
APA StyleAl Kalbani, F., & Zhang, J. (2023). Inferential Composition Control of a Distillation Column Using Active Disturbance Rejection Control with Soft Sensors. Sensors, 23(2), 1019. https://doi.org/10.3390/s23021019