Flexible Optimal Control of the CFBB Combustion System Based on ESKF and MPC
Abstract
:1. Introduction
- (1)
- For the first time, a method of enhancing the robustness of MPC control using the ESKF algorithm is applied to the combustion system of a circulating fluidized bed boiler with complex coupling characteristics, in order to effectively improve the overall performance of the control system during the flexible operation process. This solution helps to reduce the frequent fluctuations of the main steam pressure and the bed temperature, ensuring the efficiency of the operation process;
- (2)
- The extended state Kalman filter is used to ensure the accuracy and stability of the collected signals. This is especially true for the bed temperature signals in the high-temperature furnace during the combustion fluctuation process, providing stable and accurate signals for feedback control. Based on this control system, unnecessary frequent actions and wear of equipment can be reduced, equipment failures can be decreased, and the service life of equipment can be extended;
- (3)
- Combining the ESKF to conduct online estimation and compensation of the “external disturbances” of the system significantly reduces the dependence of the MPC control strategy on an accurate model. This improves the adaptability and eases the modeling difficulty during the implementation of the MPC strategy. It is conducive to the widespread application of its online optimization features.
- (4)
- During the continuous load-rising and load-falling process of CFB units, the combustion system adopting the ESKF-MPC control strategy exhibits faster tracking ability, better anti-disturbance performance, and enhanced robustness compared to the PI control strategy. Simulation results show that, for a 330 MW CFB unit at the rated capacity, when the load condition fluctuates by up to 50%, the controller still demonstrates reliable robust control performance.
2. CFB Boiler Combustion System Description
3. Control Strategy Design
3.1. ESKF-MPC Algorithm
3.2. Controller Design
4. Simulation Results and Analysis
4.1. Controller Parameter Setting
- (1)
- The influence of the prediction horizon .
- (2)
- The influence of the control horizon .
- (3)
- The influence of the discrete time .
- (4)
- The influence of the adjustment weight .
- (5)
- The influence of the error weight .
- (6)
- The influence of the control weight .
4.2. Tracking Performance Comparison
4.3. Comparison of Anti-Interference Performance
4.4. Comparison of Robust Performance
4.5. Application in Actual Continuous Change Working Conditions
5. Conclusions
- (1)
- For the multi-variable, strongly coupled, and nonlinear CFBB combustion system, the ESKF-MPC control strategy is well suited to handle this complex multi-input and multi-output control scenario. This strategy takes into account the interactions between system variables during the parameter setting process of the controller, thereby ensuring optimal overall control performance. For a system with such coupling, the control algorithm of PI and LADRC designed for single-loop systems must implement a decoupling strategy to achieve the desired control performance.
- (2)
- By expanding the “total disturbance” inside and outside the system into new observed variables, the ESKF can accurately estimate the values of all state variables and disturbances in the system at each moment. This approach effectively addresses the issue of low control performance caused by system model errors and overcomes the traditional MPC reliance on an accurate prediction model.
- (3)
- Compared to MPC control, ID-PI control, and ID-LADRC control with decoupling strategies, the proposed ESKF-MPC composite control method demonstrates the shortest adjustment time during the set point tracking process, with almost no overshoot. When disturbances are introduced to the two coupled control loops of the system, each loop exhibits minimal overshoot and the fastest recovery time. Additionally, when model parameters undergo changes, the ITAE index value remains relatively small under the ESKF-MPC strategy.
- (4)
- Under continuously changing operating conditions, the main steam pressure loop of the CFBB combustion system using the ESKF-MPC strategy achieves rapid tracking and disturbance elimination, with no significant overshoot or output shock. This effectively prevents operational instability caused by frequent fluctuations in the main steam pressure. In the coupled bed temperature loop, the ESKF-MPC strategy significantly reduces the bed temperature fluctuation range compared to the PI strategy, which helps to ensure the economic operation of the unit.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Nomenclature
The real-time combustion heat discharge | The state vector of the system | ||
The coal instruction | The control input vector of the system | ||
The primary air | The disturbance of the system | ||
The secondary air | The measurement output vector of the system | ||
The boiler water supply | The measurement noise vector | ||
The heat absorption of the heat exchange medium | The coefficient matrix | ||
The bed temperature | The input matrix | ||
The main steam pressure | The output matrix | ||
The state matrix of the system after discretization | The error matrix | ||
The input matrix of the system after discretization | The prior estimation covariance at time k | ||
The output matrix of the system after discretization | The covariance matrix for measuring noise | ||
The expanded state estimate | The posterior estimation covariance at k time | ||
The actual output value | The posterior estimation covariance at k−1 time | ||
The output estimate | The noise covariance matrix of the system | ||
The Kalman gain coefficient changing with time | The system’s augmented matrix coefficients | ||
The reference track of the controlled object | The system’s augmented matrix coefficients | ||
The output vector of the system | The system’s augmented matrix coefficients | ||
The control increment of the system | The state variables under the augmented matrix | ||
The weight coefficient | The amount of coal fed | ||
The prediction time domain | The primary air volume | ||
The control time domain | The main steam pressure | ||
The weight coefficient of output error | The bed temperature | ||
The control increment weight coefficient |
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Control Strategy | Main Steam Pressure Loop | Bed Temperature Loop | ||
---|---|---|---|---|
Adjustment Time/s | Overshoot/% | Adjustment Time/s | Overshoot/% | |
ID-PI | 3163 | 0.83 | 1949 | 1.75 |
ID-LADRC | 2611 | 1.61 | 1675 | 1.47 |
MPC | 1268 | 0 | 592 | 0 |
ESKF-MPC | 794 | 0.63 | 476 | 1.81 |
Control Strategy | Adjustment Time | ITAE Range | |
---|---|---|---|
Distribution Range of Adjustment Time | Time Span | ||
ID-PI | 2900~6000 s | 3100 s | [0.87 × 106, 2.84 × 106] |
ID-LADRC | 2600~5000 s | 2400 s | [0.7 × 106, 1.99 × 106] |
MPC | 1000~2600 s | 1600 s | [1.02 × 105, 3.56 × 105] |
ESKF-MPC | 770~1600 s | 830 s | [0.615 × 105, 1.74 × 105] |
Control Strategy | Distribution Range of Adjustment Time | ITAE Range | Mean Value of Overshoot |
---|---|---|---|
ID-PI | 2000~4000 s | [1.59 × 107, 2.54 × 107] | 2.13% |
ID-LADRC | 1590~3500 s | [1.4 × 107, 2.14 × 107] | 1.85% |
MPC | 520~1600 s | [4.44 × 106, 8.11 × 106] | 2.08% |
ESKF-MPC | 460~1100 s | [3.9 × 106, 6.75 × 106] | 2.25% |
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Han, L.; Wang, L.; Meng, E.; Liu, Y.; Yin, S. Flexible Optimal Control of the CFBB Combustion System Based on ESKF and MPC. Sensors 2025, 25, 1262. https://doi.org/10.3390/s25041262
Han L, Wang L, Meng E, Liu Y, Yin S. Flexible Optimal Control of the CFBB Combustion System Based on ESKF and MPC. Sensors. 2025; 25(4):1262. https://doi.org/10.3390/s25041262
Chicago/Turabian StyleHan, Lei, Lingmei Wang, Enlong Meng, Yushan Liu, and Shaoping Yin. 2025. "Flexible Optimal Control of the CFBB Combustion System Based on ESKF and MPC" Sensors 25, no. 4: 1262. https://doi.org/10.3390/s25041262
APA StyleHan, L., Wang, L., Meng, E., Liu, Y., & Yin, S. (2025). Flexible Optimal Control of the CFBB Combustion System Based on ESKF and MPC. Sensors, 25(4), 1262. https://doi.org/10.3390/s25041262