Constraint Optimal Model-Based Disturbance Predictive and Rejection Control Method of a Parabolic Trough Solar Field
<p>The diagram of the PTSF (<b>a</b>); the sectional drawing of A-A (<b>b</b>).</p> "> Figure 2
<p>The scheme of the proposed C-ODPRC.</p> "> Figure 3
<p>Response curves of different controllers with field disturbances under constant conditions. (<b>a</b>) Field disturbances and lumped disturbance; (<b>b</b>) Field outlet temperature; (<b>c</b>) The flow rate of heat transfer fluid; (<b>d</b>) Control degree of freedom of C-ODPRC.</p> "> Figure 4
<p>Response curves of different controllers with field disturbances under setpoint tracking conditions. (<b>a</b>) Field disturbances and lumped disturbance; (<b>b</b>) Field outlet temperature; (<b>c</b>) The flow rate of heat transfer fluid; (<b>d</b>) The control of degree of freedom of C-ODPRC.</p> ">
Abstract
:1. Introduction
- A real-time correction strategy for steady-state target sequence is designed to modify the equilibrium by compromising constraint satisfaction and disturbance rejection with the integration of the future dynamics of the lumped disturbance.
- A dynamic construction method of a maximum controlled allowable set is proposed with the disturbance prediction part based on the obtained steady-state target sequence to convert an infinite number of constraint inequalities into finite ones.
- The infinite horizon constrained optimization problem is converted into an equivalent quadratic programming problem, which is then solved by dual-mode control law and the constructed maximum controlled allowable set.
2. Modeling of Parabolic Trough Solar Field
2.1. Analytical Model and Model Validation
2.2. Control Model of PTSF
3. Methods
3.1. Lumped Disturbance Estimation and Prediction
3.1.1. Lumped Disturbance Estimation by ESO
3.1.2. Lumped Disturbance Prediction Based on LS-SVM
3.2. Dynamic Correction of Steady-State Target Sequence
3.3. The Construction of MCAS with Disturbance Prediction Compensation
- ①
- Define n = 0, F = G, t = h.
- ②
- Solve the following linear programming problem
- ③
- If the solution in step ② violates constraint set (24), it means that the holding of the previous (n + 1) inequalities does not guarantee that (GΩn+1) sk ≤ h also holds. In this case, let n = n + 1, , . Then, to step ②, otherwise, to step ④.
- ④
- If the solution in step ② satisfies the constraint set (24), it is proved that ‘n’ is large enough.
3.4. Solving of Infinite Time Domain Constraint Optimization Problem
4. Results and Analysis
- Optimal disturbance predictive and rejection controller (ODPRC) proposed in [19], in which the future dynamics are considered in controller design without constraint handling mechanism.
- A special case of the C-ODPRC without considering the disturbance prediction (C-ODRC), namely na = 0.
4.1. Simulation Research and Analysis Under Constant Operating Conditions
4.2. Simulation Research and Analysis Under Setpoint Tracking Conditions
- The PTSF operates at typical operating condition #2 from the beginning of the simulation to the 3000th second.
- The PTSF undergoes a step change from typical operating condition #2 to #1 at the 3000th second.
- The PTSF operates at typical condition #1 from the 3000th second to the 7000th second.
- The PTSF works from typical operating condition #1 to #3 (from the 7000th second to the 8000th second).
- The PTSF operates at typical condition #1 from the 8000th second to the 10,000th second.
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Parameter | Value | Parameter | Value | Parameter | Value |
---|---|---|---|---|---|
η1 | 0.94 | Pa,i | 0.066 | ρH | 1487 |
η2 | 0.96 | Pa,o | 0.070 | cH | 2454 |
η3 | 0.94 | Pg,i | 0.109 | ρa | 7850 |
η4 | 0.93 | Pg,o | 0.115 | ca | 460 |
η5 | 0.94 | w | 5.77 | ρg | 2400 |
η6 | 0.94 | l | 600 | cg | 840 |
η7 | 0.95 | εa | 0.18 | Tatm | 25 |
η8 | 0.95 | εg | 0.88 | Tsky | 10 |
TH,out,r/°C | qH,r/(kg/s) | In,r/(W/m2) | Tin,r/°C | Tatm,r/°C | Tsky,r/°C | |
---|---|---|---|---|---|---|
#1 | 390.5 | 6.5 | 785 | 275 | 25 | 10 |
#2 | 390 | 7 | 851 | 275 | 25 | 10 |
#3 | 388 | 8 | 947 | 275 | 25 | 10 |
Methods | ODPRC | C-ODRC | C-ODPRC |
---|---|---|---|
Case 1 | 0.104 | 0.100 | 0.120 |
Case 2 | 0.092 | 0.098 | 0.103 |
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Wei, S.; Gao, X.; Li, Y. Constraint Optimal Model-Based Disturbance Predictive and Rejection Control Method of a Parabolic Trough Solar Field. Energies 2024, 17, 5804. https://doi.org/10.3390/en17225804
Wei S, Gao X, Li Y. Constraint Optimal Model-Based Disturbance Predictive and Rejection Control Method of a Parabolic Trough Solar Field. Energies. 2024; 17(22):5804. https://doi.org/10.3390/en17225804
Chicago/Turabian StyleWei, Shangshang, Xianhua Gao, and Yiguo Li. 2024. "Constraint Optimal Model-Based Disturbance Predictive and Rejection Control Method of a Parabolic Trough Solar Field" Energies 17, no. 22: 5804. https://doi.org/10.3390/en17225804
APA StyleWei, S., Gao, X., & Li, Y. (2024). Constraint Optimal Model-Based Disturbance Predictive and Rejection Control Method of a Parabolic Trough Solar Field. Energies, 17(22), 5804. https://doi.org/10.3390/en17225804