Gain-Scheduled Equivalent-Cascade IMC Tuning Method for Water Level Control System of Nuclear Steam Generator
Abstract
:1. Introduction
2. Problem Formulation
2.1. AP1000 Steam Generator
2.2. Control Problems of Steam Generator Water Level
- The open-loop dynamics of SG exhibit unstable behavior;
- The shrink and swell effects lead to strong inverse response behavior, which is remarkable at low power;
- Highly nonlinear characteristics, i.e., the dynamics of the process, vary with changes in operating power.
2.3. AP1000 Water Level Control System
3. Equivalent-Cascade IMC Tuning Method
3.1. IMC-PID Tuning Theory
- Step 1.
- The process model can be expressed as , where contains any time delays and the right-half plane zeros with a steady-state gain of 1, and is the rest of .
- Step 2.
- The IMC controller is specified as , where f represents a low pass filter with a gain of 1. The filter f typically has the form , where r is sufficiently large to guarantee that the IMC controller is a proper transfer function. The parameter is the desired closed-loop time constant, which determines the speed of the response. The closed-loop transfer function for set-point changes is .
- Step 3.
- The equivalent feedback controller can be derived from Equation (1) and rearranged into the PID controller form.
3.2. Structure Analysis of Water Level Control System
3.3. Equivalent-Cascade IMC-PID Tuning Method
- Step 1.
- Designing an equivalent secondary controller
- Step 2.
- Designing of an equivalent primary controller
- Step 3.
- By using Equation (5), controller parameters of the AP1000 water level control system are obtained as follows:
3.4. Summary
- Step 1.
- The operating power level is discretized by 10% from 20% to 100% and the linearized model of nuclear SG at each power level is identified;
- Step 2.
- Using the equivalent-cascade IMC-PID tuning method, local controller parameters at each power level are obtained based on the linearized model;
- Step 3.
- Piecewise linear function is utilized to construct a gain-scheduling module of controller parameters, in which the scheduling variable is the operating power level.
4. Experiment Result
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Case | Model | Controller | Kc | ti | td |
---|---|---|---|---|---|
A | |||||
B | |||||
C |
Power | k1 | k2 | t1 | t2 | t3 | t4 | ||
---|---|---|---|---|---|---|---|---|
20% | 4.5101 | 0.1827 | 1.4846 | 5.4187 | 0.3000 | 1.4376 | 9.1116 | 0.9112 |
30% | 5.6275 | 0.1857 | 1.5352 | 3.5098 | 0.3000 | 1.4391 | 11.3479 | 1.1348 |
40% | 6.8527 | 0.1887 | 1.5922 | 2.3823 | 0.3000 | 1.4406 | 13.7997 | 1.3800 |
50% | 8.1047 | 0.1920 | 1.6538 | 1.7115 | 0.3000 | 1.4423 | 16.3055 | 1.6305 |
60% | 9.2895 | 0.1956 | 1.7213 | 1.3078 | 0.3000 | 1.4441 | 18.6767 | 1.8677 |
70% | 10.5954 | 0.1994 | 1.7973 | 1.0088 | 0.3000 | 1.4460 | 21.2904 | 2.1290 |
80% | 11.3089 | 0.2034 | 1.8823 | 0.8875 | 0.3000 | 1.4480 | 22.7195 | 2.2720 |
90% | 12.0898 | 0.2078 | 1.9786 | 0.7784 | 0.3000 | 1.4502 | 24.2834 | 2.4283 |
100% | 12.8437 | 0.2126 | 2.0877 | 0.6912 | 0.3000 | 1.4526 | 25.7937 | 2.5794 |
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Xu, Z.; Fan, Q.; Zhao, J. Gain-Scheduled Equivalent-Cascade IMC Tuning Method for Water Level Control System of Nuclear Steam Generator. Processes 2020, 8, 1160. https://doi.org/10.3390/pr8091160
Xu Z, Fan Q, Zhao J. Gain-Scheduled Equivalent-Cascade IMC Tuning Method for Water Level Control System of Nuclear Steam Generator. Processes. 2020; 8(9):1160. https://doi.org/10.3390/pr8091160
Chicago/Turabian StyleXu, Zuhua, Qingli Fan, and Jun Zhao. 2020. "Gain-Scheduled Equivalent-Cascade IMC Tuning Method for Water Level Control System of Nuclear Steam Generator" Processes 8, no. 9: 1160. https://doi.org/10.3390/pr8091160