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According to the high control quality requirements of nuclear power plants and the features of the pressurizer pressure with large inertia, time-varying, nonlinear, multi-interference, difficulty in obtaining accurate mathematical model, and open-loop unstable dynamic characteristic, the advanced control strategy is needed for pressurizer pressure control performance optimization. To tackle the problem, an adaptive predictive control method for pressurizer pressure is devised in this paper. Firstly, the non-self-regulating system is stabilized and the adaptive dynamic matrix controller is designed by identifying the controlled object online. In order to realize the engineering application for this controller, then the control signal output is obtained. Finally, the control system simulation platform is built. Simulation results reveal a superior control performance, disturbance rejection, and adaptability. Furthermore, it provides a solution for the application of dynamic matrix control algorithm in non-self-regulating system.

Load changes or core reactivity disturbances may cause pressure changes in the primary circuit of a nuclear power plant. If the primary circuit pressure is too high, it may lead to equipment fatigue and pipeline rupture. If the pressure is too low, the risk of melting the fuel element may increase [

An internal model PID control system is applied to the pressurizer pressure control, which shows superior control performance compared with PID [

Predictive control algorithm has lower requirements on model and has characteristics of rolling optimization and feedback correction. Dynamic Matrix Control (DMC) has been widely used in industrial process control, but it will produce truncation error when modeling non-self-regulating objects. The DMC algorithm is improved based on the objects’ step response characteristics of an approximate straight line in the final stage [

Adaptive control can adapt to changes in the dynamic characteristics of objects and disturbances. Adaptive control and fuzzy control are combined and applied to the pressurizer pressure regulation of nuclear power plant with pressurized water reactor (PWR) [

Therefore, an advanced control strategy for non-self-regulating system and its practical value of engineering are two main problems of pressurizer pressure control performance optimization. In this paper, the pressurizer pressure adaptive predictive control method based on DMC algorithm is designed. Firstly, a feedback structure is used to self-stabilize the non-self-regulating system and the adaptive predictive controller is designed by identifying the controlled object online. Then, the control signal output is solved to make this controller easy to be implemented in engineering. Finally, the feasibility of the controller design is verified by simulation comparison and disturbance test.

In Section

Article structure layout.

The pressurizer is an important equipment in primary circuit for a nuclear power plant. The basic functions of the pressurizer are pressure control, pressure protection, and compensation of primary circuit coolant volume change. According to the different structure and operating principles, the pressurizer can be divided into gas tank pressurizer and electrothermal pressurizer. The structure of the gas tank pressurizer is simple, but there are certain nuclear safety issues in the process of compressing air or high-pressure inert gas. Therefore, the electrothermal pressurizer is often used in modern nuclear power plants.

The structure of the electrothermal pressurizer is shown in Figure

Structure of the electrothermal pressurizer.

In order to obtain an equivalent nonparametric model, it is necessary to self-stabilize the non-self-regulating controlled object. The model of non-self-regulating controlled object can be described as

Given the feedback channel gain

Structure of controlled object with feedback.

The model in Figure

The stability of

Substituting (

If

Mathematical model of the controlled object.

Operating condition | 100% | 90% | 80% |
---|---|---|---|

Transfer function (MPa/%) |

The equivalent nonparametric model of DMC is easily obtained from

The structure of the pressurizer pressure control system based on adaptive prediction algorithm is shown in Figure

Structure of control system based on adaptive predictive algorithm.

The adaptive predictive controller is composed of online identification algorithm module, DMC controller module, and feedback channel module. The online identification algorithm module is an online identification layer. The DMC controller module and the feedback channel module are control layer. The online identification layer and the control layer work in parallel. The online identification algorithm uses the current and the historical values of control increment

The online identification algorithm continuously detects the instantaneous

Flowchart of online identification algorithm.

At each time

In every moment, the relationships between control increment, pressure output, and nonparametric model elements are shown in (

Equation (

The matrix form of (

The nonparametric model

Equation (

It is easy to get a new dynamic matrix

The prediction time domain

The vector form of (

The vector form of (

Substituting (

The optimal control increment

The “rolling optimization” strategy means that the DMC only takes the immediate control increment

Since

Model mismatch, environmental disturbances (such as load changes or core reactivity disturbances) and other factors, may cause the output error

The initial prediction value at time

The simulation test platform is based on Visual Studio2010 and MATLAB/Simulink. The function of adaptive DMC controller of pressurizer pressure control system in nuclear power plant is realized in Visual Studio2010. It is connected with MATLAB/Simulink through OLE for Process Control (OPC) interface. MATLAB/Simulink simulation model is shown in Figure

Simulation model based on pressurizer pressure adaptive predictive control.

The feedback channel gain

Response curves with different control systems.

Control output curves.

Disturbance is inevitable in an industrial process. Load changes and core reactivity disturbances are ultimately reflected in changes of pressure. It is necessary to test the disturbance rejection ability of the adaptive predictive controller with a pressure disturbance. The feedback channel gain

Response curves with different control systems under disturbance.

In order to further verify the adaptability of adaptive predictive controller to the change of controlled object model, take 90% operating condition (as shown in Table

The feedback channel gain

Response curves with different systems under 100% operating condition.

The operating condition is changed from 90% to 80% at

Response curves with different systems under 80% operating condition.

Stimulated by the control performance optimization of pressurizer pressure, the adaptive predictive control method based on DMC algorithm is proposed in this paper. Some conclusions could be drawn as follows.

The pressurizer pressure adaptive predictive controller has good control performance and dynamic characteristic. It is characterized by rapid response, small overshoot, strong disturbance rejection ability, and guaranteed robustness.

The stabilization of non-self-regulating system overcomes the disadvantages of DMC in modeling non-self-regulating object.

The acquisition of control signal output shows the adaptive predictive controller is effective and practical value of engineering application.

The online identification of models helps to improve the ability of predictive controller to adapt to changes in controlled objects.

The physical constraints of valve have been ignored for the time being, and further research and improvement are needed.

The data used to support the findings of this study are available from the corresponding author upon request.

The authors declare that they have no conflicts of interest.

The research was partially supported by the Shanghai Science and Technology Committee (no. 18020500900), the Nation Natural Science Foundation of China (no. 61503237), the Shanghai Natural Science Foundation (no. 15ZR1418300), and the Shanghai Key Laboratory of Power Station Automation Technology (no. 13DZ2273800).