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An output constrained control with input delay is proposed for a central heating system. Due to the delay of signal transmission and valves opening time, an input delay is considered into the system and an auxiliary system is employed to handle this issue by converting the delayed input into a delay-free one. Moreover, to ensure the output supply water temperature within a limited range, Barrier Lyapunov algorithm is involved to achieve desired control accuracy. Finally, external disturbance and model uncertainty are incorporated into the dynamic system and neural networks (NN) are trained in an online fashion for the compensation. The stability of the control system is guaranteed through rigorous Lyapunov analysis and the excellent control performance over traditional PID control is demonstrated via numerical simulation study.

Currently, central heating system is playing an essential role to human’s daily life and the boast of economy in everywhere all over the world. Due to the development of technology, advanced and intelligent central heating system has been widely researched and deployed to the municipal service system. This kind of system has the advantages of energy saving and contributes a lot to the less-pollution environment. Typically, this system measures the indoor/outdoor temperature and other information to control the valve opening degree in primary pip network which indirectly controls the supply water temperature in secondary network and provides heating service to the users.

In literature, many researches have been done to estimate or calculate the heating load which subsequently can help to adjust the heating control scheme [

Apart from input delay, the accuracy of supply water temperature in the secondary network is also of significance to the heating quality. Therefore, in this work, the output tracking error constraints are novelly taken into consideration for the control design. Some of the existing researches offer good results such as the ones using artificial potential field [

Control system architecture diagram.

The contributions of this paper are threefold:

Different from existing heating system control research, input delay due to the action of valve and signal transmission is novelly considered in the nonlinear system. The delay system is converted into a delay free one through an axillary updating system for the compensation.

The input delay control is proposed in combination with output constraints that can regulate the tracking accuracy of the supply water temperature in the secondary loop with specifically designed BLF method.

The external disturbance of the system and the model error are considered and handled with an NN approximator. Weights updating law is developed with rigorous mathematical verification. And the outstanding performance is demonstrated through simulation study.

The organization of this paper is as follows. Section

In this work, the target heat supply system is an indirectly connected central heating system with excellent efficiency and energy conservation capability. The whole picture of this system can be depicted as Figure

System architecture of indirectly connected district heating system.

Secondary network usually has 3-5 % heat loss. For simplicity purpose, in this work, the loss is neglected.

In this paper, the daily real-time heating load and desired secondary network supply water temperature

Radial Basis Function Neural Network (RBFNN) has been demonstrated to have outstanding function approximation and learning capabilities. If we have a continuous nonlinear function

If we are already given the supply water temperature

Even though the parameters

In actual system, external disturbance as well as the model uncertainty should be considered in model (

Besides the remarks and assumption made above, one more variable

In many researches, only single primary/secondary pipe network is considered; i.e., aforementioned model is defined as an SISO system. In this paper, system is extended to be an MIMO system which can produce multiple water temperatures in secondary pipe network to satisfy different operating requirements.

The inertia matrix

With Assumption

In this paper, the output constraints, i.e., the tracked secondary loop water temperature errors, will also be considered to regulate within a desired range. In order to handle the output constraint problem, Symmetry Barrier Lyapunov Function (SBLF) [

Denote

In practical application, the initial conditions of water temperature and temperature variation are the same with the desired values. Hence,

Time derivative of

Invoke an auxiliary state

Differentiate

Given bounded initial conditions, if there exists a

Combining Lemma

Due to the system parameter uncertainty and external disturbance, the dynamic model is augmented with a disturbance term in the following format.

The disturbance

In order to approximate the unknown disturbance, a RBF neural network is employed.

Denote the optimal weights as

With similar deduction of Remark

In this simulation, a numerical case study is conducted on a dual subnetwork heating system in the presence of output constraints and input delay.

In this subsection, the control performance of proposed control is investigated first. As mentioned above, the complicated nonlinear system model is employed and the mass matrix

As for the control parameters, the main coefficients of

Tracking control result of

Temperature tracked of

Temperature tracked of

Constrained control errors with output limitation.

Tracking error of subnetwork 1

Tracking error of subnetwork 2

Control input and temperature variation speed.

Control input of proposed control

Temptation variation speed

From the result, it can be observed that the overall control performance is excellent with proposed control in the presence of output constraints and input delay as well as disturbance and model uncertainty. In Figure

To further illustrate the advantages of proposed control, a comparative study using PID control is conducted under the same system settings with input delay and disturbance. Due to the involvement of these challenging factors, the stability of the PID control can hardly be achieved. After many tuning trials, the best performance that PID control can achieve is as Figures

PID control output.

PID tracking control of subnetwork1

PID tracking control of subnetwork1

PID control tracking error and input.

PID tracking error

PID control input

Although all the close-loop signals including control error and control input are bounded, the errors are very large compared to the proposed control. It demonstrates that, under such challenging situation, traditional simple control cannot provide satisfactory performance and the proposed control manages to handle the issues efficiently.

In this paper, a novel adaptive NN based constrained control has been proposed to a city central heating system in the presence of input delay. The valve opening degree in the primary loop is controlled such that the supply water temperature in secondary loop can follow the desired values. In order to handle output tracking error constraints problem, BLF method is involved with designed Lyapunov candidate function. The input delay due to the slow action of valves and system signal transmission is resolved with an auxiliary system which facilitates to convert the delay system into a delay-free one. Finally, the unknown external disturbance and model uncertainty are approximated through neural network with developed adaptation law. Thorough simulation study is carried out to demonstrate that the proposed control can outperform traditional control scheme in such operation conditions.

The simulation results data used to support the findings of this study are included within the article.

The authors declare that there are no conflicts of interest regarding the publication of this paper.

This work is supported by the Natural Science Guide Foundation of Liaoning Province under Project no. 20170540747.