Research on Real-Time Control Strategy of Air-Conditioning Water System Based on Model Predictive Control

Abstract

The optimization of the operation strategy for building HVAC systems is the key to achieving energy conservation and consumption reduction in air-conditioning systems. This study proposes an online real-time control strategy for the air-conditioning water system based on the model predictive control (MPC) principle, implemented and validated on the integrated energy experimental platform. The experimental system simulates load generation and dissipation processes using a water tank, where hourly varying heating power output emulates the dynamic cooling loads of buildings. By regulating the chilled water system through different algorithms, the temperature tracking control performance and cooling supply regulation accuracy were rigorously validated. The control module was written in the Python 3.8 environment, and Niagara 4 software was used as an intermediate software to achieve data interaction and logical control with the laboratory system. The experimental results show that this algorithm can follow the hourly optimized parameters with a low overshoot in the short-term domain. Meanwhile, it can achieve the optimal control of cooling capacity and energy consumption in the long-term domain. Compared with the PID strategy, the temperature following control accuracy can be improved by 9.64%, and the cooling capacity can be saved by 6.24%. Compared with the day-ahead MPC algorithm, the temperature following control accuracy can be relatively improved by 16.52%, and the cooling capacity can be saved by 1.24%.

1. Introduction

According to statistics, the whole-process energy consumption of buildings accounts for 36.3% of China’s total energy consumption, with the heating, ventilation, and air-conditioning (HVAC) systems contributing approximately 50% of the total building energy consumption, demonstrating significant potential for energy conservation and carbon reduction [1,2]. Traditional air conditioning system control strategies predominantly employ Proportional–Integral–Differential (PID) methods [3,4]. This method relies on the error between controlled parameters and setpoint values to dynamically adjust manipulated variables for achieving control objectives. However, for air-conditioning systems characterized by significant time delays and strong time-varying properties, high-precision PID controllers exhibit significantly degraded robustness under substantial dynamic disturbances, fail to achieve precise cooling supply and refined energy management, resulting in suboptimal system energy efficiency and elevated carbon emissions [5,6]. The adoption of advanced intelligent control methods has been demonstrated to significantly mitigate energy waste [7,8].

Model predictive control (MPC) demonstrates significant advantages in solving optimal control problems involving nonlinearity, multi-variable dynamics, and large time-delay characteristics [9,10]. Its inherent robustness against system disturbances and uncertainties makes it particularly advantageous for HVAC system control applications [11,12]. Ding et al. addressed the complex phase change delay characteristics of ice storage air-conditioning systems by constructing a dynamic time-delay module based on an enthalpy model, and proposed a two-objective MPC strategy that balances cost-effectiveness and dynamic response performance, achieving reductions of 6.5% in power load and 8.5% in operating costs [13]. Zhao et al. addressed data center cooling systems by coupling cooling load prediction model with server room temperature prediction model, developed a supply–demand balance MPC strategy for the cooling capacity of multiple chillers, achieving a 27.77% improvement in stability compared to PID control and an 18.08% improvement compared to fuzzy control, with energy savings of 11.81% and 7.58%, respectively [14]. Ra et al. addressed factory building cooling systems by utilizing deep neural networks (DNN) to construct models for HVAC supply air temperature and indoor temperatures in different zones, and incorporated an HVAC thermal behavior prediction model into MPC, achieving a 35.1% reduction in energy consumption while maintaining the cooling setpoint temperature [15]. Chen et al. addressed radiant ceiling cooling systems by developing a physics-based three-dimensional model of radiant ceiling systems and proposed an MPC strategy, compared to PID control and conventional bang-bang control. This approach achieved energy savings of 21–27% and 6%, respectively [16]. Zhu et al. developed an advanced double-layer model predictive control (DMPC) strategy for the hybrid cooling system of data centers, quantified the impact of uncertain parameters on the performance of the DMPC strategy, effectively shortening chiller runtime and increasing natural cooling duration [17]. Borja-Conde et al. addressed HVAC systems with multiple chillers by developing an economic MPC strategy through individual allocation of each chiller’s cooling power. Compared with quadratic programming control, this strategy achieved a 5.19% reduction in energy consumption [18].

In summary, the MPC strategy demonstrates strong feasibility in optimizing and regulating the operation of HVAC across diverse scenarios, including large-scale buildings, industrial plants, and data centers. It significantly enhances energy efficiency, reduces operational consumption, and improves equipment operational effectiveness. The application of MPC in building HVAC systems can be characterized by constructing precise building load models and equipment performance models to predict future thermal/cooling demands over a defined time horizon, thereby enabling precise regulation of cooling/heating system outputs. However, current real-world implementations of MPC for HVAC optimization remain limited, with most studies focusing on validating its advantages and feasibility in specific application scenarios [19,20].

Previous studies primarily focus on developing mathematical or predictive models for key equipment (e.g., phase change delay models, data center temperature models) based on different system characteristics, or incorporating specialized objective functions (e.g., overall economy, power load) into the MPC framework to achieve optimized control in specific scenarios [21,22]. These studies emphasize how to plan the operational state settings of different devices over time and establish objective–function-oriented operation baselines. However, due to the complexity of fluid flow and heat transfer in air-conditioning water systems, few studies delve into the transient dynamics of chilled water systems during control execution, specifically, the dynamic interactions between actual system states and setpoint values after control commands are issued. Although MPC offers advantages in feedback correction and receding horizon optimization, it still exhibits certain overshoot or delay in the operation of real-world systems [23]. This volatility is difficult to quantify, and there remains a research gap in understanding how deviations from the planned operation baselines affect energy consumption.

Therefore, this study proposes a real-time online MPC strategy that incorporates load prediction, heat dissipation process modeling, receding horizon optimization, and feedback correction. By defining a cost function to track setpoints and cooling capacity, the strategy achieves precise regulation of the planned operation baselines. Additionally, the PID control strategy, as a common solution for HVAC systems, is used as the benchmark comparison scenario. The day-ahead offline MPC serves as a simplified variant of real-time online MPC, utilizing one-time load prediction to reduce algorithmic complexity, thereby validating the impact of control horizon configurations on system performance. Experiments were conducted on the Integrated Energy Experimental Platform of Tianjin University. The control module was written in the Python language environment, and Niagara software was used as an intermediate software to achieve data interaction and logical control with the laboratory system. This study investigates the control performance and reliability of different control strategies in real-world applications by comparing their tracking accuracy for set operational targets and cooling energy consumption under various load input scenarios on an experimental platform.

2. Methodology

2.1. Real-Time Online MPC Strategy

The real-time online MPC strategy for the air-conditioning water system consists of three modules: the prediction model, rolling optimization, and feedback correction. The algorithm framework is shown in Figure 1. The prediction model is used to describe the dynamic behavior of the system. The rolling optimization is carried out to obtain the optimal value of the required performance indicators so as to determine the future control actions of the system. By comparing the measured actual value of the system output with the output result of the prediction model, feedback correction of the prediction model is conducted to enhance its ability to resist disturbances and overcome system uncertainties, enabling the system output to continuously approach the reference trajectory curve and reach the set value. It includes the following four steps:

(1)

At each time step, online prediction of future output parameters is performed through real-time acquisition and analysis of system state variables. Based on the current system state, the future output trajectory is predicted over a defined prediction horizon.

(2)

A cost function incorporating key manipulated variables and time-step weights is formulated according to HVAC system dynamics. This enables rolling optimization to determine the optimal control sequence at each decision interval.

(3)

Model prediction errors are dynamically compensated by calculating the deviation between predicted values and actual measured outputs at each time step.

(4)

The control software autonomously interfaces with the HVAC system through the Niagara framework, completing state parameter acquisition and optimization within 1 s per cycle. Optimized control commands are then transmitted to actuators for system regulation. The overall operation flowchart is shown in Figure 2.

2.1.1. Prediction Model

Artificial Neural Networks (ANNs) demonstrate significant advantages in nonlinear modeling and multivariable integration, making them a prevalent method for building energy prediction [24]. Each neuron represents a specific output function termed an activation function, while connections between neurons are weighted values that modulate signal transmission, referred to as synaptic weights. Through the adjustment of weight matrices and activation functions, ANNs achieve universal approximation capabilities for arbitrary nonlinear mappings [25]. Based on previous research, the key prediction parameters for next-step building temperature forecasting typically include outdoor environmental parameters, previous and current indoor temperatures, building cooling load, system cooling output, and projected cooling demand [26]. However, given the controlled laboratory environment in this study where outdoor parameters are excluded, an ANN model with seven inputs and one output was constructed using the following as input parameters: temperatures at the previous and current time steps, cooling capacities at the previous and current time steps, and cooling loads at the previous, current, and next time steps. Through trial-and-error validation, the ANN configuration with one hidden layer (containing four neurons), the Tanh function as the activation function for the hidden layer, and the ReLU function as the activation function for the output layer was found to achieve the best performance. The simplified prediction model for temperature forecasting reduces input variables, as illustrated in Figure 3.

2.1.2. Rolling Optimization Process

The receding optimization process seeks to minimize a predefined cost function at each sampling period to derive optimal control strategies under desired performance criteria. This study employs Particle Swarm Optimization (PSO) to perform iterative online global optimization of the cost function, which integrates temperature prediction models, water tank temperature setpoints, and cooling output parameters. The PSO algorithm demonstrates advantages in rapid convergence rate and effective handling of multivariable, high-dimensional optimization challenges [27]. In this study, the number of particles was set to 50, the maximum number of iterations to 100, the inertia weight to 0.6, and the acceleration constants to 2. The position parameters of the particles represent the control strategy for the air-conditioning system, with their maximum and minimum values defined by the cooling capacity range when the chillers in the air-conditioning system are activated. The rolling optimization architecture is illustrated in Figure 4.

The dual objectives of this study are to maintain water tank temperature within a minimal deviation from the setpoint while minimizing system cooling output. Constraint handling is implemented to prevent cooling output from exceeding chiller operational limits. The mathematical formulation of the cost function is presented in Equation (1).

$$\left\{\begin{array}{l}\min J(t)={\displaystyle \sum _{i=1}^{N}q(\mathrm{t}+i)}{[y^{*}(t+i)-y_{set}(t+i)]}^2+{\displaystyle \sum _{i=0}^{N-1}{[u(t+i)]}^2}\\ 0\le u(t+i)\le u_{\max },i=0,1,\dots ,p-1\end{array}\right.$$

(1)

where $q$ is weighting coefficient; $y_{set}$ is temperature setpoint, °C; $u$ is cooling capacity, kW.

2.1.3. Feedback Correction

Due to uncertain factors such as nonlinearity, model mismatch, and disturbances in the actual operation of the system, the established prediction model cannot always match the actual situation. A feedback correction mechanism is, therefore, implemented by comparing real-time system outputs with predicted values, utilizing the resultant error to iteratively refine the prediction model for subsequent optimization cycles. The feedback correction architecture is illustrated in Figure 5. At each time step t, the actual temperature y(t) is compared with the predicted temperature $y^{*}(t)$, generating a deviation signal e(t) that dynamically adjusts the temperature prediction model. This updated model is then embedded into the cost function for the next receding horizon optimization, yielding optimized cooling output commands for the plant. The closed-loop process continues with real temperature acquisition at t + 1, followed by subsequent feedback correction iterations. Continuously using measured temperature values to perform feedback correction on the prediction results of the temperature prediction model, thereby avoiding model mismatch.

2.2. Evaluation Index

To evaluate the performance of the developed model, five commonly used evaluation metrics are used, as shown below:

(1)

The Root Mean Square Error (RMSE) is mathematically defined as shown in Equation (2):

$$RMSE=\sqrt{{\displaystyle \frac{{{\displaystyle \sum _{\mathrm{i}=1}^N(G_{Pi}-{\overline{G}}_{Mi})}}^2}{N}}}$$

(2)

(2)

The Normalized Mean Bias Error (NMBE) is mathematically expressed as shown in Equation (3):

$$NMBE={\displaystyle \frac{{\displaystyle {\sum }_{i=1}^N(G_{Pi}-{\overline{G}}_{Mi})}}{N\times {\overline{G}}_{Mi}}}\times 100\%$$

(3)

where $N$ is the number of samples, $G_{Pi}$ is the predicted value of the sample, ${\overline{G}}_{Mi}$ is the mean value of the measured sample.

3. Case Study

3.1. Experimental System

The experiments in this study were conducted on the Integrated Energy Experimental Platform of Tianjin University [28]. The experimental system performs sufficient heat exchange in a water tank to simulate the generation and elimination process of cooling loads. The water tank contains multiple sets of cooling and heating coils, which are respectively connected to cooling and heating pipelines. The tank is equipped with multiple cooling/heating coils connected to chilled/hot water supply pipelines, respectively. Each coil’s heat (cooling) output capacity corresponds to a single energy conversion unit, enabling multi-stage load conditions through coordinated activation/deactivation of coil groups. The cooling load of real buildings is jointly composed of external disturbances caused by factors such as outdoor weather and internal disturbances caused by factors such as indoor occupants. The HVAC system supplies cooling capacity to offset these heat gains, thereby maintaining a stable indoor thermal environment. In this experimental system, the building cooling load is conceptualized as time-varying heat inputs with different power levels at different time steps, and the heat exchange in the water tank simulates the maintenance of the indoor thermal environment. The cooling side comprises three chiller units, while the heating side integrates two air-source heat pumps and one electric boiler. Motorized control valves installed on the piping networks regulate water flow rates entering the thermal exchange modules. The system schematic is shown in Figure 6, with the physical test platform depicted in Figure 7.

3.2. Software Platform

The laboratory platform’s operational control and monitoring are managed by an information management system employing the MODBUS + RS485 communication protocol. This architecture enables real-time acquisition and archival of operational parameters from all devices and instrumentation while providing remote system control capabilities. The platform integrates a comprehensive sensor array that continuously streams data to the supervisory interface. The Niagara framework serves as middleware for executing MPC and PID control strategies, receiving optimized control parameters from strategy modules, and interfacing with the laboratory’s platform for actuator command generation. The system schematic of the laboratory information management system is illustrated in Figure 8.

3.3. Comparison Cases

In real building operations, daily cooling loads fluctuate in response to variations in outdoor environmental parameters, necessitating dynamic cooling output adjustments [29]. The experimental setup employs heating coils to emulate actual cooling load profiles, with time-varying cooling load setpoints for each operational period as specified in

Table 1. The cooling load setpoints for each operational period.

Time	9:00	10:00	11:00	12:00	13:00	14:00	15:00	16:00	17:00
Simulated load 1 (kW)	5	27	36	32	36	27	35	11	-
Simulated load 2 (kW)	5	31	32	39	35	25	33	13	-

.

To validate the control performance of online real-time MPC in the air-conditioning water system, comparative experiments were conducted with PID control and day-ahead MPC strategies:

The PID strategy generates control corrections by calculating the error between setpoints and measured process variables, adjusted through proportional, integral, and derivative coefficients. Its mathematical formulation is given by Equation (4):

$$u(k)=K_p\times [e(k)+{\displaystyle \frac{T_s}{K_I}}{\displaystyle \sum _{j=0}^{k}e(j)+K_D\frac{e(k)-e(k-1)}{T_s}}]$$

(4)

where K_P, K_I, K_D denote the proportional, integral, and derivative gains, respectively; e(k) represents the deviation between measured indoor temperature and reference trajectory; T_S indicates the sampling time interval.

The day-ahead MPC serves as a simplified variant of real-time MPC. “Day-ahead” refers to single-shot load prediction before daily system operation, whereas real-time online MPC performs rolling prediction at each time step, precomputing hourly cooling load forecasts and required cooling outputs before system operation to evaluate the impact of prediction horizon length on control efficacy.

4. Results

4.1. Prediction Models

The experimental setup employs a water tank as the thermal exchange terminal for both load simulation and energy supply sides, featuring well-defined heat transfer mechanisms. A total of 173 operational datasets were extracted from the laboratory’s historical database for temperature prediction model development and validation. The data partitioning follows a 70–30 split, with 70% (122 datasets) allocated for model training and 30% (51 datasets) reserved for testing. Through iterative validation, an ANN model was finally established with a structure of one hidden layer containing four neurons, the Tanh function as the activation function for the hidden layer, and the ReLU function as the activation function for the output layer. The model demonstrates prediction accuracy with test set evaluation metrics of RMSE = 1.02 and NMBE = 0.37%. Comparative results between measured and predicted temperature values are presented in Figure 9.

4.2. Water Temperature Tracking Control Performance

4.2.1. Comparison Between Online MPC and PID

Comparative experimental results of water tank temperature control under real-time online MPC and PID algorithms are shown in Figure 10. The target temperature setpoint was configured at 22 °C. At the start of the experiment, the water tank temperature was 26 °C for both control methods. The PID control exhibited an overcooling phenomenon shortly after the experiment began: the temperature reached a minimum of 20 °C at 10:00, with a 2 °C deviation from the setpoint. It then gradually increased, approaching 23 °C around 10:40, followed by sustained oscillations around the setpoint until the experiment conclusion at 17:00.

In contrast, the real-time online MPC strategy demonstrated mitigated overcooling effects, maintaining a minimum temperature of 21 °C (1 °C deviation) through optimized cooling output adjustments derived from predictive calculations. Quantitative analysis revealed RMSE values of 0.83 °C and 0.91 °C for MPC and PID strategies, respectively, indicating a 9.64% improvement in tracking accuracy. The real-time MPC algorithm demonstrated superior precision and stability in thermal regulation.

4.2.2. Comparison Between Real-Time MPC and Day-Ahead MPC

Comparative temperature control performance between real-time online MPC and day-ahead outline MPC algorithms is shown in Figure 11. With the target temperature setpoint fixed at 22 °C, both strategies achieved rapid temperature convergence during the initial operation. However, the day-ahead MPC failed to maintain thermal stability under load demand variations, exhibiting significant deviations without effective setpoint recovery. In contrast, the real-time online MPC dynamically adjusted cooling output based on real-time load profiles and temperature deviations, sustaining minor oscillations around the setpoint. The quantitative evaluation revealed RMSE values of 1.15 °C and 1.34 °C for real-time and day-ahead MPC, respectively, demonstrating a 16.52% improvement in tracking accuracy. The real-time MPC exhibited superior control stability and dynamic responsiveness, validating its enhanced adaptability to operational uncertainties.

4.3. Cooling Capacity Control Performance

Since the time-varying cooling loads, dynamic modulation of the cooling supply is essential to maintain temperature setpoints. This section systematically evaluates control accuracy disparities among different algorithms by quantifying deviations between optimized cooling supply trajectories and operational baselines, with further analysis of their impacts on energy consumption.

4.3.1. Comparison Between Online MPC and PID

Comparative cooling output profiles between real-time online MPC and PID control algorithms are shown in Figure 12. In the initial stage of the experiment, both control methods provided more cooling capacity than the instantaneous cooling load to quickly bring the temperature close to the setpoint. Due to slight thermal energy storage in the system, the optimized cooling capacity was slightly lower than the cooling load between 11:00 and 12:00. After the temperature reached the setpoint, the cooling capacity of the real-time online MPC accurately matched the cooling load demand.

In contrast, the PID controller exhibited significant cooling supply–demand mismatches, particularly during load transitions, with overshoot magnitudes reaching 64%. Extreme changes in cooling capacity also caused wear and tear on the equipment. Calculations show that the RMSE of the real-time online MPC and PID control experiments were 3.61 MJ and 8.21 MJ, respectively, with cumulative cooling capacities of 766 MJ and 817 MJ. The real-time online MPC saved 6.24% of the cooling capacity compared to PID control, demonstrating a closer match between the calculated cooling capacity and real-time load, and reducing cooling capacity overshoot.

4.3.2. Comparison Between Real-Time MPC and Day-Ahead MPC

Comparative cooling output profiles between real-time online MPC and day-ahead MPC algorithms are presented in Figure 13. The day-ahead MPC strategy, which precomputes load forecasts and operational plans prior to system activation, exhibits heightened dependence on feedback correction, resulting in supply–demand mismatches during dynamic operation. In contrast, the real-time MPC dynamically optimizes chiller operations based on continuously updated load profiles, achieving enhanced supply–load synchronization. Quantitative evaluation shows RMSE values of 6.29 MJ and 7.53 MJ for real-time and day-ahead MPC, respectively, with cumulative cooling outputs of 793 MJ versus 803 MJ. The real-time online MPC saves 1.24% of the cooling capacity compared to the day-ahead MPC algorithm. The real-time MPC demonstrates superior cooling supply regulation fidelity compared to its offline counterpart.

4.4. Operational Energy Consumption

The energy consumption comparison between the real-time online MPC algorithm and the PID algorithm experiments is shown in Figure 14. The energy consumption of the cooling tower, water pumps, and chillers controlled by the real-time online MPC algorithm is lower than that of PID control. Specifically, the cooling tower achieves a 14.2% energy saving, water pumps 13.3%, chillers 12.4%, and the total energy savings reach 14.5%.

5. Discussion

This study embedded the MPC strategy into the laboratory’s HVAC cooling water system, demonstrating precise temperature and cooling capacity tracking control performance through experiments while reducing the energy consumption of individual devices. Due to the simple unit types and all fixed-frequency equipment used in this study, as well as the lack of consideration for occupant disturbances and weather factors, the experiments have certain limitations. However, the stable control performance still demonstrates good scalability. In the application of large-scale real-building HVAC systems, the PID control strategy faces challenges in quantifying control accuracy and convergence speed when dealing with complex internal and external disturbances. In contrast, MPC’s architecture allows predictive accuracy enhancement through multi-model integration and algorithmic refinements, effectively mitigating stochastic fluctuations during load transitions while improving control fidelity via rolling optimization and feedback correction.

With advancements in AI and IoT technologies, smart buildings represent an inevitable evolution in modern architecture [30,31]. By installing temperature sensors in critical building zones and integrating thermal power meters at key HVAC nodes, and leveraging cloud computing technology, the system enables dynamic model updating and real-time optimization. An MPC framework is then constructed to address the specific needs of the building, facilitating online rolling optimization and solution computation. Using edge-cloud collaboration technology, the optimized control parameters are transmitted to HVAC controllers, enabling feedback correction and coordination with actual control nodes.

Under the human-centric intelligent regulation paradigm for thermal environments, translating management objectives into HVAC control sequences is critical. As MPC operationalizes control targets through cost function formulations, domain-specific cost functions can be developed via multi-objective optimization to accommodate diverse building typologies. Future grid-responsive implementations could integrate electricity price forecasting and thermal storage prediction, enabling tri-objective optimization encompassing energy cost, storage utilization, and thermal comfort [32,33,34]. MPC’s extremely short response time and high-precision tracking control enable optimal power distribution among HVAC devices, reducing the impact of deviations from the planned operation baseline on energy consumption compared to PID. Future research will further enhance the adaptability of MPC in different scenarios and improve control accuracy by integrating system-specific characteristics with control objectives.

6. Conclusions

This study developed an MPC algorithm for HVAC hydronic systems and validated its performance through Niagara platform experiments, enabling automated operational optimization via real-time equipment data acquisition. The key findings are summarized as follows:

(1)

Enhanced Control Precision: The real-time online MPC algorithm achieves 9.64% higher temperature tracking accuracy compared to PID control and 16.52% improvement over day-ahead MPC, demonstrating superior dynamic response to load fluctuations.

(2)

Energy Efficiency Optimization: The real-time online MPC algorithm optimizes cooling supply–demand matching, reducing energy consumption significantly. Compared to PID control, it achieves 6.24% savings in cooling energy and 14.5% savings in total system energy. Compared to day-ahead MPC, it also reduced cooling energy consumption by 1.24%.

(3)

Multi-timescale Control Advantages: The real-time online MPC algorithm can achieve hourly optimization parameter operation with a low overshoot in a short-term horizon, enabling real-time optimization control of the air-conditioning water system. It can also achieve optimal control of cooling capacity and energy consumption in the long-term horizon, providing theoretical guidance for the intelligent control of HVAC systems in actual buildings.