Data-driven methods for model parameters identification can be applied after system structures are determined (e.g. a simplified lowerorder models). These data-driven methods are better at handing random variables such as weather prediction data. Various methods including least squares method [32], regression method [33], Kalman filter [23], ensemble Kalman filter [34], ARMAX model identification and subspace identification [35] have been employed to estimate the model parameters. Models developed through random variables can be obtained by these methods. Some research works treat manipulated variables such as temperatures and flow rates of supply chilled water, as random variables [13]. For example, Li et al., pointed out that model accuracy and calculation efficacy cannot be guaranteed through the model identification methods which lack of active building excitation [13]. This is because database data does not contain plenty of useful information about systems, in other words, data rich and information poor [36]. Fig. 1 shows a summary of models and parameter identification methods mentioned above.

Although a number of successful cases of modeling can be found, some issues still need to be solved to apply MPC in the real practice. These include:

•Models inevitably have errors. The system control error cannot be eliminated successfully even with high-order models because it is difficult to determine the model parameters.

•The presence of external uncertain disturbance such as weather prediction has significant impacts on the control quality.

Concerning the above problems, this article aims to develop a strategy of MPC with feedforward control structure, which has both the MPC feedback structure and the feedforward structure [37,38]. As mentioned above, the inputs of the controlled system can usually be pided into two categories, one is manipulated variables, and the other is uncontrollable variables, which are often random variables. The purpose of control is to continuously adjust manipulated inputs to overcome the influence of uncontrollable inputs, and make the output has the desired dynamic characteristics. For irregular disturbances such as measurement errors, this adjustment can only be made if it is reflected to the detectable variables such as outputs, and therefore the feedback method must be used. However, for those random variables (e.g. weather condition) that can be predicted, it is unreasonable if they can be corrected by feedback as disturbances. The feedback control only works when the error has impact on the output, which results in a certain hysteresis. Furthermore, the feedback control does not take full advantage of the known information of this part of the inputs. Thus, it is more reasonable to implement a feedforward control which can take advantage of the known dynamic characteristics of this part of the inputs, and can effectively compensate the errors caused by these inputs [39].

This paper is as follows: Section 2 introduces the workflow of this study including building and HVAC description. The bypass valve control model is presented in Section 3, which use step response method for manipulated variables and PSD method for random variables. Section 4 introduces the proposed MPC strategy with feedforward control structure. In Section 5, a case study is used to demonstrate the effectiveness of the proposed modeling and control strategy. Conclusion and a future research plan are given in Section 6.

2. System description

2.1. Description of working flow

Various inputs, such as occupancy, electricity, outdoor temperature etc., to the HVAC system have tremendous impacts on the system behavior. Various inputs should be analyzed respectively due to their different roles and impacts. And they can be pided into some categories: constants, ignored variables, manipulated variables and random variables.

In this study, two types of variable are pre-defined such that manipulated variables and random variables to develop a simplified control model. The step response method is used to model the system under manipulated variables, where the system model is the bypass valve control model. PSD method is applied to model the system under random variables that are outdoor temperature and solar radiation. In applying the PSD method, some parameters may be adjusted to make the model more matched with the real system. These models are expressed in the form of transfer functions, and then applied in a MPC method with feedforward control structure to the system. The whole flow of the study is shown in Fig. 2.