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Two-loop robust model predictive control for the temperature control of air-handling units.

Article Excerpt
INTRODUCTION

It is known that maintaining the supply air temperature from a typical air-handling unit (AHU) in air-conditioning systems at a specified setpoint under different operating conditions is not easy because of high nonlinearities associated with the heat exchange process (Salsbury 1998; Thompson and Dexter 2005). Proper setpoint tracking becomes important, not only for improved comfort control and system energy efficiency, but also for better process control performance (Wang and Xu 2002; Wang 1999).

A number of approaches have been proposed for the temperature control of AHUs. Earlier control strategies were mostly based on the proportional-integral-derivative (PID) control (Wang et al. 2001). Given prior knowledge of AHUs' characteristics, a PID controller can be manually tuned to achieve a desired closed-loop response at a given operating point. For example, the well-known Ziegler-Nichols approach has been widely applied in tuning the parameters of PID controllers. However, in practice, the system cannot always operate at the conditions where it is tuned due to the variations of the environment. Since a manually tuned PID controller is unable to deal with such variations, its performance may be unsatisfactory (Hepworth et al. 1994; Salsbury 1998). The drawback of manual tuning can be avoided using self-tuning control schemes based on linear dynamic models of AHUs (Dexter and Haves 1989; Astrom et al. 1993). Since a suitable process model is difficult to obtain (e.g., the parameters of the controller that are estimated online can drift if there are model order mismatches and/or unmodeled process disturbances), the closed-loop response may vary greatly with operating conditions. This may explain why the regulation performance of self-tuning controllers is often no better in practice than that of a manually tuned PID controller.

Recent developments in artificial intelligence techniques have been applied to the temperature control of AHUs. Capitalizing on the strong modelling capabilities of neural networks, a more accurate nonlinear model can be obtained and the corresponding controller can be designed by using adaptive or other control techniques (Ahmed et al. 1996; Geng and Geary 1997). The main drawback of neural network control is that gaining information over the full operating range of an AHU necessitates the collection of a large amount of training data, which cannot be easily achieved in practice. Another problem is that the learning algorithm is often complex. The time-consuming on-line identification process makes this approach infeasible in practice. A fuzzy control has been recognized as an attractive alternative. Because linguistic models can be easily realized, they have been proposed for use in AHU applications (Dexter and Trewhella 1990; Gouda et al. 2001). Although this type of controller is more robust than a PID controller, the method suffers for lack of a systematic way of generating control rules. Besides, they do not contain, in an explicit form, any objective knowledge about the system unless such knowledge can be expressed and/or incorporated into the fuzzy set framework (Yager and Filev 1994). The fuzzy decision-making approach, based on a fuzzy relational model (a type of linguistic model), has also been proposed for AHU applications (Thompson and Dexter 2005). Fuzzy goals and fuzzy cost functions are defined for thermal comfort, and the control scheme is designed using predictive control techniques. The accuracy of the fuzzy relational model, however, depends on the training data, which is required to be complete and sufficient, as is the case with neural networks.

Robust control, such as [H.sub.[infinity]] control, has also been found in the temperature control of AHUs (Underwood 1999; Anderson et al. 2002). In this method, nonlinearities are transferred into uncertainties. A linear uncertain model is used instead of nonlinear models. The difficulty with [H.sub.[infinity]] control is the selection of the control parameters, including model uncertainty weights and optimization criteria weights, which is the major part of the controller design process.

Current developments in control literature focus on model predictive control (MPC). MPC can be viewed as a successful practical control technique, and its industrial applications are supported by the fact that there are several large engineering companies that specialize in providing software for predictive control solutions to different kinds of industries (Bars et al. 2005; Henze et al. 2005). It may be used in the future to replace current typical local-loop controllers that are now widely used in industry, such as proportional (P) control, integral control (I), or their combination, PI (or PID) control (Maciejowski 2002). The application of predictive control to air-conditioning systems can be found in Linkens and Kandiah (1996) and Sousa and Kaymak (2001). The risk of using MPC is model mismatch, which might cause the predictive controller to misbehave. Robust MPC deals with uncertainties directly. It solves the problems of robust stability, control performance, and constraints in the same framework. In order to ensure robust stability, an extra constraint--say, terminal constraint--is required, which limits the last predicted state or output to a robust positively invariant set (Mayne et al. 2000). It is not easy to compute such a set; therefore, current robust MPC may be complex and still risky for practical applications when it is used to replace local controllers. This paper develops a two-loop robust control strategy and investigates the possibility of integrating the robust MPC techniques with the local-loop controllers.

The dynamic behavior of AHUs is described using low-order dynamic models (Underwood 1999, 2000). For this type of system, it is not difficult to achieve the closed-loop stability using a simple proportional, integral, or PID controller. However, the control performance cannot always...

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