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Stability of temperature control in VAV systems.

Article Excerpt
INTRODUCTION

Traditional proportional-integral-derivative (PID) controllers have been used in air-conditioning systems for a long time. The PID parameters must be carefully selected to avoid system instabilities. Even a PID controller that is well tuned during commissioning may perform poorly because of changes in operating conditions. However, when the conventional PID controllers are installed by carefully selecting parameters, the control loops often slip into hunting-a crucial problem faced by field operators.

Today, a variable air volume (VAV) system is universally accepted as a means of achieving an energy-efficient and comfortable building environment. While VAV control strategies provide a high-quality environment for building occupants, VAV system analysis rarely receives the attention it deserves. As a result, basic control strategies for VAV systems have seen little significant change (Hartman 2003).

The indoor air temperature control of a single zone space in air-conditioning systems is a practical problem of considerable interest. This problem is also of economic significance, since an improved control strategy can reduce cooling/heating costs without sacrificing the thermal comfort of the occupants. The room model, as a controlled plant, is assumed to be a first-order lag plus deadtime system. The output feedback consists of two control modes, namely P and PI actions (Kasahara et al. 2000, 2001; Kotaki et al. 2004; and Yamakawa et al. 2005). An overall system model may be formulated as a bilinear system with time-delayed feedback. Though many papers have been published regarding the stability of a bilinear system with feedback, most results focus on sufficient conditions for stability and seem to be quite impractical (Yamawaki et al. 1990; Yang et al. 1993).

A typical example of hunting observed at a building in Tokyo, Japan, is shown in Figure 1. The response of the supply air temperature seems to be a steady oscillation around a setpoint value, 16.4[degrees]C, not unlike a sine wave. This, of course, is unstable behavior, which is considered one of the crucial problems faced by field operators. Therefore, in order to avoid such unstable behavior, it is very important to make a stability analysis of the VAV control system.

[FIGURE 1 OMITTED]

In the previous papers (Matsuba et al. 1998; Kasahara et al. 2001), the authors presented a parametric analysis of stability for the VAV control system. A comparison of stability limits for the bilinear and linear systems suggested no great difference between the two. As a result, it can be concluded that traditional tuning methods to find the PID parameters are directly applicable to the VAV systems. Practical VAV systems, however, can easily indicate unstable and unsatisfactory performance due to instabilities. A shortcoming identified in the previous stability analysis is that quantitative information about instabilities can be obtained from simulations for free responses only at the initial value arbitrarily fixed. But it should be noted that the unstable characteristics differ for excessively large setpoint values (namely, as well as variable initial values).

Since stability is affected by component sizing and by controller tuning, the effects of operating points, of setpoint values, and nonlinearities of actuators (saturation and dead-zone) on the stability should be examined. This paper makes the causes for instability quite obvious and specifies the stability conditions based on experimental data. Results showing the stability regions allow a practical and useful selection of the PID parameters.

OVERALL VAV SYSTEM MODEL

The VAV system is fundamentally a cooling technique where air is maintained at an indoor temperature sufficiently low to minimize the amount of cooling energy used. Figure 2 shows a typical indoor air temperature control system using VAV technology. With this system, the indoor air temperature ([theta]) can be maintained at a setpoint value ([[theta].sub.r]) by varying the airflow rate ([f.sub.s]) to the air-conditioned room. The supply air temperature ([[theta].sub.s]) can be controlled by varying cooling water flow rate in the cooling coil. The daily changes in outdoor temperature ([[theta].sub.0]) are not taken into account in this paper, and the outside air intake is neglected to construct the simple model. Thus, the overall system considered in this study contains two major control loops-namely, the control loop for the supply air temperature and that for the supply airflow rate to the room.

[FIGURE 2 OMITTED]

From a control point of view, the VAV control system consists of an air-conditioned room (10 x 10 x 2.7 m), an air-handling unit (AHU), and duct work. It also includes feedback controllers that control the cooling coil and the motorized damper. By taking...

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