1、 VOLUME 15, NUMBER 6 HVAC accepted May 27, 2009While the dynamics of most HVAC Dexter and Haves 1989). Techniques for robust PID control design have also been suggested based on modern controltheory (e.g., Noda et al. 2003). While potentially effective, the complexity of the underlyingtheory means t
2、hat the majority of users may be unaware of the subtleties or the possible pitfallsof such approaches. Although the potential of these advanced control strategies to increase HVAC ASHRAE 2005; USDOE 2001), in general the industry has not yet enthusiasticallyadopted the strategies (Brambley et al. 20
3、05), and commercially available adaptive, predictive,and robust controllers comprise a minority of the controllers in operation. Fixed PID controllerscontinue to make up the bulk of commercial HVAC the reader is referred to the appendix for definitionsof essential terminology. 2009, American Society
4、 of Heating, Refrigerating and Air-Conditioning Engineers, Inc. (www.ashrae.org). Published in HVAC Finn and Doyle 2000;Outtagarts et al. 1997). This approach attempts to capture the dynamic response of the systemin question in terms of a constant gain k0, a first-order time constant , and time dela
5、y Td, asshown in the following transfer function:(1)To simplify the analysis, a Pad approximation of the time delay may be used to obtain a lin-ear transfer function (Franklin et al. 2006). For example, a first-order Pad approximationresults in the following transfer function: (2)For systems with de
6、lays that are small relative to the dominant time constant, this simple sub-stitution leads to a close approximation of the open-loop behavior of the system. A majority of HVAC ODwyer 2006). These tuning approaches require either an explicit modelfor the system or data from simple experiments, such
7、as an impulse or step-response test. Forexample, the Ziegler-Nichols tuning method presented in most introductory control textbooks(Franklin et al. 2006) involves applying a proportional control to the system and increasing thecontroller gain until the systems step response borders on instability. O
8、ne can then calculate thePID control gains using the values for the period of oscillations and the critical control gain.Other approaches identify a simple model of the transient response and then design the PID con-troller using classical model-based approaches (e.g., Root-Locus, frequency domain d
9、esign,etc.) (Franklin et al. 2006). These techniques, whether empirical or model based, inherently focus on tuning a controllerfor a single operating condition. This is in contrast with the techniques presented in this paper,which have the unique capability of being able to simultaneously address st
10、ability and perfor-mance of an HVAC however, recent advances in control theory overcomemany of these challenges, allowing users to define a set of linear inequalities that define the sta-bilizing range of PID controller gains and, to some extent, the range of PID gains that meet spec-ified transient
11、 performance characteristics. In essence, the final objective of these techniques is to provide the control designer with simplefigures (e.g., Figure 1 or 5) that denote the range of PID control gains that stabilize the given sys-Figure 1. Example figure of stabilizing control gains and meeting sett
12、ling time specifications. 2009, American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc. (www.ashrae.org). Published in HVAC whereas, the latter scenar-ios may represent the task of tuning a series of building HVAC Stoecker 1966;Najork 1973; Broersen and van der Jagt 1980; Bro
13、ersen and ten Napel 1983; Zhijiu et al. 2002).The electronic expansion valve (EEV) allows much greater freedom in valve control, generallyusing an electronically controlled stepper motor to adjust the valve opening. This allows imple-mentation of PID (Gruhle and Isermann 1985; Finn and Doyle 2000) o
14、r alternative control strat-egies (Outtagarts et al. 1997). Most proposed approaches schedule the controller gains to obtainacceptable performance. Synthesis of PID ControllerIn this section, a set of models for an EEV-controlled evaporator are utilized to illustrate howthe PID design techniques pre
15、sented previously may be applied. The system gain, time constant,and time delay are obtained from the data presented in Outtagarts et al. (1995). In this publica-0.8 Hpjk()Hpjk()Hpjk()1.2Hpjk()123 l, when ik1=Ak()KT0.4 K2bk0.2 bk, for k 30 for allmodels and settling time contours for the low-temp, l
16、ow-flow model.Figure 20. Closed-loop step response for proposed PI controller as applied to all models. 2009, American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc. (www.ashrae.org). Published in HVAC&R Research, Vol. 15, No. 6, November 2009. For personal use only. Addition
17、al reproduction, distribution, or transmission in either print or digital form is not permitted without ASHRAEs prior written permission.1016 HVAC&R RESEARCHNote that these results, based on a first order Pad approximation, are slightly more conservativethan the control design results based on a hig
18、her order approximation.CONCLUSIONThis paper makes several key contributions to the design of PID controllers for nonlinearHVAC&R systems. First, recently developed techniques for determining the set of all stabilizingPID controller gains for a given system are presented. These use the interlacing p
19、roperty of Hur-witz polynomials to derive sets of linear equations that can be solved quickly and efficiently.Second, extensions for determining PID controller gains that satisfy performance and robustnessmetrics are given, and methods for applying these to nonlinear systems are discussed. Finally,t
20、he two examples illustrate the simple and intuitive nature of the control design tools, allowingthe user to select appropriate controller gains while avoiding the complexity of modern optimaland robust control synthesis techniques.REFERENCESARTI. 2004. Basic research driving the future of americas h
21、eating, ventilation, air conditioning and refrig-eration technologies. Report by the Air-Conditioning and Refrigeration Technology Institute, Inc.http:/www.arti-21cr.org/documents/roadmap.pdf.ASHRAE. 2006. Navigation for a sustainable future: ASHRAE research strategic plan, 20052010. Reportby the Am
22、erican Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc., Atlanta.http:/www.ashrae.org/docLib/200641713376_347.pdf.Astrom, K.J., and F.T. Hagglund. 1995. PID Controllers: Theory, Design, and Tuning. Research TrianglePark, NC: International Society for Measurement and Control.Fig
23、ure 21. Stabilized plants and plants guaranteed phase margin 30 for proposedcontroller. 2009, American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc. (www.ashrae.org). Published in HVAC&R Research, Vol. 15, No. 6, November 2009. For personal use only. Additional reproduction, distribution, or transmission in either print or digital form is not permitted without ASHRAEs prior written permission.
