1、2010 ASHRAE 303ABSTRACTIn the heating, ventilating, and air-conditioning (HVAC)systems, Proportional-plus-integral (simply, PI) controllers areby far the most common control algorithm and this situation hasnot yet changed greatly. With a simple Proportional (P) control-ler, there would be an offset,
2、 which the operator could eliminateby the manual reset to compensate for thermal loads change. Theautomatic reset with an Integral (I) controller is absolutely neces-sary to make the control output be returned to the setpoint auto-matically. PI controller, however, often leads to a poorly dampedresp
3、onse. Proportional-plus-integral-plus-derivative (PID)controllers have been more desirable than PI controllers due tothe stabilizing effect of a Derivative (D) action. In practice,however, the D action has been frequently switched off for thesimple reason that it is difficult to tune properly. In so
4、me situa-tions, it might be possible to estimate thermal loads (or distur-bances) before they entered the plant. A typical example is acertain system for HVAC systems in which the outdoor thermom-eter detects sudden weather changes and the occupant roughlyanticipates thermal loads changes. Disturban
5、ces should be offsetby the compensation of the manual reset. This control strategycan be called a type of feed-forward control. The control schemewith lower (or no) I action may be interpreted as a PD controller.The thrust of this paper is to offset thermal loads before they affectthe control output
6、 and to confirm the effectiveness of compensa-tion of the manual reset. For the sake of comparison, simulationresults to demonstrate the validity of compensation method aresomewhat superior to those with a traditional PI controller.INTRODUCTIONAbout one hundred years ago, applying the thermostatand
7、the control valve to home heating controls, the automaticcontrol system has been initially realized. Since then, the heat-ing, ventilating, and air-conditioning (HVAC) systems havebeen considered from viewpoint of control engineering. Thecomplexity of multi-variable system, interacting system, anddi
8、stributed system are the common characteristics for anyprocess industries. The HVAC systems, however, have notbeen advanced compared to chemical and steel processes thatexploited the advantages of digital control (Hartman 2003).The HVAC systems have huge different characteristics incontrol engineeri
9、ng from chemical plants. One of the charac-teristics is that the equilibrium point (or the operating point)usually changes with disturbance such as outdoor tempera-ture, control input, and thermal loads etc. The change of theequilibrium point means the change of plant parameters. Thus,the HVAC contr
10、ol system is extremely difficult to obtain anexact mathematical model.Today, a variable air volume (VAV) system is universallyaccepted as means of achieving energy efficient and comfort-able building environment. While the VAV control strategiesprovide a high quality environment for building occupan
11、ts, theVAV system analysis rarely receives the attention it deserves.As a result, basic control strategies for the VAV system haveseen little significant change up to now (Hartman 2003).Recently, applying the model prediction control to theHVAC systems, the control performance has been highlyimprove
12、d by pursuing the perturbation of equilibrium point ofplant (Taira 2004). In this paper, recognizing the operatingpoint of control input and calculating the optimal control inputabout the perturbation for equilibrium point on next samplingtime, the control system gives better responses than the trad
13、i-tional feedback control systems.Compensation of Manual Reset to Offset Thermal Loads Changefor PID ControllerYuji Yamakawa Takanori Yamazaki, PhDKazuyuki Kamimura, PhD Shigeru Kurosu, PhDMember ASHRAEYuji Yamakawa is a graduate student in the Department of Information Physics and Computing at the
14、University of Tokyo, Tokyo, Japan.Takanori Yamazaki is a research associate in the Department of Mechanical Engineering at Oyama National College of Technology, Oyama,Japan. Kazuyuki Kamimura is a director in the Research & Development division, Yamatake Co., Ltd., Tokyo, Japan. Shigeru Kurosu is ad
15、irector at the Research Institute “Crotech,” Chikusei, Japan.OR-10-033 2010, American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc. (www.ashrae.org). Published in ASHRAE Transactions 2010, Vol. 116, Part 1. For personal use only. Additional reproduction, distribution, or tra
16、nsmission in either print or digital form is not permitted without ASHRAEs prior written permission. 304 ASHRAE TransactionsOne of the primary objectives of the HVAC systems is tomaintain the indoor temperature and humidity at the setpointvalues to provide a high quality environment for building occ
17、u-pants. Proportional-plus-integral (PI) controllers are by far themost common control algorithm and the situation has not yetchanged greatly. With a simple Proportional (P) controller, therewould be an offset (or a steady-state error), which the operatorcould eliminate by the manual reset to compen
18、sate for thermalloads change. The supply air flowrate (the control input) to theroom (the controlled plant) should offset thermal loads changeimposed on the room due to the function of an Integral (I) action.PI controller, however, often leads to a poorly damped response.Proportional-plus-integral-p
19、lus-derivative (PID) controllershave been more desirable than PI controllers due to the stabi-lizing effect of a Derivative (D) action. In practice, however, theD action has been frequently switched off for the simple reasonthat it is difficult to tune properly (Shilling 1963, Shinsky 1967,Takahashi
20、 1969).In some applications, thermal loads (or disturbances) canbe estimated in advance before they entered the plant. A typicalexample is a certain system for HVAC systems in which theoutdoor thermometer detects sudden weather changes and theoccupant roughly anticipates thermal loads changes. Distu
21、r-bances should be offset by the compensation of the manualreset. This control strategy can be called a type of feed-forwardcontrol. The control scheme with lower (or no) I action may beinterpreted as a Proportional-plus-derivative (PD) controller. Inthis paper, of special interest to us is how to m
22、ake the D actionmore effective for HVAC systems. At first, this paper proposesa compensation method of the manual reset to offset thermalloads before they affect the control output and confirms theeffectiveness of compensation.PLANT DYNAMICS AND CONTROL STRUCTUREDynamics of HVAC SystemTo explore the
23、 application of a PID controller to HVACsystem, we consider a single-zone environmental space cool-ing system, as shown in Figure 1. The system is composed ofa constant volume, single-zone air-handling unit (AHU oractuator), a PID controller, and an environmental space(controlled plant). With this s
24、ystem, the indoor temperature ofthe space () is measured with a thermometer (sensor). Theoutput signal from the sensor is amplified and then fed back tothe PID controller. Using the error defined as the differencebetween the setpoint value (r) and the measured value of thecontrolled variable (), the
25、 PID controller generates thecontrol input for the actuator so that the error is reduced. Theair-handling unit responds to the control input (ws) by provid-ing the appropriate thermal power to the supply airflow. Airenters the AHU at a warm temperature, which decreases as airpasses through the cooli
26、ng coil. The cooling water valve isused to supply cooling air at moderately cool temperature tothe indoor environmental space by changing chilled waterflow through the cooling coil. Because a room space is acomplex thermal system, it is extremely difficult to describethe exact model that will achiev
27、e accurate control perfor-mance. However, simplifying this thermal system to be a spaceenclosed by an envelope exposed to certain outdoor conditionsis of significant interest to look roughly into room dynamics(Zhang 1992, Matsuba 1998, Yamakawa 2009). This simpli-fied thermal system is governed by t
28、he following equation:(1)where,C = overall heat capacity of air-conditioned space kJ/K, = overall transmittance-area factor kJ/min K,qL= thermal load from internal heat generation kJ/min,Q = thermal load from infiltration kJ/min,ws= acpfskJ/min K, which is heat of supply air flowrate,a= density of a
29、ir kg/m3,cp= specific heat of air kJ/kg K,fs= supply air flowrate m3/min.The first term on the right-hand side is the heat loss which iscontrolled by the supply air flowrate. The second term is theheat gain through the room envelope, including the warm airinfiltration due to the inside-outside tempe
30、rature differential.The third and fourth terms are the thermal loads from the inter-nal heat generation and the infiltration. In this simplifiedmodel, any other uncontrolled inputs (e.g., ambient weatherconditions, solar radiation and inter-zonal airflow, etc) are notconsidered.Table 1 summarizes al
31、l of the plant parameters used in thecurrent analysis. All numerical values given in parenthesesFigure 1 Overall structure of VAV control system.Cddt- wss()0()qLQ+= 2010, American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc. (www.ashrae.org). Published in ASHRAE Transaction
32、s 2010, Vol. 116, Part 1. For personal use only. Additional reproduction, distribution, or transmission in either print or digital form is not permitted without ASHRAEs prior written permission. ASHRAE Transactions 305may be determined from experimental data or calculatedsystem design data (National
33、 Institute for Environment Stud-ies in Tsukuba). From the open-loop responses, the roomdynamics can be approximated by a first-order lag plus dead-time system described by.(2)In this plant, if the room model is represented by Equation1, the plant gain (KP) and the time constant (TP) can be approx-im
34、ately given by,.(3)Equation 3 implies that KPand TPmust be changable with thecontrol input (the supply air flowrate fs). In addition, thecurrent analysis assumes that the deadtime corresponds to thecontrol input in similar way:.(4)where, LP0is determined so that LPis equal to 2.4 min whenfsis equal
35、to 50 %. Namely, LP0is equal to 49.4 kJ/K.Control SystemTaking the PID control algorithm into account, the controlinput related to the error e(t) can be given by the following:(5)where, fs0(t) is the manual reset and e(t) (= (tLP) r) isthe error and ris the setpoint value of the indoor tempera-ture,
36、 and LP(= 2.4 min) is the deadtime. The PID controlparameters (the proportional gain kp, the integral gain ki, andthe derivative gain kd) must be carefully chosen to avoidsystem instabilities. Since the objective of this controlsystem is to minimize the effect of thermal loads changes onthe control
37、output, the initial estimates of these parameterscan be determined by the well-known ultimate sensitivitymethod (Ziegler and Nichols 1942). The PID controlparameters can be obtained (Table 2): kp= 11.65, ki= 2.55,and kd= 13.28.These parameters are indeterminate and therefore can beadjusted to allevi
38、ate instabilities caused by poor tuning. Inparticular, unstable response can result from too much high Iaction and the I control action can generally be less effectiveexcept that offset is eliminated. The function of the I controlaction, however, can be improved by varying the manual resetenough to
39、compensate for thermal loads change (distur-bances). When thermal loads are changing continuously inHVAC systems, the manual reset fs0(t) can be estimated byknowledge of the plant dynamics. The inherent advantages ofthe compensation of the manual reset for thermal loadschanges are highlighted in thi
40、s paper.From Equation 1, the equilibrium (operating) point at itssteady-state can be written:(6)The manual reset (fs0) can be obtained by the solution ofEquation 6, namely. (7)This represents the exact compensation of the manual reset.Such exact compensation, however, is not always realizable.Thus,
41、a new compensation method should be considered.Figure 2 shows a block diagram for a new compensation of themanual reset that would be implemented in VAV controlsystem in Figure 1.In Equation 7, the supply air temperature (s), the outdoortemperature (0), the indoor temperature ( ), and the setpoint(r
42、) can be easily measured. However, little information existson the behavior of thermal loads (qL+Q). In practice, thermalloads cannot be specified in advance, i.e., their magnitudes areTable 1. Selected Parameters of Room ModelOverall heat capacity of air-conditioned space C 370.44 kJ/KSpecific heat
43、 of air cp1.3 kJ/kg KDensity of air a1.006 kg/m3Overall transmittance-area factor 9.69 kJ/min KThermal loads from internal heat generation qL94.2 kJ/minThermal loads from infiltration Q 27.52 kJ/minMaximum supply air flowrate fsmax16.66 m3/minMinimum supply air flowrate fsmin0.00 m3/minOutdoor tempe
44、rature 028 CSupply air temperature s13.1 CDeadtime L 2.4 minPs()KPTPs 1+- eLPs0.6418s 1+-e2.4s=KPsws+- TP,Cws+-=LPLP0ws+-=fst() kpet() kiet()dt kdde t()dt- fs0t()+=Table 2. PID Controller ParametersProportional Gain, kpIntegral Gain(Integral Time)ki(Ti)Derivative Gain(Derivative Time)kd(Td)(a) USM 1
45、1.65 2.55 (4.57) 13.26 (1.16)(b) PMM 11.8 2.22 (5.32) 8.13 (0.69)(c) Modified PI 8.73 0.8 (10.9) 0 (0)(d) Modified PD8.73 0.8 (10.9) 10 (1.15)wss()0()qLQ+ 0 wsacpfs=()=fs0qLQ 0r()+cpars()-= 2010, American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc. (www.ashrae.org). Publis
46、hed in ASHRAE Transactions 2010, Vol. 116, Part 1. For personal use only. Additional reproduction, distribution, or transmission in either print or digital form is not permitted without ASHRAEs prior written permission. 306 ASHRAE Transactionssuddenly changed from the minimum to the maximum values.C
47、onsequently, it outlines some recommendations thatoccupants can roughly estimate thermal loads to improve theaccuracy of the control output at arbitrary adequate samplinginterval. For example, three of the estimates used forcompensation are listed in the following: the maximum (75%),the medium (50%)
48、, and the minimum (25%).At any given point of operation, the manual reset (fs0) tooffset thermal loads can be easily calculated. Thus, it can beconcluded that the controller with lower I action is superior tothat with no I action and there would be no offset due to thediscrepancies in thermal loads.
49、 The control scheme with lowerI action may be interpreted as a PD controller.COMPARISON OF CONTROL STRATEGIESTo illustrate the control performance of the two majorcontrol schemes (with fixed manual reset and adjustable one),a comparative study is carried out. The two major controlschemes are conducted to examine the PID parameters withdif
