1A CONTROLLER FOR HVAC SYSTEMS WITH FAULT DETECTIONCAPABILITIES BASED ON SIMULATION MODELS

T. I. SalsburyLawrence Berkeley National Laboratory

Berkeley, California 94709, USA

ABSTRACTThis paper describes a control scheme with faultdetection capabilities suitable for application toHVAC systems. The scheme uses static simulationmodels of the system under control to generate feed-forward control action, which acts to supplement aconventional PI(D) feedback loop. The feedforwardaction reduces the effect of plant non-linearity oncontrol performance and provides more consistentdisturbance rejection as operating conditions change.In addition to generating feedforward control action,the models act as a reference of correct operation.Faults that occur in the HVAC system under controlcause the PI(D) controller to provide a greater thannormal control action to compensate for fault-induced inaccuracies in the feedforward models. Thecontroller monitors the level of feedbackcompensation and generates alarms when thresholdsare exceeded. The paper presents results from testingthe controller with a dual-duct air-handling unit.

INTRODUCTIONHeating, ventilating, and air-conditioning (HVAC)systems are typically controlled using proportionalplus integral (and sometimes plus derivative) PI(D)control law. In practice, HVAC systems exhibit non-linear operating characteristics, which causes controlperformance to vary when operating conditionschange. Poor control performance can lead tooccupant discomfort in a building, greater energyconsumption, and increased wear on controlledelements, such as actuators, valves, and dampers.

In a conventional PI(D) feedback loop, the controllerdoes not contain much information about the processit is controlling. Faults that lead to performancedeterioration or a change in system behavior areoften masked within a feedback loop. The controlscheme described in this paper uses a model of thecorrectly operating system to supplement aconventional PI(D) feedback loop. The model isused as part of a feedforward control regime in orderto reduce the effects of plant non-linearity on controlperformance. In addition, the model acts as areference of correct behavior, which facilitates thedetection of faults that develop in the controlledsystem.

Several researchers (e.g. Gertler, 1998; Glass et al.,1994; Isermann, 1995; Patton et al., 1995) have

proposed fault detection and diagnosis schemesbased on the use of models. The main trade-off withmodel-based schemes is configuration effort versusmodel accuracy. Generally, the greater the potentialaccuracy of the models, the greater the effort requiredto configure the models for operation. The models inthe proposed controller have therefore been selectedto be configurable from performance informationtypically available during a system life cycle.Although model accuracy and fault sensitivity aresacrificed to a certain extent, the paper demonstratesthat the proposed scheme is capable of detecting twoimportant faults in the air-handling unit tested.

DESCRIPTION OF THE CONTROLLERFigure 1 shows the control and fault detectionscheme. A conventional PI(D) feedback loopgenerates control action (uPI) based on the errorbetween the setpoint and the controlled variable.This feedback control action is then supplemented bya control signal (uFF) generated by a simulationmodel, which is an inverse representation of thesystem. The model is in static form and produces acontrol action appropriate for the current setpoint andmeasured disturbances. The control scheme issimilar to that proposed by Hepworth and Dexter(1994), which used an adaptive neural network as theinverse system model.

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Figure 1: The control and fault detection scheme

The inverse model acting in isolation of the feedbackloop would produce responses equivalent to the openloop dynamics of the system. The feedback loopserves to speed the response time of the controllerand eliminate offsets resulting from modelinaccuracies and unmeasured disturbances. If theapplication allows the assumption to be made that theeffect of unmeasured disturbances is small, the(steady-state) feedback control action (uPI) serves asan indication of the model/system mismatch. By

2configuring the model to represent a correctlyoperating system, the level of uPI acts as an indicationof fault development. Faults occurring in the system,which change its behavior or performance, thuscreate a mismatch between the model and systemleading to an increase in feedback control action.The control scheme incorporates a procedure formonitoring the feedback action so that an alarm isgenerated if uPI exceeds a threshold for a sustainedperiod.

APPLICATION SYSTEMThe control scheme is evaluated using a simulationof an air-handling unit developed in the MATLABenvironment using component models adapted fromHVACSIM+ (Clark, 1985). The unit is modeled on areal system, which is installed in a large federalbuilding in downtown San Francisco, USA. Figure 2depicts the air-handling unit, which is a dual-ducttype having three thermal subsystems: mixing box,cooling coil, and heating coil. The air-handling unithas the capacity to deliver 74kg/s of air and provide850kW of heating and 1260kW of cooling.

Each thermal subsystem has its own controller. Themixing box controller modulates three sets ofdampers in sequence to maintain a mixed air setpoint.There is a minimum outside-air requirement based ondamper position (20% minimum outside-air byposition) and a temperature economizer. The hotduct houses a steam-to-air heating coil regulated by atwo-port valve, and there is a water-to-air coolingcoil having a three-port valve in the cold duct. In thereal system, the fan speed is varied according to loadchanges in the zones in a conventional VAVarrangement whereby a constant duct static pressureis maintained. In the simulated system, artificial stepchanges in airflow rate were applied in order tomaintain excitation but avoid the need for modelingthe zones and VAV boxes.

SIMULATION MODELS USED IN THEFEEDFORWARD CONTROLLERThe models used in the feedforward controller aresimplified versions of the models in the simulation.Three separate models are employed; one in each ofthe three separate control-loops in the air-handler:mixing box, heating coil, and cooling coil. Details ofthe model equations can be found in (Salsbury,1998). The models used in the feedforwardcontroller differ from the models used in thesimulation in several respects. In particular, thecontroller models do not treat:x variations in coil thermal conductance with

fluid flow rates;x dehumidification in the cooling process;x non-linearity for variations in control signal

when all other operating conditions arefixed.

The latter simplification is made becausecharacterization of this non-linearity requiresparameters that are not easily obtainable or reliable,such as those related to valve and damper inherentcharacteristics and authorities. Although linearbehavior is rarely achieved in practice, thesimplification is reasonable, as this is one of thegoals of the design and commissioning processes.Although the model simplifications reduce potentialaccuracy and performance of the scheme, a majoradvantage is that the model parameter values may beobtained from typical available information, ratherthan requiring training data and additional tuningeffort.

Table 1: Configuration parameters

PARAMETER/DESIGN SPECIFICATIONS UNITSHEATING/COOLING COIL

Heat transfer rate kWCold fluid inlet air temperature CCold fluid mass flow rate kgs-1

Hot fluid inlet temperature CHot fluid mass flow rate kgs-1

MIXING BOXMinimum fractional outside air flow %

Table 1 lists the parameters required by the controllerand Table 2 lists the required sensormeasurements/variables. Note that in the dual-ductair handling unit, air temperatures and flow rates arerequired before the coils in both the hot and coldducts.

Table 2: Required sensor signals/variables

SENSOR SIGNAL UNITSReturn air temperature COutside air temperature CAir flow rates kgs-1

Pre-coil air temperatures CSetpoints kgs-1

TEST RESULTSThe control scheme is evaluated in two respects:x setpoint tracking performance;x ability to detect faults in the three thermal

subsystems.Twelve hours of test data, sampled at 5-secondintervals are used to evaluate the control scheme.The test data contain real measurements of ambientand return air temperatures from the real building.Airflow rate is artificially varied in a sequence ofarbitrary steps and ramps. The setpoints for each ofthe three subsystems are also varied artificially inorder to facilitate a rigorous assessment of thecontrollers.

3Control PerformanceThis section compares the performance of thefeedforward controller with the performance of a PIcontroller acting in isolation. Each of the PI controlloops was tuned using the Zeigler-Nichols open looptest procedure making use of the highest gainsexhibited in the range of conditions in the test data.

Figure 3 shows the performance of the PI controllerwhen subjected to the test data. The upper graphshows the three controlled variables and setpoints.The middle graph shows the ambient and return airtemperatures and the air flow rate (right axis scale),and the lower graph shows the control signals to eachof the subsystems. For these conditions, the PIcontroller provides satisfactory performance for thetest data. Control performance is characterized bythe sum of the mean absolute errors (MAE), listed inTable 3.

Figure 4 shows the performance of the same PIcontrollers, but this time with the inclusion ofsupplemental feedforward action. The graphs showminor improvements in the responses to thedisturbances. This is particularly evident for theheating coil control-loop, which shows tighter controltoward the end of the test data.

Table 3 lists the mean absolute errors in each controlloop over the period of the data. There is littlechange in the performance of the mixing control-loop, which shows only a 4% improvement. This isdue to the ambient air temperature not varyingsignificantly during the test data leading to areasonably invariant gain in this subsystem. Inpractice, variations in ambient air temperaturedirectly affect the mixing box gain and lead toinstability in this loop. Previous work has shown thatthe feedforward controller can significantly improvethe mixing box control-loop in the face of highlyvariable environmental conditions (Salsbury, 1998).The cooling coil control performance improves by18%, while the heating coil shows the greatestimprovement of 52%.

Table 3: Comparative performance of controllers

MAE (K)PROCESS COOL MIX HEATPI control in isolation 0.22 0.45 0.25PI + feedforward control 0.18 0.43 0.12Improvement (%) 18 4 52

FAULT DETECTION PERFORMANCEThe ability of the control scheme to detect faults isevaluated using the same test data used in the controlperformance evaluation.

No Fault ConditionThe control scheme is tested firstly using the systemin its correctly operating condition. Figure 5 showsthe indices associated with the fault detection. Thetop graph shows the control signals generated by thethree feedback loops in the air-handler. If the modelsused in the controller were perfect representations ofthe system under control, these control signals wouldasymptotically approach zero following eachdisturbance.

Figure 5 shows that there are modeling errors in eachof the models. The errors vary during the data due totransient effects and because the models approximatethe system better in certain parts of the operatingrange than in others. The cooling coil exhibits thegreatest level of inaccuracy during the test data; thismost likely being due to the extra simplifications inthis model, such as non-treatment ofdehumidification. The heating coil model appears torepresent the system well, with the feedbackcontribution being the lowest of the threesubsystems. Correlating Figure 5 with Figure 4,shows that the greatest errors in the mixing boxmodel are in the mid-range of operation, this beingdue to the simplification of linearity between the twoextreme load points.

The bottom three graphs in Figure 5 show the faultdetection output for each loop. A fault is deemed tohave occurred if the feedback control signal risesabove the threshold and stays above the threshold fora sustained period (30 minutes).The selection of a threshold is fundamental to theperformance of the fault detection scheme. Thethreshold was selected here based only on themaximum feedback control actions exhibited for thecorrectly operating data. In practice, the mostreliable way in which to establish thresholds wouldbe to perform closed loop tests on the subsystemsduring the commissioning process. These tests couldbe set up so that selected setpoints exercise thesystems at strategic points in their operating ranges.Alternatively, thresholds could be identified duringan on-line learning phase, whereby maximumfeedback action is monitored over an assignedperiod. Another possibility would be to determinedefault threshold values for particular classes ofHVAC systems based on statistically significant testson similar equipment.

Valve LeakageLeakage through the control valve of a heatexchanger is a common fault in HVAC systems,which often persists unnoticed due to feedbackmasking and compensatory actions of other systems.This fault can lead to wastage of energy, not only inthe subsystem where the fault occurs, but also in theother systems forced to provide compensatory action.

4In this test, the cooling coil valve model in thesimulation is amended so that it leaks by 20% ofmaximum flow when the valve is supposed to beclosed.

Figure 6 shows the behavior of the control schemefor the leakage fault. The 20% leakage causes thecooling coil to provide too much cooling during mostof the test data, which makes the feedback controlsaturate the control signal at zero. The setpoint isonly attained when a high cooling demand is neededduring the middle of the data.

Figure 7 shows the fault detection indicators for theleakage fault case. The top graph shows that thefeedback loop control action exceeds the thresholdfor a large portion of the day. Correspondingly, themixing process graph (second from bottom in thefigure) indicates a fault for much of the data. Thefeedback error is largest when the cooling coilcontrol signal is zero due to this being the part of theoperating range where the fault is most evident.When the coil operates at a higher load, the feedbackcompensation drops below the threshold. Thescheme therefore only detects faults when theconsidered subsystem is operating at a point wherethe effects of the fault are evident.

Stuck Return Air DamperA stuck damper in the mixing box is anothercommon fault in HVAC systems. This fault can bedue to various causes, such as a failed actuator,damper obstruction, de-coupled linkage, etc. Thefault is difficult to detect in practice as it does notcause failure of the mixing process but instead altersits characteristics and restricts the operating range.Figure 8 shows the performance of the controllerwhen the re-circulation damper is stuck at 50% open.The fault is masked for the majority of the test datawith the fault condition only affecting controlperformance in the middle of the day when thecontroller demands 100% outside air.

Figure 9 shows the fault indicator variables for thestuck damper condition. The feedback control actionto the mixing box increases during the periods whenthe dampers are supposed to be providing 100%outside air. Unwanted re-circulation through themixing box reduces its operating range so thatsetpoints close to the ambient air temperature becomeunattainable. The fault is less apparent in the parts ofthe range where setpoints are closer to the return airtemperatures. The fault proves difficult to detect andthe threshold is only exceeded for a short time aroundnine hours into the test data. However, the periodover which the feedback action remains above thethreshold is sufficient to trigger an alarm for themixing box. Note that 30 minutes is set as the timelimit for a threshold transgression in order to triggeran alarm.

CONCLUSIONSThis paper has demonstrated the potential for usingsimplified simulation models as part of an HVACcontrol scheme. The tests results presented in thepaper showed that the scheme was able to improvecontrol performance and detect two different types offaults in the considered air-handling unit.

The performance of the control scheme and its abilityto detect faults in the controlled process depends onthe accuracy of the models. Realizable accuracy islimited by errors in the structural formulation of themodel, selection of correct parameter values, and bythe reliability of the sensor signals used by themodels. More research is needed to ascertain theoptimum model complexity for particular faultdetection applications.

Thresholds need to be related to model accuracy,which, under ideal conditions, should be establishedthrough rigorous testing on the application system.There is a trade-off between the time invested inestablishing thresholds, and the reliability of thescheme. In the paper, a threshold was establishedheuristically based on one set of correct operationdata. In practice, data of this sort may be to costly toobtain. Other means of ascertaining thresholds, suchas on-line learning, or the use of default values maybe more practical alternatives.

ACKNOWLEDGEMENTSThis work was supported by the Assistant Secretaryfor Energy Efficiency and Renewable Energy, Officeof Building Technology and Community Systems,and the Federal Energy Management Program, of theUS Department of Energy under Contract No. DE-AC03-76SF00098.

REFERENCESClark, R. C. 1985. HVACSIM+ Building Systemsand Equipment Simulation Program ReferenceManual. Published by the U.S. Department ofCommerce, Gaithersburg, MD 20899.

Gertler, J. 1988. Survey of Model-Based FailureDetection and Isolation in Complex Plants. IEEEControl Systems Magazine. Number 6. Volume 8.Page 3.

Glass, A. S., P. Gruber, M. Roos, and J. Tdtli. 1994.Preliminary Evaluation of a Qualitative Model-Based Fault Detector for a Central Air-HandlingUnit. Proceedings of 3rd IEEE Conference onControl Applications, Glasgow.

Hepworth, S. J., A . L. Dexter. 1994. NeuralNetwork Control of a Non-Linear Heater Battery.Building Services Engineering Research andTechnology. Volume 15. Number 3. Page119.

5Isermann, R. 1995. Model-Based Fault Detectionand Diagnosis Methods. Proceedings of theAmerican Control Conference, Seattle, Washington,USA. Page 1605.

Patton, R. J. J. Chen, S. B. Nielsen. 1995. Model-Based Methods for Fault Diagnosis: SomeGuidelines. Transactions of the Institute ofMeasurement and Control. Volume 17. Number 2.Page 73.

Salsbury, T. I. 1998. A Temperature Controller forVAV Air-Handling Units Based on SimplifiedPhysical Models. ASHRAE HVAC&R ResearchJournal. Volume 4. Number 3.

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Figure 5: Diagnostic indicator variables no fault condition

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Figure 7: Fault indicator variables leaking cooling valve fault

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Figure 8: Control behavior when the return air damper is stuck at 50%

Figure 9: Fault indicator variables - return air damper stuck at 50%

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