Neuro PID Tracking Control Air Discharger

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Neuro-PID tracking control of a discharge

air temperature system

M. Zaheer-uddin *, N. Tudoroiu

Department of Building, Civil and Environmental Engineering, Concordia University, Montreal, Canada H3G 1M8

Received 15 April 2003; received in revised form 15 September 2003; accepted 23 November 2003Available online 22 January 2004

Abstract

In this paper, the problem of improving the performance of a discharge air temperature (DAT) system

using a PID controller and augmenting it with neural network based tuning and tracking functions is

explored. The DAT system is modeled as a SISO (single input single output) system. The architecture of the

real time neuro-PID controller and simulation results obtained under realistic operating conditions are

presented. The neural network assisted PID tuning method is simple to implement. Results show that the

network assisted PID controller is able to track both constant and variable set point trajectories efficiently

in the presence of disturbances acting on the DAT system.

2003 Elsevier Ltd. All rights reserved.

Keywords: Discharge air temperature system; SISO system; HVAC systems; Temperature control; Neural network

control; PID control; Neuro-PID tuning; Tracking control

1. Introduction

The control of heating, ventilating and air conditioning (HVAC) systems is a difficult problem

because even the simplest HVAC system models are multi-variable and nonlinear. Furthermore,these systems are acted upon by multiple disturbances. For these reasons, there is considerableinterest in developing real time control strategies to improve the performance of HVAC systems.

Several specific aspects of HVAC systems modeling and control have been considered in theliterature. For example, the issue of discharge air temperature (DAT) control in HVAC systemshas been studied by Shavit [1], Nesler [2], Dexter and Haves [3] and Seem [4]. In our research, we

Energy Conversion and Management 45 (2004) 24052415

www.elsevier.com/locate/enconman

* Corresponding author. Tel.: +1-514-848-3194; fax: +1-514-846-7965.

E-mail address: [email protected] (M. Zaheer-uddin).

0196-8904/$ - see front matter

2003 Elsevier Ltd. All rights reserved.doi:10.1016/j.enconman.2003.11.016
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are interested in adapting some neuro-modeling procedures to build a real time neuro-PID

controller for a DAT system.Single loop feedback controllers are used to maintain the temperature, humidity and pressure at

their respective set points in HVAC systems in commercial buildings. Some work has already beendone in this area. For instance, the development of control strategies for improving the perfor-mance of PID controllers using self tuning and adaptive control techniques has been studied byDexter and Haves [3], Nesler [2] and Seem [4,5]. The authors conclude that the magnitude of the

disturbances found in the HVAC industry causes problems when applying self tuning andadaptive control methods. Also, it has been reported that unmodeled process disturbances andactuator hysteresis limit the effectiveness of the RLS self tuner as such. More recently, adaptive

techniques that utilize statistical experimental design methods have been designed [4,5]. Here, weare interested in finding a simple neural network based strategy for tuning the proportional

integral-derivative (PID) controller so that the control loop performance is improved while thecontroller remains in the closed loop.

2. DAT system oriented structure

A typical configuration of a DAT system is shown in Fig. 1. Outdoor air (OA) and room return

air (RA) are mixed, and the mixed air is filtered and circulated in the cooling and dehumidifyingcoil. The chilled water flow rate is modulated using a valve, a motor-actuator and a PID con-troller. The discharge air temperature [CCOTS] is controlled to track a chosen set point by

regulating the valve position [VALOP], which varies the mass flow rate [CWFRG] (gpm) ofchilled water entering the coil. The experimental setup also includes measurements of chilled watertemperatures entering [CWSTS] and leaving [CWRTS] the cooling coil. The temperature of air

entering the cooling coil was measured by the sensor [CCITS], and the airflow rate was recordedby a differential pressure sensor [DPS]. Measurements were made of the above variables every 4 s.Several tests were conducted to gather the data needed for training the neural networks. The data

collected represented three different operating points of the system, the low, medium and highload conditions that typically occur in HVAC systems.

CWFRG4.40 GPM

VALOP58.78 PCT

CWSTS7.0 DEG. C

DPS260.5 CFM

CWRTS12.0 DEG. C

OA

RA

CoolingCoil

CCITS25.6 DEG. C

CCOTS11.0 DEG.CDischarge Air

Temperature System

Fig. 1. The discharge air temperature (DAT) control system.

2406 M. Zaheer-uddin, N. Tudoroiu / Energy Conversion and Management 45 (2004) 24052415


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From the point of view of modeling, it is useful to conceptualize the DAT system as a multi-

input multi-output (MIMO) and single-input single-output (SISO) system as shown, respectively,in Figs. 2 and 3. In the MIMO system, the inputs to the model is chilled water flow rate mw,

[CWFRG](gpm), air flow rate Qa, [DPS](cfm), chilled water supply temperature Twi, [CWSTS](F)and cooling coil inlet temperature Tai, [CCITS](F), and its outputs are cooling coil outlet

mwTao

Qa

Twi Two

Tai

Cooling Coil

Fig. 2. DAT systemMIMO model input/output functional block: cooling and dehumidifying coil model

(mw CWFRG; Qa DPS; Twi CWITS; Tai CCITS; Tao CCOTS; Two CWRTS).

mwTao

Cooling Coil

Fig. 3. DAT systemSISO model input/output functional block: sensible coil-model (mw CWFRG; Tao CCOTS).

K

error backpropagation

p K*p target Kp

_ gain parameter

ynn (k+1)_ _

+

y*

(k+1)

ICKi Kd Kp

u(k) y(k+1)

y*(k) e(k)

-

PI D

Controller

DAT Plant

Hp(z)

z-1

z-1

z-1

z-1

z-1

Ziegler-Nichols

IC

Fig. 4. Neuro-PID controller structure.

M. Zaheer-uddin, N. Tudoroiu / Energy Conversion and Management 45 (2004) 24052415 2407


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temperature Tao, [CCOTS](F) and chilled water return temperature Two, [CWRTS](F). On theother hand, in the SISO model, a more simplistic point of view is taken in order to reduce themodel complexity. In the SISO model, the discharge air temperature Tao, is the output, and

the chilled water mass flow rate mw, is considered as the input to the system. The other variableswere considered as disturbances on the system.

In a previous study [6], the predictions from the MIMO and SISO models were compared. It

was shown that the SISO model predictions are close to those of the MIMO model. As such, forcontrol design, a simpler model, such as the SISO model, is more suitable than the MIMO model.

The resulting inaccuracies in modeling can be compensated by designing robust controllers thatcan compensate for the model uncertainties. With this as the motivation, we propose to use theSISO model to design a neuro-tracking controller for the DAT system. By tightly regulating thedischarge air temperature close to an optimal set point, the overall performance of the system

could be improved.

3. Neuro-PID controller

Precise modeling of the DAT process is difficult to perform due to its high nonlinearity. Re-

cently, models derived using neural networks have been shown to offer advantages in bothaccuracy and robustness over more traditional statistical approaches (regression methods). The

Fig. 5. Neuro-PID controller-discharge air temperature response for u3 2 F.



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neural networks are capable of generalizing and learning dynamic relationships between the in-puts and outputs of the plant. Furthermore, the neural networks can constantly update theirconnection weights to respond to changes in the plant dynamics. Our objective in this research is

to determine an accurate neural network based PID controller for the DAT system. The controlleris assumed to have the transfer function:

Hcz Kp Ki

1 z1 Kd1 z

1

and is shown in this paper to provide good tracking performance for the temperature output andto reduce substantially the effect of the disturbances. The self learning feature of the neural

networks can be exploited in autotuning the PID gain parameters (proportional gain Kp, integralgain Ki and derivative gain Kd) where there are nonlinearities that cannot be expressed in closed

form or some unidentified dynamic modes [7]. Recent work has developed advanced structuresand algorithms, such as adaptive neuro-controllers and exponentially weighted moving average(EWMA) neuro-controllers. In this study, an inputoutput data set was used to train feed forward

neural networks using the error back propagation algorithm. For this purpose, we consider aneural network configuration that consist of three layers [7], namely 522, shown in Fig. 4,trained by an error back propagation technique [8,9]. The neural network training was continued

until an error goal, defined by the mean square root error (MSE) criterion, was met. The MSEcriterion was defined as

Fig. 6. Neuro-PID controller-chilled water flow rate response for u3 2 F.



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E 12Xi

kyi tik2 1

The back propagation technique in the training of neural networks looks for the minimum of the

network error function in weight space using the method of gradient descent, where yi representsthe output of the neural network, and ti represents the output target value in the supervised

learning mode.To this end, we consider the neural network architecture shown in Fig. 4. In Fig. 4, the plant

error and its delayed signals are used as inputs. It was found that five delayed error signals wereneeded to capture the dynamics of the DAT control loop accurately. Furthermore, the errorbetween the neural network output and the plant output, as well as the error in the predicted

proportional gain and the target proportional gain, were back propagated as shown in Fig. 4.To initiate the training process, one could assign arbitrary values for the PID gain parameters.Alternately, the PID gain parameters could be computed using well known techniques, such as theZieglerNichols method, and used as initial values. The system error ek was defined

ek yk 1 yk 1

and was used in the supervised training mode. For greater efficiency, we consider the neural

network structure with one parameter fixed, for example, the proportional gain KP, and the otherparameters (Ki;Kd) are then determined directly by the neural network structure, as the outputs of

Fig. 7. Neuro-PID controller-discharge air temperature response for u3 4 F.



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the hidden layer. The idea behind this scheme is to let the neural network find all three parameters(Kp;Ki;Kd) by presenting the inputoutput data set of the DAT system. We note that the use of

initial PID parameter values obtained using the ZieglerNichols procedure greatly improved theconvergence of the algorithm as compared to Ahn [7] where the initiation of the process in closed

loop is not specified. Also, the architectural structure of the PID neuro-control strategy is sim-plified using one single hidden layer, and this eliminates ambiguity in the selection of the output

parameters Kp, Ki, Kd. Even though this technique still requires one to specify a target gain (suchas Kp when a full PID control is implemented), its advantage is obvious when using only the PIcontrol. In the PI mode, only two gain parameters are needed, which can be updated by thenetwork by back propagating the neural network output and the plant error. Since in many

HVAC systems, including the DAT systems, the derivative action is rarely used as such, thenetwork structure shown in Fig. 4 can be readily simplified to a neuro-PI controller by eliminatingthe target Kp gain.

4. Simulation results

In this paper, we consider the case with changes in the discharge air temperature set points(target values): y 55 F for the first 300 samples, y 60 F for the next 200 samples and

Fig. 8. Neuro-PID controller-chilled water flow rate response for u3 4 F.



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y 50 F for the last 200 samples. The results of the simulations subjected to the changes in setpoints and disturbances are presented in Figs. 58. We consider changes in chilled water supply

temperature Twiu3 as a disturbance on the DAT system. The results depicted in Figs. 58 showthe output responses of the system to the changes in set points by 5 F when a 2 F rise in inletwater temperature occurs. In the initial 100 s (25 samples) the valve response (Fig. 6) goes from

a full closed to full open position before it stabilizes. This suggests that significant changes in setpoints impose a large error on the controller, thus causing rapid movements of the actuators over

a short period of time. The control operation is otherwise stable and tracks the desired set point.In the simulations results presented here, the set point of 60 F corresponds to almost no load

conditions. Because of this, the control valve is almost closed at this set point as shown in Fig. 6.

The sets of responses in Figs. 7 and 8 (with a 4 F rise in chilled water inlet temperature) showsimilar trends. The effect of increasing the chilled water temperature can be seen by comparing

Figs. 5 and 6 (a 2 F change) and 7 and 8 (a 4 F change). Given that in both Figs. 5 and 7, the setpoints remain the same, it is apparent from Fig. 8 that a higher water flow rate is needed tomaintain the same set point when the water temperature is increased by 4 F compared to the

water flow rates shown in Fig. 6.These figures reveal a good tracking performance (with zero steady state error), good transient

behavior, but a 5 F overshoot in output temperature. Also, the neuro-controller input responses

show periods of transients following the disturbance. To eliminate this situation, we have adapted

Fig. 9. New set point trajectory for the neuro-PID tracking controller.



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a tracking control technique presented by Anderson and Moore [10]. In the technique used, wehave built a neuro-PID tracking controller that tracks a reference trajectory such as the one

shown in Fig. 9. The simulation results from this neuro-PID tracking controller are depicted inFigs. 10 and 11. It is apparent that the control input responses are smooth even when a 4 Fchange in chilled water temperature is imposed as a disturbance on the system.

The neuro-PID tracking control is useful in minimizing the overshoot. This is achieved byletting the PID controller track a given trajectory. The advantage of this technique is that the

steady state time can be chosen a priori to achieve a desired tracking trajectory. The trackingtrajectory considered in this paper is shown in Fig. 9. The corresponding DAT responses are

depicted in Fig. 10. The speed of response can be improved by selecting a trajectory that reachesthe set point faster.

5. Performance evaluation

The magnitude of temperature oscillations in the neuro-control strategy is somewhat large dueto the fact that the model of the DAT system is nonlinear. For this reason, the actuator responsesduring the initial few samples seems to be more oscillatory. We have addressed this issue by

presenting a tracking solution that represents a new point of view. The responses from this neuro-PID tracking controller leads to better performance, reducing the oscillations and the actuator

Fig. 10. Neuro-PID tracking controller-discharge air temperature for u3 4 F.



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acts smoothly. This represents a big advantage in practical applications. Overall, taking intoaccount the fact that for the neuro-control strategy, the dynamics of the DAT system could beunknown and the nonlinearity of the actuator is incorporated in its dynamics, we consider the

neuro-control strategy very useful for tuning the PID parameters. Experimental work is beingplanned for validating the control strategy reported in this paper.

6. Conclusion

In this paper, we developed real time DAT control strategies for tuning the PID gainparameters. The simulation results reveal that the neuro-PID controller gives good trackingperformance. Furthermore, the neuro-PID controller structure proposed can be applied to DAT

systems with unknown dynamics and, consequently, eliminate the need for extensive identifica-tion. The values obtained for the PID gain parameters are not unique. They represent only one ofthe solutions for the triplet among infinitely many possible ones. In spite of this, this technique

still remains useful for HVAC systems for tuning of the PID gain parameters. To avoid over-fitting, we have limited the number of neurons to as few as possible that yield convergence to thedesired error level, and we cut off the training once that error level was reached. The proposed

neuro-PID structure gave the best fit for the inputoutput data set with the smallest standarddeviation error.

Fig. 11. Neuro-PID tracking controller-chilled water flow rate response for u3 4 F.



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Acknowledgements

This work was funded by a research grant (OGP 0036380) from the Natural Sciences and

Engineering Research Council (NSERC) of Canada.

References

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[3] Dexter AL, Haves P. A robust self-tuning controller for HVAC applications. ASHRAE Trans 1989;95(1):4318.

[4] Seem JE. A new pattern recognition adaptive controller. In: IFAC 13th Triennial World Congress, San Francisco;

1996. p. 1216.

[5] Seem JE. Implementation of a new pattern recognition adaptive controller developed through optimization.

ASHRAE Trans 1997;103(1).[6] Zaheer-uddin M, Tudoroiu N. Neuro-models for discharge air temperature system. Energy Convers Manage

2004;45(6):90110.

[7] Ahn S. Self-tuning PID controller design using neural networks: intelligent engineering systems through artificial

neural networks. In: Proceedings of the Artificial Neural Networks in Engineering (ANNIE 93) Conference, vol. 3.

New York: ASME Press; 1993.

[8] Zurada JM. Introduction to artificial neural systems. West Publishing Company; 1991.

[9] Rojas R. Neural networksa systematic introduction. Berlin, New York: Springer-Verlag; 1996.

[10] Anderson BDO, Moore JB. Optimal control: linear quadratic methods. Prentice-Hall; 1990.


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Neuro PID Tracking Control Air Discharger