Application of adaptive neural predictive control for an

Applied Thermal Engineering 73 (2014) 1242e1252

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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng

Application of adaptive neural predictive control for an automotive air conditioning system Boon Chiang Ng, Intan Zaurah Mat Darus*, Hishamuddin Jamaluddin, Haslinda Mohamed Kamar Department of Applied Mechanics and Design, Faculty of Mechanical Engineering, Universiti Teknologi Malaysia, 81310 Johor, Malaysia

h i g h l i g h t s
An adaptive neural predictive controller is applied for an AAC system.
A neural network model is used to identify the AAC dynamic system.
Set point tracking and disturbance rejection tests are performed experimentally.
The proposed controller is compared with MPC using offline trained ANN.
The proposed controller delivered superior performance.

a r t i c l e i n f o

a b s t r a c t

Article history: Received 8 April 2014 Accepted 20 August 2014 Available online 30 August 2014

In this paper, a Model Predictive Controller (MPC) using an online trained artificial neural network (ANN) as the nonlinear plant model is implemented for an automotive air conditioning (AAC) system equipped with a variable speed compressor (VSC). The training scheme using LevenbergeMarquardt algorithm and sliding stack window technique is incorporated to train the ANN model in real time so that the time varying dynamics of the AAC system can be captured throughout the control process. The ANN model is initially identified offline using the training and testing data obtained from the experimental AAC system. Validation of the neural network is performed using one-step-ahead and 10-steps-ahead prediction tests. Subsequently, several experimental tests are carried out on the AAC test bench to verify the capability of the proposed controller in tracking set point changes and rejecting disturbances. In order to show the advantages of incorporating an online trained ANN in the proposed controller, comparative assessment is performed between the proposed adaptive controller and two other control schemes, namely a MPC using an offline trained ANN model and a conventional PID controller. The experimental results signify the superiority of the proposed control scheme in terms of reference tracking as well as disturbance rejection due to its adaptation capability in capturing the real time AAC system behaviour over the wide range of operation conditions. © 2014 Elsevier Ltd. All rights reserved.

Keywords: Neural networks Adaptive control Model predictive control Variable speed compressor Automotive air conditioning

1. Introduction The reinforcement of more stringent environmental regulations has posed a great challenge to automotive industry to fulfil the demand for fuel saving and energy efficiency. Since the air conditioner compressor is the single largest auxiliary load on an automobile engine [1], the manufacturers are concerned with the

* Corresponding author. Tel.: þ6075557061. E-mail addresses: [email protected] (B.C. Ng), [email protected], [email protected], [email protected] (I.Z.M. Darus), [email protected] (H. Jamaluddin), [email protected] (H.M. Kamar). http://dx.doi.org/10.1016/j.applthermaleng.2014.08.044 1359-4311/© 2014 Elsevier Ltd. All rights reserved.

design of a more efficient automotive air conditioning (AAC) system. A conventional AAC system operates with its compressor belt driven by a combustion engine. The compressor is cycled on-off via engagement and disengagement of a magnetic clutch in order to maintain the demanded cooling capacity during partial load condition. The main drawbacks of this control method are the energy loss associated with the pressure equalization during compressor stoppage, friction losses due to the pulley belt mechanism and poor cooling performance. Reduction in power consumption can be achieved for an air conditioning system [2,3] by converting the control strategy from the conventional compressor on-off cycling to a variable speed

B.C. Ng et al. / Applied Thermal Engineering 73 (2014) 1242e1252

operating mode. The reason for energy saving lies in the fact that establishment of a proper speed control of the variable speed compressor (VSC) can insure a continuous matching between the cooling capacity and the varying thermal load. Furthermore, variable speed operation can deliver better temperature control and faster response to sudden change in thermal load in comparison to the fixed speed operation [4]. This control method is technically applicable for heavy trucks, buses, electric vehicles, in which high voltage battery supply is available. Recently, it has become a prospective application in conventional vehicles, as the key German carmakers are working on the stepping up of the current 12 V power supply to the proposed 48 V power net system [5]. This transition will facilitate the integration of an electric VSC in the conventional vehicle powered fully by the 48 V battery. In view of the promising improvement brought about by the VSC application, several controllers for VSC have been proposed in the literature. Investigations related to the implementation of proportional-integral and derivative (PID) control in regulating the compressor speed of an air conditioning system are reported in the literature [2,6,7]. However, under consideration of the inherently nonlinear dynamic behaviour of the air conditioning system [8], a simple PI/PID controller with fixed control parameters is not adequate to consistently deliver optimal control performance over the wide range of operating conditions. Researches on linear model based controller for an air conditioning system has been reported in the literature [9,10]. The proposed control methods require preliminarily a detailed nonlinear physical model of the vapour compression cycles derived from first principle to back up the controller design [9,11,12]. However, developing an adequate physical model with satisfactory prediction accuracy is a challenging task, as the physical system is highly nonlinear and there are complex interconnections between the subsystems that mutually influence one another. Artificial neural network (ANN) has been well-known for its capability as a universal approximator to fit nonlinear dynamic system without prior physical knowledge of the plant [13,14]. When nonlinear model is required for real time control implementation, the choice of ANN model can potentially reduce the development effort and computational burden as compared to the first principle based model. Many studies have reported the success of ANN's application for advanced model based control of air conditioning system [15,16]. However, the ANN based controllers developed in these studies often deal with an offline trained ANN, which is identified using data collected at one operating point. Once the ANN is properly trained, the established model produces output prediction without further update of the connection weights and biases as the process continues. Application of an offline trained ANN model for the thermal control of housing air conditioning and industrial refrigeration systems is considered adequate, as these applications usually work under static conditions. The controller is capable to operate efficiently as long as the operating condition is not drifted away from a given range of the ANN training point. However, an offline trained ANN alone is incapable of capturing the dynamics of a mobile AAC system over its entire operating range, as it is consistently subjected to a wide range of transient disturbances such as the sun radiation, environmental temperature and incoming air speed of heat exchangers [17]. Following this, an ANN based adaptive controller is developed in this work for an AAC system equipped with VSC. The ANN model adopted in the proposed controller is trained online using real time collected data and its connection weights are updated on a regular basis in order to ensure an optimal representation of the real time system dynamics. Out of the several ANN based control approaches available in the literature, model predictive control appears to be successfully

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applied in a wide variety of areas including chemical, food processing, automotive and aerospace applications [18]. As a result, an adaptive ANN based model predictive controller (A-NNMPC) is developed in this work for the thermal control of the AAC system. Even though intelligent thermal control for the AAC system has been analysed intensively using computer aided simulation results [17,19,20], limited laboratory experimental implementation associated with this control system have been published. Considering the great potential of the VSC application in the AAC system, all the set point tracking and robustness tests against disturbances in this work are conducted on an experimental bench. In comparison to numerical simulation, experimental validation process is more challenging due to the presence of environmental uncertainties, unmeasured noises, computation delays and nonlinear dynamics. In this study, the experimental setup for the AAC system equipped with VSC is first introduced. Secondly, the working principle of the proposed controller with an ANN online training algorithm is presented. Subsequently, offline identification of the AAC system using an ANN model is performed to predict the average cabin temperature under random modulation of the compressor speed. One-step-ahead and 10-steps-ahead prediction tests are carried out to evaluate the performance of the ANN model based on the training and testing data. Finally, experimental tests comprising the command following test and disturbance rejection tests are carried out to verify the control performance of A-NNMPC. Comparative assessment is performed between the proposed ANNMPC and two other control schemes, namely the conventional MPC with an offline trained ANN model (O-NNMPC) and the conventional PID controller tuned using the Ziegler Nichols method. 2. Experimental setup Depicted in Fig. 1 is an experimental rig developed to emulate an actual AAC system working under different operating conditions. It comprised a refrigeration circuit working with HFC134a and air distribution subsystems. The key components of the vapour compression system were the original off-the-shelf units for a compact vehicle, which consisted of a condenser, an evaporator and a thermostatic expansion valve. Additionally, an electric power hermetic compressor was integrated as the replacement of the engine driven wobble plate compressor. This rig was specifically designed for the performance evaluation of an AAC system operating with the hermetic VSC. The VSC is of compact hermetic compressor type powered by 48 V Direct Current (DC) supply. This feature enables direct implementation of the compressor in a conventional vehicle supplemented with 48 V power net. The compressor was regulated between the bounded set speed interval ranging from 1800 to 5500 RPM. The thermally insulated air ducting systems serve to guide the air flow through the heat exchangers with minimum disturbance from the ambience. The air duct containing the evaporator is a closed loop conduit resembling the air recirculation in an actual car, while the duct section for the condenser is of open tunnel type that served to simulate the running wind crossing the condenser located at the front of a moving vehicle. Air circulation in the evaporator ductwork was driven by a centrifugal fan with three manually adjustable face velocities (2.3, 3.0 and 4.25 m/s). These velocity selections were chosen by comparison with the outlet air speeds measured at the AAC vent of a compact vehicle. Air was forced into the condenser tunnel using an upstream variable speed blower. The condenser face velocity was controlled by a frequency inverter within the range of 1.0e5.3 m/s, representing an idling vehicle as well as driving speed up to 96 km/h [21]. Electrical finned heaters were installed upstream of the heat exchangers to provide

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Fig. 1. Schematic diagram of the complete experimental AAC system.

sensible loads. Additionally, a steam humidifier was installed in the evaporator ductwork to produce latent loads. Both actuators were controlled by PID controllers. The vehicle cabin was measured at 1.85  1.4  1.2 m, equivalent to the interior volume of the referenced car. The temperature at four different locations in the cabin, covering the driver seat, front passenger seat and two rear seats, were recorded with RTD sensors of type Pt1000. The mean value of these four temperatures represents the average cabin temperature. In addition, a radiant heater with 550 W power output was installed in the cabin to simulate the space cooling load. The power output of the heater was modulated by a computerized Pulse-Width Modulation (PWM) signal using an on/off relay. The period of the PWM signal was set as 20 s and its duty cycle can be varied from 5% to 100%. The setting of the 5% lower limit was intended to protect the relay from drastic switching action. Other measurement instruments in the system included a flow rate sensor, pressure transducers, temperature and humidity sensors. All the sensor signals were recorded, monitored, and displayed in real time through a National Instrument (NI) compact data acquisition (DAQ) system. This DAQ system was equipped with built-in signal conditioning circuits such as an anti-aliasing filter. 3. Adaptive ANN based model predictive control As depicted in Fig. 2, the proposed algorithm in this study is an amalgamation of four major components: a reference model, a cost function optimizer (CFO), an offline trained and an online trained ANN predictive model. The reference model is incorporated to specify the desired performance of the plant. The CFO serves to determine the best control input needed to produce the desired trajectory of the AAC system, while the neural network models are used to predict the plant output over a receding prediction horizon [22]. In this figure, r is the set point of the cabin temperature, yn

represents the reference trajectory, u is the control input voltage of the VSC, z1 denotes the time delay operator that store previous value of the model input signal, ym and b y m are the actual and predicted cabin temperature respectively. The dotted arrow line represents the training of the ANN in real time using past prediction errors. The general working principle of the A-NNMPC algorithm at time step n is summarized in Fig. 3. It involves the ANN prediction, cost function optimization, plant control and training operation, which are performed iteratively in order to achieve optimum cabin comfort control. The switching between these operations is realized by the use of two double-pole double throw switches (S1 and S2), while the selection of the plant predictor out of the two ANN variants: online trained ANN and offline trained ANN, is determined by the position of S3. The control system is initially operating with an offline trained ANN predictor. Only when indications are that the ANN model is readily trained in real time with sufficient data is the model transferred to become the tuner model. Even though this flow chart is meant for the A-NNMPC algorithm, operation of O-NNMPC can be achieved using the identical working principle by skipping the training operation. In the following subsections, the implementation of the A-NNMPC algorithm is further discussed by presenting the details of each module in the control algorithm, namely the reference model, the CFO algorithm and the ANN online training scheme. 3.1. Reference model The reference model is intended to produce the reference trajectory ym that prescribes the behaviour of the closed loop system. Since the step response results in a previous study [8] indicate that the dynamics of the cabin temperature can be approximated as a first order system, in this work, the discrete reference model is

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Fig. 2. Schematic of the A-NNMPC control scheme.

designed with similar model order to introduce the reference trajectory over the prediction horizon Np: TTs ðnþjÞ

yn ðn þ jÞ ¼ rðn þ jÞ þ e

ref

ðyi  rðn þ jÞÞ

j ¼ 1; …; Np

(1)

where Ts is the sampling time, Tref is the model time constant, r is the target set point, yi is the initial model output and n is the present time instant. The time constant Tref can be varied to specify the desired performance of the plant. Lower value of time constant can force the system to have a more aggressive response and therefore lead to a shorter rise time. However, if the reference trajectory is much faster than the process, the system may behave as if a step input has been introduced as the reference trajectory. 3.2. Neural network architecture In this work, an ANN based nonlinear autoregressive exogenous (NARX) model is implemented as a plant predictive model in the

control scheme to predict the system output over a specified prediction horizon. The predicted output of this class of ANN at time instant n is given mathematically by:

   b y m ðnÞ ¼ f uðn  1Þ; /; uðn  mu Þ; ym ðn  1Þ; /; ym n  my (2) where u and y denote the inputs and outputs of the system respectively and f(.) represents the nonlinear function of its arguments, mu and my specify the model orders. Dynamic network model can be applied in two different network configuration: series parallel and parallel architectures. The series parallel architecture illustrated in Fig. 4(a) is an NARX representation of Eq. (2), which performs its prediction based on the past measured outputs and inputs. In view of its purely feedforward architecture, standard backpropagation can easily be implemented for the training of ANN with the series parallel architecture. However, such expression of the ANN predictor is only limited to one-step-ahead prediction. For

Fig. 3. Flowchart of the A-NNMPC algorithm.

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Fig. 4. Network architecture of the MLP based NARX model.

the implementation of multiple-steps-ahead predictor, the series parallel architecture is converted to a parallel network (see Fig. 4(b)), which performs the multi-steps-ahead prediction using the previous predicted outputs as part of the model inputs. The isteps-ahead predictor can be defined as:

 b y m ðn þ i  1Þ; /; y m ðn þ iÞ ¼ f uðn þ i  1Þ; /; uðn  mu þ iÞ; b   b y m k  my þ i

(3)

Since the proposed control system involves online training and multi-step ahead prediction operation, the NARX network is applied in such a way that it is convertible from one to the other according to the need of the operation. The ANN model structure opted in this research is a three layered multilayer perceptron (MLP) model with model order mu ¼ 5,my ¼ 3 and five hidden neurons. This model architecture is determined based on the suggestion in previous empirical studies [8]. The suggested model structure has been proven to deliver onestep-ahead and 20-steps-ahead prediction of the cabin temperature to a satisfactory degree. With reference to Fig. 2, switches S1 and S2 are set to the ANN model during the prediction operation. The input of ANN model with the parallel configuration is first initialized with the past data sample collected from the AAC system. It performs the multiplesteps-ahead prediction using the optimal control input delivered from the CFO. 3.3. Cost function optimization There are several nonlinear minimization algorithms that have been implemented in ANN based predictive control such as gradient descent, Newton-Rahpson and LevenbergeMarquardt algorithms [23]. In this study, the Newton-Rahpson method, a quadratically converging algorithm, has been chosen to optimize the cost function. It is reported that this optimization technique can achieve convergence with significant reduced number of iteration in comparison to other technique [22]. Despite the expensive computation of the Hessian and its inverse in this algorithm, Newton-Rahpson appears to be a faster and more efficient

algorithm for real time predictive control due to the lower number of optimization iterations. The operation of cost function optimizer (CFO) is activated by setting S1 and S2 to the ANN predictive model. Using the system output prediction produced by the ANN model and the reference trajectory from the reference model, the optimization routine computes the optimal intermediate control input that minimizes the specified cost function over a receding prediction horizon. The objective function of interest to this application is.

J¼

Np X

½yn ðn þ jÞ  b y m ðn þ jÞ

2

j¼1

þ

Nu X

lðjÞ$½uðn þ jÞ  uðn þ j  1Þ2

(4)

j¼1

where Nu is a parameter specifying the control horizon, Np is the prediction horizon, yn is the reference trajectory, b y m is the ANN predicted output, u is the control input and l is the weighting factor, which acts as a damper on the predicted control input. Proper setting of weighting factor can avoid excessive movement of the compressor speed, resulting in the longer lifetime of the actuator and a more stable system output. Using Newton-Rahpson as the optimization algorithm, the objective function J is minimized iteratively to determine the optimal control input. The control input vector U at each iteration k is denoted as.

3 uðn þ 1Þ 6 uðn þ 2Þ 7 7 UðkÞ ¼ 6 5 4 « uðn þ Nu Þ 2

k ¼ 1; /; kmax

(5)

j ¼ 1; /; Nu

(6)

and subject to

umin  uðn þ jÞ  umax

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where kmax is the predefined maximum iteration, umin and umax are the upper and lower limit of the control input defined by the maximum and minimum input control voltage of the VSC. The Newton-Rahpson update rule for U(kþ1) is.

Uðk þ 1Þ ¼ UðkÞ 

d2 J ðkÞ dU 2

!1

dJ ðkÞ dU

(7)

where dJ/dU(k) and d2J/dU2(k) are respectively the Hessian and Jacobian matrix, which involve the first second derivative of the cost function with respect to the control input vector. Detailed computational issues of the Hessian and Jacobian are addressed in Ref. [22]. The optimisation step using Eq. (7) is iterated until the maximum iteration kmax is exceeded and optimum control input vector is readily solved. Subsequently S1 and S2 (see Fig. 2) are set to the plant and the plant control operation is performed by delivering the first control input u(n þ 1) to the AAC system for the regulation of the compressor speed. 3.4. ANN online training A sliding stack window technique is adopted to manage the training data during the ANN online training process. With the proposed technique, a constant stack size of previous training data is stored and it is updated continuously in a first-in first-out fashion, by which the data set is augmented by the newest data, replacing the oldest. As a result, the computational effort of the training scheme remains unchanged and the model is more sensitive to the new information. The main drawback of this method is that the model may perform erroneously when the system remains in steady state over a long period, as the model is consistently trained with data sets lacking of persistent excitation. However this condition rarely takes place in the AAC system as it is consistently subjected to varying degrees of environmental disturbances that preserve the rich input excitation required for the system identification [17]. In this work, a stack window size with 125 data points and sampling interval 8 s is predefined. It takes approximately 17 min of waiting time for the controller to introduce an online trained ANN as the plant predictor. Before the online trained ANN is ready for control implementation, the offline trained ANN is temporarily used for system output prediction as well as the calculation of the Jacobian and Hessian in Eq. (7). The backpropagation algorithm is the well-known training algorithm implemented as the standard training method for a feedforward neural network with more than one layer of neurons [24]. In this study, the backpropagation algorithm with LevenbergeMarquardt (LM) learning method is adopted to update the synaptic weights of the ANN due to its faster speed of convergence in comparison to other methods, such as steepest descent, GaussNewton and quasi-Newton methods [25]. The commonly used cost function for the ANN training is specified as the mean square error:

X 1 nþN VðnÞ ¼ eðiÞ2 2N i¼n

(8)

where J is the Jacobian matrix, E is the error vector, I is the identity matrix, and m is denoted as the combination coefficient, which is introduced as a positive real number to ensure that the approximated Hessian matrix JjT Jj þ mI is always invertible. In this study, this coefficient is initialized as 1 and it is multiplied by 10 whenever an update results in the increment of the cost. On the other hand, m is divided by 10 when a step leads to the cost decrement [25]. The LM training at each time instant is terminated when the maximum number of iteration jmax is exceeded or when the cost in Eq. (8) drops below the predetermined threshold. 4. ANN based system identification Offline training of the ANN model is not only important for the O-NNMPC algorithm, but also to ensure a stable control by ANNMPC during the first 17 min before the online trained ANN model is ready for implementation. In this study, amplitude modulated PRBS (APRBS) was applied to generate series of amplitude- and hold time-varying compressor set speeds over the entire operating space, which served as the excitation signal to the AAC rig. Open loop experimental tests were conducted to obtain a total of 2000 data sets, which were divided into training set (75%) and testing set (25%). Testing set is the unseen data used to evaluate the generalization capability of the ANN model. In order to avoid overfitting of the ANN, 20% of the training data was reserved for validation purpose during the training phase, in which early stopping was executed after the performance with the validation test stops improving. The working conditions of the experimental rig during the data collection were specifically chosen to represent as closely as possible to the conditions encountered by an AAC system. In order to simulate a late morning drive at moderate speed 60 km/h, the flow rate and temperature of the incoming air towards the condenser were fixed at 3.0 m/s and 30  C respectively [21]. The incoming air temperature of the evaporator was set at 30  C, assuming that air circulation in the evaporator ducting system operates with the supply of ambient air. The face air velocity of the evaporator was set to ‘high speed’, equivalent to air stream crossing the vent at speed value 4.25 m/s. The thermal load in the cabin was set to the minimum value by adjusting the heater duty cycle to 5%. Relative humidity inside the closed loop ductwork was maintained in equilibrium state within 50%e60%. Two evaluation tests namely one-step-ahead and 10-stepsahead prediction tests were carried out to examine the prediction performance of the ANN model. The performance criteria taken into account included the mean square error MSE and the linear correlation coefficient R. Linear correlation coefficient has been used to measure the strength of a relationship between the predicted outputs of the ANN model and the target values. The mathematical formula used to compute R for n data sets is:

P P P b n ym b ym y m  ym qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P P P 2 P 2 2 2 ymÞ n ym  ð ym Þ n b ym  ð b

m ¼ 1; :::; n (10)

where N is the stack size of the training data and e(i), the error term at time instant i is defined as the difference between the measured and the predicted output value. At iteration j, the connecting weight vector is computed using the LevenbergeMarquardt update rule as:

 1 Wj ¼ Wj  JjT Jj þ mI Jj Ej

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(9)

where b y m is the ANN's predicted output and ym is the target value. The comparison between the experimental and the predicted cabin temperature with respect to the modulated compressor speed is shown in Fig. 5 and Fig. 6. As illustrated in these figures, the ANN based NARX model performed the one-step-ahead and 10-steps-ahead prediction of the training and testing data to a satisfactory degree, as the predicted outputs tracked closely the plant output. Prediction of the

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Fig. 5. Comparison between the one-steps-ahead AAC system output prediction by the ANN model and the experimental results.

testing data with low order of prediction error implies a good generalization capability of the ANN model. It is worth mentioning that the feedback of the past predicted output using ANN with parallel architecture during 10-steps-ahead prediction resulted in an accumulation of prediction error, therefore leading to a poorer overall prediction performance. Fig. 6 provides a good virtualisation of the error accumulation by the zoom in predicted output trajectory in the form of sawtooth wave. Each cycle of the sawtooth wave trajectory represents a complete 10-steps-ahead prediction. The predicted output deviated from the plant output due to the accumulation of the prediction errors. Error resetting took place at the beginning of each new prediction cycle, as the input layer of the model was reinitialised with the sample data. The low order of the performance indices MSE in Table 1 infers that the MLP based NARX model was capable of capturing the underlying dynamic behaviour of the plant to a satisfactory accuracy. In addition, the correlation coefficients of all tests were close to unity, indicating a strong positive linear correlation between the predicted output and plant output.

5. Results and discussion In this section, several tests were performed using the AAC rig in order to examine the control performance of the proposed controller. In order to show the advantages of the A-NNMPC controller, comparative assessment was carried out between the proposed A-NNMPC and two other control methods, namely the ONNMPC control system using the offline trained ANN model and the conventional PID controller tuned using the Ziegler Nichols method. The parameterisation of both controller variants is tabulated in Table 2. A-NNMPC and O-NNMPC controllers shared the same control parameter settings for all of the experimental tests to avoid biased conclusion due to comparison of both controllers with different parameterisation. These control parameters were determined empirically using the trial and error method. Nominal test conditions are readily defined in Section 4, under which the system identification was carried out. External disturbances were introduced during the experiments by manipulating

Fig. 6. Comparison between the 10-steps-ahead AAC system output prediction by the ANN model and the experimental results.

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Table 1 Performance indices of the ANN model in the prediction tests.

One-step-ahead 10-steps-ahead

MSETrain

MSETest

RTrain

RTest

3.163  106 3.163  104

4.069  106 1.650  104

0.9999 0.9997

0.9999 0.9992

the evaporator air speed, incoming air temperature of evaporator and condenser, and the cabin thermal load. The time interval between two subsequent control actions of compressor speed was set at 8 s, identical to the data sampling rate for the ANN system identification. In this study, quantitative criteria adopted to measure the performance of the respective controller comprise the rise time tr, the absolute overshooting/undershooting Mp and the Integral Absolute Error (IAE). The IAE is computed by integrating the absolute value of the error over time as follows:

Zt2 IAE ¼

jyn  ym j dt

(11)

Fig. 7. Reference tracking by A-NNMPC and O-NNMPC under nominal condition.

t1

where t1 and t2 represent the start and end time of the integration process. Activation of the integration is triggered during the step change of the set point or the moment when disturbances are first introduced according to the need of the respective test evaluation. Termination of the integration is normally set when the process has reached its settling condition. 5.1. Comparison of A-NNMPC and O-NNMPC In this section, comparative assessment was performed on the proposed controller and the O-NNMPC control scheme. This investigation was intended to show the necessity of using an online trained ANN in the predictive controller. Four different tests were carried out to evaluate the capability of the proposed controller in tracking the changing reference as well as rejecting the disturbances. Details of each test are listed as below: 1) 2) 3) 4)

Reference tracking under nominal condition (Exp. I). Disturbance rejection with constant reference (Exp. II). Time varying disturbance rejection (Exp. III). Disturbance rejection with changing reference (Exp. IV).

5.1.1. Reference tracking under nominal condition (Exp. I) The control performance of the proposed controller A-NNMPC and the offline trained neural predictive controller O-NNMPC was examined under nominal condition using the step change in the set point. As seen in Fig. 7, the cabin temperature setting was initially fixed at 21  C. At 350 s, the set point was altered to 23  C, and both controllers responded immediately by simultaneously decreasing

Table 2 Parameterisation of the controllers. Controller

Control parameter

Value setting

O-NNMPC & A-NNMPC

Prediction horizon Np Control horizon Nu Weighting factor l Max. number of optimization iteration kmax Max. number of training iteration jmax P I D

8 8 0.3 10

PID

the compressor speed to the minimum limit to ensure that maximum speed is achieved by the system in approaching the set point. Based on the performance indices presented in Table 3, ONNMPC responded to the set point changes more aggressively by reaching the set point within a shorter rise time. However, this took place at the expense of a higher overshooting, and this was then followed by a lower undershooting. On the other hand, A-NNMPC delivered a better overall control performance by achieving a lower IAE and over/undershooting. The improvement shown by the ANNMPC over O-NNMPC can be explained by the insufficient offline ANN training as well as the unmeasured disturbances during the experimental test, which eventually resulted in poorer control performance of the O-NNMPC. All these factors can be overcome by the implementation of ANN online training, as latest information regarding the plant was continuously delivered to the predictive model by the online training at each sampling interval. 5.1.2. Disturbance rejection with constant reference (Exp. II) This disturbance rejection test was conducted by introducing the abrupt change of evaporator speed and the set point remained unchanged throughout the experiment. Prior to the introduction of disturbance, the cabin temperature was maintained steadily at 22  C under nominal conditions. At 600 s, the AAC system was subjected to disturbance by switching the evaporator fan mode from ‘high speed’ to ‘medium speed’, equivalent to a decrement of fan speed from 4.25 m/s1 to 3.00 m/s1. As depicted in Fig. 8, the cabin temperature gradually decreased in response to the disturbance. Obviously, the O-NNMPC has failed to bring the cabin temperature back to the set point 22  C throughout the experiment period. Steady state cabin temperature of 21.75  C was attained at 1100 s with 0.25  C tracking errors. Since the ANN model used in the O-NNMPC was offline trained using the data under one operating condition, the changing evaporator fan

Table 3 Performances measure of the A-NNMPC and O-NNMPC in different test conditions. A-NNMPC

10 2.3 54.0 13.5

Exp. I Exp. II Exp. III

O-NNMPC

tr (s)

Mp ( C)

IAE

tr

Mp( C)

IAE

210 e 152

0.05 0.25 0.06

133 79 72

200 e 173

0.09 0.3 0.13

152 300 755

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that A-NNMPC outperformed O-NNMPC by delivering satisfactory control actions to reject the sudden operational disturbance (see Table 3).

Fig. 8. The response of O-NNMPC under disturbance of step change in evaporator fan speed.

speed caused a poorer model representation and therefore leading to the incapability of the O-NNMPC to trace the reference trajectory. From Fig. 9, it can be seen that A-NNMPC delivered stable and improved steady state response. Initially, the cabin temperature deviated from the reference when the system was subjected to the disturbance, but it was successfully regulated back to the desired value within 175 s. Subsequently the temperature oscillated around the set point with decreasing amplitude. The cabin temperature settled down at 1300 s and remained within 0.05  C tolerance thereafter. Based on the decreasing prediction error shown in Fig. 9(b), it is clear that the continuous online weights training using the feedback prediction error improved the prediction performance of the ANN predictor and therefore resulting in a convergence of the temperature oscillation to the reference point. This test indicates

Fig. 9. The response of A-NNMPC under disturbance of step change in evaporator fan speed.

5.1.3. Time varying disturbance rejection (Exp. III) In this test, the cabin temperature was initially maintained at 23.5  C and the cabin thermal load was kept at nominal state by setting the duty cycle of the heater at 5%. At 200 s, the set temperature was reduced to 22.5  C. Simultaneously, the duty cycle of the heater was increased from 5% to 30% for the next 2000 s. As seen in Fig. 10, after all the changes were imposed, the proposed controller ANNMPC responded immediately by regulating the compressor speed accordingly. The cabin temperature reached the new set point in 150 s, and steadily maintained within the tolerance 0.1  C for the rest of the test period. It can be seen that the compressor input speed continued to increase from t ¼ 600 s to t ¼ 2000 s, even though the cabin temperature remained in a steady state within this period. The compressor speed was forced to increase in an attempt to raise the cooling capacity, thereby compensating the increment of the thermal load produced by the heater. On the other hand, the O-NNMPC managed to bring the cabin temperature back to the set point at t ¼ 375 s, but it failed to hold to this value thereafter. The relatively lower increment rate of the compressor speed from t ¼ 600 s till t ¼ 2200 s was not sufficient to balance the increasing thermal load. Consequently, the cabin temperature continued to increase as the experiment went on. The disturbance rejection characteristics exhibited by O-NNMPC in this test indicates the inadequacy of using offline trained predictive model in handling the control task under time varying disturbances. 5.1.4. Disturbance rejection with changing reference (Exp. IV) The aim of this disturbance rejection test is to check whether the proposed controller is able to track the changing reference signal under the presence of disturbance. The disturbance was induced at t ¼ 0 by having the incoming air temperature of the heat exchangers set at 34  C, instead of the nominal state 30  C. In other words, a mismatch between the initial state of the ANN model and the actual testing condition was imposed during the initialisation of the controller. To make the controlling task more challenging, the set point was alternately switched between 21  C and 22  C every 500 s. As shown in Fig. 11, the O-NNMPC was first implemented and

Fig. 10. The response of A-NNMPC and O-NNMPC in the presence of time varying disturbance.

B.C. Ng et al. / Applied Thermal Engineering 73 (2014) 1242e1252

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Fig. 11. Disturbance rejection by O-NNMPC and A-NNMPC at changing references. Fig. 12. Cabin temperature control under the effect of disturbance using A-NNMPC and PID controller.

the cabin temperature was poorly regulated in the first cycle. Activation of the ANN online training was triggered at t ¼ 1000 s and significant improvement in term of rise time, over/undershooting and IAE was achieved by A-NNMPC in the following two cycles. Optimal control performance was attained in the third cycle with minimum rise time and trivial overshooting. In addition, the control system achieved its lowest IAE at 45 and 35 for both set points in the third cycle (see Table 4). The continuous improvement delivered by the A-NNMPC is attributed to the rich excitation induced by the periodical changes in set point, which had in turn facilitated the ANN online training. As a result, optimal control of the AAC system was delivered in the third cycle when model mismatch was minimized as a result of the adequate information provided for the adaptation of the ANN model. 5.2. Comparison of A-NNMPC and PID controller In this test, the set point was alternately switched between 23.5  C and 24.5  C every 500 s. The incoming air temperature of the evaporator was maintained at 30  C. At time t ¼ 1500 s, a heater placed upstream of the evaporator was switched on in order to introduce additional 500 W thermal load on the heat exchanger. It can be observed in Fig. 12 that both controllers responded to the increment of thermal load by increasing the average compressor speed in order to maintain the demanded cooling capacity. The ANNMPC brought the cabin temperature to the set points by the gradual adjustment of the compressor, which gave smooth control response. The PID controller in turn brought the cabin temperature to the set point by rigorous regulation of the compressor speed, which resulted in shorter rise time and significant over/undershooting of the process response. Table 5 shows the quantitative results of the control performance for each control scheme. Cycle A and cycle B represent the process response before and after the introduction of the disturbance respectively. As compared to the

Table 4 Performance indices of the controllers in the disturbance rejection test at changing references. Cycle (controller)

1 (O-NNMPC)

2 (A-NNMPC)

3 (A-NNMPC)

Ref. ( C) tr (s) Mp( C) IAE ( C)

21 e e 82

21 220 0.06 61

21 218 0.03 45

22 120 0.16 48

22 150 0.02 44

22 140 0.03 35

PID controller, A-NNMPC delivered satisfactory results with less over/undershooting and lower IAE values for both cycles. These results signify the superiority of the proposed controller over the conventional PID controller in both cases, where the system worked under nominal operating condition as well as under the presence of disturbance. 6. Conclusion This study investigated the feasibility of implementing an adaptive neural network based predictive controller in AAC thermal control system. The predictive control scheme was realized by adopting the Newton-Rahpson method to solve the nonlinear cost optimisation problem. An ANN based NARX model was incorporated as a plant predictive model to provide the future plant output predictions as well as process knowledge to the controller. In order to enhance the robustness of the controller with respect to model mismatch and time varying disturbances, online training of the ANN predictive model was implemented using the LevenbergeMarquardt algorithm and sliding stack window technique. The performance of the ANN model was verified with the one-stepahead and 10-steps-ahead prediction tests using the data recorded from an AAC experimental bench. Several experimental tests involving set point tracking and disturbance rejection were carried out on the proposed adaptive controller A-NNMPC. Comparative assessments were performed on the proposed A-NNMPC and two other control schemes, namely the O-NNMPC with offline trained ANN predictive model and the conventional PID controller tuned using the Ziegler Nichols method. The experimental results indicated that A-NNMPC outperformed O-NNMPC and PID controller due to its capability to Table 5 Performance indices of PID and A-NNMPC control schemes in the reference tracking test under the effect of disturbance. Cycle

A

Ref ( C)

24.5

23.5

24.5

23.5

145 0.55 117.5 325 0.06 57.4

140 0.50 114.2 210 0 51.5

115 0.58 125 130 0.16 73.8

210 0.48 134 320 0 80.0

PID

A-NNMPC

tr (s) Mp( C) IAE ( C) tr (s) Mp( C) IAE ( C)

B

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adaptively capture the time varying dynamics of the AAC system. The poorer performance of the O-NNMPC was attributed to the mismatch between its offline trained ANN model and the actual AAC system particularly when the operating condition was drifted far away from the training point. PID controller with fixed control parameters was also found to be inadequate in handling the complex and highly nonlinear AAC thermal control process. Since the AAC system operates under a wide range of operation conditioning, it would be impractical to carry out system identification covering the entire operating range. For this reason, ANNMPC is a potential control scheme to be applied in AAC thermal control system due to its adaptation capability. Future work is to be directed towards the implementation of the proposed controller on a vehicle with exposure to actual environmental disturbance. Acknowledgements The authors wish to thank the Ministry of Higher Education (MOHE) and Universiti Teknologi Malaysia (UTM) for providing the research grant and facilities. This research is supported using UTM Research University grant, Vote No. 03H09. References [1] J.P. Rugh, T.J. Hendricks, Effect of Solar Reflective Glazing on Ford Explorer Climate Control, Fuel Economy, and Emissions, Society of Automotive Engineers (SAE), 2001. [2] H. Nasution, M.N.W. Hassan, Potential electricity savings by variable speed control of compressor for air conditioning systems, Clean. Technol. Environ. Policy 8 (2006) 105e111. [3] L.O.S. Buzelin, S.C. Amico, J.V.C. Vargas, J.A.R. Parise, Experimental development of an intelligent refrigeration system, Int. J. Refrig. 28 (2005) 165e175. [4] S.A. Tassou, T.Q. Qureshi, Performance of a variable-speed inverter motor drive for refrigeration applications, Comput Control Eng. J. 5 (1994) 193e199. [5] O. Sirch, 48 Volt and its threats and opportunities, in: Automotive 48 V Power Supply System, vol. 1, 2013. Frankfurt/Main, Germany. [6] J. Zhang, G. Qin, B. Xu, H. Hu, Z. Chen, Study on automotive air conditioner control system based on incremental-PID, Adv. Mater. Res. 129-131 (2010) 17e22. [7] B.C. Ng, I.Z.M. Darus, H.M. Kamar, M. Norazlan, Dynamic modeling of an automotive air conditioning system and an auto tuned PID controller using extremum seeking algorithm, in: IEEE Symposium on Computers & Informatics, Langkawi, Malaysia, 2013, pp. 92e97.

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