a hybrid digital proportional integral closed loop …control strategy of the mimo centrifugal...

International Journal of Computer Science and Applications,

©Technomathematics Research Foundation

Vol. 16, No. 1, pp. 86 – 104, 2019

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A HYBRID DIGITAL PROPORTIONAL INTEGRAL CLOSED LOOP

CONTROL STRATEGY AND MIMO ADAPTIVE NEURAL NETWORK FUZZY

INTERFERENCE SYSTEM MODEL FOR A CENTRIFUGAL CHILLER

ROXANA-ELENA TUDOROIU†

Mathematics and Informatics, University of Petrosani,

20 University Street, Petrosani, 332006, Romania

[email protected]

MOHAMMED ZAHEERUDDIN

Building Civil and Environmental Engineering, Concordia University,

1455 De Maisonneuve West Blvd, Montreal, H3G 1M8, Canada

[email protected]

SORIN MIHAI RADU

Mechanical and Electrical Engineering, University of Petrosani, 20 University Street, Petrosani, 332006, Romania

[email protected]

NICOLAE TUDOROIU Engineering Technologies Department, John Abbott College

2127 Lakeshore Road, Sainte-Anne-de-Bellevue, QC, H9X 3L9, Canada

[email protected]

DUMITRU DAN BURDESCU

Software Engineering Department, University of Craiova, Craiova, 200585, Romania

[email protected]

The basic idea of this paper lies in encouraging results disseminated in the recent paper presented in

FedCSIS 2018 conference on a significant improvement in MIMO ARMAX models’ accuracy,

simplicity and rapid implementation in real time by developing one of the most accurate adaptive

neuro-fuzzy inference system modelling, suitable for modelling the nonlinear dynamics of any

process or control systems. The novelty of this paper is a further investigation of the use and the

benefits of a hybrid closed-loop control strategy structure consisting of the improved MIMO ANFIS

model in combination with a digital PI controller in terms of performance tracking accuracy,

transient convergence speed and robustness. The effectiveness of this control strategy structure is

demonstrated by extensive simulations conducted in this direction on a MATLAB real-time

implementation platform and comparison results obtained by another control strategies.

Keywords: centrifugal chiller; PI control; Artificial Neural Network; Fuzzy Inference System;

ANFIS model; system identification; open and closed-loop control; ARMAX model;

1. Introduction

This paper investigates the use of the results disseminated in the last year

international conference paper, FedCSIS 2018, September 9-12, from Poznan, Poland.

They are the fruit of a rigorous investigation on a new modelling design methodology

to be applied on nonlinear systems dynamics, such as an adaptive neuro-fuzzy inference

mailto:[email protected]




A hybrid digital proportional integral closed loop control strategy

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system (ANFIS) models, very useful for a large amount of control systems applications

from different fields [Tudoroiu et al., (2018b)]].

Essentially, the new modelling approach is a significant enhancement of linear

discrete-time based polynomials, such as an Autoregressive Moving Average with

exogenous input (ARMAX), or simple an Autoregressive with input stimulus (ARX)

polynomials models generated by using the most popular least squares estimation (LSE)

method [Tudoroiu et al., (2018a)]. Additionally, ANFIS models are preferred for their

simplicity and fast real-time implementation, based on the typical functions imported

from System Identification ToolboxTM integrated in a MATLAB R2018b platform

[Tudoroiu et al., (2018b)]. Basically, these models are generated as a hybrid combination

of two system models, one of them is an artificial neural network (ANN) and the second

is a fuzzy logic (FL) system model as is well documented in [Zurada, (1992);

Zaheeruddin and Tudoroiu, (2004)], and [Radu et al., (2017)] respectively. The first

ANN system model was developed for information processing and is based on human

brain features, i.e. through a high processing capacity of parallel and distributed

information, of high complexity and nonlinearity, as well as local information processing

and adaptation. Thus, the ANN system model is designed to mimic the human brain systems in building architectural structures, learning and operating techniques.

Nowadays, we are truly fascinated by the promising future of applying Artificial

Intelligence (AI) technology almost everywhere by widespread implementation of

practical speech, machines learning and translations, autonomous vehicles and robotics in

households and industry. At the same time, as one of the AI's main areas, ANNs have

also made significant advances in architectural design, learning and operating techniques,

and can thus solve problems that are hard to solve or difficult to calculate traditional

[Zurada, (1992)]. Furthermore, the ANNs have been widely accepted by scientists due to

their accuracy and ability to develop complex nonlinear models and to solve a wide

variety of tasks.

Some preliminary results obtained and related to ANN in our academic research

activity over the years can be found by the reader in [Zaheeruddin and Tudoroiu, (2004)].

The FL modelling technique as a powerful tool for the formulation of expert

knowledge is a combination of imprecise information from different sources. As is

mentioned in [Tudoroiu et al., (2018b)] the FL is a suitable modelling approach for a

“complicated system without knowledge of its mathematical description”.

An interesting FL modelling approach we have developed in the research papers

[Tudoroiu et al., (2016), Radu et al., (2017)] to improve the performance of a hybrid

fuzzy sliding mode observer estimator that controls the speed of a dc servomotor in

closed-loop.

In the present research paper, the proposed SISO hybrid closed-loop control structure

is an integrated structure of a Proportional Integral and Derivative (PID) digital controller

and an ANFIS model of a centrifugal chiller system, chosen as a case study since it is one

of the most seen in Heating Ventilation and Air Conditioning (HVAC) system

applications. The centrifugal chiller is a multi-input, multi-output (MIMO) plant of a

great complexity and high nonlinearity dynamics, as is developed in detail in the research

paper [Tudoroiu et al., (2018a)]. As is stated in [Tudoroiu et al., (2018b)], the centrifugal

chillers are the most widely used devices since “they have high capacity, reliability, and

require low maintenance”. An extensive literature review made in [Tudoroiu et al.,

(2018b)] has shown a significant amount of work done in a classic way on transient and

steady state modelling of centrifugal chillers, mainly in [Braun, (1987); Beyene, (1994);

Tudoroiu et al.

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Gordon, (1995); Browne and Bansal, (1998); Popovic and Shapiro, (1998); Svensson,

(1999); Wang and Wang, (2000); Swider, (2001); Bendapudi, (2005); Pengfei, (2010)].

Additionally, it can be enlarged with the most recent investigations on a combined hybrid

control ANFIS system model for single-input, single-output (SISO) or for MIMO

models, integrated in different closed-loop control structures with centrifugal chillers

plants. An interesting integrated ANFIS modelling methodology is developed in

[Gholamrezaei and Ghorbanian, (2015)] where the learning capability of ANN is

integrated to the knowledge aspect of fuzzy inference system (FIS) to “offer enhanced

prediction capabilities rather than using a single methodology independently”.

Similar, in [Zhou, (2009)] a combined neuro-fuzzy modelling technique is integrated

to develop a fault detection, diagnosis and isolation (FDDI) strategy for a centrifugal

chiller control system. Concluding, there is a great opportunity for us to use the research

preliminary results obtained in this field, such that to explore, develop and implement in

real-time the most suitable and intelligent modelling and control strategies applicable on

centrifugal chillers control systems. The remainder of the paper is structured as follows.

In Section 2 open-loop simulations results for nonlinear chiller plant are presented. In

section 3 two SISO ARMAX and ANFIS models are generated and are shown the model

validation simulations results compare to the input-output measurements data collected

by an extensive number of MATLAB simulations in closed-loop for the nonlinear

centrifugal chiller plant. In Section 4 is developed an improved PID ANFIS closed-loop

control strategy of the MIMO centrifugal chiller plant control system as an intelligent

combined hybrid structure of ANFIS model generated in Section 3 and a standard digital

PID controller. The implementation of simulation results in real-time on the MATLAB

R2018b software platform of both PID ANFIS SISO closed-loop control strategies of the

centrifugal chiller plant are shown in the same section with a rigorous performance

analysis by comparison to the first two PID closed-loop control strategies introduced at

the beginning of Section 4 in terms of tracking accuracy, transient convergence speed and

robustness will be done. Finally, the Section 5 concludes the relevant contributions of this

research paper.

2. Input-Output Measurements Dataset – Closed-Loop Simulations

In this section is introduced a systemic description of the centrifugal chiller plant as

an oriented object in a closed-loop control system. Also, the setup to get the input-output

measurements dataset needed to build the MIMO ARX chiller plant model is briefly

described. A centrifugal chiller standard PI closed-loop control system can be considered

as a MIMO centralized system that can be represented by an interconnection of two main

standard PI closed loops control subsystems. The first control subsystem is a chilled

water temperature standard PI control loop inside an evaporator, and the second one is a

refrigerant liquid level standard PI control loop inside a condenser, as is shown in

[Tudoroiu et al., (2018a)].

Also, the overall model dynamics of the centrifugal chiller plant is of great

complexity in terms of dimension and encountered nonlinearities, thus a tight control of

the both closed-loops is required. This is possible only if for each closed-loop control

subsystem a significant improvement in terms of accuracy, dimensionality and of

implementation simplicity of each dynamic model is done through a suitable modelling

approach. Concluding, the centrifugal chiller efficiency can be improved by


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implementing advanced model-based controller design strategies, so the development of

high-fidelity centrifugal chiller dynamic model becomes a priority task in our research.

The readers interested in modelling details can access the full dynamic model of

centrifugal chiller under our investigation and some preliminary results on ARX and

ARMAX modeling approach in Annex 1 of our research work [Tudoroiu et al., (2018a)],

pp. 299-305. The first step of our control design is based on this nonlinear dynamic

model represented as a SIMULINK dynamic model on MATLAB R2018b software

platform, as is shown in in Fig. 1, Fig. 2 and Fig.3.

Fig.1. SIMULINK model of centralized centrifugal chiller in closed-loop

Fig.2. SIMULINK models of the PI control blocks (MATLAB Function) and Evaporator and Condenser

subsystems outputs block (MATLAB Function)

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Fig.3. SIMULINK model of the PI control blocks

Legend: kpT is the proportional component of Temperature PI control law, and kiT is the integral component

of the Temperature PI control law. For level control PI law, the index subscripts are replaced by kpL, kiL.

The SIMULINK model of nonlinear centrifugal chiller dynamics in a closed-loop

control structure is a very useful architecture structure setup to get the input-output

measurements dataset to build ARX or ARMAX models, i.e. linear polynomials models

represented in discrete time, characterized by a lower dimension, and significant

simplicity for real-time implementation. Based on these models can be built several

MIMO closed-loop control strategies, like those built in Section 3. Since the overall

chiller plant in fact is a distributed control system, and even if in “real-life” there exist

some interferences between the both control loops without significant effects, though the

loops can be assumed to be independent of each other, i.e. as completely two decoupled

SISO models, as is mentioned also in [Tudoroiu et al., (2018a)]. Through extensive

closed-loop simulations is generated the most appropriate input-output measurements

dataset required to build the linear SISO polynomial ARMAX models for both control

loops of the centrifugal chiller plant, i.e. for chilled water temperature and for refrigerant

liquid level respectively.

Consequently, a high accuracy model, of significant reduced dimensionality and

great implementation simplicity, capable to capture entire dynamics of the overall MIMO

chiller system under various operating conditions is essential to give more flexibility for

closed-loop control design strategies. In the Figs. 4-7 are shown the input relative speed

of the compressor Ucom, the output chilled water temperature Tchw, i.e. the input-output

of the SISO Evaporator control subsystem loop (Fig.4 and Fig.5), the input opening of

the expansion valve u_EXV, and the output refrigerant liquid level L, i.e. the input-output

of the SISO Condenser control subsystem loop (Fig.6 and Fig.7) respectively.


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Fig.4. The Evaporator input -compressor relative speed, Ucom

Fig.5. The Evaporator output -chilled water temperature, Tchw

Fig.6. The Condenser input - expansion valve relative opening, uEXV

Fig.7. The Condenser output – refrigerant liquid level, Level

3. ARMAX MIMO Centrifugal Chiller Model

In this section we build the both SISO models of the open-loop Evaporator and

Condenser control subsystems based on the input-output measurements dataset of MIMO

chiller plant closed-loop control system collected in the previous Section 2.

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3.1. ARMAX and ANFIS SISO Evaporator subsystem models

Basically, arx or armax two specific functions provided by a control system

identification MATLAB Toolbox estimate the parameters of two polynomials, each one

assigned to a linear discrete-time model, known as autoregressive with an exogenous

input (ARX) or autoregressive moving average with a similar exogenous input

(ARMAX) respectively, thru LSE method, like in [Tudoroiu et al., (2018a)].

Furthermore, MATLAB’s System Identification Toolbox provides users with the option

of simulating data as would have been obtained from a physical process to generate

IDDATA objects that package the input-output measurement dataset into a suitable

MATLAB format. Both MATLAB functions are based on a prediction error method and

the specified polynomial orders. Additionally, a pure transport delay of the signal flow in

the feedback path from measurement sensors to each closed-loop controller is specified

as a new argument of these two specific MATLAB functions. The ARX and ARMAX

models are “inherently linear” and the advantage is to design the “model structure and

parameter identification rapidly”, as is mentioned also in [Tudoroiu et al., (2018a)]. To

generate both models is preferred that the dataset samples to be divided in two subsets,

first one required for the prediction phase, and the second one consisting of the remaining

samples is used in the validation phase.

Basically, a general description of a noise corrupted linear control system can be

described by: u ey yy H u H e= + (1)

where u , y are the control system input and output, while e is a unmeasured white

noise disturbance source [7]. uyH and

eyH denote the input-output transfer function and

the description of the noise disturbance respectively that will be estimated thru different

ways of parametrizing of parametrization.

The discrete-time ARMAX model corresponding to the general description (1) is

given by:

11

10 1

11

( ) ( ) ( ) ( ) ( ) ( )

( ) 1 ...

( ) ...

( ) 1 ...

a

a

k k k b

b

c

c

nn

n n n nn

nn

A q y t B q u t C q e t

A q a q a q

B q b q b q b q

C q c q c q

−−

− − − − −

−−

= +

= + + +

= + + +

= + + +

(2)

where , ,a b cn n n denote the l orders of the polynomials ( ), ( )A q B q and ( )C q while kn is

the pure transport delay. Here q is a forward shift time operator, i.e.

( ) ( 1), ( ) ( 1), ( ) ( 1)qy t y t qu t u t qe t e t= + = + = + while 1q− is the backward shift time

operator, i.e. 1 1 1( ) ( 1), ( ) ( 1), ( ) ( 1)q y t y t q u t u t q e t e t− − −= − = − = − , ,t kT k += Z is for

discrete time description, and T is the sampling time. In the ARMAX model structure (2)

is easy to identify the three specific terms, namely AR (Autoregressive) corresponding to

the ( )A q -polynomial, MA (Moving average) related to the noise ( )C q -polynomial, and

X denoting the "eXtra" exogenous input ( ) ( )B q u t . In terms of the general transfer

functions uyH and

eyH , the ARMAX model corresponds to a following parameterization:


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( ) ( )

( ) , ( )( ) ( )

u ey y

B q C qH q H q

A q A q= = (3)

with common denominators, that in complex domain (frequency domain)

, , , 1, 2Tsz e z C s j j f = = + = − = ,

where f is the signal frequency, measured in hertz, (3) can be written as

( ) ( )( ) , ( )

( ) ( )

u ey y

B z C zH z H z

A z A z= = (4)

The Command Window provides the following useful information about the SISO

ARMAX model of chilled water temperature of the Evaporator subsystem generated in

MATLAB:

mARMAX_T = Discrete-time ARMAX model:

( ) ( ) ( ) ( ) ( ) ( ) A z y t B z u t C z e t= +

1 2 3 4 5( ) 1 2.332 1.497 0.02349 0.2059 0.01763A z z z z z z− − − − −= − + + − +

1 2 3 4 5( ) 0.000362 0.001476 0.00294 0.008282 0.004236B z z z z z z− − − − −= − + + − +

1( ) 1 0.9908C z z−= −

Sample time: 1 seconds

Parameterization:

Polynomial orders: 5 , 5 , 1 , 1a b c kn n n n= = = =

Number of free coefficients: 11

Status:

Estimated using ARMAX on time domain data.

Fit to estimation data: 99.92% (prediction focus)

FPE: 7.319e-10, MSE: 7.293e-10

Concluding, the dynamics of the SISO ARMAX model is of fifth order, the dynamics

of “colored noise” is of first order, and the input signal is delayed by one single time

sample. Thus, the state space dimension of the original nonlinear centrifugal chiller

dynamics, approximatively 39, is drastically reduced to fifth order, but still higher.

The validation of this model is shown in Fig. 8, that reveal a reasonable accuracy but

not higher, only 89.03 %, where zvT denotes the subset of the last half of measurements

dataset chosen for validation phase.

Invoking the anfis command, which can be opened directly to the MATLAB R2018b

software package command line related to an Adaptive Neuro-Fuzzy training of Sugeno-

type FIS, a SISO chilled water temperature model ANFIS is generated and the simulation

results are shown in Fig. 9.

This specific subroutine command anfis uses a hybrid learning algorithm to identify

the membership function parameters of SISO, Sugeno - type FISs. A combination of LSE

and backpropagation gradient descent methods are used for training FIS membership

function parameters to model a given set of input-output (u, y) data.

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For a set of data for input-output measurement data (u, y), for example, the following

MATLAB R2018b code lines are the core of an ANFIS model:

options = genfisOptions('GridPartition');

options. NumMembershipFunctions = 5;

in_fis = genfis (u, options);

options = anfisOptions;

options. InitialFIS = in_fis;

options. Epoch Number = 30;

out_fis = anfis ([u y], options);

evalfis (u, out_fis)

Fig.8. SISO ARMAX Evaporator chilled water temperature model validation, Tchw (y1)

Fig.9. SISO ANFIS Evaporator chilled water temperature model validation, Tchw

Comparing the MATLAB simulation results shown in Fig.8 and Fig. 9, of both

models, ARMAX and ANFIS we can see a huge improvement in ANFIS model accuracy

for chilled water temperature. This improvement will be a real advantage to build one of

the most suitable PID ANFIS control strategy for the closed-loop Evaporator control

subsystem.


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3.2. ARMAX and ANFIS SISO Condenser subsystem models

Like the previous subsection 3.1 the Command Window provides the following useful

information about the SISO ARMAX model of refrigerant liquid level in Condenser

subsystem generated in MATLAB:

mARMAX_L = Discrete-time ARMAX model

( ) ( ) ( ) ( ) ( ) ( ) A z y t B z u t C z e t= +

1 2( ) 1 1.903 0.9032A z z z− −= − +

1 2 3 4 5( ) 0.07757 0.1534 0.2824 1.059 1.112B z z z z z z− − − − −= + − − +

1 2( ) 1 0.8242 0.1757C z z z− −= − −

Sample time: 1 seconds

Parameterization:

Polynomial orders: 2 , 5 , 2 , 1a b c kn n n n= = = =

Number of free coefficients: 9

Status:

Estimated using ARMAX on time domain data.

Fit to estimation data: 98.78% (prediction focus)

FPE: 0.00081, MSE: 0.0008075

The model description reveals that the dynamics of the SISO ARMAX model is of

second order, the dynamics of “colored noise” is of second order, and the input signal is

delayed by one single time sample. Thus, the state space dimension of the original

nonlinear centrifugal chiller dynamics, approximatively 39, is drastically reduced to the

second lowest possible order.

The validation of this model is shown in Fig. 10, that reveal a great accuracy better

than for chilled water temperature SISO model, at 98.78 %, where zvL denotes the subset

of the last half of measurements dataset chosen for validation phase.

Fig.10. SISO ARMAX Condenser refrigerant liquid level model validation, Level (y2)

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Invoking also the anfis command, which can be opened directly to the MATLAB

R2018b software package command line related to an Adaptive Neuro-Fuzzy training of

Sugeno-type FIS, a SISO refrigerant liquid level model ANFIS is generated and the

simulation results are shown in Fig. 11.

Fig.11. SISO ANFIS Condenser refrigerant liquid level model validation, Level (y2)

4. Centrifugal Chiller PID Closed-Loop Control Strategies – Performance

Analysis

For performance comparison in this section is performed a rigorous analysis of at

least three PID closed-loop control strategies, namely for the original nonlinear

centrifugal chiller model documented in detail in [Tudoroiu et al., (2018a)], for two linear

discrete-time SISO ARMAX closed-loop models for a MIMO centrifugal chiller plant

developed in Section 3, and finally for two SISO ANFIS improved closed-loop models of

the same centrifugal chiller plant developed also in Section 3 based on a same MIMO

ARMAX centrifugal chiller control system.

To have a good insight of the closed-loop performance in all three cases under

investigation the simulation results performed in real-time on a MATLAB R2018b

attractive environment are shown in separate figures for different time scales. Thus, in

Fig. 12 and Fig.13 are shown the MATLAB simulations results for a PID closed-loop

centrifugal chiller model presented also in [Tudoroiu et al., (2018a)] for both closed-loop

SISO models, attached to chilled water temperature in Evaporator control subsystem and

refrigerant liquid level in Condenser control subsystem respectively. In Fig.14 are shown

two digital PID Simulink closed-loop control strategies, based on the SISO ARMAX

models developed in Subsection 3, with the corresponding simulation results shown in

Fig. 15 and Fig.16. Further, in Fig. 17 and Fig. 18 are shown the MATLAB simulation

results for two other PID closed-loop control strategies, based on a significant

improvement brought to the both SISO ARMAX models previous mentioned, thru an

ANFIS hybrid combined intelligent structure developed in Section 3.

In Fig.12 and Fig.13 the parameters kp and ki (proportional and integral respectively)

of both PID controllers are adjusted according to a PI control law setup to the following

values:

kp = 0.001, ki = 0.001 for first SISO loop, and kp = 0.5, ki = 0.001 for second one.


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The MATLAB simulation results show that the settling time for temperature is

approx. 3000 seconds, i.e. 50 minutes, and for refrigerant liquid level the settling time is

much shorter, namely approx. 2000 seconds, i.e. almost 34 minutes.

However, the overall performance in terms of tracking accuracy is high, but in terms

of transient convergence speed is realistic but not remarkable.

.

Fig.12. PID SISO Evaporator chilled water temperature set point tracking performance, Tchw

Fig.13. PID SISO Condenser refrigerant liquid level set point tracking performance, Level

In Fig. 14 the PID SISO ARMAX closed-loop SIMULINK model in a state-space

representation for Evaporator chilled water temperature situated in the top of the figure,

and its parameters are tuned to the following values: kp = 19.17 (proportional

component), ki = 0.3641 (integral component), kd = 91.62 (derivative component), and

the filter coefficient of the PID transfer function is N = 0.05658. Similar, the PID SISO

ARMAX closed-loop SIMULINK model for Condenser refrigerant liquid level in state-

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space representation is situated to the bottom in Fig.14, and its parameters are tuned to

the following values: kp = 0.0649, ki = 0.00007643, kd = -0.14, and the filter coefficient

of the PID transfer function is N = 0.0009533.

Fig.14. PID SISO ARMAX Simulink models for Evaporator Temperature and Condenser refrigerant liquid

level closed-loop control subsystems

Since the SISO ARMAX models are linear discrete-time polynomials, it is

noteworthy that for both PIDs SIMULINK models structures the controllers’ parameters

can be easily tuned by using the advance option built-in each controller MATLAB block

incorporated in SIMULINK library, i.e. such those shown in Fig. 15 for a better insight.


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Fig.15. MATLAB PID Tuner block of SISO ARMAX Simulink models for Evaporator Temperature

Compared to nonlinear centrifugal chiller plant MATLAB simulation results shown in

Fig.12 and Fig.13, the SIMULINK simulation results for both PID SISO ARMAX

closed-loop control strategies shown in Fig.16 and Fig.17 reveal a significant

improvement in terms of tracking accuracy and transient convergence speed, but further

remains an enough room for significant improvements to be done. It is a little bit strange

the behavior of the PID algorithm in the first samples of the transient that is noticed an

unrealistic sharp decrease from the initial conditions, i.e. 8℃ for chilled water

Temperature in Evaporator and 50% for refrigerant liquid level in Condenser. This is a

MATLAB algorithm solver issue, but after approx. 15 seconds for chilled water

Temperature, and 60 seconds for refrigerant liquid level respectively, the algorithm

performs in realistic way.

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Fig.16. PID SISO ARMAX Evaporator chilled water temperature set point tracking performance, Tchw

Fig.17. PID SISO Condenser refrigerant liquid level set point tracking performance, Level

Important improvments are revealed by the MATLAB simulation results shown in

Fig.18, Fig.19, Fig.20 and Fig.21, for both PID ANFIS SISO, first one for a closed-loop

intelligent control strategy of the Evaporator chilled water temperature, the second one

for closed-loop intelligent control strategy of the Condenser refrigerant liquid level.


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Fig.18. PID ANFIS SISO Evaporator chilled water temperature set point tracking performance, Tchw

Fig.19. The robustness of PID ANFIS SISO Evaporator chilled water temperature to changes in set point

tracking performance, Tchw

The last two figures, Fig.18 and Fig.19 represent a complete picture of the great overall

performance obtained by a PID ANFIS SISO control strategy applied on Evaporator

chilled water temperature in terms of high tracking accuracy, very fast transient speed,

and great robustness to the changes in the tracking setpoints compare to the MATLAB

simulation results obtained in the previous two cases. Similar, great results are performed

in closed-loop the PID ANFIS control strategy applied on Condenser refrigerant liquid

level shown in Fig.20 and Fig.21, in terms of the tracking accuracy, transient speed

convergence and robustness to changes in the tracking setpoints. The parameters of

ANFIS PID controllers are tuned to the following values: kp = 0.00001, ki = -0.001 and

kd = 0 for Evaporator chilled water temperature closed-loop control subsystem, and kp =

0.000001, ki = 0.01, and kd =0.001.

It is also worth to mention that all MATLAB simulations are performed for a

sampling time Ts = 1 second.

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Fig.20. PID ANFIS SISO Condenser refrigerant liquid level set point tracking performance, Level

Fig.21. Robustness of PID ANFIS SISO Condenser refrigerant liquid level to changes in set point tracking

performance, Level

However, a small number of oscillations we notice in the refrigerant liquid level

during the transient, and an overshoot whose amplitude is not significant for the overall

performance of the controlled Condenser.

5. Conclusions

This research paper is an extension and in the same time a dissemination of the

preliminary results obtained by authors during the years in this research field. The

novelty of the paper consists of the improvement brought to the linear discrete-time

polynomials autoregressive moving average models of multi-input and multi-output

centrifugal chiller plant of high nonlinearity and complexity, especially due to its high

state-space dimensionality. The adaptive neuro-fuzzy inference models of centrifugal

chiller plant are built by using the same input-output measurements data used to generate


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the autoregressive moving average models, and the proportional integral derivative

control strategy structures based on these models are intelligent hybrid combination of an

adaptive neuro-fuzzy structures and proportional integral derivative controllers.

The implementation of simulation results in real-time on the MATLAB R2018b

software platform of the multi-input and multi-output nonlinear centrifugal chiller plant

decomposed into two single-input single-output closed-loop control loops reveals that

the proportional integral derivative adaptive neuro-fuzzy inference system closed-loop

strategy control outperforms clearly and without doubt the first two standard

proportional integral derivative single-input and single-output closed-loop control

strategies in terms of setpoints tracking accuracy, transient convergence speed, number

of oscillations, overshoot and robustness to changes in tracking setpoints. The future

research work will focus on expanding these preliminary results, using the proposed

modeling and control approach for a wide range of applications across industries.

Also, to provide a real-time implementation of the same approach for some hardware

development based on microcontrollers and a field-programmable gate array (FPGA) will

be a great challenge for us.

Acknowledgments

Research funding (discovery grant) for this project from the Natural Sciences and

Engineering Research Council of Canada (NSERC) is gratefully acknowledged.

References

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