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Decoupling Fuzzy-Neural Temperature and Humidity Control in HVAC Systems
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ScienceDirect IFAC PapersOnLine 52-25 (2019) 299–304
Decoupling Fuzzy-Neural Decoupling Fuzzy-Neural Decoupling Fuzzy-Neural Decoupling Fuzzy-Neural Temperature and Humidity Control in HVAC Systems Temperature and Humidity Control in HVAC Systems Temperature and Humidity Temperature and Humidity Control Control in in HVAC HVAC Systems Systems
Ivan Ganchev, Albena Taneva, Krum Kutryanski, Michail Petrov Ivan Ganchev, Albena Taneva, Krum Kutryanski, Michail Petrov Ivan Ivan Ganchev, Ganchev, Albena Albena Taneva, Taneva, Krum Krum Kutryanski, Kutryanski, Michail Michail Petrov Petrov Technical University of Sofia, Branch Plovdiv, Control Systems Department, Plovdiv, Technical University of Sofia, Branch Plovdiv, Control Systems Department, Plovdiv, (Tel: +359 Branch 32 659 585; e-mail: [email protected]) Technical University of Plovdiv, Control Systems TechnicalBulgaria University of Sofia, Sofia, Branch Plovdiv, Control Systems Department, Department, Plovdiv, Plovdiv, Bulgaria (Tel: +359 32 659 585; e-mail: [email protected]) Bulgaria Bulgaria (Tel: (Tel: +359 +359 32 32 659 659 585; 585; e-mail: e-mail: [email protected]) [email protected])
Abstract: This paper presents a neuro-fuzzy structure of a decoupling fuzzy neural PID controller with Abstract: This paper presents aa neuro-fuzzy structure aa decoupling fuzzy neural PID controller with self-tuning parameters. This structure is appropriate forof ventilation air conditioning HVAC Abstract: paper structure of fuzzy neural PID with Abstract: This This paper presents presents a neuro-fuzzy neuro-fuzzy structure ofheating, a decoupling decoupling fuzzyand neural PID controller controller with self-tuning parameters. This structure is appropriate for heating, ventilation and air conditioning HVAC nonlinear plants. The main advantage here is that the equation of classical PID control with decoupling self-tuning parameters. This structure is appropriate for heating, ventilation and air conditioning HVAC self-tuning parameters. This structure is appropriate for heating, ventilation and air conditioning HVAC nonlinear plants. The main here is into that the of classical control with decoupling coefficients are used as a advantage Sugeno function the equation consequent part of PID the fuzzy the nonlinear The advantage here that equation of PID control with decoupling nonlinear plants. plants. The main main advantage here is is into that the the equation of classical classical PID controlrules. with Hence, decoupling coefficients are fuzzy rules. Hence, the used as a Sugeno function the consequent part of the designed decoupling fuzzy PID controller could be viewed as a natural similarity to the conventional PID coefficients are used as a Sugeno function into the consequent part of the fuzzy rules. Hence, the coefficients are usedfuzzy as a PID Sugeno function into the consequent partsimilarity of the fuzzy rules. Hence, PID the designed decoupling controller could be viewed as a natural to the conventional controller with decoupling elements. A benchmark HVAC system with temperature and humidity control designed decoupling fuzzy PID controller could be viewed as a natural similarity to the conventional PID designed decoupling fuzzy elements. PID controller could be HVAC viewed system as a natural similarity to the conventional PID controller with decoupling A benchmark with temperature and humidity control is considered illustrate the benefitsA the design HVAC paradigm. The with performance of this up was studied controller withtodecoupling decoupling elements. Aofbenchmark benchmark HVAC system with temperature andsethumidity humidity control controller with elements. system temperature and control is considered to illustrate the benefits of the design paradigm. The performance of this set up up was was studied studied for reference tracking and disturbance rejection cases. Simulation results confirm the effectiveness of the is considered to illustrate the benefits of the design paradigm. The performance of this set is considered to illustrate the benefits of the design paradigm. The performance of this set up was studied for reference tracking and disturbance rejection cases. Simulation results confirm the effectiveness of the proposed control system. for reference tracking and disturbance rejection cases. Simulation results confirm the effectiveness for reference tracking and disturbance rejection cases. Simulation results confirm the effectiveness of of the the proposed control system. proposed control system. proposed control system. © 2019, IFAC (International Federation Automatic Control) Hosting by PID Elsevier Ltd. All rights reserved.and Keywords: Decoupling control, Fuzzyof PID controller, Self-Tuning controller, Temperature Keywords: Decoupling control, Fuzzy PID controller, Self-Tuning PID controller, Temperature and Humidity control Keywords: Decoupling control, Fuzzy PID controller, Self-Tuning PID controller, Temperature and Keywords:control Decoupling control, Fuzzy PID controller, Self-Tuning PID controller, Temperature and Humidity Humidity control Humidity control Alli 2009], are to improve the performance of the HVAC 1. INTRODUCTION Alli 2009], are to improve the performance of the HVAC system. Alli 2009], 1. INTRODUCTION Alli 2009], are are to to improve improve the the performance performance of of the the HVAC HVAC 1. INTRODUCTION system. 1. INTRODUCTION system. Heating, ventilation, and air conditioning (HVAC) systems system. Fuzzy logic controllers (FLC) have emerged as one of the Heating, ventilation, and air conditioning (HVAC) ensure supply and maintain the comfortable indoorsystems air for Fuzzy logic controllers (FLC) have emerged as one of the Heating, ventilation, and (HVAC) systems Heating,to ventilation, and air air conditioning conditioning (HVAC) systems most useful research areas emerged in fuzzy control Fuzzy logic controllers (FLC) as of ensure to supply and maintain the comfortable indoor air for Fuzzyactive logicand controllers (FLC) have have emerged as one one theory. of the the occupants with the ensure to and maintain the comfortable indoor for active and useful research areas in fuzzy control theory. ensure to supply supply and desired maintainair thetemperature, comfortable humidity indoor air air and for most That is why fuzzy logic controllers have been successfully most active and useful research areas in fuzzy control theory. occupants with the desired air temperature, humidity and most active and useful research areas in fuzzy control theory. quality. The comfortable air inside these buidlings depends occupants with the desired air temperature, humidity and is why fuzzy logic controllers have been successfully occupants with the desired air temperature, humidity and That applied for control of various physical On the That is fuzzy controllers have been quality. The comfortable air inside these buidlings is why why fuzzy logic logic controllers have processes. been successfully successfully on the acurate temperature and relative humidity depends process That quality. The comfortable air inside these buidlings depends applied for control of various physical processes. On the quality. The comfortable air inside these buidlings depends other hand the best-known industrial process controller applied for control of various physical processes. On the on the acurate temperature and relative humidity process applied forthe control of various physical processes. Onis the control in HVAC systems [Soyguder S.,humidity H. Alli, process 2009]. other on the acurate temperature and relative hand best-known industrial process controller is the on the acurate temperature and relative humidity process PID controller because of its simple structure and robust other hand the best-known industrial process controller is control in HVAC systems [Soyguder S., H. Alli, 2009]. other controller hand the best-known industrial process controller is the the Hence, it is necessary to design temperature and humidity control in HVAC systems [Soyguder S., H. Alli, 2009]. PID because of its simple structure and robust control itin isHVAC systems [Soyguder S., H.and Alli,humidity 2009]. performance in because a wide range operating conditions. This PID controller controller because of its its ofsimple simple structure and robust robust Hence, necessary to design temperature PID of structure and control strategies in order to improve the performance of Hence, it is necessary to design temperature and humidity performance in a wide range of operating conditions. This Hence, itstrategies is necessary to design temperature and humidity paper is aimed study theof of previously performance in wide range operating This control in order tosystems improve performance of performance in aa to wide range ofperformance operating conditions. conditions. This HVAC forthe indoor building air control strategies in order improve the performance of is aimed to study the performance of previously control systems. strategiesThe in control order to tosystems improve the performance of paper achieved good simulation results of the presented fuzzy – paper is aimed to study the performance of previously HVAC systems. The control for indoor building air paper is aimed to study the performance of previously can be mainly classified into two categories according to the HVAC systems. The systems for building air good simulation results of the presented fuzzy – HVAC systems. The control control systems for indoor indoor building air achieved neural PID (FNPID) controller in real time applications achieved good simulation results of the presented fuzzy can be mainly classified into two categories according to the good simulation results in of real the presented fuzzy – – employed approaches: the two conventional controllersto can be be mainly mainly classified into into two categories according according to and the achieved neural PID (FNPID) controller time applications can classified categories the [Petrov et al.,(FNPID) 2002]. controller neural PID in real time applications employed approaches: the conventional controllers and neural PID (FNPID) controller in real time applications computational intelligence techniques. employed approaches: the conventional controllers and et al., 2002]. employed approaches: the conventional controllers and [Petrov [Petrov et 2002]. computational intelligence techniques. [Petrov et al., al., 2002]. to this problem and describes some of computational intelligence techniques. This paper is devoted computational intelligence techniques. The popular Proportional Integral Derivative (PID) controller This paper is devoted to this problem and describes some of the the problem fuzzy PID controllers with This paper devoted to and some of The popular Proportional Integral Derivative (PID) controller This design paper is isaspects devoted of to this this problem and describes describes some of is employed in conventional HVAC systems, because its the The popular Integral Derivative (PID) controller design aspects of the fuzzy PID controllers with The popular Proportional Proportional Integral Derivative (PID) controller application to TITO nonlinear plants [Ganchev et al. 2016]. the design aspects of the fuzzy PID controllers with is employed in conventional HVAC systems, because its the design toaspects of the fuzzy PID controllers with simplicity, easy installation, and use. However, PID is employed in conventional HVAC systems, because its application TITO nonlinear plants [Ganchev et al. 2016]. is employedeasy in conventional HVAC systems, becausePID its Nonlinear fuzzy functions are et to application to to TITOmembership nonlinear plants plants [Ganchev etutilized al. 2016]. 2016]. simplicity, installation, and use. However, application TITO nonlinear [Ganchev al. controller may not solve successfully some nonlinear simplicity, easy installation, and use. However, PID Nonlinear fuzzy membership functions are utilized to simplicity, easy installation, and use. However, PID implement in the network structure, called fuzzy neural Nonlinear fuzzy membership functions are utilized to controller may not solve successfully some nonlinear Nonlinear fuzzy membership functions are fuzzy utilized to problems, and not satisfying the demand about the indoor air controller may not solve successfully some nonlinear implement in the network structure, called neural controller and maynotnot solve the successfully some nonlinear network (FNN). Thus, the FNN has more design degrees of implement in the network structure, called fuzzy neural problems, satisfying demand about the indoor air implement in the network structure, called fuzzy neural quality. Intelligent controllers,the fuzzy logicabout or neural networks problems, and demand the air Thus, the FNN has moreofdesign degrees of problems, and not not satisfying satisfying the demand about the indoor indoor air network freedom (FNN). to enhance performance the fuzzy network (FNN). Thus, the has degrees of quality. Intelligent controllers, logic or (FNN). Thus, the the FNN FNN has more moreofdesign design degreesPID of have recently become practical fuzzy as a fast, accurate andnetworks flexible network quality. Intelligent controllers, fuzzy logic or neural neural networks freedom to enhance the performance the fuzzy PID quality. Intelligent controllers, fuzzy logic or neural networks controller. A simple fuzzy PID type method based on freedom to enhance the performance of the fuzzy PID have recently become practical as a fast, accurate and flexible freedom to enhance the performance of the fuzzy PID tool to HVAC control strategy, modeling, simulation and have recently become practical as a fast, accurate and flexible controller. A simple fuzzy PID type method based on have recently become practical as amodeling, fast, accurate and flexible Sugeno’s fuzzy technique introduced by Petrov et al. [Petrov controller. A fuzzy PID method based on tool to HVAC control strategy, and controller. A simple simple fuzzy PID type type method based on design [Soyguder, S. et al., 2009]. Withsimulation the designed tool to HVAC control strategy, modeling, simulation and Sugeno’s fuzzy technique introduced by Petrov et al. [Petrov tool to HVAC control strategy, modeling, simulation and et al., 2002] is extended with decoupling control elements in Sugeno’s fuzzy technique introduced by Petrov et al. [Petrov design [Soyguder, S. et al., 2009]. With the designed Sugeno’s fuzzy techniquewith introduced by Petrov etelements al. [Petrov intelligent controllers, the performance of a HVAC system design [Soyguder, S. et al., 2009]. With the designed et al., 2002] is extended decoupling control in design [Soyguder, S. the et performance al., 2009]. of With the designed order to improve the performance of the controller. et al., 2002] is extended with decoupling control elements intelligent controllers, a HVAC system et al., to 2002] is extended with decoupling control elements in in can be significantly improved [Terzyiska M. et al., 2006]. intelligent controllers, the performance of a HVAC system order improve the performance of the controller. intelligent controllers,improved the performance ofM. a HVAC system order to to improve improve the the performance performance of of the the controller. controller. can be significantly [Terzyiska et al., 2006]. order Moreover, there are several disadvantages that limit the can be significantly improved [Terzyiska M. et al., 2006]. The paper is organized as follows: Section 2 presents can be significantly improved [Terzyiska M. that et al.,limit 2006]. Moreover, there are several disadvantages the The paper is organized as follows: Section 2 presents aa performance of current control technologies, such as: the Moreover, there are several disadvantages that limit system structure and2 introducesaa The organized as Section Moreover, there are several disadvantages that limit the decoupling The paper paper is iscontrol organized as follows: follows: Section 2 presents presents performance of current control technologies, such as: the decoupling control system structure and introduces causes of the system switching working state too frequently; performance of current control technologies, such as: the control scheme using the adaptive FNN. The decoupling control system structure and performance of current controlworking technologies, such as: the decoupling control system structure and introduces introduces causes of the system switching state too frequently; decoupling control scheme using the adaptive FNN. The and neural networks are hard to put into application; causes of of the the system system switching switching working working state state too too frequently; frequently; decoupling implemented design of the decoupled FNN controller and the control scheme using the adaptive FNN. The causes decoupling control scheme using the adaptive FNN. The and neural networks are hard to put into application; implemented design of the decoupled FNN controller and the controller is so complex. The results of applying the selfand neural networks are hard to put into application; developed on-line learning algorithm are presented in section implemented design of the decoupled FNN controller and the and neural networks are hard to put into application; implemented design of the decoupled FNN controller and the controller is so complex. The results of applying the selfdeveloped on-line learning algorithm are presented in section tuning intelligent PID controller, fuzzy adaptive PID controller is so complex. The results of applying the self3. Simulation results and some concluding remarks are given developed on-line learning algorithm are presented in section controller is so complex. The results of applying the selfdeveloped on-line learning algorithm are presented in section tuning intelligent PID controller, fuzzy adaptive PID 3. Simulation results and some concluding remarks are given controller, adaptive PID predictive decoupling tuning intelligent controller, fuzzy adaptive PID in 4 and 5 respectively. Simulation results and tuning intelligent PID controller, fuzzy control, adaptive fuzzy PID 3. 3. section Simulation results and some some concluding concluding remarks remarks are are given given controller, adaptive predictive decoupling control, fuzzy in section 4 and 5 respectively. control combined with neural network, in [Soyguder S., H. controller, adaptive predictive decoupling control, fuzzy in controller, adaptive predictive decoupling control, S., fuzzy in section section 4 4 and and 5 5 respectively. respectively. control combined with neural network, in [Soyguder H. control control combined combined with with neural neural network, network, in in [Soyguder [Soyguder S., S., H. H. 2405-8963 © 2019, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Peer review under responsibility of International Federation of Automatic Control. 10.1016/j.ifacol.2019.12.539
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2. DECOUPLING CONTROL STRUCTURE OF HVAC SYSTEM The goal of decoupling control is used to eliminate complicated loop interactions so that a change in one process variable will not cause corresponding changes in other process variables. To do this a non-interacting or decoupling control scheme is designed. In this scheme, a compensation structure called a decoupler is used to the process - G11 , G12 , G22 , G21. This decoupler is the inverse of the gain array and allows for all measurements to be passed through it in order to give full decoupling of all of the loops. This is shown on Fig.1.
∆e1 (k ) = e1 (k ) − e1 (k − 1) , ∆e2 (k ) = e2 (k ) − e2 (k − 1)
(2)
Each FNPID controller can use as a third input signal the sum of the system errors δe(k) or the acceleration error ∆2e(k) , which are calculated using the equations: δ e1,2 (k ) = δ e1,2 (k − 1) + e1,2 (k ) ∆e1,2 (k ) = e1,2 (k ) − 2e1,2 (k − 1) + e1,2 (k − 2)
(3) (4)
The third input ((3) or (4)) of the proposed controller depends on the selected structure for the PID controller. It is known from discrete control theory, that the most frequently used discrete PID control algorithm can be described with the well-known equations as follows [Astrom, K. and B. Witenmark 1997]: Positioning PID controller: u ( k ) = k p e( k ) + kiδ e( k ) + kd de( k )
Incremental PID controller: ∆u (k ) = k p de(k ) + ki e(k ) + kd d 2e(k )
(5) (6)
where ki = k p Tk Ti , kd = k p Td Tk , Tk is the sample time of the discrete system, Ti is the integral time constant of the conventional controller, Td is the differential time constant, kp is the proportional gain, u(k) is the output control action and ∆u(k) is the incremental control action. Fig. 1. Structure of decoupling control system. In the structure of the decoupling control system each Controller consists of a conventional PD controller working in parallel with the main FNPID controller. This is according the learning schema introduced by [Gomi and Kawato, 1993]. As it could be seen in [Petrov et.al., 2002] the conventional PD controller is used both as an ordinary feedback controller to guarantee global asymptotic stability in a compact space and as an inverse reference model of the response of the controlled object. The proposed decoupled FNPID control algorithm ensures adaptive properties and deals with system disturbances and uncertainties. It combines the features of conventional PID control algorithm with intuitiveness of fuzzy logic and the adaptation abilities of artificial neural networks 3. DESIGN OF DECOUPLED FUZZY-NEURAL PID CONTROLLER FOR HVAC SYSTEMS The traditional FLC works usually with input signals of the system error e(k) and the change rate ∆e(k) in the error. The system errors for the first and second control loops are defined as a difference between the set point r(k) and the plant output y(k) at the moment k, for each controller respectively in Fig. 1.
e1 (k ) = r1 (k ) − y1 (k ) , e2 (k ) = r2 (k ) − y2 (k )
(1)
Hence the change rate in the errors ∆e1,2(k) at the moment k will be:
The final control action for implementation of the second type controller (6) can be calculated according to the previous value of the control output u(k-1) as follow: u (k ) = u (k − 1) + ∆u (k )
(7)
The Sugeno’s fuzzy rules [Takagi and Sugeno, 1985] into each FNPID controller can be composed in the generalized form of ‘if-then’ composition with a premise and an antecedent part to describe the control policy. The rule base comprises a collection of N rules (8) and (9), where the upper index (r) represents the rule number: First decoupled FNPID controller: R1( r ) : if e1 is E1 and ∆e1 is ∆E1 and δ e1 is δ E1 then f u(1r ) = k1(pr ) e1 (k ) + k1(ir )δ e1 (k ) + k1(dr ) ∆e1 (k ) + k21( r ) e2 (k ) + k1(or )
(8)
Second decoupled FNPID controller: R2( r ) : if e2 is E 2 and ∆e2 is ∆E 2 and δ e2 is δ E 2 then f u(2r ) = k2( rp) e2 (k ) + k2( ir )δ e2 (k ) + k2( rd) ∆e2 (k ) + k12( r ) e1 (k ) + k2( ro)
(9)
where e, ∆e, ∆2e , δe are the input variables for each controller. This way a similarity between the equations of the conventional digital PID controllers (5), (6) and the Sugeno’s output functions fu1, fu2 in (8) and (9) could be found, where k12 and k21 are decoupling coefficients. In this case, each FNPID controller can be considered as a collection of many local PID controllers, which are represented by the Sugeno’s functions into the different fuzzy rules. Thus, it is possible to approximate the nonlinear characteristic of the controlled plant.
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output defuzzification and it is expressed as a weighted mean value:
3.1. The structure of the proposed fuzzy-neural PID controllers
N
The proposed FNPID controllers with self-tuning parameters are represented by adaptive properties of two artificial neural networks. The fuzzy-neural structure has 5 layers (Fig. 2) with particular for fuzzy logic control functionalities.
uF (k ) =
∑f
(r ) u
µu( r )
(13)
i =1
N
∑µ
(r ) u
i =1
where fu(r) are the Sugeno output functions (8,9) and μu(r) are the correspond membership degrees of the quantization levels (11,12). This layer also consists of tunable parameters – the coefficients of the FNPID controllers joined in the parameter β jr . 3.2. The proposed learning algorithm The described fuzzy-neural PID controller implements the basic control function in the system, and the conventional feedback PD controller (uPD(k) = kpe(k)+kd∆e(k)) is used for the learning algorithm [Gomi, H. and M. Kawato, 1993]. The control action is obtained as a sum of the output signal from the FNPID controller uF and the output signal from the conventional PD controller uPD, working in parallel: u = u PD + u F
Fig.2. Fuzzy-neural network architecture for each FNPID controller. The first layer simply propagates the input variables towards next layers. Gaussian membership functions with uncertain standard deviation are implemented into the second layer in order to perform the fuzzification of the inputs. The Gaussian membership functions with uncertain deviation are expressed by: 1 ( xi − cij ) 2 (10) µij ( xi ) = exp − 2 σ ij where cij is the mean value of the jth fuzzy set for the ith input signal and σ ij is the deviation of membership function respectively . The input signals are xi (e, ∆e, ∆2e or δe). The parameters of the Gaussian function are adjustable. Their values (joined in the parameter αij) are going to be tuned by the learning algorithm introduced below. The nodes in the third layer are used to perform precondition matching of the fuzzy logic rules. Hence, the rule nodes Rr should carry out a collection of the membership degrees of the fired fuzzy sets. The fourth layer implements the fuzzy ‘product’ operation according to (11) or (12) and to integrate the fired rules which have the same consequent.
µ1(ur ) = µe( r ) ∗ µ∆( re) ∗ µδ( re) ∗ µ∆( re)
(11)
µ2( ru) = µe( r ) ∗ µ∆( re) ∗ µδ( re) ∗ µ∆( re)
(12)
1
2
1
2
1
2
2
1
where µij specify the membership degrees upon the fired fuzzy sets of the input signals into the (r)th fuzzy rule. They are determined according to (10). The single node in the fifth layer computes the decision signal out of the network and in this way acts as Sugeno’s
(14) The learning algorithm is based on instant minimization of an error measurement function, which is defined as E =ε2 / 2
(15)
where ε is calculated as a difference ε = u − uF = uPD , in which u denotes the desired control action and the output uF is calculated by the fuzzy - neural network. The algorithm performs two-step gradient learning procedure [Petrov at al., 2002]. Assuming that βjr is an jth adjustable parameter (e.g. the constant kp, ki , kd, or k0 in the Sugeno output function fu (8) or (9) into the (r)th activated rule, which is represented as a connection for the output neuron in the layer 5, the general parameter learning rule used is [Petrov at al., 2002]: ∂E ∂β jr
β jr (k + 1) = β jr (k ) + η −
j=0,1,2,3; (r)=1,2,…,N
(16)
where the parameter η is so called learning rate, and the derivative of the error is calculated by partial derivatives:
∂ E ∂ E ∂ uF ∂ f u( r ) = ⋅ ⋅ ∂β jr ∂ uF ∂ f u( r ) ∂β jr
(17)
where:
∂ f u( r ) ∂E ∂ uF µ (r ) = xi = −(u − uF ) , = N u , (r ) ∂β jr ∂ uF ∂ fu (r ) µ ∑ u
(18)
j =1
After calculating the partial derivatives, the final recurrent equation for each adjustable parameter βjr (kp, ki, kd, kij , k0) in the layer 5 for two controllers are:
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xi (k ) − cij (k )
First decoupled FNPID controller:
cij (k + 1) = cij (k ) +ηuPD µu(r ) (k ) f u(r ) (k ) − uF (k )
k (k + 1) = k (k ) + η u PD1 (k ) µ (k )e1 (k ) (r ) 1p
(r ) 1p
(r ) 1u
xi (k ) − cij (k ) σ ij (k + 1) = σ ij (k ) +ηuPD µu( r ) (k ) f u( r ) (k ) − uF (k ) σ ij3 (k )
k1(ir ) (k + 1) = k1(ir ) (k ) + η u PD1 (k ) µ1(ur ) (k )δ e1 (k ) k (k + 1) = k (k ) + η u PD1 (k ) µ (k )∆e1 (k ) (r ) 1d
(r ) 1d
2
(27)
(r ) 1u
(r ) (r ) k21 (k + 1) = k21 (k ) + η u PD1 (k ) µ1(ur ) (k )e2 (k )
k (k + 1) = k (k ) + η u PD1 (k ) µ (k ) (r ) 1o
(26)
cij2 (k )
(r ) 1o
(r ) 1u
(19)
The final recurrent equations (19), (20), (26) and (27) are used in the software implementation of the developed algorithm for the FNPID controllers.
Second decoupled FNPID controller: 4. SIMULATION RESULTS k2( rp) (k + 1) = k2( rp) (k ) + η u PD2 (k ) µ 2( ru) (k )e2 (k )
The investigations have been carried out by simulations of the decoupling fuzzy neural algorithm in MATLAB&Simulink environment with a nonlinear plant – HVAC system, described in [Mien, 2016].
k2( ir ) (k + 1) = k2( ir ) (k ) + η u PD2 (k ) µ 2( ru) (k )δ e2 (k ) k2( rd) (k + 1) = k2( rd) (k ) + η u PD2 (k ) µ 2( ru) (k )∆e2 ( k )
k12( r ) (k + 1) = k12( r ) (k ) + η u PD2 (k ) µ 2( ru) (k )e1 (k ) k2( ro) (k + 1) = k2( ro) (k ) + η u PD2 (k ) µ 2( ru) (k )
(20)
The internal two layers 4 and 3 do not contain adjustable parameters or they have constant link weights equal to 1. Therefore the output error E can be propagated back directly to the layer 2, where there are the adjustable parameters αij. The output error function E is propagated through the links composed by corresponding membership degrees µu - µij from the layer 5 to the layer 2. Hence, the learning rule for the second group of the adjustable parameters in the layer 2 can be taken from [Petrov et.al., 2002]: ∂E (21) α ij (k + 1) = α ij (k ) + η − ∂α ij where the derivative of the output error function E is distributed as follow: ∂ E ∂ E ∂ uF ∂µij (22) = ⋅ ⋅ ∂α ij ∂ uF ∂µij ∂α ij The first partial derivative has been calculated in (18) and the second one is: ∂ uF f u( r ) − uF (23) = N
∂µij
∑µ
(r ) u
j =1
There are two possibilities to calculate the third partial derivative in (22) for each adjustable parameter according to the equations (10) for each Gaussian membership function (24) for the center cij or (25) for the deviations σ ij of Gaussian membership function: ∂ µij xi (k ) − cij = ∂ cij cij2
∂ µij xi (k ) − cij = ∂σ ij σ ij3
(24)
Here it is studied a room, equiped with the base HVAC system which has the heater by hot/cold water and the humidifier by steam, such as Fig.3. Depending on the mixed air temperature after the filter, the outside air is heating or cooling by the heating/cooling coil. Then, the outside air can be humidified by the steam humidifier, and then it is supplied into the room by the supply fan. The exhaust air is conducted out the room by the return fan. The heating/cooling coil gives the indoor air a thermal-humid energy P by changing the hot/cold water flowrate Fp through the hot water return/chilled water return (HWR/CHR) control valve. The steam humidifier also gives the indoor air a thermal-humid energy Q by varying the steam flowrate Fq through the control steam valve. This system uses the temperature & humidity controller to adjust the position coefficients αp and αq of hot/cold water, steam valves, and then can change flowrates Fp, Fq following equations: P = αp.Fp; Q = αq.Fq
(28)
4.1. Mathematical model of the indoor air temperature The indoor air temperature is affected by the outside air temperature, initial indoor air temperature, volume of the room, heat loss from the wall, hot/cold water flowrate and steam flowrate as it is presented in Fig. 3. Thus, the indoor air temperature can be expressed as follow:
T(t) = Tp (t) +Tq (t)
(29)
The main temperature Tp is supplied by the hot/cold water flowrate through the heating/cooling coil. The temperature Tq is after the humidifier and To is the outdoor temperature. Hence, it can be expressed as follows based on energy conservation principle:
2
(25)
After calculating the partial derivatives, the final recurrent equation for each adjustable parameter for ith input variable and its jth fuzzy set is:
ρ a C pVi
dTp dt
= a p Fp (t ) − U w Aw [Tp (t ) − To (t )]
(30)
Assuming To=0 and considering the effect of the time delay of the heat transfer process in the room, such as θtp, then (30) can be
Ivan Ganchev et al. / IFAC PapersOnLine 52-25 (2019) 299–304
simply transferred as follows: −q s ρ a C pVi Tp ( s ) ktp e tp ; ttp = G11 = = U w Aw Fp ( s ) ttp s + 1
4.3. Dynamic models of control valves
; ktp =
ap U w Aw
(31)
The indoor air temperature is also affected by the steam humidifier. Calculating the same as the main temperature, the temperature Tq caused by the steam humidifier, is expressed
G12 =
Tq ( s ) Fq ( s )
=
ktq e
− qtq s
ttq s + 1
; ttq =
303
aq at Vi ; ktq = fa f a ρa E p
(32)
In most of the control valves the flowrate through the valve is a nearly linear function of the signal to the valve actuator. Therefore, a first-order transfer function is an adequate model [Mien, 2016] for the dynamic characteristic of the electricpneumatic valve in this case:
Gvt =
Fp ( s ) It (s)
=
Fq ( s ) kvh e − qvh s kvt e − qvt s ; Gvh = = I h ( s ) tvh s + 1 tvt s + 1
(37).
4.2. Mathematical model of the indoor air humidity The indoor air humidity is directly affected by the steam humidifier, initial indoor air humidity, heating/cooling coil as in Fig.3. The indoor air humidity can be expressed as it follows: H(t) = Hp (t) +Hq (t) (33) The main indoor air humidity Hq is produced by adjusting the position of the steam valve. Humidity Hp is after heating/cooling coil and Ho is outdoor humidity. So that Hq can be described based on the energy conservation principle as follows: dH q (34) ρ a E pVi = aq Fq (t ) − ρ a f a E p [ H q (t ) − H o (t )] dt Assume Ho=0 and consider the time delay of the humidity spread process in the room, such as θhq, then (34) can be presented using the Laplace transform, as follows:
G22 =
H q (s) Fq ( s )
=
khq e
− qhq s
thq s + 1
; thq =
Vi fa
; khq =
aq fa ρa E p
(35)
The indoor air humidity is also affected by the heating/cooling coil. In order to simplify the equation (34) and the transfer function of indoor humidity can be expressed as: −q s a a ρCV H p ( s ) khq e hp ; thp = a p i ; khp = p h (36) G21 = = U w Aw U w Aw Fp ( s ) thp s + 1
4.4. The mathematical model of the control object in the indoor air temperature and humidity control system When considering interaction between temperature and humidity, the indoor air temperature and humidity processes is a two-inputs two-outputs (TITO) model. The matrix transfer function of the control object in the indoor air temperature T and humidity H control (Y1 and Y2 respectively according Fig. 1), when adding the model of the control valve, it is given as follows: T Gvt G11 GvhG12 Fp H = G G vt 21 GvhG22 Fq
(38)
The simulation results of the temperature T and humidity H control with the proposed decoupling fuzzy-neural PID control and classical PID control are presented graphically. The results illustrate the performance of the both control strategies. The parameters of the experimental studies included in (28) – (37) are given in Table 1. Fig. 4 shows temperature and humidity control results with the classical PID controllers and figure 5 shows the same control results with the proposed decoupling FNPID controllers. The different quantities are marked as follows: the two set points – R1 and R2, system outputs – Y1 and Y2, (temperature T [0C] and humidity H [%] respectively) and control actions Fp [%] and Fq [%]. The advantage of the discussed tuned fuzzyneural controller with decoupling effect is that it improves the system performance. Simulation results confirm the effectiveness of the proposed control system.
Fig. 4. Temperature and humidity control results with the classical PID controllers. Fig. 3. Basic view of the HVAC system.
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The advantage of fuzzy - neural control is that the controller can be taken as a collection of many local linear parallel distributed controllers, which usually have analytical solutions. The simulation results have proved the proposed FNPID decoupling controller. The advantage of the discussed tuned fuzzy-neural controller with decoupling effect is that it improves the system performance. Simulation results confirm the effectiveness of the proposed control system. In other words the FNPID decoupling controllers are suitable for controlling simultaneously the indoor air temperatue and humidity processes in the HVAC system. The FNPID decoupling controller can improve the indoor air quality, increase the process efficiency and bring economic benefits to the user. Fig. 5. Temperature and humidity control results with decoupling FNPID controllers Table 1. Experimental parameters Parameters
ρa Cp Ep
3
kg/m J/kgoC
kJ/kg
Vi m3 Aw m2 dw m fa m3/s Uw W/m2. ha W/m. oC Kb W/m. oC
Description Air density Heat capacity of air Vapour enthalpy Volume of the room Area of the wall Thickness of the wall Fl h supplied li d air i Flow rate off the Overall heat transfer coefficient Convection heat transfer coefficient f i Thermal conductivity of the brick
Value 1.2 1005 2538 24 36 0.3 0.015 1.43 10 0.6
3
3
Ep=2538kJ/kg,Cp=1005J/kg. C,Kb=0.6W/m. C, ρa=1.2kg/m3, ha=10W/m. C. Finally, the coefficients in described models (28 – 37) are calculated as follows: Uw=1.43, ktp=0.019, τtp=562.24, ktq=0.009, τtq=1600, khp=0.006, τhp=562.24, khq=0.022, τhq=1600, αt=0.4, αh=0.3,θtp=5.6, θtq=6.4, θhp=1.7, θhq=16, kvt=22, τvt=1.5, θvt=0.6, kvh=23.75, τvh=2.5, θvh=1.2. o
The authors would like to acknowledge Research and Development Center of the Technical University Sofia, Joint Research Project No: 19 000. REFERENCES
In this paper, the length of the testing room is 4m, width is 2m, heigh is 3m; the thickness of the brick wall is 0.3m; and the desired indoor temperature is 20 oC. Therefore Vi=24m , Aw=36 m , dw=0.3 m, fa=0.015m /s. From [Mien, 2016] they are received values as follows: 2
ACKNOWLEDGMENTS
o
o
6. CONCLUSIONS This paper is focused on the design of an algorithm for decoupling fuzzy neural PID control and its application to control of a HVAC system. To handle the nonlinearities, a Takagi–Sugeno FNN is suggested as a means to control the plant with nonlinearities depending on the operating region. The proposed technique has been tested and evaluated using this simulated HVAC plant.
Astrom, K-J. and B. Witenmark (1997). Computer Controlled Systems. 3 Ed., Prentice Hall, Ganchev I., S. Ahmed, A. Taneva, M. Petrov (2016). Decoupling Fuzzy-Neural PID Controller for TITO Nonlinear Systems. Information technologies and control, Vol. 2, pp. 12 – 19. Gomi, H. and M. Kawato (1993). Neural Network Control for a Closed-Loop System Using Feedback-ErrorLearning. − Neural Networks, 6, Mien T. (2016). Design of Fuzzy-PI Decoupling Controller for the Temperature and Humidity Process in HVAC System. International Journal of Engineering Research & Technology (IJERT), pp. 589 – 594. Petrov, M., I. Ganchev, A. Taneva (2002). Fuzzy PID Control of Nonlinear Plants. Proceedings of the IEEE International Symposium on “Intelligent Systems”, Varna, Bulgaria, pp. 30-35. Soyguder, S., Karakose, M., Alli, H. (2009) Design and simulation of self-tuning PID-type fuzzy adaptive control for an expert HVAC system; Expert Systems with Applications, 36.. Soyguder S., H. Alli (2009). An expert system for the humidity and temperature control in HVAC systems using ANFIS and optimization with Fuzzy Modeling Approach; Energy and Buildings 41. pp. 814–822. Takagi, T. and Sugeno, M., (1985). Fuzzy identification of systems and its applications to modeling and control, IEEE Transactions on Systems, Man, and Cybernetics, vol. 15, no. 1, pp. 116–132. Terzyiska M., Y. Todorov, M. Petrov (2006). Fuzzy-Neural Model Predictive Control of a Building Heating System. Proceedings of the IFAC WS ESC’06 Energy Saving Control in Plants and Buildings, Bansko, Bulgaria, pp. 69 - 74.
ScienceDirect IFAC PapersOnLine 52-25 (2019) 299–304
Decoupling Fuzzy-Neural Decoupling Fuzzy-Neural Decoupling Fuzzy-Neural Decoupling Fuzzy-Neural Temperature and Humidity Control in HVAC Systems Temperature and Humidity Control in HVAC Systems Temperature and Humidity Temperature and Humidity Control Control in in HVAC HVAC Systems Systems
Ivan Ganchev, Albena Taneva, Krum Kutryanski, Michail Petrov Ivan Ganchev, Albena Taneva, Krum Kutryanski, Michail Petrov Ivan Ivan Ganchev, Ganchev, Albena Albena Taneva, Taneva, Krum Krum Kutryanski, Kutryanski, Michail Michail Petrov Petrov Technical University of Sofia, Branch Plovdiv, Control Systems Department, Plovdiv, Technical University of Sofia, Branch Plovdiv, Control Systems Department, Plovdiv, (Tel: +359 Branch 32 659 585; e-mail: [email protected]) Technical University of Plovdiv, Control Systems TechnicalBulgaria University of Sofia, Sofia, Branch Plovdiv, Control Systems Department, Department, Plovdiv, Plovdiv, Bulgaria (Tel: +359 32 659 585; e-mail: [email protected]) Bulgaria Bulgaria (Tel: (Tel: +359 +359 32 32 659 659 585; 585; e-mail: e-mail: [email protected]) [email protected])
Abstract: This paper presents a neuro-fuzzy structure of a decoupling fuzzy neural PID controller with Abstract: This paper presents aa neuro-fuzzy structure aa decoupling fuzzy neural PID controller with self-tuning parameters. This structure is appropriate forof ventilation air conditioning HVAC Abstract: paper structure of fuzzy neural PID with Abstract: This This paper presents presents a neuro-fuzzy neuro-fuzzy structure ofheating, a decoupling decoupling fuzzyand neural PID controller controller with self-tuning parameters. This structure is appropriate for heating, ventilation and air conditioning HVAC nonlinear plants. The main advantage here is that the equation of classical PID control with decoupling self-tuning parameters. This structure is appropriate for heating, ventilation and air conditioning HVAC self-tuning parameters. This structure is appropriate for heating, ventilation and air conditioning HVAC nonlinear plants. The main here is into that the of classical control with decoupling coefficients are used as a advantage Sugeno function the equation consequent part of PID the fuzzy the nonlinear The advantage here that equation of PID control with decoupling nonlinear plants. plants. The main main advantage here is is into that the the equation of classical classical PID controlrules. with Hence, decoupling coefficients are fuzzy rules. Hence, the used as a Sugeno function the consequent part of the designed decoupling fuzzy PID controller could be viewed as a natural similarity to the conventional PID coefficients are used as a Sugeno function into the consequent part of the fuzzy rules. Hence, the coefficients are usedfuzzy as a PID Sugeno function into the consequent partsimilarity of the fuzzy rules. Hence, PID the designed decoupling controller could be viewed as a natural to the conventional controller with decoupling elements. A benchmark HVAC system with temperature and humidity control designed decoupling fuzzy PID controller could be viewed as a natural similarity to the conventional PID designed decoupling fuzzy elements. PID controller could be HVAC viewed system as a natural similarity to the conventional PID controller with decoupling A benchmark with temperature and humidity control is considered illustrate the benefitsA the design HVAC paradigm. The with performance of this up was studied controller withtodecoupling decoupling elements. Aofbenchmark benchmark HVAC system with temperature andsethumidity humidity control controller with elements. system temperature and control is considered to illustrate the benefits of the design paradigm. The performance of this set up up was was studied studied for reference tracking and disturbance rejection cases. Simulation results confirm the effectiveness of the is considered to illustrate the benefits of the design paradigm. The performance of this set is considered to illustrate the benefits of the design paradigm. The performance of this set up was studied for reference tracking and disturbance rejection cases. Simulation results confirm the effectiveness of the proposed control system. for reference tracking and disturbance rejection cases. Simulation results confirm the effectiveness for reference tracking and disturbance rejection cases. Simulation results confirm the effectiveness of of the the proposed control system. proposed control system. proposed control system. © 2019, IFAC (International Federation Automatic Control) Hosting by PID Elsevier Ltd. All rights reserved.and Keywords: Decoupling control, Fuzzyof PID controller, Self-Tuning controller, Temperature Keywords: Decoupling control, Fuzzy PID controller, Self-Tuning PID controller, Temperature and Humidity control Keywords: Decoupling control, Fuzzy PID controller, Self-Tuning PID controller, Temperature and Keywords:control Decoupling control, Fuzzy PID controller, Self-Tuning PID controller, Temperature and Humidity Humidity control Humidity control Alli 2009], are to improve the performance of the HVAC 1. INTRODUCTION Alli 2009], are to improve the performance of the HVAC system. Alli 2009], 1. INTRODUCTION Alli 2009], are are to to improve improve the the performance performance of of the the HVAC HVAC 1. INTRODUCTION system. 1. INTRODUCTION system. Heating, ventilation, and air conditioning (HVAC) systems system. Fuzzy logic controllers (FLC) have emerged as one of the Heating, ventilation, and air conditioning (HVAC) ensure supply and maintain the comfortable indoorsystems air for Fuzzy logic controllers (FLC) have emerged as one of the Heating, ventilation, and (HVAC) systems Heating,to ventilation, and air air conditioning conditioning (HVAC) systems most useful research areas emerged in fuzzy control Fuzzy logic controllers (FLC) as of ensure to supply and maintain the comfortable indoor air for Fuzzyactive logicand controllers (FLC) have have emerged as one one theory. of the the occupants with the ensure to and maintain the comfortable indoor for active and useful research areas in fuzzy control theory. ensure to supply supply and desired maintainair thetemperature, comfortable humidity indoor air air and for most That is why fuzzy logic controllers have been successfully most active and useful research areas in fuzzy control theory. occupants with the desired air temperature, humidity and most active and useful research areas in fuzzy control theory. quality. The comfortable air inside these buidlings depends occupants with the desired air temperature, humidity and is why fuzzy logic controllers have been successfully occupants with the desired air temperature, humidity and That applied for control of various physical On the That is fuzzy controllers have been quality. The comfortable air inside these buidlings is why why fuzzy logic logic controllers have processes. been successfully successfully on the acurate temperature and relative humidity depends process That quality. The comfortable air inside these buidlings depends applied for control of various physical processes. On the quality. The comfortable air inside these buidlings depends other hand the best-known industrial process controller applied for control of various physical processes. On the on the acurate temperature and relative humidity process applied forthe control of various physical processes. Onis the control in HVAC systems [Soyguder S.,humidity H. Alli, process 2009]. other on the acurate temperature and relative hand best-known industrial process controller is the on the acurate temperature and relative humidity process PID controller because of its simple structure and robust other hand the best-known industrial process controller is control in HVAC systems [Soyguder S., H. Alli, 2009]. other controller hand the best-known industrial process controller is the the Hence, it is necessary to design temperature and humidity control in HVAC systems [Soyguder S., H. Alli, 2009]. PID because of its simple structure and robust control itin isHVAC systems [Soyguder S., H.and Alli,humidity 2009]. performance in because a wide range operating conditions. This PID controller controller because of its its ofsimple simple structure and robust robust Hence, necessary to design temperature PID of structure and control strategies in order to improve the performance of Hence, it is necessary to design temperature and humidity performance in a wide range of operating conditions. This Hence, itstrategies is necessary to design temperature and humidity paper is aimed study theof of previously performance in wide range operating This control in order tosystems improve performance of performance in aa to wide range ofperformance operating conditions. conditions. This HVAC forthe indoor building air control strategies in order improve the performance of is aimed to study the performance of previously control systems. strategiesThe in control order to tosystems improve the performance of paper achieved good simulation results of the presented fuzzy – paper is aimed to study the performance of previously HVAC systems. The control for indoor building air paper is aimed to study the performance of previously can be mainly classified into two categories according to the HVAC systems. The systems for building air good simulation results of the presented fuzzy – HVAC systems. The control control systems for indoor indoor building air achieved neural PID (FNPID) controller in real time applications achieved good simulation results of the presented fuzzy can be mainly classified into two categories according to the good simulation results in of real the presented fuzzy – – employed approaches: the two conventional controllersto can be be mainly mainly classified into into two categories according according to and the achieved neural PID (FNPID) controller time applications can classified categories the [Petrov et al.,(FNPID) 2002]. controller neural PID in real time applications employed approaches: the conventional controllers and neural PID (FNPID) controller in real time applications computational intelligence techniques. employed approaches: the conventional controllers and et al., 2002]. employed approaches: the conventional controllers and [Petrov [Petrov et 2002]. computational intelligence techniques. [Petrov et al., al., 2002]. to this problem and describes some of computational intelligence techniques. This paper is devoted computational intelligence techniques. The popular Proportional Integral Derivative (PID) controller This paper is devoted to this problem and describes some of the the problem fuzzy PID controllers with This paper devoted to and some of The popular Proportional Integral Derivative (PID) controller This design paper is isaspects devoted of to this this problem and describes describes some of is employed in conventional HVAC systems, because its the The popular Integral Derivative (PID) controller design aspects of the fuzzy PID controllers with The popular Proportional Proportional Integral Derivative (PID) controller application to TITO nonlinear plants [Ganchev et al. 2016]. the design aspects of the fuzzy PID controllers with is employed in conventional HVAC systems, because its the design toaspects of the fuzzy PID controllers with simplicity, easy installation, and use. However, PID is employed in conventional HVAC systems, because its application TITO nonlinear plants [Ganchev et al. 2016]. is employedeasy in conventional HVAC systems, becausePID its Nonlinear fuzzy functions are et to application to to TITOmembership nonlinear plants plants [Ganchev etutilized al. 2016]. 2016]. simplicity, installation, and use. However, application TITO nonlinear [Ganchev al. controller may not solve successfully some nonlinear simplicity, easy installation, and use. However, PID Nonlinear fuzzy membership functions are utilized to simplicity, easy installation, and use. However, PID implement in the network structure, called fuzzy neural Nonlinear fuzzy membership functions are utilized to controller may not solve successfully some nonlinear Nonlinear fuzzy membership functions are fuzzy utilized to problems, and not satisfying the demand about the indoor air controller may not solve successfully some nonlinear implement in the network structure, called neural controller and maynotnot solve the successfully some nonlinear network (FNN). Thus, the FNN has more design degrees of implement in the network structure, called fuzzy neural problems, satisfying demand about the indoor air implement in the network structure, called fuzzy neural quality. Intelligent controllers,the fuzzy logicabout or neural networks problems, and demand the air Thus, the FNN has moreofdesign degrees of problems, and not not satisfying satisfying the demand about the indoor indoor air network freedom (FNN). to enhance performance the fuzzy network (FNN). Thus, the has degrees of quality. Intelligent controllers, logic or (FNN). Thus, the the FNN FNN has more moreofdesign design degreesPID of have recently become practical fuzzy as a fast, accurate andnetworks flexible network quality. Intelligent controllers, fuzzy logic or neural neural networks freedom to enhance the performance the fuzzy PID quality. Intelligent controllers, fuzzy logic or neural networks controller. A simple fuzzy PID type method based on freedom to enhance the performance of the fuzzy PID have recently become practical as a fast, accurate and flexible freedom to enhance the performance of the fuzzy PID tool to HVAC control strategy, modeling, simulation and have recently become practical as a fast, accurate and flexible controller. A simple fuzzy PID type method based on have recently become practical as amodeling, fast, accurate and flexible Sugeno’s fuzzy technique introduced by Petrov et al. [Petrov controller. A fuzzy PID method based on tool to HVAC control strategy, and controller. A simple simple fuzzy PID type type method based on design [Soyguder, S. et al., 2009]. Withsimulation the designed tool to HVAC control strategy, modeling, simulation and Sugeno’s fuzzy technique introduced by Petrov et al. [Petrov tool to HVAC control strategy, modeling, simulation and et al., 2002] is extended with decoupling control elements in Sugeno’s fuzzy technique introduced by Petrov et al. [Petrov design [Soyguder, S. et al., 2009]. With the designed Sugeno’s fuzzy techniquewith introduced by Petrov etelements al. [Petrov intelligent controllers, the performance of a HVAC system design [Soyguder, S. et al., 2009]. With the designed et al., 2002] is extended decoupling control in design [Soyguder, S. the et performance al., 2009]. of With the designed order to improve the performance of the controller. et al., 2002] is extended with decoupling control elements intelligent controllers, a HVAC system et al., to 2002] is extended with decoupling control elements in in can be significantly improved [Terzyiska M. et al., 2006]. intelligent controllers, the performance of a HVAC system order improve the performance of the controller. intelligent controllers,improved the performance ofM. a HVAC system order to to improve improve the the performance performance of of the the controller. controller. can be significantly [Terzyiska et al., 2006]. order Moreover, there are several disadvantages that limit the can be significantly improved [Terzyiska M. et al., 2006]. The paper is organized as follows: Section 2 presents can be significantly improved [Terzyiska M. that et al.,limit 2006]. Moreover, there are several disadvantages the The paper is organized as follows: Section 2 presents aa performance of current control technologies, such as: the Moreover, there are several disadvantages that limit system structure and2 introducesaa The organized as Section Moreover, there are several disadvantages that limit the decoupling The paper paper is iscontrol organized as follows: follows: Section 2 presents presents performance of current control technologies, such as: the decoupling control system structure and introduces causes of the system switching working state too frequently; performance of current control technologies, such as: the control scheme using the adaptive FNN. The decoupling control system structure and performance of current controlworking technologies, such as: the decoupling control system structure and introduces introduces causes of the system switching state too frequently; decoupling control scheme using the adaptive FNN. The and neural networks are hard to put into application; causes of of the the system system switching switching working working state state too too frequently; frequently; decoupling implemented design of the decoupled FNN controller and the control scheme using the adaptive FNN. The causes decoupling control scheme using the adaptive FNN. The and neural networks are hard to put into application; implemented design of the decoupled FNN controller and the controller is so complex. The results of applying the selfand neural networks are hard to put into application; developed on-line learning algorithm are presented in section implemented design of the decoupled FNN controller and the and neural networks are hard to put into application; implemented design of the decoupled FNN controller and the controller is so complex. The results of applying the selfdeveloped on-line learning algorithm are presented in section tuning intelligent PID controller, fuzzy adaptive PID controller is so complex. The results of applying the self3. Simulation results and some concluding remarks are given developed on-line learning algorithm are presented in section controller is so complex. The results of applying the selfdeveloped on-line learning algorithm are presented in section tuning intelligent PID controller, fuzzy adaptive PID 3. Simulation results and some concluding remarks are given controller, adaptive PID predictive decoupling tuning intelligent controller, fuzzy adaptive PID in 4 and 5 respectively. Simulation results and tuning intelligent PID controller, fuzzy control, adaptive fuzzy PID 3. 3. section Simulation results and some some concluding concluding remarks remarks are are given given controller, adaptive predictive decoupling control, fuzzy in section 4 and 5 respectively. control combined with neural network, in [Soyguder S., H. controller, adaptive predictive decoupling control, fuzzy in controller, adaptive predictive decoupling control, S., fuzzy in section section 4 4 and and 5 5 respectively. respectively. control combined with neural network, in [Soyguder H. control control combined combined with with neural neural network, network, in in [Soyguder [Soyguder S., S., H. H. 2405-8963 © 2019, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Peer review under responsibility of International Federation of Automatic Control. 10.1016/j.ifacol.2019.12.539
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2. DECOUPLING CONTROL STRUCTURE OF HVAC SYSTEM The goal of decoupling control is used to eliminate complicated loop interactions so that a change in one process variable will not cause corresponding changes in other process variables. To do this a non-interacting or decoupling control scheme is designed. In this scheme, a compensation structure called a decoupler is used to the process - G11 , G12 , G22 , G21. This decoupler is the inverse of the gain array and allows for all measurements to be passed through it in order to give full decoupling of all of the loops. This is shown on Fig.1.
∆e1 (k ) = e1 (k ) − e1 (k − 1) , ∆e2 (k ) = e2 (k ) − e2 (k − 1)
(2)
Each FNPID controller can use as a third input signal the sum of the system errors δe(k) or the acceleration error ∆2e(k) , which are calculated using the equations: δ e1,2 (k ) = δ e1,2 (k − 1) + e1,2 (k ) ∆e1,2 (k ) = e1,2 (k ) − 2e1,2 (k − 1) + e1,2 (k − 2)
(3) (4)
The third input ((3) or (4)) of the proposed controller depends on the selected structure for the PID controller. It is known from discrete control theory, that the most frequently used discrete PID control algorithm can be described with the well-known equations as follows [Astrom, K. and B. Witenmark 1997]: Positioning PID controller: u ( k ) = k p e( k ) + kiδ e( k ) + kd de( k )
Incremental PID controller: ∆u (k ) = k p de(k ) + ki e(k ) + kd d 2e(k )
(5) (6)
where ki = k p Tk Ti , kd = k p Td Tk , Tk is the sample time of the discrete system, Ti is the integral time constant of the conventional controller, Td is the differential time constant, kp is the proportional gain, u(k) is the output control action and ∆u(k) is the incremental control action. Fig. 1. Structure of decoupling control system. In the structure of the decoupling control system each Controller consists of a conventional PD controller working in parallel with the main FNPID controller. This is according the learning schema introduced by [Gomi and Kawato, 1993]. As it could be seen in [Petrov et.al., 2002] the conventional PD controller is used both as an ordinary feedback controller to guarantee global asymptotic stability in a compact space and as an inverse reference model of the response of the controlled object. The proposed decoupled FNPID control algorithm ensures adaptive properties and deals with system disturbances and uncertainties. It combines the features of conventional PID control algorithm with intuitiveness of fuzzy logic and the adaptation abilities of artificial neural networks 3. DESIGN OF DECOUPLED FUZZY-NEURAL PID CONTROLLER FOR HVAC SYSTEMS The traditional FLC works usually with input signals of the system error e(k) and the change rate ∆e(k) in the error. The system errors for the first and second control loops are defined as a difference between the set point r(k) and the plant output y(k) at the moment k, for each controller respectively in Fig. 1.
e1 (k ) = r1 (k ) − y1 (k ) , e2 (k ) = r2 (k ) − y2 (k )
(1)
Hence the change rate in the errors ∆e1,2(k) at the moment k will be:
The final control action for implementation of the second type controller (6) can be calculated according to the previous value of the control output u(k-1) as follow: u (k ) = u (k − 1) + ∆u (k )
(7)
The Sugeno’s fuzzy rules [Takagi and Sugeno, 1985] into each FNPID controller can be composed in the generalized form of ‘if-then’ composition with a premise and an antecedent part to describe the control policy. The rule base comprises a collection of N rules (8) and (9), where the upper index (r) represents the rule number: First decoupled FNPID controller: R1( r ) : if e1 is E1 and ∆e1 is ∆E1 and δ e1 is δ E1 then f u(1r ) = k1(pr ) e1 (k ) + k1(ir )δ e1 (k ) + k1(dr ) ∆e1 (k ) + k21( r ) e2 (k ) + k1(or )
(8)
Second decoupled FNPID controller: R2( r ) : if e2 is E 2 and ∆e2 is ∆E 2 and δ e2 is δ E 2 then f u(2r ) = k2( rp) e2 (k ) + k2( ir )δ e2 (k ) + k2( rd) ∆e2 (k ) + k12( r ) e1 (k ) + k2( ro)
(9)
where e, ∆e, ∆2e , δe are the input variables for each controller. This way a similarity between the equations of the conventional digital PID controllers (5), (6) and the Sugeno’s output functions fu1, fu2 in (8) and (9) could be found, where k12 and k21 are decoupling coefficients. In this case, each FNPID controller can be considered as a collection of many local PID controllers, which are represented by the Sugeno’s functions into the different fuzzy rules. Thus, it is possible to approximate the nonlinear characteristic of the controlled plant.
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output defuzzification and it is expressed as a weighted mean value:
3.1. The structure of the proposed fuzzy-neural PID controllers
N
The proposed FNPID controllers with self-tuning parameters are represented by adaptive properties of two artificial neural networks. The fuzzy-neural structure has 5 layers (Fig. 2) with particular for fuzzy logic control functionalities.
uF (k ) =
∑f
(r ) u
µu( r )
(13)
i =1
N
∑µ
(r ) u
i =1
where fu(r) are the Sugeno output functions (8,9) and μu(r) are the correspond membership degrees of the quantization levels (11,12). This layer also consists of tunable parameters – the coefficients of the FNPID controllers joined in the parameter β jr . 3.2. The proposed learning algorithm The described fuzzy-neural PID controller implements the basic control function in the system, and the conventional feedback PD controller (uPD(k) = kpe(k)+kd∆e(k)) is used for the learning algorithm [Gomi, H. and M. Kawato, 1993]. The control action is obtained as a sum of the output signal from the FNPID controller uF and the output signal from the conventional PD controller uPD, working in parallel: u = u PD + u F
Fig.2. Fuzzy-neural network architecture for each FNPID controller. The first layer simply propagates the input variables towards next layers. Gaussian membership functions with uncertain standard deviation are implemented into the second layer in order to perform the fuzzification of the inputs. The Gaussian membership functions with uncertain deviation are expressed by: 1 ( xi − cij ) 2 (10) µij ( xi ) = exp − 2 σ ij where cij is the mean value of the jth fuzzy set for the ith input signal and σ ij is the deviation of membership function respectively . The input signals are xi (e, ∆e, ∆2e or δe). The parameters of the Gaussian function are adjustable. Their values (joined in the parameter αij) are going to be tuned by the learning algorithm introduced below. The nodes in the third layer are used to perform precondition matching of the fuzzy logic rules. Hence, the rule nodes Rr should carry out a collection of the membership degrees of the fired fuzzy sets. The fourth layer implements the fuzzy ‘product’ operation according to (11) or (12) and to integrate the fired rules which have the same consequent.
µ1(ur ) = µe( r ) ∗ µ∆( re) ∗ µδ( re) ∗ µ∆( re)
(11)
µ2( ru) = µe( r ) ∗ µ∆( re) ∗ µδ( re) ∗ µ∆( re)
(12)
1
2
1
2
1
2
2
1
where µij specify the membership degrees upon the fired fuzzy sets of the input signals into the (r)th fuzzy rule. They are determined according to (10). The single node in the fifth layer computes the decision signal out of the network and in this way acts as Sugeno’s
(14) The learning algorithm is based on instant minimization of an error measurement function, which is defined as E =ε2 / 2
(15)
where ε is calculated as a difference ε = u − uF = uPD , in which u denotes the desired control action and the output uF is calculated by the fuzzy - neural network. The algorithm performs two-step gradient learning procedure [Petrov at al., 2002]. Assuming that βjr is an jth adjustable parameter (e.g. the constant kp, ki , kd, or k0 in the Sugeno output function fu (8) or (9) into the (r)th activated rule, which is represented as a connection for the output neuron in the layer 5, the general parameter learning rule used is [Petrov at al., 2002]: ∂E ∂β jr
β jr (k + 1) = β jr (k ) + η −
j=0,1,2,3; (r)=1,2,…,N
(16)
where the parameter η is so called learning rate, and the derivative of the error is calculated by partial derivatives:
∂ E ∂ E ∂ uF ∂ f u( r ) = ⋅ ⋅ ∂β jr ∂ uF ∂ f u( r ) ∂β jr
(17)
where:
∂ f u( r ) ∂E ∂ uF µ (r ) = xi = −(u − uF ) , = N u , (r ) ∂β jr ∂ uF ∂ fu (r ) µ ∑ u
(18)
j =1
After calculating the partial derivatives, the final recurrent equation for each adjustable parameter βjr (kp, ki, kd, kij , k0) in the layer 5 for two controllers are:
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302
xi (k ) − cij (k )
First decoupled FNPID controller:
cij (k + 1) = cij (k ) +ηuPD µu(r ) (k ) f u(r ) (k ) − uF (k )
k (k + 1) = k (k ) + η u PD1 (k ) µ (k )e1 (k ) (r ) 1p
(r ) 1p
(r ) 1u
xi (k ) − cij (k ) σ ij (k + 1) = σ ij (k ) +ηuPD µu( r ) (k ) f u( r ) (k ) − uF (k ) σ ij3 (k )
k1(ir ) (k + 1) = k1(ir ) (k ) + η u PD1 (k ) µ1(ur ) (k )δ e1 (k ) k (k + 1) = k (k ) + η u PD1 (k ) µ (k )∆e1 (k ) (r ) 1d
(r ) 1d
2
(27)
(r ) 1u
(r ) (r ) k21 (k + 1) = k21 (k ) + η u PD1 (k ) µ1(ur ) (k )e2 (k )
k (k + 1) = k (k ) + η u PD1 (k ) µ (k ) (r ) 1o
(26)
cij2 (k )
(r ) 1o
(r ) 1u
(19)
The final recurrent equations (19), (20), (26) and (27) are used in the software implementation of the developed algorithm for the FNPID controllers.
Second decoupled FNPID controller: 4. SIMULATION RESULTS k2( rp) (k + 1) = k2( rp) (k ) + η u PD2 (k ) µ 2( ru) (k )e2 (k )
The investigations have been carried out by simulations of the decoupling fuzzy neural algorithm in MATLAB&Simulink environment with a nonlinear plant – HVAC system, described in [Mien, 2016].
k2( ir ) (k + 1) = k2( ir ) (k ) + η u PD2 (k ) µ 2( ru) (k )δ e2 (k ) k2( rd) (k + 1) = k2( rd) (k ) + η u PD2 (k ) µ 2( ru) (k )∆e2 ( k )
k12( r ) (k + 1) = k12( r ) (k ) + η u PD2 (k ) µ 2( ru) (k )e1 (k ) k2( ro) (k + 1) = k2( ro) (k ) + η u PD2 (k ) µ 2( ru) (k )
(20)
The internal two layers 4 and 3 do not contain adjustable parameters or they have constant link weights equal to 1. Therefore the output error E can be propagated back directly to the layer 2, where there are the adjustable parameters αij. The output error function E is propagated through the links composed by corresponding membership degrees µu - µij from the layer 5 to the layer 2. Hence, the learning rule for the second group of the adjustable parameters in the layer 2 can be taken from [Petrov et.al., 2002]: ∂E (21) α ij (k + 1) = α ij (k ) + η − ∂α ij where the derivative of the output error function E is distributed as follow: ∂ E ∂ E ∂ uF ∂µij (22) = ⋅ ⋅ ∂α ij ∂ uF ∂µij ∂α ij The first partial derivative has been calculated in (18) and the second one is: ∂ uF f u( r ) − uF (23) = N
∂µij
∑µ
(r ) u
j =1
There are two possibilities to calculate the third partial derivative in (22) for each adjustable parameter according to the equations (10) for each Gaussian membership function (24) for the center cij or (25) for the deviations σ ij of Gaussian membership function: ∂ µij xi (k ) − cij = ∂ cij cij2
∂ µij xi (k ) − cij = ∂σ ij σ ij3
(24)
Here it is studied a room, equiped with the base HVAC system which has the heater by hot/cold water and the humidifier by steam, such as Fig.3. Depending on the mixed air temperature after the filter, the outside air is heating or cooling by the heating/cooling coil. Then, the outside air can be humidified by the steam humidifier, and then it is supplied into the room by the supply fan. The exhaust air is conducted out the room by the return fan. The heating/cooling coil gives the indoor air a thermal-humid energy P by changing the hot/cold water flowrate Fp through the hot water return/chilled water return (HWR/CHR) control valve. The steam humidifier also gives the indoor air a thermal-humid energy Q by varying the steam flowrate Fq through the control steam valve. This system uses the temperature & humidity controller to adjust the position coefficients αp and αq of hot/cold water, steam valves, and then can change flowrates Fp, Fq following equations: P = αp.Fp; Q = αq.Fq
(28)
4.1. Mathematical model of the indoor air temperature The indoor air temperature is affected by the outside air temperature, initial indoor air temperature, volume of the room, heat loss from the wall, hot/cold water flowrate and steam flowrate as it is presented in Fig. 3. Thus, the indoor air temperature can be expressed as follow:
T(t) = Tp (t) +Tq (t)
(29)
The main temperature Tp is supplied by the hot/cold water flowrate through the heating/cooling coil. The temperature Tq is after the humidifier and To is the outdoor temperature. Hence, it can be expressed as follows based on energy conservation principle:
2
(25)
After calculating the partial derivatives, the final recurrent equation for each adjustable parameter for ith input variable and its jth fuzzy set is:
ρ a C pVi
dTp dt
= a p Fp (t ) − U w Aw [Tp (t ) − To (t )]
(30)
Assuming To=0 and considering the effect of the time delay of the heat transfer process in the room, such as θtp, then (30) can be
Ivan Ganchev et al. / IFAC PapersOnLine 52-25 (2019) 299–304
simply transferred as follows: −q s ρ a C pVi Tp ( s ) ktp e tp ; ttp = G11 = = U w Aw Fp ( s ) ttp s + 1
4.3. Dynamic models of control valves
; ktp =
ap U w Aw
(31)
The indoor air temperature is also affected by the steam humidifier. Calculating the same as the main temperature, the temperature Tq caused by the steam humidifier, is expressed
G12 =
Tq ( s ) Fq ( s )
=
ktq e
− qtq s
ttq s + 1
; ttq =
303
aq at Vi ; ktq = fa f a ρa E p
(32)
In most of the control valves the flowrate through the valve is a nearly linear function of the signal to the valve actuator. Therefore, a first-order transfer function is an adequate model [Mien, 2016] for the dynamic characteristic of the electricpneumatic valve in this case:
Gvt =
Fp ( s ) It (s)
=
Fq ( s ) kvh e − qvh s kvt e − qvt s ; Gvh = = I h ( s ) tvh s + 1 tvt s + 1
(37).
4.2. Mathematical model of the indoor air humidity The indoor air humidity is directly affected by the steam humidifier, initial indoor air humidity, heating/cooling coil as in Fig.3. The indoor air humidity can be expressed as it follows: H(t) = Hp (t) +Hq (t) (33) The main indoor air humidity Hq is produced by adjusting the position of the steam valve. Humidity Hp is after heating/cooling coil and Ho is outdoor humidity. So that Hq can be described based on the energy conservation principle as follows: dH q (34) ρ a E pVi = aq Fq (t ) − ρ a f a E p [ H q (t ) − H o (t )] dt Assume Ho=0 and consider the time delay of the humidity spread process in the room, such as θhq, then (34) can be presented using the Laplace transform, as follows:
G22 =
H q (s) Fq ( s )
=
khq e
− qhq s
thq s + 1
; thq =
Vi fa
; khq =
aq fa ρa E p
(35)
The indoor air humidity is also affected by the heating/cooling coil. In order to simplify the equation (34) and the transfer function of indoor humidity can be expressed as: −q s a a ρCV H p ( s ) khq e hp ; thp = a p i ; khp = p h (36) G21 = = U w Aw U w Aw Fp ( s ) thp s + 1
4.4. The mathematical model of the control object in the indoor air temperature and humidity control system When considering interaction between temperature and humidity, the indoor air temperature and humidity processes is a two-inputs two-outputs (TITO) model. The matrix transfer function of the control object in the indoor air temperature T and humidity H control (Y1 and Y2 respectively according Fig. 1), when adding the model of the control valve, it is given as follows: T Gvt G11 GvhG12 Fp H = G G vt 21 GvhG22 Fq
(38)
The simulation results of the temperature T and humidity H control with the proposed decoupling fuzzy-neural PID control and classical PID control are presented graphically. The results illustrate the performance of the both control strategies. The parameters of the experimental studies included in (28) – (37) are given in Table 1. Fig. 4 shows temperature and humidity control results with the classical PID controllers and figure 5 shows the same control results with the proposed decoupling FNPID controllers. The different quantities are marked as follows: the two set points – R1 and R2, system outputs – Y1 and Y2, (temperature T [0C] and humidity H [%] respectively) and control actions Fp [%] and Fq [%]. The advantage of the discussed tuned fuzzyneural controller with decoupling effect is that it improves the system performance. Simulation results confirm the effectiveness of the proposed control system.
Fig. 4. Temperature and humidity control results with the classical PID controllers. Fig. 3. Basic view of the HVAC system.
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The advantage of fuzzy - neural control is that the controller can be taken as a collection of many local linear parallel distributed controllers, which usually have analytical solutions. The simulation results have proved the proposed FNPID decoupling controller. The advantage of the discussed tuned fuzzy-neural controller with decoupling effect is that it improves the system performance. Simulation results confirm the effectiveness of the proposed control system. In other words the FNPID decoupling controllers are suitable for controlling simultaneously the indoor air temperatue and humidity processes in the HVAC system. The FNPID decoupling controller can improve the indoor air quality, increase the process efficiency and bring economic benefits to the user. Fig. 5. Temperature and humidity control results with decoupling FNPID controllers Table 1. Experimental parameters Parameters
ρa Cp Ep
3
kg/m J/kgoC
kJ/kg
Vi m3 Aw m2 dw m fa m3/s Uw W/m2. ha W/m. oC Kb W/m. oC
Description Air density Heat capacity of air Vapour enthalpy Volume of the room Area of the wall Thickness of the wall Fl h supplied li d air i Flow rate off the Overall heat transfer coefficient Convection heat transfer coefficient f i Thermal conductivity of the brick
Value 1.2 1005 2538 24 36 0.3 0.015 1.43 10 0.6
3
3
Ep=2538kJ/kg,Cp=1005J/kg. C,Kb=0.6W/m. C, ρa=1.2kg/m3, ha=10W/m. C. Finally, the coefficients in described models (28 – 37) are calculated as follows: Uw=1.43, ktp=0.019, τtp=562.24, ktq=0.009, τtq=1600, khp=0.006, τhp=562.24, khq=0.022, τhq=1600, αt=0.4, αh=0.3,θtp=5.6, θtq=6.4, θhp=1.7, θhq=16, kvt=22, τvt=1.5, θvt=0.6, kvh=23.75, τvh=2.5, θvh=1.2. o
The authors would like to acknowledge Research and Development Center of the Technical University Sofia, Joint Research Project No: 19 000. REFERENCES
In this paper, the length of the testing room is 4m, width is 2m, heigh is 3m; the thickness of the brick wall is 0.3m; and the desired indoor temperature is 20 oC. Therefore Vi=24m , Aw=36 m , dw=0.3 m, fa=0.015m /s. From [Mien, 2016] they are received values as follows: 2
ACKNOWLEDGMENTS
o
o
6. CONCLUSIONS This paper is focused on the design of an algorithm for decoupling fuzzy neural PID control and its application to control of a HVAC system. To handle the nonlinearities, a Takagi–Sugeno FNN is suggested as a means to control the plant with nonlinearities depending on the operating region. The proposed technique has been tested and evaluated using this simulated HVAC plant.
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