sensors Article

Self-Tuning Fully-Connected PID Neural Network System for Distributed Temperature Sensing and Control of Instrument with Multi-Modules Zhen Zhang, Cheng Ma * and Rong Zhu Department of Precision Instrument, Tsinghua University, Beijing 100084, China; [email protected] (Z.Z.); [email protected] (R.Z.) * Correspondence: [email protected]; Tel.: +86-10-6277-1694 Academic Editor: Vittorio M. N. Passaro Received: 24 August 2016; Accepted: 12 October 2016; Published: 14 October 2016

Abstract: High integration of multi-functional instruments raises a critical issue in temperature control that is challenging due to its spatial–temporal complexity. This paper presents a multi-input multi-output (MIMO) self-tuning temperature sensing and control system for efficiently modulating the temperature environment within a multi-module instrument. The smart system ensures that the internal temperature of the instrument converges to a target without the need of a system model, thus making the control robust. The system consists of a fully-connected proportional–integral–derivative (PID) neural network (FCPIDNN) and an on-line self-tuning module. The experimental results show that the presented system can effectively control the internal temperature under various mission scenarios, in particular, it is able to self-reconfigure upon actuator failure. The system provides a new scheme for a complex and time-variant MIMO control system which can be widely applied for the distributed measurement and control of the environment in instruments, integration electronics, and house constructions. Keywords: MIMO; self-tuning; temperature control; instrument; high reliability

1. Introduction Miniaturization, modularization, and multi-functionalization have become development trends in instrumentation [1–4]. For example, Christian et al. [5] introduced one of the smallest real-time polymerase chain reaction (PCR) systems with a size of 100 × 60 × 33 mm3 and a weight of approximately 90 g. Segyeong et al. [6] presented a portable microfluidic flow cytometer with dual detection ability of impedance and fluorescence that is 150 × 100 × 100 mm3 in size and weighs nearly 800 g. Roda et al. [7] designed a simple and versatile portable device based on chemiluminescence lensless imaging that can simultaneously perform different types of bioassays. For the instruments with multi-modules, internal temperature control becomes an important issue, since the different functions are achieved by several modules integrated in one box, and the modules’ thermal characters vary. For instance, the typical PCR temperatures are approximately 90 ◦ C in denaturation, 55 ◦ C in annealing, and 72 ◦ C in extension [1]. Thus, these are three different temperatures in one cycle. The loop-mediated isothermal amplification (LAMP) temperature is set to a fixed value of 55 ◦ C [2]. However, general modules require the environment temperature to be constant and near to room temperature. This is a challenge, since the modules are shaped differently and placed very close to each other due to spatial constraints. Distributed temperature control is a general problem in various fields. Song et al. [8] introduced a method using artificial neural networks to optimize the temperature control in data centers. Shen et al. [9] designed a novel decoupling control system for high-dimensional, multi-input,

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multi-output (MIMO) room temperature control. Pohjoranta et al. [10] presented a method to control the temperature difference over the solid oxide fuel cell stack based on the predicted model. Moon et al. [11] introduced a temperature control method for an ultrasupercritical once-through boiler–turbine system using MIMO dynamic matrix control technology. The distributed MIMO temperature control problem is complex because of strong coupling and time-variance in the internal structure. The modeling method is a common decoupling method with the estimation of the action object. Li et al. [12] introduced a decoupling method in a double-level air flow dynamic vacuum system based on neural networks and prediction principle. Gil et al. [13] presented a constrained nonlinear adaptive model-based control framework applied to a distributed solar collector field. Shen et al. [14] presented the temperature uniformity control of large-scale vertical quench furnaces with a proportional–integral–derivative (PID) decoupling control system to eliminate the strong coupling effects of multi-heating zones. Although the modeling method is an effective approach to dealing with the coupling effects in some cases, it cannot meet all the demands in practical application. Furthermore, the control performances of this method usually depend on the accuracy of the developed model, which highly restricts the robustness of the system. The proportional–integral–derivative neural network (PIDNN) controller is independent of system modeling, and it is suitable for fan speed control [15–17]. Lee et al. [15] presented a PIDNN controller for a server fan cooling system. Rossomando et al. [16] used an adaptive neural PID controller for mobile robots’ trajectory tracking control. Maraba et al. [17] introduced a PIDNN-based speed control method for an asynchronous motor. To control a MIMO coupling fan cooling system, PIDNN controllers were used separately and thus could not deal with the coordination among the fans, which degraded the effectiveness of the control. In this paper, a novel MIMO temperature sensing and control system based on a fully-connected PID neural network (FCPIDNN) is developed for an integrated instrument with multi-modules. The system takes the advantages of a PIDNN controller and full-connection neural networks, and capably adjusts the internal temperature of the instrument independent of object modeling. It enables the achievement of a global optimization by self-tuning, and makes a reconfiguration under failure event. The effectiveness of the control methodology is demonstrated and validated experimentally. 2. Problem Model and Design of Self-Tuning FCPIDNN Temperature Sensing and Control System 2.1. Temperature Control Problem Formulation Due to the complexity of the thermohydrodynamic operation, it is generally difficult to build an accurate model for an instrument system. Stafford et al. [18] have made a thorough study at flat plate heat transfer with axial fan flows. They used infrared thermography to quantify a two-dimensional profile of the heat transfer coefficient on a flat plate for a range of fan speeds and the distances from fan to plate. A relationship between the fan speed and heat transfer intensity was presented. Generally, when the other conditions were kept stable, the faster the fan speed, the higher the Nusselt number in their experiments. Thus, the convective heat transfer characteristics can be changed by adjusting the fans’ speeds. Grimes et al. [19] have researched air flow and heat transfer in fan-cooled electronic systems. In their works, we can see that the heat transfer processes situated in the inlet and exit air flow from the fan varies significantly. The fan exhaling flow is unsteady and swirling, and the Nusselt number is higher, which enhances the heat transfer. However, this method makes the internal air more disordered. Based on the previous research, when the other influencing factors keep invariant, we can get the function relation of temperature and fan speed in the presented mockup as: Ti = fi (F1 , . . . , Fj , . . . , F6 ), i = 1, . . . , 6

(1)

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where Ti is the sensor’s temperature around module i, and Fj is the speed of cooling fan j. That is, the temperature variation is infulenced by the fans’ speed. As mentioned above, due to the complexity Sensors 2016, 16, 1709 configuraiton and the thermohydrodynamic coupling, the function f cannot 3 of 12be of the structural i obtained exactly. We can convert Equation (1) to another form: complexity of the structural configuraiton and the thermohydrodynamic coupling, the function fi 6Equation (1) to another form: cannot be obtained exactly. We can T convert ( aik ·F ), k = 1, . . . , 6 (2) i =

∑ k =1

k

Ti = ∑6k=1 (aik·Fk), k = 1,…, 6 aik = aik (F1 , . . . , Fj , . . . , F6 ), j = 1, . . . , 6

(2) (3)

aik = aisik (decided F1,…, Fby j,…, F6 ), j = 1,…, 6 (3)of where aik is the coefficient of Fk , which Fj (j = 1, . . . , 6). So, we can get the matrix form the function as: of Fk, which is decided by Fj (j = 1,…, 6). So, we can get the matrix form of where aik is therelation coefficient the function relation as: 

  T1 a11  ..  T1 .. a11  . = . ⋮ = ⋮ T6 T6 a61a61

  . . . a16 F1  F1 .  . .… a.. 16   .⋱ . ⋮   ..= A ⋮ . .… . a66 a66 F6 F6



 F1 F1 A  ..  =  .  ⋮ F6 F6

(4) (4)

where whereAAstands standsfor forthe therelation relationmatrix. matrix. 2.2. 2.2.MIMO MIMOTemperature TemperatureSensing Sensingand andControl ControlSystem System AsAsmentioned on the the object’s object’s model. model.The Thestructure structureof mentionedabove, above,the thePIDNN PIDNNcontroller controller does does not not rely rely on ofthe thePIDNN PIDNNcontroller controller is a three-layer network whose hidden layer neurons’ activation functions is a three-layer network whose hidden layer neurons’ activation functions work work as a controller PID controller [15–17]. The improved FCPIDNN controller proposed this takes papera takes as a PID [15–17]. The improved FCPIDNN controller proposed in this in paper seriesaof series of PIDNN controllers basic controllers adds a full connection layer the between the basic PIDNN controllers as basic as controllers and addsand a full connection layer between basic controllers controllers and the cooling fans. and the cooling fans.

PIDNN1 R1 P1

Fan1

MultiModules F1 Instrument T1

N1

PIDNNi Ri Pi

Fani

Fi

Ti

F6

T6

Ni

PIDNN6 R6 P6

Fan6

N6

Figure Structureof of fully-connected proportional–integral–derivative neural (FCPIDNN) network Figure1. 1. Structure the the fully-connected proportional–integral–derivative neural network temperature controller for an instrument. (FCPIDNN) temperature controller for an instrument.

The Thestructure structureofofthe theFCPIDNN FCPIDNNcontroller controllerisisshown shownininFigure Figure1.1.It Itcontains containsa afour-layer four-layerneural neural network. The symbol i represents the serial number (i = 1,..., 6). R i is a target temperature. Ni is the network. The symbol i represents the serial number (i = 1, ..., 6). Ri is a target temperature. Ni is fourth layer layer neuron. Pi is Ptheis pulse width modulation (PWM) control signal inputting to to fanfan i, i, the fourth neuron. the pulse width modulation (PWM) control signal inputting i which is used to control fan speed. F i is the speed of fan i. Ti is the local temperature of sensor i. The which is used to control fan speed. Fi is the speed of fan i. Ti is the local temperature of sensor i. MIMO controller includes two main parts. OneOne is six PIDNN controllers. The other is isthe The MIMO controller includes two main parts. is separate six separate PIDNN controllers. The other the full connection structure of the neural network. The structure of the PIDNN controller is shown in Figure 2, where Ri is the target temperature. Ti is the actual local temperature. Yi is the output of the PIDNN controller [15]. There are three layers in the PIDNN, including an input layer, a hidden layer, and an output layer. Each neuron has an input o and an output x. The input layer is used to estimate the difference between the set-point and the actual value. The hidden layer is composed of P, I, and D neurons, which implement a PID algorithm combined with connection weights from the

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full connection structure of the neural network. The structure of the PIDNN controller is shown in Figure 2, where Ri is the target temperature. Ti is the actual local temperature. Yi is the output of the PIDNN controller [15]. There are three layers in the PIDNN, including an input layer, a hidden layer, and an output layer. Each neuron has an input o and an output x. The input layer is used to estimate the difference between the set-point and the actual value. The hidden layer is composed of P, I, and Sensors 2016, 16, 1709 implement a PID algorithm combined with connection weights from the hidden 4 of 12 D neurons, which layer to the output layer. The output layer contains one neuron, summing the outputs of the hidden hidden layer to the output layer. Thethis output contains one neuron, summing the outputs of the layer with weights. Here we utilize kindlayer of independent PIDNN mainly to reduce the complex hidden layer with weights. Here we utilize this kind of independent PIDNN mainly to reduce the calculating cost to achieve a real-time online training. complex calculating cost to achieve a real-time online training. PIDNN P Ri

oih1 xih1 oi1 xi1 I

oiy xiy

oih2 xih2 Ti

oi2 xi2

Yi

D

oih3 xih3

Figure Figure 2. 2. Structure Structure of of the the PIDNN. PIDNN.

The full-connection the fourth layer is mainly used to full-connection structure structurefrom fromthe theoutput outputofofthe thePIDNN PIDNNtoto the fourth layer is mainly used link thethe basic controllers to the fans. As seen in Equation (4), (4), the relationship between the six and to link basic controllers to the fans. As seen in Equation the relationship between thefans six fans the temperatures can becan represented as a dimensional matrix.matrix. Under Under a slightachange of the fan andoutput the output temperatures be represented as a dimensional slight change of speed, this relationship can be approximately linear. Thereby, Equation (4) can be simplified as: the fan speed, this relationship can be approximately linear. Thereby, Equation (4) can be simplified

as: T  1



 . . . a16 l1 P1   a16 . . . a11.. …  . . .  . ⋱ ⋮ = ⋮ . . . a61 a66 … al666 P6 T6

a11  .   .  .  =  . T1  .   . ⋮ T6 a61





l 1P 1  = ⋮ = l6P6 



  a11 . . . a16 l1 wo11 . . . l1 wo61   ..a11 . … a.. 16   l1wo11 .. … . .l.1wo61 .. Y1  .. . .  . .  ⋮ ⋱ ⋮ ⋮ ⋮ ⋱ ⋮ l w . . . l w a61 . . . a 6 o16 6 o66 a61 … a6666

l6wo16 …

l6wo66

Y6

 Y1 ..   .  Y6

(5)

(5)

where woij and llii is is the the scale scale factor factor between between PPii to toFFi.i . where oij is is the the weight weight from from Y Yii to Njj, and In the toto thethe second layer areare wi11wi11 =w the PIDNNi, PIDNNi, the theweights weightsfrom fromthe thefirst firstlayer layer second layer = i12 wi12==wwi13 i13 = 1 and wi21 = i23 w=i23−1, =− 1, and weight from hidden layer to the output layer = 1, ...,The 3). i21 ==ww i22 =w and the the weight from the the hidden layer to the output layer is wisihl w(lihl= (l1,...,3). i22 The weight the third tofourth the fourth woij , where j present the serial number weight fromfrom the third layerlayer to the layerlayer is woijis, where i and ijand present the serial number from from PIDNNi to neuron Nj. goal The of goal the FCPIDNN controller to minimize the deviation of PIDNNi to neuron Nj. The theofFCPIDNN controller is to isminimize the deviation of the the actual temperature from targettemperature. temperature.The Theweights weightsare areupdated updated online online using using the actual temperature from thethe target back-propagation (BP) (BP) algorithm. algorithm. So, the cost function is is defined defined as: as: 6

11 6 J(n)J(n = )= ∑ ee2m2m((n) n) 2 2mm=1 =1

(6)

where eerepresents representsthethe difference between the target and actual temperatures, m represents the where difference between the target and actual temperatures, m represents the number number of temperature control channels, and n represents the sample number. The BP updated of temperature control channels, and n represents the sample number. The BP updated algorithm is algorithm used as: is used as: ∂J (n) ∂J(n) woij (n) =woij (n − 1) − ηo (7) woij (n) = woij (n − 1) − η∂w (7) oij ( n ) o ∂w oij (n) ∂J (n) wihl (n) =wihl (n − 1) − ηh (8) ∂J(n) ∂wihl (n) wihl (n) = wihl (n − 1) − ηh (8) ∂wihl (n) where ηo and ηh are the learning coefficients. The partial derivative terms in Equations (7) and (8) can be written as: ∂J = ∂woij

m=1

∂J ∂em ∂Tm ∂Fj ∂Pj ∂em ∂Tm ∂Fj ∂Pj ∂woij

(9)

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where ηo and ηh are the learning coefficients. The partial derivative terms in Equations (7) and (8) can be written as: ! 6 ∂J ∂J ∂em ∂Tm ∂F j ∂P j = ∑ (9) ∂woij ∂em ∂Tm ∂F j ∂P j ∂woij m =1 " !#) ( 6 6 ∂J ∂Tm ∂F j ∂P j ∂Yi ∂J ∂em = ∑ (10) ∂wihl ∂em ∂Tm j∑ ∂F j ∂P j ∂Yi ∂wihl m =1 =1 ∂Tm ∂F j

Due to the absence of the system model of the instrument, we use a sign function to deduce as: " # ∂Tm Tm ( n ) − Tm ( n − 1 ) = sgn (11) ∂F j F j ( n ) − F j ( n − 1)

2.3. Convergence Analysis Based on Equation (5) to Equation (6) and Figure 2, the difference between J(n) and J (n − 1) can be written as: !  6 3  6 6 ∂J(n) ∂J(n) (12) 4 J( n ) = J( n ) − J( n − 1) = ∑ ∑ 4 wihl (n) + ∑ ∑ 4 woij (n) ∂wihl (n) ∂woij (n) i =1 l =1 i =1 j =1 According to Equation (7) to Equation (8), we can get

4 woij (n) = woij (n) − woij (n − 1) = −ηo

∂J(n) ∂woij (n)

(13)

4 wihl (n) = wihl (n) − wihl (n − 1) = −ηh

∂J(n) ∂wihl (n)

(14)

Introducing Equations (13) and (14) into Equation (12), we can get 6

4 J( n ) = J( n ) − J( n − 1) =

3

∑∑

i =1 l =1



∂J(n) ∂J (n) − ηh ∂wihl (n) ∂wihl (n)



6

+∑

6

∑

i =1 j =1

∂J (n) ∂J (n) − ηo ∂woij (n) ∂woij (n)

! (15)

Equation (15) indicates that 4J(n) ≤ 0, meaning that the cost function J(n) converges to the minimum, implying that the system is stable. 3. Experiments and Discussion 3.1. Instrument Mockup In practical applications, the different modules in an instrument have different power consumptions. To evaluate the proposed self-tuning FCPIDNN for temperature sensing and control, a mockup of a real instrument was constructed. The 3D model of the mockup is shown in Figure 3. The mockup is 350 mm × 350 mm × 415 mm in volume with six modules inside. These modules have different shapes and volumes. Inside each module, there is a heater to generate heating and a small ventilation fan. The six heaters have different power, and the ventilation fans drive the heat out of the modules into internal public space of the mockup. Each module has a temperature sensor around itself, and there are six main cooling fans set at the back of the mockup. These cooling fans serve as temperature-tuning actuators to modulate the internal temperature of the instrument. Therefore, a temperature sensing and control system is built up with the modules, temperature sensors, and cooling fans.

3.1. Instrument Mockup In practical applications, the different modules in an instrument have different power consumptions. To evaluate the proposed self-tuning FCPIDNN for temperature sensing and control, a mockup of a real instrument was constructed. The 3D model of the mockup is shown Sensors 2016, 16, 1709 6 of 12 in Figure 3.

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The mockup is 350 mm × 350 mm × 415 mm in volume with six modules inside. These modules have different shapes and volumes. Inside each module, there is a heater to generate heating and a small ventilation fan. The six heaters have different power, and the ventilation fans drive the heat out of the modules into internal public space of the mockup. Each module has a temperature sensor around itself, and there are six main cooling fans set at the back of the mockup. These cooling fans serve as temperature-tuning actuators to modulate the instrument. (a) (b) the internal temperature of (c) Therefore, a temperature sensing and control system is built up with the modules, temperature Figure (a)The Theappearance appearanceof of the the instrument; instrument; (b) model with sixsix Figure 3. 3.(a) (b) The Theperspective perspectiveview viewofofthe the3D3D model with sensors, and cooling fans. modules inside and six cooling fans at the backplane; (c) The internal configuration of the modules inside and six cooling fans at the backplane; (c) The internal configuration of the instrument. instrument.

3.2. Experimental System and Results 3.2. Experimental System and Results The temperature sensing and control system was applied to a mockup of an instrument with multi-modules, as illustrated Figure 4a. system The instrumentation a mockup, power supply The temperature sensing in and control was appliedincludes to a mockup of anainstrument with (KEITHLEY 2260b-30-72), a temperature sensors (DS18B20) array, a tailor-designed data processing multi-modules, as illustrated in Figure 4a. The instrumentation includes a mockup, a power supply circuit, and2260b-30-72), a data monitoring computer. The system usedarray, the FCPIDNN controller mentioned (KEITHLEY a temperature sensors (DS18B20) a tailor-designed data processing above to perform the online temperature control. The details of the mockup have been presented circuit, and a data monitoring computer. The system used the FCPIDNN controller mentioned above previously. Figure 4b shows the back view of the mockup, with six fans indicated as fan1 to fan6. to perform the online temperature control. The details of the mockup have been presented previously. Figure 4c shows the internal layout of the mockup. The power supply was used to provide electrical Figure 4b shows the back view of the mockup, with six fans indicated as fan1 to fan6. Figure 4c energy to the heaters inside the six modules, simulating the heating behavior of the modules. The shows the internal layout of the mockup. The power supply was used to provide electrical energy powers of the heaters inside modules 1 and 6, modules 2 and 3, and modules 4 and 5 are set to 24W, to the heaters inside the six modules, simulating the heating behavior of the modules. The powers 48W, and 96W, respectively. The temperature sensors were used to detect the local temperatures of the heaters inside modules 1 and 6, modules 2 and 3, and modules 4 and 5 are set to 24W, 48W, around the six modules. The data processing circuit, including a field-programmable gate array and 96W, respectively. The temperature sensors were used to detect the local temperatures around (FPGA, EP2C35F484), acquired the temperatures around the six modules from temperature sensors thethrough six modules. The data processing circuit, including (UART) a field-programmable gate (FPGA, universal asynchronous receiver and transmitter port, implemented thearray developed EP2C35F484), acquired the temperatures around the six modules from temperature sensors through self-tuning temperature control and outputted the PWM control signals to the fans. The data universal asynchronous receiver (UART) port, implemented developedcomputer self-tuning processing circuit also outputand thetransmitter temperature information to the datathe monitoring temperature control and outputted the PWM control signals to the fans. The data processing circuit through the UART port. also output the temperature information to the data monitoring computer through the UART port.

(a) Figure 4. Cont.

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(b) (b)

(c) (c)

Figure 4. (a) Structure of the temperature sensing and control system; (b) Back view of the Figure 4. (a) Structure of the temperature sensing and control system; (b) Back view of the instrument instrument (c) Internal temperature layout of the sensing mockup.and PCB:control printedsystem; circuit board. Figure 4. Internal (a)mockup; Structure (b) Back view of the mockup; (c) layoutofofthe the mockup. PCB: printed circuit board. instrument mockup; (c) Internal layout of the mockup. PCB: printed circuit board.

Figure 5 shows the top level structure diagram of the FPGA’s program. The temperature Figure 5 shows thethe top level structure diagram of Then, the program. The temperature signals are transported to top the FPGA by a UART port. theFPGA’s temperatures are extracted by asignals data Figure 5 shows level structure diagram of FPGA’s the program. The temperature aresignals transported to the FPGA by a UART port. Then, the temperatures are extracted by a data converter sent to the FCPIDNN together with set-points.are Finally, the calculated are and transported to the FPGA bycontroller a UART port. Then, the the temperatures extracted byconverter a data and sent toare the FCPIDNN with the set-points. Finally, the calculated results are results converted to controller the PWM together signals and output to thethe fans. The number of the the calculated total logic converter and sent to the FCPIDNN controller together with set-points. Finally, converted toused the PWM and output to and the fans. The number thetotal totalcombination logic used elements in thesignals FPGA 32,754. Specifically, the ofofthe functions results are converted to the was PWM signals output tonumber the fans. The number of elements the total logic in and dedicated logic registers are32,754. 32,020 and 4382, respectively. theelements FPGA was 32,754. the number of the total combination and dedicated logic used in theSpecifically, FPGA was Specifically, the number of the functions total combination functions and dedicated logic registers are 32,020 and 4382, respectively. registers are 32,020 and 4382, respectively.

Figure 5. Structure of the FCPIDNN temperature controller for the instrument. PWM: pulse width Figure 5. 5. Structure ofofthe temperature controller for the theinstrument. instrument.PWM: PWM: pulse width modulation. UART: universal asynchronous receiver and transmitter. Figure Structure theFCPIDNN FCPIDNN temperature controller for pulse width modulation. UART: universal asynchronous receiver and transmitter. modulation. UART: universal asynchronous receiver and transmitter.

To demonstrate the control performances of the proposed method in a MIMO temperature sensing and control we conducted three andmethod compared the temperature conventional To demonstrate the control performances ofexperiments the proposed in awith MIMO To demonstrate thesystem, control performances of the proposed method in a MIMO temperature sensing method. The first experiment was conducted by comparing the temperature responses of the sensing and control system, we conducted three experiments and compared with the conventional and control system, we conducted three experiments and compared with the conventional method. instrument using FCPIDNN controller and a traditional controller. The second method. Thebyfirst experiment was conducted by comparing the PIDNN temperature responses of the The first experiment wasa conducted by comparing the temperature responses of the instrument experiment was conducted to demonstrate the self-tuning of the controller when the target instrument by using a FCPIDNN controller and a traditional PIDNN controller. The second by using a FCPIDNN controller and a traditional PIDNN controller. The second experiment was temperaturewas changed in-process. The third experiment was to simulate the experiment conducted demonstrate the controller self-tuningwhen of the controller when the changed target conducted to demonstrate thetoself-tuning of the theconducted target temperature reconfiguration of the control systemThe whenthird a pop-up actuator fail temperature changed in-process. experiment wasoccurred. conducted to simulate the in-process. The third experiment was conducted to simulate the reconfiguration of the control system reconfiguration of the control system when a pop-up actuator fail occurred. when a pop-up actuator fail occurred.

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60 60 55 55 50 50 45 45

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Figures and show the control Figures666and and 777 show show the the control control results using conventional conventional PIDNN and FCPIDNN controllers, Figures results using conventionalPIDNN PIDNNand andFCPIDNN FCPIDNNcontrollers, controllers, respectively. Figure 6a shows the results using a PIDNN controller to control respectively. Figure 6a shows single module respectively. shows the the results results using using aa PIDNN PIDNN controller controller to to control controlaaasingle singlemodule module temperature. Figure 6b shows the results using six separate PIDNN controllers to control temperature. Figure 6b shows the results using six separate PIDNN controllers to control the temperature. Figure 6b shows the results using six separate PIDNN controllers to controlthe the temperatures of the six modules. Each controller worked in its own separate control loop. We can temperatures of of the the six six modules. modules. Each Each controller temperatures controller worked worked in in its its own own separate separatecontrol controlloop. loop.We Wecan can see from the results that the PIDNN could temperature of one module seefrom fromthe the results results that that the the PIDNN PIDNN could could control control the the environmental environmental see control the environmental temperature temperatureof ofone onemodule module very well, but brought steady-state errors when controlling for multiple modules. The steady-state very well, but brought steady-state errors when controlling for multiple modules. The steady-state very well, but brought steady-state errors when controlling for multiple modules. The steady-state temperatures of several controlled not converge to the target, due to the presence of the temperatures of of several several controlled controlled objects objects did did temperatures objects did not not converge converge to to the thetarget, target,due dueto tothe thepresence presenceofofthe the mutual interference among the cooling fans. To solve this problem, we need to build connections mutual interference among the cooling fans. To solve this problem, we need to build connections mutual interference among the cooling fans. To solve this problem, we need to build connections among the controllers and thus ensure the controlling global optimization. amongthe thecontrollers controllersand andthus thus ensure ensure the the controlling controlling processes processes tending tending to to among processes tending to global global optimization. optimization. 60 60 55 55 50 50 45 45

T-1 T-1 T-2 T-2 T-3 T-3 T-4 T-4 T-5 T-5 T-6 T-6 T-target T-target

Controller started working Controller started working

40 40 35 35 30 30 25 250 0

(a) (a)

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(b) (b)

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(a) (a)

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Figure (a) Control results of aa PIDNN controller for module; (b) results of Figure6.6. 6.(a) (a)Control Control results PIDNN controller for single single module; (b) Control Control of six six Figure results of aofPIDNN controller for single module; (b) Control results results of six separate separate PIDNN controllers for the six modules (Target temperature is 33 °C). ◦ separate PIDNN controllers for the six modules (Target temperature is 33 °C). PIDNN controllers for the six modules (Target temperature is 33 C).

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Figure (a) Control results of the FCPIDNN controller (Target temperature °C); Variation ◦ C); Figure7.7. 7.(a) (a)Control Controlresults resultsof ofthe theFCPIDNN FCPIDNNcontroller controller(Target (Target temperature 33 °C); (b) Variation of Figure temperature 3333 (b)(b) Variation of of the p ( J(n)). the square root of the cost function the square ofcost the cost function square root root of the function ( J ((nJ(n)). )).

Figure 7a shows the results using the FCPIDNN controller. experimental condition was Figure 7a 7a shows shows the the results results using using the the FCPIDNN FCPIDNN controller. controller. The The Figure The experimental experimentalcondition conditionwas was the same as Figure 6a. Figure 7b shows the corresponding variation of square root thesame same as as that that in in shows thethe corresponding variation of the the root of of the theof the that in Figure Figure6a. 6a.Figure Figure7b7b shows corresponding variation of square the square root cost function. We can see that the temperature of different modules tended to the setting targets costcost function. WeWe cancan seesee that thethe temperature ofof different the function. that temperature differentmodules modulestended tendedtotothe thesetting settingtargets targets simultaneously, and the cost function’s variation shows that the difference between the actual and simultaneously, and and the the cost cost function’s function’s variation variation shows simultaneously, shows that that the the difference differencebetween betweenthe theactual actualand and target temperatures decreased and approached the minima. There were no steady-state errors in target temperatures decreased and approached the minima. There were no steady-state errors in the the target temperatures decreased and approached the minima. There were no steady-state errors in the temperature, temperature, and and the the control control obtained obtained aa global global convergence. convergence. temperature, and the the control obtained a using globalFCPIDNN convergence. Figure 8 shows control results Figure 8 shows the control results using FCPIDNN controller controller when when target target temperature temperature varied varied Figure 8There shows the three control results control using FCPIDNN controller when target temperature varied in process. were different processes. Figure 8a,b (process 1) in process. There were three different control processes. Figure 8a,b (process 1) shows shows the the control control in process. There were three differenttarget control processes. Figure 8a,b In (process 1) showscontrollers the control results results when when one one temperature temperature control control target changed changed in in aa stable stable state. state. In the the process, process, six six controllers results when one temperature control target changed in a stable state. In the process, six controllers maintained at the maintained the the six six modules’ modules’ temperature temperature at at 32 32 °C °C the beginning. beginning. Then, Then, the the target target temperature temperature of of ◦ C at maintained the six modules’ temperature at 32 at the beginning. Then, the target temperature of module module six six was was changed changed to to 34 34 ◦°C, °C, and and others’ others’ temperatures temperatures remained remained unchanged. unchanged. After After aa period period of of module six wasthe changed to 34controller, C, and others’temperatures temperatures remained unchanged. After a period of self-tuning self-tuning by by the FCPIDNN FCPIDNN controller, the the temperatures of of all all modules modules approached approached to to their their own own self-tuning by the FCPIDNN controller, the temperatures of all modules approached to their own targets, targets, and and the the cost cost function function gradually gradually reduced reduced to to the the minima. minima. Figure Figure 8c,d 8c,d (process (process 2) 2) show show targets, and the cost function gradually reduced tochanged the minima. Figure 8c,d (process 2) show another another control result when temperature target to different values. In the process, another control result when temperature target changed to different values. In the process, the the control result when temperature target changedthe to different values. In themodules process, the2,temperature temperature temperature initially initially remained remained at at 35 35 °C. °C. Then, Then, the target target temperature temperature for for modules 1, 1, 2, and and 66 was was

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initially remained at 35 Then, the target temperature for modules 1, 2, and 6 was changed to changed to 33.5 andtemperature the target temperature 3, 4,changed and 5 was to 32 °C. After 33.5 ◦ C, and the °C, target for modulesfor 3, modules 4, and 5 was to changed 32 ◦ C. After a period of aself-tuning, period of all self-tuning, all modules approached their target temperatures separately. Figure 8e,f modules approached their target temperatures separately. Figure 8e,f (process 3) shows (process 3) results showswhen the control results when the temperature for all twice modules was changed the control the target temperature fortarget all modules was changed in the process; i.e., ◦ C, andthen twice in the thebeginning, process; i.e., °C at the beginning, changed andFCPIDNN finally changed to 35 ◦ C at then35changed to 32.5 finally changedtoto32.5 30 ◦°C, C. The controller 30 °C. The FCPIDNN controller successfully modulated the temperature of the modules to the successfully modulated the temperature of the modules to the setting targets and the square roots of setting and the roots of the cost function got to minima at last. the costtargets function got tosquare minima at last.

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Figure 8. (a) (a)Control Controlresults results of the FCPIDNN controller one temperature control target Figure 8. of the FCPIDNN controller when when one temperature control target changed pfunction ( J(n)) in process (a); changed in a stable state; (b) Variation of the square root of the cost in a stable state; (b) Variation of the square root of the cost function ( J (n)) in process (a); (c) Control (c) Control results of thecontroller FCPIDNN controller when control temperature targets changed to ones two results of the FCPIDNN when temperature targetscontrol changed to two different p different halfway;of(d) of the square root of the ( J(n)) in Control process results (c); (e) halfway; ones (d) Variation theVariation square root of the cost function ( cost J (n)function ) in process (c); (e) Control results of the FCPIDNN controller when temperature control targets changed twice in the of the FCPIDNN controller when temperature control targets changed twice in the control process; p control process; (f) Variation of the square root of the cost function ( J(n)) in process (e). (f) Variation of the square root of the cost function ( J (n)) in process (e).

Reliability of temperature control is generally very important in practical use. When a fan fails Reliability of temperature control is generally very important in practical use. When a fan fails to to work, the system can make a self-reconfiguration to adapt to this situation. To validate the work, the system can make a self-reconfiguration to adapt to this situation. To validate the reliability, reliability, we conducted an experiment by setting the target temperature of all modules to 32.5 °C we conducted an experiment by setting the target temperature of all modules to 32.5 ◦ C at the beginning at the beginning of the process, and then shut off one fan. Figure 9a,b shows the control results of the process, and then shut off one fan. Figure 9a,b shows the control results when all fans were when all fans were working. Figure 10 shows the control results when fan 2 failed. Figure 11 shows the control results when fan 3 failed. We can see that the temperatures of the modules could be modulated to the setting targets, even though one fan failed.

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working. Figure 10 shows the control results when fan 2 failed. Figure 11 shows the control results when fan 3 failed. We can see that the temperatures of the modules could be modulated to the setting Sensors 2016, 16, 1709 10 of 12 Sensors 1709 10 targets, even though Sensors2016, 2016,16, 16, 1709 one fan failed. 10of of12 12

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Figure results of the controller when were working (target Figure 9. (a) Control results of the FCPIDNN controller when all fans were working (target Figure 9. (a) (a) Control Control results ofFCPIDNN the FCPIDNN FCPIDNN controller when all fans fans were (target working (target Figure 9. 9. (a) Control results of the controller when all fans all were working temperature pfunction ( J(n)). temperature is 32.5 °C); (b) Variation of the square root of the cost ◦ temperature is 32.5 °C); (b) Variation of the square root of the cost function ( J(n)). temperature is 32.5 °C);of(b) Variation of the root of the cost is 32.5 C); (b) Variation the square root ofsquare the cost function ( Jfunction (n)). ( J(n)).

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Figure 10. results of the when Figure 10. (a) (a) Control Control results of the FCPIDNN controller when fan fan 222 failed failed (target (target temperature temperature is isis Figure Controlresults resultsof of the the FCPIDNN FCPIDNN controller controller Figure 10.10.(a)(a)Control FCPIDNN controller when whenfan fan 2failed failed(target (targettemperature temperature is p 32.5 °C); (b) Variation of the square root of the cost function ( J(n)). 32.5 °C); (b) Variation of the square root of the cost function (( J(n)). 32.5 °C); (b) Variation of the square root of the cost function J(n)). ◦ 32.5 C); (b) Variation of the square root of the cost function ( J (n)).

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Figure Figure 11. (a) (a) Control Control results of the FCPIDNN controller when fan failed (target (target temperature temperature is isis Figure11. Control results results of of the the FCPIDNN FCPIDNN controller controller when when fan fan 333 failed Figure 11.11. (a)(a) Control results of the FCPIDNN controller when fan 3failed failed(target (targettemperature temperature is 32.5 °C); (b) Variation of the square root of the cost function ( J(n)). p 32.5 °C); (b) Variation of the square root of the cost function ( J(n)). 32.5 °C); (b) Variation of the square root of the cost function ( J(n)). 32.5 ◦ C); (b) Variation of the square root of the cost function ( J (n)).

From From the experiments, we can see that both FCPIDNN and PIDNN can control the system From the the experiments, experiments, we we can can see see that that both both FCPIDNN FCPIDNN and and PIDNN PIDNN can can control control the the system system without the need of the model. The FCPIDNN can successfully deal with the coupling From experiments, we can see that both FCPIDNN and PIDNN can control the system without without MIMO without the the need need of of the the model. model. The The FCPIDNN FCPIDNN can can successfully successfully deal deal with with the the coupling coupling MIMO MIMO system with global optimum, but PIDNN can only control the temperature for one module, and the need of theglobal model. The FCPIDNN can successfully dealthe with the coupling system with system with optimum, but can temperature for one and system with global optimum, but PIDNN PIDNN can only only control control the temperature forMIMO one module, module, and will bring errors when controlling multiple coupling modules. In addition, FCPIDNN can make will bring errors when controlling multiple coupling modules. In addition, FCPIDNN can make global optimum, but PIDNN can only control the temperature for one module, and will bring errors will bring errors when controlling multiple coupling modules. In addition, FCPIDNN can make self-reconfiguration to actuator fail. capabilities enhance the robustness of self-reconfiguration to the actuator fail. The above capabilities enhance the robustness of the control when controlling multiple In addition, FCPIDNN can make self-reconfiguration self-reconfiguration tothe thecoupling actuatormodules. fail.The Theabove above capabilities enhance the robustness ofthe thecontrol control to system and make the system smart, aiming at any possible scenario. system and make the system smart, at possible scenario. the actuator The capabilities enhance robustness of the control system and make the system andfail. make theabove system smart,aiming aiming atany anythe possible scenario.

system smart, aiming at any possible scenario. 4. 4. Conclusions 4.Conclusions Conclusions In In this paper, we developed MIMO self-tuning temperature sensing and control system with Inthis thispaper, paper,we wedeveloped developedaaaMIMO MIMOself-tuning self-tuningtemperature temperaturesensing sensingand andcontrol controlsystem systemwith with aaanovel FCPIDNN controller for an instrument with multi-modules. A mockup system was built novel FCPIDNN controller for an instrument with multi-modules. A mockup system was built up novel FCPIDNN controller for an instrument with multi-modules. A mockup system was builtup up

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4. Conclusions In this paper, we developed a MIMO self-tuning temperature sensing and control system with a novel FCPIDNN controller for an instrument with multi-modules. A mockup system was built up to mimic the complicated environment in the instrument and test the effectiveness of the MIMO self-tuning system. The MIMO temperature sensing and control system can adjust the internal temperature environment of the instrument without the need for system modeling. It can get to a global optimal result by on-line self-tuning. The system is applicable to effectively control the internal temperature of an instrument aiming at various mission scenarios, in particular, it is able to self-reconfigure upon actuator failure. Acknowledgments: This study was supported by the National Key Scientific Instrument and Equipment Development Projects, China (Grant No. 2013YQ19046705). Author Contributions: Zhen Zhang and Cheng Ma conceived and designed experiments; Zhen Zhang performed the experiments; Zhen Zhang and Cheng Ma analyzed the data; Cheng Ma and Rong Zhu contributed materials and analysis tools; Zhen Zhang wrote the paper; Cheng Ma and Rong Zhu revised the manuscript. Conflicts of Interest: The authors declare no conflict of interest.

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