A novel intelligent adaptive control of laser-based ground thermal test

Gan Zhengtao,Yu Gang,Li Shaoxia,He Xiuli,Chen Ru,Zheng Caiyun,Ning Weijian

Key Laboratory of Mechanics in Advanced Manufacturing,Institute of Mechanics,Chinese Academy of Sciences,Beijing 100190,China

A novel intelligent adaptive control of laser-based ground thermal test

Gan Zhengtao,Yu Gang*,Li Shaoxia,He Xiuli,Chen Ru,Zheng Caiyun,Ning Weijian

Key Laboratory of Mechanics in Advanced Manufacturing,Institute of Mechanics,Chinese Academy of Sciences,Beijing 100190,China

Laser heating technology is a type of potential and attractive space heat flux simulation technology,which is characterized by high heating rate,controlled spatial intensity distribution and rapid response.However,the controlled plant is nonlinear,time-varying and uncertainty when implementing the laser-based heat flux simulation.In this paper,a novel intelligent adaptive controller based on proportion–integration–differentiation(PID)typefuzzy logic is proposed to improve the performance of laser-based ground thermal test.The temperature range of thermal cycles is more than 200 K in many instances.In order to improve the adaptability of controller,output scaling factors are real time adjusted while the thermal test is underway.The initial values of scaling factors are optimized using a stochastic hybrid particle swarm optimization(H-PSO)algorithm.A validating system has been established in the laboratory.The performance of the proposed controller is evaluated through extensive experiments under different operating conditions(reference and load disturbance).The results show that the proposed adaptive controller per forms remarkably better compared to the conventional PID(PID)controller and the conventional PID typefuzzy(F-PID)controller considering performance indicators of overshoot,settling time and steady state error for laser-based ground thermal test.It is a reliable tool for effective temperature control of laser-based ground thermal test.

1.Introduction

Thermal test processes are implemented during the qualification process of space device development.Environmental conditions in space contain the transient thermal load and vacuum are simulated to guarantee that a given space device will operate efficiently when subjected to real environments much different from those on earth.1It has been proved that the ground based testing method plays a highly important role in the development of the space device.2–4The external thermal flux simulation system is essential for the effective working of the thermal tests.At present,the conventional external thermal flux simulation system includes solar simulator,infrared heater and contact electric heater.5,6It has been reported that there were plenty of successful thermal tests using these external thermal flux simulation systems.7–10However,as the requirements appear for complex structure,accurate temperature control and rapid heating-up in some applications of thermal tests such as parabolic antennas,solar panels and precision optical systems,11there is an urgent need for better external thermal flux simulation techniques capable of handling better steerability of space and time than the conventional thermal flux simulation techniques.

Laser-based external thermal flux simulation technique is a promising candidate for ground thermal test for two major reasons.Firstly,laser beam has remarkable steerability of space.The spatial intensity distribution of laser beam can be shaped into the non-symmetry and non-uniform pattern by geometrical trans form method12–19to meet the pressing needs of thermal tests of complex structures.Instead of the complicated design process of the conventional thermal flux simulation system by combining the infrared heaters and contact electric heaters,the intensity distribution of laser beam can be directly and specially designed based on the orbital temperaturefield of space devices to have better alignment between the real space environment and ground test environment.Secondly,the time response of laser heat flux simulation system is much faster than the conventional external thermal flux simulation systems.It might be difficult to precede high-accuracy transient thermal test by combining the infrared heater and contact electric heater due to the limit of the time response of heat flux simulation system.11However,the time response of laser heat flux simulation system is less than 100 ms.Using the laser heat flux simulation system can improve greatly the accuracy of transient thermal test and simulate the change of the real on-orbit temperature of space devices.There fore,this paper presents a well-designed laser heat flux simulation system to improve the suitability and stability of the ground thermal test.

Effective thermal controller for heat flux simulation system is crucial for reliable working of the ground thermal test.Some befitting approaches of temperature control for ground thermal tests have been reported.The conventional PID controllers were improved based on arranging the transient process for the ground thermal test.20A real-time process simulator used by PLC programming for the ground thermal test was reported.21In many instances of ground thermal test,such as solar panels,the temperature range of thermal cycles is more than 200 K.11In order to develop the adaptability of controller,in recent years,several self-tuning controllers that continuously update the parameters of controller were proposed.The advantage of these controllers is that the parameters can be adjusted on-line to improve their adaptability.A fuzzy-PID controller was put forward for the thermal tests of space devices.22A fuzzy reference gain-scheduling control approach(FRGS)was investigated to control thermal vacuum chambers automatically and satisfy testing requirements.23,24A approach based on particle swarm optimization(PSO)and Takagi–Sugeno(TS)fuzzy model for describing dynamical behavior was proposed for thermal vacuum test systems.25,26The main limitation of the most reported works is that these controllers are used to thefirst-order or second-order linear system with dead time while it is difficult to apply these controllers to the processes of higher order nonlinear systems.

However,introducing the laser heat flux simulation system makes the controlled plant extremely nonlinear,time-varying and uncertainty.The performance of the above controllers for laser-based ground thermal test might be unsatisfactory in terms of large overshoot and excessive oscillation.There fore,the aim of this paper is to develop a new intelligent adaptive controller based on thefuzzy logic to improve the performance of the laser-based ground thermal test.An adaptive PID typefuzzy logic controller is proposed by continuously adjusting the scaling factors of controller using an updating factor.A stochastic hybrid particle swarm optimization(H-PSO)algorithm is introduced to tune the initial values of scaling factors.To verify the performance of the proposed controller,a validating thermal test system has been established in the laboratory and the performance of the proposed controller is compared with the conventional PID(PID)controller and the conventional PID typefuzzy(F-PID)controller considering performance indicators of overshoot and settling time.

2.System description and dynamical modeling

2.1.Apparatus of laser-based thermal tests

The proposed laser-based thermal vacuum test system consists of a chamber,laser thermal flux simulation system,temperature measure system,intelligent adaptive thermal control system,center control,laserbeam shaping system18and cryogenic vacuum pump system(Fig.1).An Nd:YAG highpower continuous solid laser HLD1001.5 was used as the heat source of the laser-based ground thermal test.For simulating the orbit environmental conditions,firstly,vacuum was reached by using cryogenic vacuum pump system,and then the space device was heated for simulating orbit thermal cycles.For precisely emulating the temperature distribution of the space device in space,laser beam was shaped in a nonuniform spatial intensity distribution by the laser beam shaping system.In order to implement the transition thermal test,the surface temperatures of key points were measured by two infrared thermometers.The thermometers which were produced by Raytek Company were collected with the sampling interval 100 ms.The measurements of the thermometers were taken as the input of the intelligent adaptive controller.The output of the controller was the change of power of the laser beam.The main parameters of the laser-based thermal test are provided in Table 1.

2.2.Dynamical modeling of laser-based thermal test

As described in previous section,since the heating rate of laser is much faster than the rate of heat conduction inside the space device,temperature gradient of the space device should not be neglected.Thus heat conduction and radiation are the major heat sources of heat transfer for the space device.27The differential Eq.(1)of the laser-based thermal test process depends nonlinearly on local temperature T,as follows:

Fig.1 Schematic of laser-based thermal vacuum test system.

Table 1 Parameters of laser-based thermal test.

where ?T/?t denotes the transition rate,T denotes the mean temperature on the measure point,Tabis the ambient temperature,?T/?x,?T/?y and ?T/?z denote the temperature gradient in the coordinate direction,k denotes the thermal conductivity,cpdenotes the heat capacity,ρ denotes the density of the space device,σ denotes the Stefan–Boltzmann constant,ε denotes the emission capacity,and A denotes the equivalent radiated area of measure point.

From Eq.(1),the controlled plant is nonlinear.Because the the rmophysical property of space device depends on temperature,the controlled plant is time-varying.The controlled plant is also time-delaying because of the optical properties of the space devices under test as well as its physical properties such as specific heat capacity and equivalent thermal conductivity.Furthermore,it is extremely difficult to obtain all the thermophysical property depending on temperature as well as the optical parameters such as absorptivity and reflectivity of laser,so the controlled plant is uncertainty.Based on the above points,the conventional control method might be inappropriate for the laser-based ground thermal test.This paper advocates the use of an adaptive PID typefuzzy logic control approach for thermal control.Fuzzy logic control,as an intelligent control approach,can count human experience into control system.28Because the fuzzy logic control systems have ability to handle uncertain nonlinear system,this method is a beneficial choice for controlling laser-based thermal test.

3.Intelligent adaptive control strategy

An intelligent adaptive PID fuzzy logic control strategy is proposed and explained.The proposed control system is shown in Fig.2.It includes a PI and a PD fuzzy logic control.

Fig.2 Intelligent adaptive control system structure diagram.

The control system shown in Fig.2 consists of process and controller and there is a load disturbance affecting the control process.Due to the load disturbance,controlled plant tends to drive away from its desired temperature.The process variable Tobis the real temperature of measure point which is controlled.In this study,only one measure point is chosen.This measure point is located in the center of the laser irradiation where the local temperature is the highest than that in other locations.Using the measure point layout,the maximum temperature in the specimen can be controlled during the thermal test process.The controlled plant is affected by the control variable UPID_AF.In this paper,the output signals of controller can be equivalent to the laser output power,since the used laser machine HLD1001.5 is controlled by the digital control(i.e.,PROFIBUS).The controller has two inputs and one output.The inputs are the measured temperature T and the reference temperature Trefand the output is the control signal(i.e.,laser power)UPID_AF.θ and θ*are adaptive factors of the controller.

The proposed controller can be divided into three parts:a PI typefuzzy logic controller(PI-FLC),a conventional PD controller and an adaptivefuzzy controller.The combination of the PI-FLC and PD controller can provide a concise and worthy control configuration.By tuning the parameters(scaling factors)of PI-FLC and PD controller,relative great control performance can be obtained for laser-based ground thermal test.However,the main limitation of the PI-FLC and PD controller is that the performance of the controller directly depends on the scaling factors which arefixed during the process.So an extra adaptive fuzzy part is introduced into the proposed controller to on-line adjust the scaling factors of PI-FLC and PD controller.The proposed controller contains seven tuning parameters(α1-α7)to adjustthe control response.As shown in Fig.2,α1and α2are the scaling factors of input,α3and α4are defined as the scaling factors of PI-FLC controller,and α5and α6represent the scaling factors of PD controller.A novel on-line approach is proposed to adaptively adjust the output scaling factors via the parameter of α7.There fore,the benefits of the proposed intelligent adaptive control over the conventional PID control(PID)or conventional PID typefuzzy logic control(F-PID) for laser-based thermal test system are as follows:

(1)The output laser power(UPID_AF)is approximately proportional to the temperature error(input).The proposed controller has reason to be a great substitution of the PID control.

(2)Each section of the proposed controller can be improved independently for the outstanding performance of controller.

(3)The controller contains seven necessary parameters(α1-α7),and thus it has capacity to be optimized to have better performance.

(4)Because the scaling factors are real time adjusted during the ground thermal test, the control performance like overshoot and settling time can be minimized.

3.1.Membership functions

The membership functions of fuzzy control 1 and fuzzy control 2 for the inputs on the normalized interval[-1,1](e*and ce*)and the outputs on the normalized interval[0,1](kP_Fand kI_F)are shown in Fig.3.The Gauss membership function is used.The inputs and outputs related to rule bases are presented in Table 2.The membership functions of thefuzzy control 2 for output on the normalized interval[0,1](θ)are presented in Fig.4.Thefuzzy sets and linguistic values are shown in Table 3.

3.2.Stability analysis

In order to obtain the stability condition of controlled system,firstly,by analyzing the structure of proposed controller(Fig.2),the fuzzy gains(K′P_F,K′I_F,K′D_F,TI_Fand TD_F)and transfer function can be obtained.In this section,the adaptive factor θ*is neglected to simplify the analysis.Then,the bounded-input/bounded-output(BIBO)stability of the proposed controlled system can be analyzed by using the‘small-gain theorem”.29

From the block diagram(Fig.2),the proposed controller is designed to have its own fuzzy proportional factor(K′P_F),fuzzy integral factor(K′I_F)and fuzzy derivation factor(K′D_F),which can be formulized as follows(F{α}denotes the fuzzy transfer function):

Fig.3 Membership functions.

Table 2 Rule base for kP_Fand kI_F.

Fig.4 Membership functions for θ.

Table 3 Fuzzy sets and linguistic values.

Theorem.A sufficient condition for the nonlinear fuzzy PID control system to be BIBO stable is that the given nonlinear process has a bounded norm(gain)as‖Φ‖＜∞ and the parameters of the fuzzy PID controller,we,wΔe,wu,wΔu,(or K′P_F,TI_Fand TD_Fin Eqs.(3)–(8)),satisfy

where ‖Φ‖ is the operator norm of the given Φ（·）,or the gain of the given nonlinear system,usually defined as30

If a nonlinear control system can be given,the stability condition of controlled system can be obtained by substituting Eq.(3)–(8)into the Eq.(9).

3.3.Output scaling factors

To adjust the output scaling factors on-line,an adaptive method using fuzzy rule base is presented to tune θ.The dynamic relationships between the parameters of the proposed controller and the scaling factors are listed below:

3.4.Rule bases of fuzzy control 2

For improving the adaptation of the proposed controller,the rule bases of fuzzy control 2 are presented to adjust θ(Table 4).The following fuzzy rule clauses have been taken into account:

(1)For achieving the better performance in terms of overshoot and settling time,when e*is big,while e*and ce*are opposite signs,the gain θ is modified larger.This can be written in IF-THEN clauses:if e*is PB and ce*is NB,then θ is VB.

(2)For decreasing the impacts caused by delays,a small value of θ is modified to ensure the controller work within the excepted range.When e*is positive and big,but e*and ce*have the same sign,the gain θ should be adjusted small to prevent performance of controller deterioration.This can be written in IF-THEN clauses:if e*is PB and ce*is PB,then θ is Z.

(3)Based on the demand of thermal test,there should be a

sharp variation of the gain θ around the reference temperature to avoid overlarge overshoots.For example,if e*is Z and ce*is NB,then θ is VS.This clause denotes that the controlled process is just near the reference temperature and rapidly away from it.In this case,a relative small θ should be modified to prevent the upward more excessively resulting in a relatively acceptable overshoot.

3.5.Design method of scaling factors

The proposed intelligent adaptive controller is engaged with both the PI-FLC and PD effects and the influence of adaptivefactor θ makes the gain design more complicated and timeconsuming.Thus,in this study,a H-PSO algorithm is applied to tune scaling factors(α1-α7).It has been proved that the HPSO algorithm can combine the benefits of the PSO and BFO algorithm as well as avoid their defects.31It is reported that the performance of PSO and BFO is limited because of premature convergence.The particles are easy to converge in the local optimal point;however,the global optimal point has been passed.32The H-PSO algorithm breaks through this shortcoming by using the method of elimination dispersal of bacteria,and hence the ability of converging to the global optimal point is improved.The details of H-PSO algorithm are presented in the literature.31,33,34

Table 4 The proposed rule bases for θ.

The performance of the proposed stochastic algorithm extremely depends on the objective function and incorporated performance indicators.Because the conventional indicators of integral absolute error (IAE)and integral-of -timemultiplied absolute error(ITAE)hardly accurately represent the performance of the controller,35this paper contains the objective function listed below:

where e is the error of controlled system,UPID_Fis the controller output at the time t,β1-β4are the weight factors,tris the rising time of controlled plant and△T=T(t)-T(t-1).

4.Experimental results

To validate the effectiveness of the proposed intelligent adaptive controller,three different controllers including PID control,PID type fuzzy controland proposed intelligent adaptive control were considered in a verifying laser-based ground thermal test system,which is shown in Section 2.1.The Ziegler–Nichols method was used to design the PID and the stochastic genetic algorithm(GA)method34was used to tune the scaling factors of F-PID while the proposed H-PSO algorithm was used for the intelligent adaptive control.The tuned gains for each method are shown in Table 5.

Figs.5(a)and(b)show the reference temperature and load disturbance for the verifying laser-based thermal test.The variation of the output fuzzy part 2 gains(θ)is shown in Fig.5(c).Fig.5(d)indicates the responses with the reference and load disturbance changes.The details of Fig.5(d)are shown in Figs.5(e)and(f).The performance indicators of settling time and overshoot are shown in Table 6.The error band of τ*is 0.05 K for temperatures and 2%final value for others,and units for σ*are ‘K” for temperatures and% for others in Table 6.

As it can be seen in Fig.5 and Table 6,the proposed intelligent adaptive control remarkably improves the performance of the F-PID and PID controller.The F-PID decreases the settling time and overshoot partly compared with the PID controller;however it causes the fluctuation of controlled temperature.This shortcoming has been tackled by combining the self-adjusted scaling factors and θ(Fig.5(c)).The stability of the thermal test is improved.The overshoot of the proposed controller is smaller compared with the values in PID and F-PID controller,which are 0.9%,7.7%and 15.9%respectively.The settling time is also smaller than the values of PID and F-PID controller,which are 5.5 s,9.1 s and 11.6 srespectively.Furthermore,the recovery time of the proposed controller is smaller than PID and F-PID controller under the given load disturbance.Thesefacts illustrate that the proposed intelligent adaptive controller per forms more excellent and stable compared with the PID and F-PID controllers.

Table 5 Design methods and tuned gains for each method.

Fig.5 Transient responses with PID,F-PID and proposed method.

Table 6 Settling time τ and overshoot σ of PID,F-PID and proposed method.

To verify the adaptability of the temperature control system,the different reference temperature was set.The reference temperature was set as 50 °C,100 °C,150 °C and 200 °C,respectively.The results are shown in Fig.6.The overshoot,settling time and steady state error using the PID,F-PID and proposed adaptive controller are shown in Table 7.The error band of τ*is 0.05 K for temperatures and 2%final value for others,units for σ*and ε*are ‘K” for temperatures,and τ*is ‘s” for steady state time and% for others in Table 7.As can be seen,when reference temperature changed,PID had relatively large fluctuation for settling time and overshoot(from 6.2%to 15.4%).However, for the proposed adaptive controller,the overshoot was more stable and much lower(less than 3%),and besides,settling time was shorter(less than 10 s).This demonstrates that the adaptability of the proposed adaptive controller improves greatly compared with the PID and F-PID controller.

Table 7 Settling time τ,overshoot σ and steady state error ε of PID,F-PID and proposed controller under different reference temperatures.

Fig.6 Transient responses with PID,F-PID and proposed control under reference temperatures of 50 °C,100 °C,150 °C and 200°C.

5.Conclusions

In this paper,a novel intelligent adaptive controller based on PID typefuzzy logic is proposed to improve the performance of laser-based ground thermal test.The output scaling factors of proposed controller are real time adjusted by introducing a fuzzy coefficient θ.The stochastic method based on an advanced H-PSO algorithm is improved to calculate the initial scaling factors of the proposed controller.The transient performance of the proposed intelligent controller is compared with the PID and F-PID designed by the Ziegler–Nichols and GA methods.The performance indicators considered contain the overshoot,settling time and steady state error.Some important conclusions are listed as follows:

(1)The overshoot of the proposed controller is smaller compared with the values in PID and F-PID controller,which are 0.9%,7.7%and 15.9%respectively.The settling time is also smaller than the values of PID and F-PID controller,which are 5.5 s,9.1 s and 11.6 s respectively.Furthermore,the recovery time of the proposed controller is smaller than PID and F-PID controller under the given load disturbance.

(2)The proposed controller can enhance capacity of laser heat flux simulation system,and it is a reliable tool for effective temperature control of laser-based ground thermal test.The proposed controller per forms more excellent and stable compared to the above mentioned controllers for laser-based ground thermal test.The other advantage of the proposed controller is that the adaptability and robustness were improved greatly.

(3)Since the proposed control method only uses the commercial equipment,implementation of it in industrial applications is straight forward.Furthermore,it is a promising approach which can be applied to other industrial processes where the temperature needs to be controlled accurately.

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Gan Zhengtao is a Ph.D.candidate at Institute of Mechanics,Chinese Academy of Sciences.He received his B.S.degreefrom Chongqing University.His major research interest is mechanics in advanced manufacturing.

Yu Gang went to UK to study high-resolution molecular spectroscopy in 1987.In 1992,prof essor Yu received the Ph.D.degree in physics from University of Strathclyde.From 1992 to 1995,he went on with postdoctoral research at Heriot-Watt University.He returned to China at the end of 1995 and has become a researcher in Institute of Mechanics,Chinese Academy of Sciences since then.

13 October 2015;revised 26 April 2016;accepted 13 May 2016

Available online 23 June 2016

Adaptive control;

Fuzzy logic;

Ground thermal test;Laser heating;

Thermal control

?2016 Chinese Society of Aeronautics and Astronautics.Production and hosting by Elsevier Ltd.Thisisan open access article under the CC BY-NC-ND license(http://creativecommons.org/licenses/by-nc-nd/4.0/).

*Corresponding author.Tel.:+86 10 82544250.

E-mail address:gyu@imech.ac.cn(G.Yu).

Peer review under responsibility of Editorial Committee of CJA.

Production and hosting by Elsevier

http://dx.doi.org/10.1016/j.cja.2016.06.015

1000-9361?2016 Chinese Society of Aeronautics and Astronautics.Production and hosting by Elsevier Ltd.

This is an open access article under the CC BY-NC-ND license(http://creativecommons.org/licenses/by-nc-nd/4.0/).