Research of fuzzy-PID control system based on fuzzy weights

Xiu-shuang CAO（Department of Information and Engineering，Tangshan College，Tangshan 063000，China）

Research of fuzzy-PID control system based on fuzzy weights

Xiu-shuang CAO*
（Department of Information and Engineering，Tangshan College，Tangshan 063000，China）

Aiming at merits and faults of control system between the classical fuzzy and PID，a kind of Fuzzy-PID hybrid control system was set up.Linear PID controller and fuzzy controller were combined in parallel.The fuzzy control plays a major role in the region that strays from work point distantly，by contrary PID linear control.And aiming at faults of switch about threshold value and single fuzzy set，the hybrid control system based on fuzzy weights controller is proposed.Simulation results show that the capability of hybrid control system based on fuzzy switch is improved and increased.

Fuzzy weights，Threshold value switch，Fuzzy-PID

Hydromechatronics Engineering

http：//jdy.qks.cqut.edu.cn

E-mail：jdygcyw@126.com

1 Introduction

Because of advantages of simple structure，easy to use，strong applicability，maturity in stability design and parameter tuning method，up to now PID linear controller occupies a certain position yet in some control system.But，because of its linear performance，PID linear controller has good control capability only beside work point.When it is far from work point，owing to the nonlinearity of control object，it is hard to keep dynamic characteristics.Since fuzzy control was proposed，it has been used widely in industrial process control.One of characteristics about fuzzy control is to improve dynamic characteristics in the area far from work point.In addition，fuzzy control has superior robustness than PID linear controller when the character of control object change.But fuzzy control belongs to nonlinear control method in substance.It lacks of general systematic design method.Stability of fuzzy controller is hard to be guaranteed，and control accuracy is not high enough，also it is easy to produce limit cycle oscillation near the work point［l］.Therefore，taking their advantages into account，a kind of Fuzzy-PID hybrid control system is proposed.Conventional fuzzy-PID hybrid control system adopts threshold value switch mode，which uses different modes to realize control in difference discourse domain.Conventional fuzzy-PID hybrid control algorithm is simple，has good real-time and fast response，also can avoid of steady state error effectively.But destabilization exists on switching.Aiming at the problem of switch，many people make improvements to realize switching without disturbance.A kind of improved adaptive fuzzy-PID compound control was proposed in reference［2］that a inching regulator，which is a linear combination of fuzzy control and PID control function，was appended to its structure，which can make system transit smoothly，increase stability，decrease oscillation.But it is blind in the setting of inching regulator and function parameter of computing weighting coefficient. When system is switched to hybrid control，respective control ratio of two controllers only uses a fixed function to finish.Its accuracy is low.The compound control of fuzzy switch based on amount of dispersion is studied in reference［3-9］.When amount of dispersion is some value，deviation variation is positive value maybe，also negative value.Therefore，influence on control must take deviation and deviation variationinto account synthetically.In Reference［1］and［6］，switch control was based on deviation and deviation variation，by simple operation.However，the degree of membership of every variable was simple single mode fuzzy subsets.Its switching control was rough. The intensity component control can be changed through altering the parameter of membership grade. The parameter of membership grade is hard to obtain. For this purpose，a new fuzzy-PID hybrid control system is proposed in this paper，which adopts fuzzy weight controller to regulate weight，and considers influence on control of deviation E and deviation change rate EC synthetically.The deviation E and deviation change rate EC correspond between fuzzy weight controller and fuzzy controller，which has same fuzzy domain.Provened that it can switch without disturbance smoothly.

2 The design of Fuzzy-PID system based on fuzzy weight regulator

2.1 The structure of Fuzzy-PID control system

The structure diagram of Fuzzy-PID control system is shown in Fig.1.One important problem of Fuzzy-PID hybrid control is to overcome disturbance when switching.For general compound control，once the ratio of control for every controller is confirmed，it is hard to self-adjust along with controlled object and environmental change in the process of control，and both control effect and robustness are not ideal.In this paper，the Fuzzy-PID control system based on fuzzy weights controller to switch double mode control and general compound control.Switching between Fuzzy and PID though fuzzy rules can obtain more effect than threshold value switching.Furthermore，when controlled object or environmental change，the fuzzy rules can be optimized again in order to improve control performance and enhance the robustness.

Fig.1 Fuzzy-PID controI system based on fuzzy weight controIIer switching

2.2 The design of fuzzy weights controller

Input and output parameters region of fuzzy controller regulating weight is［-6，6］，input variable is e and ec，output is weight α whose physical parameters field is［0，1］.Fuzzy value is converted to physical quantity range of accurate value through formula（1）.

Where Umis fuzzy output，then output of system is as the formula（2）：

u=α*ufuzzy+（1-α）*upid（2）

Fuzzy control rules of fuzzy weights controller was an important section what influences on fuzzy weight regulation.In this paper，using optimization algorithm to generate fuzzy control rules.SAGACIA（SA-SAA，GA-GA，C-CA，I-Integrated，A-Algorithm）［10］optimization algorithm is a kind of hybrid stochastic optimization method，which synthesizes advantage of Simulated Annealing Algorithm（SAA），Genetic Algorithm（GA）and Chemotaxis Algorithm（CA），and increases efficiency of algorithm furthermore.SAGACIA algorithm is very strong in local and global search capability.Control rules of switching for weight controller optimized by SAGACIA optimization algorithm is shown in Table 1.

TabIe1 ControI ruIes tabIe of switching

3 The applied research

3.1 Applied simulation

General industrial process can be equivalent to a two order system along with some typical nonlinear link，such as the dead zone，saturation and pure delay etc.In this paper，the model of controlled object in reference［10］is adopted，as formula（3）：

It can represent general industrial process，and the sampling period is T=0.015，pure delay Nd= 0.02/0.01=2.The dead zone and saturated zone of control actuator are 0.07and 0.7 respectively.In hybrid control，quantitative factors and proportional factor of fuzzy controller for controlling are ke=60，kec= 2.5，ku=0.8［11-13］，and fuzzy controller for regulating weight switches from fuzzy output to accurate output through formula（1），which uses triangular，homogeneous distribution and full overlap membership function.The solution domain of input and output variables is（-6，6）.Its fuzzy sets are｛NB，NM，NS，ZO，PS，PM，PB｝.Fuzzy rules and PID parameters are optimized by SAGACIA algorithm.The comparison of output curve is shown in Fig.2 among threshold switching，single fuzzy sets switching and fuzzy weight controller switching.The curve of fuzzy weight α is shown in Fig.3.Here，the switching threshold of Fuzzy-PID hybrid control is set 1.4%set value on selecting.Triangle membership function with setting as the boundary was selected as the membership function for single fuzzy set.For every e（k）and ec（k），according to reference［1］，the ratio of every controller can be computed through formula（4）and（5）.

Fig.2 Comparison of step response of three switchings

As can be seen from the above figure，the effect based on threshold switching is the worst，especially in the system with dead time and saturation zone，where the switching threshold is set to 2.1%at a given value.The effect based on single fuzzy subsets switching is better，but it has long rise time，bad steady state performance and static difference.The effect based on fuzzy weights switching is the best that its steady state performance is very good，its rise time is also reduced at a certain extent.Although its overshoot is slightly higher，overshoot is in the very small range that can be ignored.As can be seen from the ITAE performance index，in this paper Fuzzy-PID control based on fuzzy switching is improved at a certain extent.The comparison of ITAE performance index based on three kind of switching is as shown as Table 2.

Fig.3 Output curve of fuzzy weight controIIer

TabIe2 Comparison of performance index based on different switching

As can be seen from switching curve of Fig.3，in the early stage of system response，fuzzy control plays a major role，on the contrary PID control plays a major role in the steady state.And in the process of control，the ratio of two controllers is varied，which avoid of defect of fixed ratio.The percent of fuzzy control and PID control in every stage of Fuzzy-PID control system is variable，it is an adjustment phase in a second，after program is adjusted，and the deviation is large relatively.The weight ratio of Fuzzy control is bigger than PID.When the deviation reduces slowly，the weight ratio of Fuzzy control reduce slowly accordingly，on the contrary，PID control rise.The controller for regulating weights is a basic fuzzy controller actually.So it is unavoidable that the curve of output has vibration in steady state.The rules of weights controller was optimized through SAGACIA algorithm to regulate Fuzzy-PID control system.The control effect is satisfactory.

3.2 Anti-interference tests

In the process of a system operation，it is hard to avoid of various interference.A good system can restrain interference better and transit to steady state，furthermore，the overshoot is small.In order to prove the capacity of resisting disturbance of Fuzzy-PID control system，the interference signal which lasted 0. 5seconds on 10%settings was joining in 3 seconds. After joining interference，control curve based on fuzzy weights switching and single fuzzy subset switching is as shown as Fig.4 and Fig.5.As can be seen from curve，Fuzzy-PID control based on fuzzy weights switching can transit to steady state quickly after interference，but that based on single fuzzy subset switching requires 4.5 seconds.So，the fuzzy weight switching is superior to other switching modes at present.

Fig.4 Stepresponseafterimportingdisturbance based on fuzzy weight controIIer

Fig.5 Stepresponseafterimportingdisturbance based on fuzzy controI ruIes

4 Conclusions

Aiming at the problem of bumpless switching，fuzzy-PID hybrid control based on fuzzy weight controller has good dynamic and static performance，which realizes the combination of complementary advantages between PID control and fuzzy control.

Acknowledgements

This paper is supported by Education Department of Hebei Province（Project NO.QN20132019）and Science and Technology Planning Project of Tangshan City（Project NO.131302118a）

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基于模糊權重的Fuzzy-PID控制系統研究

曹秀爽*
唐山學院信息工程系，唐山 063000

針對經典模糊控制策略和PID控制策略各自的優點和缺點，建立了一種Fuzzy-PID自適應切換的混合控制系統，在控制過程中，將PID線性控制器通過控制的權重與模糊控制器并行結合，在偏離穩定的工作點較遠的區域會以具有優勢的模糊控制為主，在穩定的工作點附近位置則會主要使用靜態性能好的PID線性控制。并針對Fuzzy-PID的混合控制系統中經常采用的閾值切換和單模糊子集進行模糊切換的缺點，提出一種利用模糊權重控制器進行的切換，應用結果表明：該模糊權重切換下的混合控制性能有所改善和提高。

模糊權重；閾值切換；Fuzzy-PID

10.3969/j.issn.1001-3881.2015.12.020Document code：A

TP273+.4

20 November 2014；revised 30 December 2014；accepted 5 January 2015

*Corresponding author：Xiu-shuang CAO，Experimentalist.

E-mail：379511725@qq.com