CN111129548B - Improved particle swarm optimization fuzzy PID fuel cell temperature control method - Google Patents
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Abstract
The invention discloses an improved particle swarm optimization fuzzy PID fuel cell temperature control method, which comprises the following steps: establishing a fuel cell dynamic model based on an MATLAB/Simulink simulation platform, and obtaining the output power and the corresponding temperature of the fuel cell through the fuel cell dynamic model; designing a fuzzy PID temperature controller aiming at the fuel cell dynamic model, and controlling the error and the error change rate of the expected temperature value and the actual temperature value by using the controller to obtain the parameter adjustment quantity of the fuzzy PID temperature controller; optimizing quantization factors and scale factors in the fuzzy PID temperature controller by adopting an improved particle swarm algorithm; and assigning the optimized quantization factor and the scale factor to a fuzzy PID temperature controller so as to control the temperature of the fuel cell in real time. The invention utilizes the improved particle swarm optimization fuzzy PID control, the control strategy is set according to the control experience rule, and the invention has the advantages of strong robustness, fast response speed and the like, and ensures that the PEMFC pile is maintained at a fixed temperature.
Description
Technical Field
The invention belongs to the technical field of thermal management of fuel cells, and particularly relates to an improved particle swarm optimization fuzzy PID fuel cell temperature control method.
Background
With the increasing energy crisis and environmental pollution problems, the development of efficient and low-pollution energy technology has become one of the major issues in all countries in the world. Fuel cells are widely regarded by the automotive industry as an efficient and clean energy conversion device. Among them, Proton Exchange Membrane Fuel Cells (PEMFCs) have the advantages of low operating temperature, fast starting speed, high power generation efficiency, mature technology, etc., and are receiving more and more extensive attention.
Temperature has a significant impact on fuel cell system performance and reliability. The temperature of the galvanic pile is increased, so that the electrochemical reaction activity is improved, the electric conductivity of the membrane is improved, and the performance of the battery is improved; however, the electrolyte membrane of PEMFCs has limited temperature resistance and, considering the problem of water-containing property of the membrane, the operating temperature is not preferably too high. For fuel cells, it is desirable that the temperature inside the stack be substantially uniform, which is beneficial for improving stack performance and extending stack life. However, the heat generated by the chemical reaction of the fuel cell is carried out of the stack by the low-temperature medium, so that a certain temperature difference is required inside the stack, and the redundant heat can be transferred from the inside of the stack to the cooling medium and carried out of the stack. The temperature of the electric pile is controlled within a certain range by controlling the flow of the cooling medium.
At present, the most widely applied PID controller is the classical PID controller, and three parameters K of the traditional PID controllerP，KI，KDThe method is fixed and unchangeable, the parameter setting method is more complicated, and the system control is more difficult; the fuzzy control has good control performance, but the fuzzy PID controller also has defects, quantization and scale factor determination, membership function selection and fuzzy rule table formulation have important influence on control effect, but can only be obtained by depending on expert experience and engineering experience, interference caused by special conditions cannot be avoided, and self-adaptive capacity and control effect are not ideal.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides an improved particle swarm optimization fuzzy PID fuel cell temperature control method, which realizes effective control of the temperature of a proton exchange membrane fuel cell.
In order to achieve the purpose, the invention adopts the technical scheme that:
an improved particle swarm optimization fuzzy PID fuel cell temperature control method comprises the following steps:
s1, according to the physical characteristics of a galvanic pile, a water pump and a heat exchanger in the proton exchange membrane fuel cell system, building a dynamic model of the fuel cell based on an MATLAB/Simulink simulation platform to obtain the temperature change of the fuel cell;
s2, designing a fuzzy PID temperature controller according to the dynamic model of the fuel cell established in the step S1, and controlling the error and the error change rate of the expected temperature value and the actual temperature value by using the fuzzy PID temperature controller to obtain the parameter adjustment of the fuzzy PID temperature controller;
s3, optimizing the quantization factor and the scale factor in the fuzzy PID temperature controller by adopting an improved particle swarm optimization;
and S4, assigning the optimized quantization factor and the scale factor to a fuzzy PID temperature controller.
In step S2, the desired temperature value T of the fuel cell is selectedS(T) error e (T) from actual temperature value T (T) ═ TS(t) -T (t) and its error rate of change
As an input variable of the PID temperature controller, the parameter adjustment quantity delta K of the fuzzy PID temperature controllerP，ΔKI，ΔKDAs output quantities, among others: Δ KP，ΔKI，ΔKDThree parameters K corresponding to proportional integral P, integral I and differential DP，KI，KDThe amount of change in (c).
In the step S3, the improved particle swarm algorithm is adopted to adjust the scale factor k of the fuzzy PID temperature controllere，
And the quantization factor k of proportion, integral and differential in PID controlup、kuiAnd kudFive parameters are optimized, and the optimization process comprises the following steps:
s301, initializing particle swarm algorithm parameters, setting the parameters in a d-dimensional search space, and initializing a population with the size of NsIn the search space of each quantization factor parameter
lowi,highiRespectively initializing the position X of each particle i of the group for the upper and lower limits of the search spaceiAnd velocity Vi；
S302, constructing a corresponding objective function:
in the formula, Fobj，iIs the objective function value; t is tp,tsAnd t∞Respectively representing peak time, adjustment time and system stabilityThe time is required; t (T)p) Representing the peak time t in the temperature control process of the subsystempThe temperature of (a); t (T)s) Representing the temperature at which the conditioning time is reached in the subsystem temperature control process; t (T)∞) Indicating the temperature of the system after the system tends to stabilize; according to the automatic control principle, if T (T)p)>T(t∞) And lim [ T (T) ]p)-T(t∞)]When T (T) is 0, the overshoot of the control system is reduced, and T (T) isp)<T(t∞) If so, the system does not have overshoot correspondingly;
represents the minimum time required for the temperature response to reach and remain within ± 5% of the final temperature value;
s303, inputting a system control parameter, namely the particle population size N for optimizingsMaximum iteration step number N of the whole optimizing processcThe dimension N, N of the problem is the number of quantization factors to be optimized, i.e. the dimension is consistent with the number of quantization factors, and the maximum tolerance epsilon allowed by the objective function0And the parameters μ, ζ, F, CRA value of (d);
s304, in the search space
Using chaos theory model internally, and locating X for each particleiInitializing and calculating corresponding target function Fobj,iAnd taking the position of the current particle as the individual historical optimal position P of the particleiThe corresponding objective function value is taken as the individual optimum objective function value pbestiRepeating the above process to obtain the optimal position of each particle individual, recording the corresponding objective function, transversely comparing the optimal position of each particle on the basis, and finding out the optimal position P of the whole populationgAnd corresponding to the objective function gbest, and making the iteration time t equal to 0;
s305, judging whether iteration is converged, if one of the following two conditions is met in the iteration process, iteratively converging, and outputting an optimal quantization factor parameter combination;
(i) historical optimum position P of total groupgHas an objective function value gbest smaller than the maximum tolerance error epsilon0I.e. gbest<ε0；
(ii) The number of iterations t is greater than a given maximum number of iteration steps NtI.e. t>Nt；
S306, updating the position X of each particleiI.e. updating the quantization factor parameter information carried by each particle, if the new position exceeds the given search space during the calculation process
The position is forced to be the upper and lower limits of the search space, i.e. lowiAnd highi；
S307, evaluating the position of each particle and calculating a corresponding objective function value Fobj，i(ii) a Judging whether the objective function value of each current particle position is better than the objective function value pbest of the corresponding individual historical optimal positioniIf F isobj，i<pbestiUpdating the historical optimal position information of the individual group, namely updating the parameter combination of the individual optimal quantization factor;
s308, calculating a mutation vector Pi,mutSum target vector Pi,tarThe target vectors, i.e. the combination of the quantization factor parameters generated by the mutation, are then compared with the objective function value pbest for the optimal position of the acceptor particle iiIf F isobj(Pi,tar)<pbestiWherein: fobj(Pi,tar) As an objective function value of the target vector, pbestiUpdating the information of the historical optimal position of the receptor particle i if the target function value of the optimal position is obtained; otherwise, if Fobj(Pi,tar)≥pbestiWhen the time is long, the time is kept unchanged;
s309, judging the historical optimal position P of each particlegObjective function value pbest ofiWhether it is better than the objective function value gbest of the optimal position of the whole group, if pbesti<gbest updates the optimal position information of the entire total group, and step S305 is executed.
In S303, N is 5.
The step S4 includes the steps of,
s401, configuring a fuzzy PID temperature controller, assigning the optimized quantization factor and the optimized scale factor to the fuzzy PID temperature controller, wherein the input of the fuzzy PID temperature controller comprises two, and one is the set temperature T of the PEMFCS(T) error e (T) from actual temperature value T (T) ═ TS(t) -T (t), the other is the error rate of change
S402, when the actual temperature of the galvanic pile is higher than the set temperature, the cooling water flow is required to be increased so as to bring away heat to achieve the purpose of cooling, otherwise, when the actual temperature of the galvanic pile is lower than the set temperature, the cooling water flow is required to be reduced;
s403, dividing input and output of the PID temperature controller into 7 fuzzy sets: NB (negative big), NM (negative middle), NS (negative small), ZE (zero), PS (positive small), PM (middle), PB (positive big), fuzzification variables of a Gaussian function are adopted for the membership function, and the membership function f (x; C, sigma) is expressed as:
wherein: chi is variable, C is corresponding abscissa used for confirming the centre of the curve, sigma is the standard deviation;
and the trigonometric membership function f (χ, a, b, c) is expressed as:
wherein: a, c are the values of the triangle function on the abscissa, and b is the vertex of the triangle function.
Compared with the prior art, the invention has the following beneficial effects:
(1) the improved particle swarm algorithm is combined with the fuzzy PID control for optimization, the defect that parameter selection of the existing fuzzy PID control method excessively depends on expert experience and engineering experience is overcome, the requirement of attitude control of the modern unmanned helicopter is met, and the control performance is improved;
(2) the fuel cell temperature is controlled by adopting the improved particle swarm optimization fuzzy PID, so that the system response time is reduced, and the robustness of the system is improved.
Drawings
FIG. 1 is a block diagram of a PEMFC thermal management system;
FIG. 2 is a basic schematic diagram of a particle swarm optimization fuzzy PID controller in the invention;
FIG. 3 is a flowchart of a fuzzy PID control procedure for particle swarm optimization according to the present invention;
FIG. 4 shows the deviation e (t) and the deviation change rate in an embodiment of the present invention
Defining a curve according to the membership degree of the target;
FIG. 5 is a graph of fuzzy controller test signals in one embodiment of the present invention;
fig. 6 is a schematic diagram of a dynamic process of a controlled temperature when a load changes according to an embodiment of the present invention.
Detailed Description
The present invention will be further described with reference to the following examples.
As shown in fig. 1, a specific thermal management structure block diagram of a pem fuel cell is shown in fig. 1, where: t isst,inIs the cooling water inlet temperature; t isstThe outlet temperature of the cooling water, namely the temperature T (t) of the galvanic pile; wclThe flow rate of the cooling water is the same.
An improved particle swarm optimization fuzzy PID fuel cell temperature control method comprises the following steps:
s1, according to the physical characteristics of a galvanic pile, a water pump and a heat exchanger in the proton exchange membrane fuel cell system, building a dynamic model of the fuel cell based on an MATLAB/Simulink simulation platform to obtain the temperature change of the fuel cell;
s2, designing a fuzzy PID temperature controller according to the dynamic model of the fuel cell established in the step S1, and controlling the error and the error change rate of the expected temperature value and the actual temperature value by using the fuzzy PID temperature controller to obtain the parameter adjustment of the fuzzy PID temperature controller;
in step S2, the desired temperature value T of the fuel cell is selectedS(T) error e (T) from actual temperature value T (T) ═ TS(t) -T (t) and its error rate of change
As an input variable of the PID temperature controller, the parameter adjustment quantity delta K of the fuzzy PID temperature controllerP，ΔKI，ΔKDAs output quantities, among others: Δ KP，ΔKI，ΔKDThree parameters K corresponding to proportional integral P, integral I and differential DP，KI，KDThe amount of change in (c).
S3, optimizing the quantization factor and the scale factor in the fuzzy PID temperature controller by adopting an improved particle swarm optimization;
in the step S3, the improved particle swarm algorithm is adopted to adjust the scale factor k of the fuzzy PID temperature controllere，
And the quantization factor k of proportion, integral and differential in PID controlup、kuiAnd kudFive parameters are optimized, and the optimization process comprises the following steps:
s301, initializing particle swarm algorithm parameters, setting the parameters in a d-dimensional search space, and initializing a population with the size of NsIn the search space of each quantization factor parameter
lowi,highiRespectively initializing the position X of each particle i of the group for the upper and lower limits of the search spaceiAnd velocity Vi；
S302, constructing a corresponding objective function:
in the formula, Fobj，iIs the objective function value; t is tp,tsAnd t∞Respectively representing peak time, adjusting time and time required by system stabilization; t (T)p) Representing the peak time t in the temperature control process of the subsystempThe temperature of (a); t (T)s) Representing the temperature at which the conditioning time is reached in the subsystem temperature control process; t (T)∞) Indicating the temperature of the system after the system tends to stabilize; according to the automatic control principle, if T (T)p)>T(t∞) And lim [ T (T) ]p)-T(t∞)]When T (T) is 0, the overshoot of the control system is reduced, and T (T) isp)<T(t∞) If so, the system does not have overshoot correspondingly;
represents the minimum time required for the temperature response to reach and remain within ± 5% of the final temperature value;
s303, inputting a system control parameter, namely the particle population size N for optimizingsMaximum iteration step number N of the whole optimizing processcThe dimension N of the problem, N, is the number of quantization factors to be optimized, i.e. the dimension coincides with the number of quantization factors, in particular N-5, and the maximum tolerance epsilon allowed by the objective function0And the parameters μ, ζ, F, CRThe value of (c).
S304, in the search space
Using chaos theory model internally, and locating X for each particleiInitializing and calculating corresponding target function Fobj,iAnd taking the position of the current particle as the individual historical optimal position P of the particleiThe corresponding objective function value is taken as the individual optimum objective function value pbestiRepeating the above process to obtain the optimal position of each particle, recording the corresponding objective function, and comparing the lateral ratio based on the optimal positionFinding out the optimal position P of the whole population by comparing the optimal position of each particlegAnd corresponding to the objective function gbest, and making the iteration time t equal to 0;
s305, judging whether iteration is converged, if one of the following two conditions is met in the iteration process, iteratively converging, and outputting an optimal quantization factor parameter combination;
(i) historical optimum position P of total groupgHas an objective function value gbest smaller than the maximum tolerance error epsilon0I.e. gbest<ε0；
(ii) The number of iterations t is greater than a given maximum number of iteration steps NtI.e. t>Nt；
S306, updating the position X of each particleiI.e. updating the quantization factor parameter information carried by each particle, if the new position exceeds the given search space during the calculation process
The position is forced to be the upper and lower limits of the search space, i.e. lowiAnd highi；
S307, evaluating the position of each particle and calculating a corresponding objective function value Fobj，i(ii) a Judging whether the objective function value of each current particle position is better than the objective function value pbest of the corresponding individual historical optimal positioniIf F isobj，i<pbestiUpdating the historical optimal position information of the individual group, namely updating the parameter combination of the individual optimal quantization factor;
s308, calculating a mutation vector Pi,mutSum target vector Pi,tarThe target vectors, i.e. the combination of the quantization factor parameters generated by the mutation, are then compared with the objective function value pbest for the optimal position of the acceptor particle iiIf F isobj(Pi,tar)<pbestiWherein: fobj(Pi,tar) As an objective function value of the target vector, pbestiUpdating the information of the historical optimal position of the receptor particle i if the target function value of the optimal position is obtained; otherwise, if Fobj(Pi,tar)≥pbestiWhen the time is long, the time is kept unchanged;
s309, judging the historical optimal position P of each particlegObjective function value pbest ofiWhether it is better than the objective function value gbest of the optimal position of the whole group, if pbesti<gbest updates the optimal position information of the entire total group, and step S305 is executed.
S4, assigning the optimized quantization factor and the scale factor to a fuzzy PID temperature controller, wherein a basic schematic diagram of the particle swarm optimization fuzzy PID controller is shown in FIG. 2; referring to fig. 3 in detail, the step S4 includes the following steps,
401, configuring a fuzzy PID temperature controller, assigning the optimized quantization factor and the optimized scale factor to the fuzzy PID temperature controller, wherein the input of the fuzzy PID temperature controller comprises two, one is the set temperature T of the PEMFCS(T) error e (T) from actual temperature value T (T) ═ TS(t) -T (t), the other is the error rate of change
And 402, performing fuzzy decision according to a fuzzy rule to obtain a fuzzy control quantity, and performing defuzzification on the fuzzy control quantity by a weighted average gravity center method to obtain an accurate control quantity suitable for the controlled object. Specifically, when the actual temperature of the galvanic pile is higher than the set temperature, the cooling water flow needs to be increased so as to bring away heat to achieve the purpose of cooling, and conversely, when the actual temperature of the galvanic pile is lower than the set temperature, the cooling water flow needs to be decreased;
the input and output of the PID temperature controller are divided into 7 fuzzy sets 403: NB (negative big), NM (negative middle), NS (negative small), ZE (zero), PS (positive small), PM (middle), PB (positive big), fuzzification variables of a Gaussian function are adopted for the membership function, and the membership function f (x; C, sigma) is expressed as:
wherein: chi is variable, C is corresponding abscissa used for confirming the centre of the curve, sigma is the standard deviation;
and the trigonometric membership function f (χ, a, b, c) is expressed as:
wherein: a and c are values of the triangular function on the abscissa, b is the vertex of the triangular function, and the membership function curves corresponding to the input and output variables are shown in fig. 4.
In step 7, fig. 5 shows a load current test signal of the stack in the working range, which is mainly represented by two step signals of rising and falling. The obtained control effect of the improved particle swarm optimization fuzzy PID and the control effect of the non-optimization fuzzy PID are compared and shown in FIG. 6. Therefore, under the action of the improved controller, the temperature response is faster and the stability is better.
The above description is only of the preferred embodiments of the present invention, and it should be noted that: it will be apparent to those skilled in the art that various modifications and adaptations can be made without departing from the principles of the invention and these are intended to be within the scope of the invention.
Claims (3)
1. An improved particle swarm optimization fuzzy PID fuel cell temperature control method is characterized by comprising the following steps:
s1, according to the physical characteristics of a galvanic pile, a water pump and a heat exchanger in the proton exchange membrane fuel cell system, building a dynamic model of the fuel cell based on an MATLAB/Simulink simulation platform to obtain the temperature change of the fuel cell;
s2, designing a fuzzy PID temperature controller according to the dynamic model of the fuel cell established in the step S1, and controlling the error and the error change rate of the expected temperature value and the actual temperature value by using the fuzzy PID temperature controller to obtain the parameter adjustment of the fuzzy PID temperature controller;
in step S2, the desired temperature value T of the fuel cell is selectedS(T) error e (T) from actual temperature value T (T) ═ TS(t) -T (t) and its error rate of change
As an input variable of the PID temperature controller, the parameter adjustment quantity delta K of the fuzzy PID temperature controllerP，ΔKI，ΔKDAs output quantities, among others: Δ KP，ΔKI，ΔKDThree parameters K corresponding to proportional integral P, integral I and differential DP，KI，KDThe amount of change in (c);
s3, adopting improved particle swarm optimization to quantize the factor k in the fuzzy PID temperature controllerup、kui、kudAnd a scale factor ke，
Optimizing, constructing an objective function according to the temperature change of the galvanic pile, and then searching a combination of the optimized objects when the objective function obtains the minimum value through a series of iterative computations by means of the algorithm;
s4, the improved particle swarm optimization algorithm is used for obtaining the minimum value of the optimized object according to the iterative solution of the constructed objective function, and the optimized quantization factor k is usedup、kui、kudAnd a scale factor ke，
And transferring the parameters to a Simulink simulation platform, and assigning the parameters to a fuzzy PID temperature controller.
2. The improved particle swarm optimization fuzzy PID fuel cell temperature control method according to claim 1, wherein in the step S3, the improved particle swarm optimization algorithm is adopted to apply the scaling factor k to the fuzzy PID temperature controllere，
And the quantization factor k of proportion, integral and differential in PID controlup、kuiAnd kudFive parameters are optimized, excellentThe chemical process comprises the following steps:
s301, initializing particle swarm algorithm parameters, setting the parameters in a d-dimensional search space, and initializing a population with the size of NsIn the search space of each quantization factor parameter
lowi,highiRespectively initializing the position X of each particle i of the group for the upper and lower limits of the search spaceiAnd velocity Vi；
S302, constructing a corresponding objective function:
in the formula, Fobj，iIs the objective function value; t is tp,tsAnd t∞Respectively representing peak time, adjusting time and time required by system stabilization; t (T)p) Representing the peak time t in the temperature control process of the subsystempThe temperature of (a); t (T)s) Representing the temperature at which the conditioning time is reached in the subsystem temperature control process; t (T)∞) Indicating the temperature of the system after the system tends to stabilize; according to the automatic control principle, if T (T)p)＞T(t∞) And lim [ T (T) ]p)-T(t∞)]When T (T) is 0, the overshoot of the control system is reduced, and T (T) isp)＜T(t∞) If so, the system does not have overshoot correspondingly;
represents the minimum time required for the temperature response to reach and remain within ± 5% of the final temperature value;
s303, inputting a system control parameter, namely the particle population size N for optimizingsMaximum iteration step number N of the whole optimizing processcThe dimension N, N of the problem is the number of quantization factors to be optimized, i.e. the dimension is consistent with the number of quantization factors, and the maximum tolerance epsilon allowed by the objective function0And the parameters μ, ζ, F, CRWherein N is 5;
s304, in the search space
Using chaos theory model internally, and locating X for each particleiInitializing and calculating corresponding target function Fobj,iAnd taking the position of the current particle as the individual historical optimal position P of the particleiThe corresponding objective function value is taken as the individual optimum objective function value pbestiRepeating the above process to obtain the optimal position of each particle individual, recording the corresponding objective function, transversely comparing the optimal position of each particle on the basis, and finding out the optimal position P of the whole populationgAnd corresponding to the objective function gbest, and making the iteration time t equal to 0;
s305, judging whether iteration is converged, if one of the following two conditions is met in the iteration process, iteratively converging, and outputting an optimal quantization factor parameter combination;
(i) historical optimum position P of total groupgHas an objective function value gbest smaller than the maximum tolerance error epsilon0I.e. gbest < epsilon0；
(ii) The number of iterations t is greater than a given maximum number of iteration steps NtI.e. t > Nt；
S306, updating the position X of each particleiI.e. updating the quantization factor parameter information carried by each particle, if the new position exceeds the given search space during the calculation process
The position is forced to be the upper and lower limits of the search space, i.e. lowiAnd highi；
S307, evaluating the position of each particle and calculating a corresponding objective function value Fobj，i(ii) a Judging whether the objective function value of each current particle position is better than the objective function value pbest of the corresponding individual historical optimal positioniIf F isobj，i＜pbestiThen, the individual group calendar is updatedHistory optimal position information, namely updating the parameter combination of the individual optimal quantization factor;
s308, calculating a mutation vector Pi,mutSum target vector Pi,tarThe target vectors, i.e. the combination of the quantization factor parameters generated by the mutation, are then compared with the objective function value pbest for the optimal position of the acceptor particle iiIf F isobj(Pi,tar)<pbestiWherein: fobj(Pi,tar) As an objective function value of the target vector, pbestiUpdating the information of the historical optimal position of the receptor particle i if the target function value of the optimal position is obtained; otherwise, if Fobj(Pi,tar)≥pbestiWhen the time is long, the time is kept unchanged;
s309, judging the historical optimal position P of each particlegObjective function value pbest ofiWhether it is better than the objective function value gbest of the optimal position of the whole group, if pbestiIf < gbest, the optimal position information of the entire total group is updated, and step S305 is executed.
3. The improved particle swarm optimization fuzzy PID fuel cell temperature control method according to claim 2, wherein the step S4 comprises the steps of:
s401, configuring a fuzzy PID temperature controller, assigning the optimized quantization factor and the optimized scale factor to the fuzzy PID temperature controller, wherein the input of the fuzzy PID temperature controller comprises two, and one is the set temperature T of the PEMFCS(T) error e (T) from actual temperature value T (T) ═ TS(t) -T (t), the other is the error rate of change
S402, when the actual temperature of the galvanic pile is higher than the set temperature, the cooling water flow is required to be increased so as to bring away heat to achieve the purpose of cooling, otherwise, when the actual temperature of the galvanic pile is lower than the set temperature, the cooling water flow is required to be reduced;
s403, dividing input and output of the PID temperature controller into 7 fuzzy sets: NB negative is large, NM negative is medium, NS negative is small, ZE zero, PS positive is small, PM positive is medium, PB positive is large, a Gaussian function fuzzification variable is adopted for the membership function, and the membership function f (x; C, sigma) is expressed as:
wherein: chi is variable, C is corresponding abscissa used for confirming the centre of the curve, sigma is the standard deviation;
and the trigonometric membership function f (χ, a, b, c) is expressed as:
wherein: a, c are the values of the triangle function on the abscissa, and b is the vertex of the triangle function.
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