CN103309233A - Designing method of fuzzy PID (Proportion-Integration-Differential) controller - Google Patents
Designing method of fuzzy PID (Proportion-Integration-Differential) controller Download PDFInfo
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Abstract
The invention discloses a designing method of fuzzy PID (Proportion-Integration-Differential) controller. The designing method comprises the following steps of fuzzifying input quantity deviation e and deviation change ec; determining parameter tuning rule and carrying out fuzzy reasoning; and establishing a fuzzy control table. The designing method has the advantages of being flexible in fuzzy control and strong in applicability by combining fuzzy control with the PID control, as well as the characteristic of being high in PID control accuracy. The controller with self-tuned PID parameter can be realized, on the basis of a conventional PID regulator, the online self-tuning fuzzy control on parameters Kp, KI and KD can be achieved by adopting the conception of fuzzy reasoning according to different absolute values of e and delta e, and the fuzzy PID controller with excellent performance can be provided.
Description
Technical field
The invention belongs to the Automation Design technical field, relate in particular to a kind of method for designing of fuzzy controller.
Background technology
As everyone knows, traditional PID regulator is most widely used general in the industrial processes, the most basic a kind of regulator, it is simple that it has an algorithm, robustness is good, high reliability, PID regulates rule to considerable Industry Control object, especially be very effective to the control of the deterministic control system that can set up mathematical models, but have non-linear for those, the time become probabilistic control object, use traditional PID regulator and just be difficult to realize effective control, fuzzy controller is the new controller that a kind of development in recent years is got up, its advantage is not require the mathematical models of grasping controlled device, and according to artificial regular weaves decision table, so and by this decide by vote the size of deciding controlled quentity controlled variable, fuzzy control or fuzzy automatic control system are with fuzzy mathematics, i.e. fuzzy set theory, the fuzzy language representation of knowledge and fuzzy logic ordination etc. are as theoretical foundation; With Computer Control Technology, the Theory of Automatic Control automatic control system as technical foundation.
At present, conventional PID regulator has been widely used in industrial control system, and obtains and control preferably effect, and by regulating PID controller parameter K
p, K
I, K
D, make it can be applied to various object, become a kind of comparatively general regulator, but because controlled parameter becomes when having, the factor such as non-linear, uncertain, conventional PID controller does not have the on-line tuning parameter K
p, K
I, K
DFunction, cause its can not satisfy system at different deviation e and Δ e to pid parameter in the requirement of certainly adjusting, thereby affected the further raising of its control effect, in addition, proofread and correct the parameter of PID even adopted various optimization algorithms, because the parametric solution process of optimization method is comparatively complicated, need just can find the optimized parameter that satisfies objective function after a complete process, and parameter is fixed after proofreading and correct, the process that can't effective control parameter changes, and fuzzy controller is the new controller that a kind of development in recent years is got up, its response characteristic is better than conventional PID control, and has preferably robustness, especially to non-linear and controlled device time variation, the control effect that can obtain to be satisfied with.On the other hand, fuzzy control is as the read statement variable take systematic error e and error change ec, therefore it has the effect that is similar to conventional PID controller, adopt the system of such fuzzy controller might obtain good dynamic perfromance, and static characteristics can not be satisfactory.
Summary of the invention
The purpose of the embodiment of the invention is to provide a kind of method for designing of fuzzy controller, is intended to solve that conventional PID controller exists does not have the on-line tuning parameter K
p, K
I, K
DFunction, solution procedure is comparatively complicated, the problem of the process that can't effective control parameter changes.
The embodiment of the invention is achieved in that a kind of method for designing of fuzzy controller, and the method for designing of described fuzzy controller may further comprise the steps:
The obfuscation of input quantity deviation e, change of error ec;
Determining and fuzzy reasoning of tuning method;
Set up fuzzy control table.
Further, the step of the obfuscation of described input quantity deviation e, change of error ec is: at first will carry out Fuzzy processing to input quantity, the Linguistic Value of input, output variable is divided into seven Linguistic Values: { NB, NM, NS, O, PS, PM, PB}, membership function adopts the strong trigonometric function of sensitivity, for strengthening the robustness of system, improve the resolution of membership function, near the function shape 0 value obtains steeper;
The basic domain of e is: [2 ℃, 2 ℃];
The basic domain of ec is: [1,1];
Δ K
pBasic domain is: [0.3,0.3];
Δ K
iBasic domain is: [0.006,0.006];
Δ K
dBasic domain is: [0.3,0.3];
The fuzzy quantity of above each variable is respectively: E, EC, Δ K
p, Δ K
i, Δ K
d
Its domain is: [6 ,-5 ,-4 ,-3 ,-2 ,-1,0,1,2,3,4,5,6];
The quantizing factor of input quantity e, ec is:
k
e=-3,k
ec=-6。
Further, the definite and fuzzy reasoning of described tuning method also comprises:
The proportional component of the deviation signal e of proportional reflection control system;
Be used for to eliminate static difference, improve system without margin, to the integral element that error is carried out integration and control has certain delayed action to system;
The variation tendency that can reflect deviation signal, and can before the deviation signal value becomes too greatly, add a corrected signal, accelerate the response speed of system, reduce the overshoot time, strengthen the differentiation element of Systems balanth.
Further, the acquiring method of described fuzzy control table is:
By between 49 fuzzy condition statements describing control be or relation, can calculate Δ K by the determined control law of first statement
p, Δ K
i, Δ K
d
Can be written as by the determined fuzzy relation of first statement:
RΔK
p=(NBe×NBec)×ΔK
ppb
RΔK
i=(NBe×NBec)×ΔK
io
RΔK
d=(NBe×NBec)×ΔK
dps
According to each bar inference rule, can obtain corresponding fuzzy relation, such as R1, R2 ... Rn, so the corresponding fuzzy relation R of the overhead control of whole system rule is:
R=R1∨R2∨...∨Rn
Had after the R, just can according to above-mentioned obtained E and the quantize value of EC, according to the computing of Fuzzy fuzzy filtering rule, draw the fuzzy set Δ K that corresponding ratio changes
p, Δ K
i, Δ K
d
ΔK
p=(E×EC)·RΔK
p
ΔK
i=(E×EC)·RΔK
i
ΔK
d=(E×EC)·RΔK
d
The output of above-mentioned fuzzy control all is a Fuzzy subset, it is a kind of combination of the different values of reflection control language, but actual controlled device can only be accepted an output quantity, therefore will be with the Fuzzy set transform to accurate output quantity de-fuzzy, we can use fuzzy judgment, namely by principles such as method of weighted mean or the maximum method of degree of membership or center of gravity methods, obtain corresponding output quantity, adopt gravity model appoach to ask for the degree of accuracy of output quantity;
Draw the clear amount C (k) behind the fuzzy judgment, draw at last control output summary table.
Further, the method for designing of described fuzzy controller comprises the algorithm of fuzzy controller:
At first to being input to the parameter initialization of PID controller;
Obtain current sampled value;
e(k)=r-y(k);
ee(k)=e(k)-e(k-1);
e(k-1)=e(k);
E (k), ec (k) obfuscation;
Through fuzzy reasoning and computing, de-fuzzy obtains Δ K
p, Δ K
i, Δ K
d
Calculate current K
p, K
i, K
d
Carry out the PID computing, amplitude limit output.
The method for designing of fuzzy controller of the present invention by fuzzy control and PID control are combined, is maximized favourable factors and minimized unfavourable ones, and has both had flexible, the adaptable advantage of fuzzy control, has again the high characteristics of PID control accuracy.For this reason, introduce a kind of fuzzy inference function of using here and realize pid parameter from the controller of adjusting, it is on the basis of conventional PID regulator, adopts the thought of fuzzy reasoning, according to different | e| and | Δ e|, to parameter K
p, K
I, K
DCarry out the fuzzy control of online self-tuning.
Description of drawings
Fig. 1 is the process flow diagram of the method for designing of the fuzzy controller that provides of the embodiment of the invention;
Fig. 2 is the schematic diagram of the membership function of the embodiment of the invention input E, the EC that provide;
Fig. 3 is the output Δ K that the embodiment of the invention provides
p, Δ K
i, Δ K
dThe schematic diagram of membership function;
Fig. 4 is the process flow diagram of Fuzzy PID in one-period that the embodiment of the invention provides.
Embodiment
In order to make purpose of the present invention, technical scheme and advantage clearer, below in conjunction with embodiment, the present invention is further elaborated.Should be appreciated that specific embodiment described herein only in order to explain the present invention, is not intended to limit the present invention.
Fig. 1 shows the flow process of the method for designing of fuzzy controller provided by the invention.For convenience of explanation, only show part related to the present invention.
The method for designing of fuzzy controller of the present invention, the method for designing of this fuzzy controller may further comprise the steps:
The obfuscation of input quantity deviation e, change of error ec;
Determining and fuzzy reasoning of tuning method;
Set up fuzzy control table.
Prioritization scheme as the embodiment of the invention, the step of the obfuscation of input quantity deviation e, change of error ec is: at first will carry out Fuzzy processing to input quantity, the Linguistic Value of input, output variable is divided into seven Linguistic Values: { NB, NM, NS, O, PS, PM, PB}, membership function adopts the strong trigonometric function of sensitivity, for strengthening the robustness of system, improve the resolution of membership function, near the function shape 0 value obtains steeper;
The basic domain of e is: [2 ℃, 2 ℃];
The basic domain of ec is: [1,1];
Δ K
pBasic domain is: [0.3,0.3];
Δ K
iBasic domain is: [0.006,0.006];
Δ K
dBasic domain is: [0.3,0.3];
The fuzzy quantity of above each variable is respectively: E, EC, Δ K
p, Δ K
i, Δ K
d
Its domain is: [6 ,-5 ,-4 ,-3 ,-2 ,-1,0,1,2,3,4,5,6];
The quantizing factor of input quantity e, ec is:
k
e=-3,k
ec=-6。
As a prioritization scheme of the embodiment of the invention, the definite and fuzzy reasoning of described tuning method also comprises:
The proportional component of the deviation signal e of proportional reflection control system;
Be used for to eliminate static difference, improve system without margin, to the integral element that error is carried out integration and control has certain delayed action to system;
The variation tendency that can reflect deviation signal, and can before the deviation signal value becomes too greatly, add a corrected signal, accelerate the response speed of system, reduce the overshoot time, strengthen the differentiation element of Systems balanth.
As a prioritization scheme of the embodiment of the invention, the acquiring method of described fuzzy control table is:
By between 49 fuzzy condition statements describing control be or relation, can calculate Δ K by the determined control law of first statement
p, Δ K
i, Δ K
d
Can be written as by the determined fuzzy relation of first statement:
RΔK
p=(NBe×NBec)×ΔK
ppb
RΔK
i=(NBe×NBec)×ΔK
io
RΔK
d=(NBe×NBec)×ΔK
dps
According to each bar inference rule, can obtain corresponding fuzzy relation, such as R1, R2 ... Rn, so the corresponding fuzzy relation R of the overhead control of whole system rule is:
R=R1∨R2∨...∨Rn
Had after the R, just can according to above-mentioned obtained E and the quantize value of EC, according to the computing of Fuzzy fuzzy filtering rule, draw the fuzzy set Δ K that corresponding ratio changes
p, Δ K
i, Δ K
d
ΔK
p=(E×EC)·RΔK
p
ΔK
i=(E×EC)·RΔK
i
ΔK
d=(E×EC)·RΔK
d
The output of above-mentioned fuzzy control all is a Fuzzy subset, it is a kind of combination of the different values of reflection control language, but actual controlled device can only be accepted an output quantity, therefore will be with the Fuzzy set transform to accurate output quantity de-fuzzy, we can use fuzzy judgment, namely by principles such as method of weighted mean or the maximum method of degree of membership or center of gravity methods, obtain corresponding output quantity, adopt gravity model appoach to ask for the degree of accuracy of output quantity;
Draw the clear amount C (k) behind the fuzzy judgment, draw at last control output summary table.
As a prioritization scheme of the embodiment of the invention, the method for designing of fuzzy controller comprises the algorithm of fuzzy controller:
At first to being input to the parameter initialization of PID controller;
Obtain current sampled value;
e(k)=r-y(k);
ee(k)=e(k)-e(k-1);
e(k-1)=e(k);
E (k), ec (k) obfuscation;
Through fuzzy reasoning and computing, de-fuzzy obtains Δ K
p, Δ K
i, Δ K
d
Calculate current K
p, K
i, K
d
Carry out the PID computing, amplitude limit output.
Below in conjunction with drawings and the specific embodiments application principle of the present invention is further described.
The method for designing of fuzzy controller of the present invention is:
At first according to theory and the method for fuzzy mathematics, operating personnel's adjustment experience and technical know-how are summed up the fuzzy rule that becomes IF (condition) THEN (result) form, and these fuzzy rules and relevant information (such as initial pid parameter) are deposited in the computing machine, response condition according to temperature, calculate the deviation e of sampling instant and the variation ec input control device of deviation, use fuzzy reasoning, carry out fuzzy operation, can obtain the K in this moment
P, K
I, K
D, realize the best adjustment to pid parameter, the Fuzzy-PID controller mainly is comprised of obfuscation, fuzzy reasoning, de-fuzzy three parts;
The Fuzzy-PID controller is on the basis of pid parameter pre-tuning, utilizes three corrected parameters of fuzzy rule real-time online Tuning PID Controller: Δ K
p, Δ K
i, Δ K
dRealization adopts the decay oscillation curve method to realize the pre-tuning K ' of parameter to the optimal control of little temperature in the literary composition
p, K '
I, K '
d, the Fuzzy-PID controller's design can divide following three parts to finish:
The first step, input quantity deviation e, the obfuscation of change of error ec, the input of fuzzy controller, output variable all is accurate amount, fuzzy reasoning carries out for fuzzy quantity, therefore, controller at first will carry out Fuzzy processing to input quantity, in the designed Fuzzy-PID controller of the present invention, input, the Linguistic Value of output variable is divided into seven Linguistic Values: { NB, NM, NS, O, PS, PM, PB}, membership function adopts the strong trigonometric function of sensitivity, for strengthening the robustness of system, improve the resolution of membership function, near the function shape 0 value obtains steeper, form such as Fig. 2, shown in 3
The basic domain of e is: [2 ℃, 2 ℃]
The basic domain of ec is: [1,1]
Δ K
pBasic domain is: [0.3,0.3]
Δ K
iBasic domain is: [0.006,0.006]
Δ K
dBasic domain is: [0.3,0.3]
The fuzzy quantity of above each variable is respectively: E, EC, Δ K
p, Δ K
i, Δ K
d
Its domain is: [6 ,-5 ,-4 ,-3 ,-2 ,-1,0,1,2,3,4,5,6]
The quantizing factor of input quantity e, ec is:
k
e=-3,k
ec=-6;
Determining and fuzzy reasoning of second step, tuning method:
The tuning rule of parameter is the core of controller, and it is the summary of operating personnel and expert's experimental knowledge, and tabulation is as follows; Programming language is shown in appendix;
Table 4-4 Δ K
pThe parameter adjustment rule list
Table 4-5 Δ K
iThe parameter adjustment rule list
Table 4-6 Δ K
dThe parameter adjustment rule list
The proportional component effect is the deviation signal e of proportional reflection control system, and deviation is in case generation is controlled immediately generation effect, to reduce deviation, if but K
PValue is excessive, can cause system oscillation, destroys dynamic performance, therefore, when deviation | when e| is larger, for improving response speed, K
PIncrease; In deviation hour, prevent the excessive generation vibration of overshoot, K
PReduce; When deviation was very little, stable as early as possible for making system, then KP should continue to reduce, and considers simultaneously the ec factor; When ec and e jack per line, output changes K towards departing from the stationary value direction
PSuitably increase; Otherwise, K
PReduce Δ K
pControl law as the table 4-4 shown in;
Integral element is mainly used in eliminating static difference, improve system without margin, it carries out integration to error, control has certain delayed action to system, and integration I effect is excessively strong, can cause system overshoot to increase, even cause vibration, in conventional PID control, saturated for preventing integration, often integral element is separated, when deviation is reduced to certain limit, just added integral element, therefore, when deviation | when e| is large or larger, for avoiding system overshoot, K
iGet null value; When | e| hour, integral element is effective, with the reducing and increase of | e|, to eliminate the Systems balanth error, improves control accuracy, Δ K
iControl law as the table 4-5 shown in;
The variation tendency of the energy-conservation reflection deviation signal of differential ring, and can before the deviation signal value becomes too greatly, add a corrected signal, accelerate the response speed of system, reduce the overshoot time, strengthen Systems balanth, but it is responsive equally to undesired signal, the ability that can make system suppress to disturb descends, therefore, at the initial stage of control procedure, when deviation | when e| is larger, for avoiding the deviation instantaneous variation, cause differential to overflow, K
dShould get less; In deviation hour, consider anti-vibration ability and the system response time of system, should make K
dSuitable value, Δ K
dControl rule table is shown in table 4-6;
Deviation e and change of error ec to input after obtaining corresponding Linguistic Value, according to the tuning rule table, draw respectively three corrected parameter Δ K
p, Δ K
i, Δ K
dFuzzy quantity;
The 3rd goes on foot, sets up fuzzy control table
Between 49 fuzzy condition statements of above-mentioned description control be or relation, can calculate Δ K by the determined control law of first statement
p, Δ K
i, Δ K
d,
Can be written as by the determined fuzzy relation of first statement:
RΔK
p=(NBe×NBec)×ΔK
ppb
RΔK
i=(NBe×NBec)×ΔK
io
RΔK
d=(NBe×NBec)×ΔK
dps
According to each bar inference rule, can obtain corresponding fuzzy relation, such as R1, R2 ... Rn, so the corresponding fuzzy relation R of the overhead control of whole system rule is
R=R1∨R2∨...∨Rn
Had after the R, just can according to above-mentioned obtained E and the quantize value of EC, according to the computing of Fuzzy fuzzy filtering rule, draw the fuzzy set Δ K that corresponding ratio changes
p, Δ K
i, Δ K
d,
ΔK
p=(E×EC)·RΔK
p
ΔK
i=(E×EC)·RΔK
i
ΔK
d=(E×EC)·RΔK
d
The output of above-mentioned fuzzy control all is a Fuzzy subset, it is a kind of combination of the different values of reflection control language, but actual controlled device can only be accepted an output quantity, therefore will be with the Fuzzy set transform to accurate output quantity (de-fuzzy), we can use fuzzy judgment, namely by principles such as method of weighted mean or the maximum method of degree of membership or center of gravity methods, obtain corresponding output quantity, to the present invention, adopt gravity model appoach to ask for the degree of accuracy of output quantity;
Draw the clear amount C (k) behind the fuzzy judgment, draw at last such as table 4-7,4-8, control output summary table shown in the 4-9, fuzzy control table is one of the simplest fuzzy controller, it can pass through the input variable quantized value of inquiry current time fuzzy controller (such as error, the error change quantized value) corresponding output valve is as the final output of fuzzy logic controller, thereby reach fast in real time control, fuzzy control rule table must be to all input language variablees (such as error, error change) the various combinations after the quantification go out the fuzzy controller output of each state by the methodology calculated off-line of fuzzy logic inference, finally generate a fuzzy control table;
The acquiring method of this control table and other method are by comparison, because it does not need to carry out compositional rule of inference by relational matrix, avoided loaded down with trivial details matrix operation, have directly perceived, simple operation, characteristics fast, and after trying to achieve control table, and it is stored in the internal memory of computing machine, working out a subroutine of searching accordingly control table gets final product again, find out from above, the foundation of fuzzy control table is that off-line carries out, therefore it shows no sign of the speed that affects the fuzzy controller real time execution, can satisfy the requirement of real-time control fully
Table 4-7 Δ K
pFuzzy control table
Table 4-8 Δ K
iFuzzy control table
Table 4-9 Δ K
dFuzzy control table
In addition, the accurate amount that each sampling provides through FUZZY ALGORITHMS FOR CONTROL is control object directly, also it must be transformed into as going in the receptible basic domain of object,
K=Y/M.
The scale factor of each corrected parameter is:
K
u(ΔK
p)=1/20
K
u(ΔK
i)=1/1000
K
u(ΔK
d)=1/20
The parameter that is input to the PID controller is calculated by following formula:
K
i=K’
i+ΔK
i
K
d=K’d+ΔK
d
Fuzzy-PID control algolithm process flow diagram:
The Fuzzy-PID algorithm of temperature control system has adopted the form of program to write, and the flow process in one-period as shown in Figure 4.
The above only is preferred embodiment of the present invention, not in order to limiting the present invention, all any modifications of doing within the spirit and principles in the present invention, is equal to and replaces and improvement etc., all should be included within protection scope of the present invention.
Claims (5)
1. the method for designing of a fuzzy controller is characterized in that, the method for designing of described fuzzy controller may further comprise the steps:
The obfuscation of input quantity deviation e, change of error ec;
Determining and fuzzy reasoning of tuning method;
Set up fuzzy control table.
2. the method for designing of fuzzy controller as claimed in claim 1, it is characterized in that, the step of the obfuscation of described input quantity deviation e, change of error ec is: at first will carry out Fuzzy processing to input quantity, the Linguistic Value of input, output variable is divided into seven Linguistic Values: { NB, NM, NS, O, PS, PM, PB}, membership function adopts the strong trigonometric function of sensitivity, for strengthening the robustness of system, improve the resolution of membership function, near the function shape 0 value obtains steeper;
The basic domain of e is: [2 ℃, 2 ℃];
The basic domain of ec is: [1,1];
Δ K
pBasic domain is: [0.3,0.3];
Δ K
iBasic domain is: [0.006,0.006];
Δ K
dBasic domain is: [0.3,0.3];
The fuzzy quantity of above each variable is respectively: E, EC, Δ K
p, Δ K
i, Δ K
d
Its domain is: [6 ,-5 ,-4 ,-3 ,-2 ,-1,0,1,2,3,4,5,6];
The quantizing factor of input quantity e, ec is:
k
e=-3,k
ec=-6。
3. the method for designing of fuzzy controller as claimed in claim 1 is characterized in that, the definite and fuzzy reasoning of described tuning method also comprises:
The proportional component of the deviation signal e of proportional reflection control system;
Be used for to eliminate static difference, improve system without margin, to the integral element that error is carried out integration and control has certain delayed action to system;
The variation tendency that can reflect deviation signal, and can before the deviation signal value becomes too greatly, add a corrected signal, accelerate the response speed of system, reduce the overshoot time, strengthen the differentiation element of Systems balanth.
4. the method for designing of fuzzy controller as claimed in claim 1 is characterized in that, the acquiring method of described fuzzy control table is:
By between 49 fuzzy condition statements describing control be or relation, can calculate Δ K by the determined control law of first statement
p, Δ K
i, Δ K
d
Can be written as by the determined fuzzy relation of first statement:
RΔK
p=(NBe×NBec)×ΔK
ppb
RΔK
i=(NBe×NBec)×ΔK
io
RΔK
d=(NBe×NBec)×ΔK
dps
According to each bar inference rule, can obtain corresponding fuzzy relation, such as R1, R2 ... Rn, so the corresponding fuzzy relation R of the overhead control of whole system rule is:
R=R1∨R2∨...∨Rn
Had after the R, just can according to above-mentioned obtained E and the quantize value of EC, according to the computing of Fuzzy fuzzy filtering rule, draw the fuzzy set Δ K that corresponding ratio changes
p, Δ K
i, Δ K
d
ΔK
p=(E×EC)·RΔK
p
ΔK
i=(E×EC)·RΔK
i
ΔK
d=(E×EC)·RΔK
d
The output of above-mentioned fuzzy control all is a Fuzzy subset, it is a kind of combination of the different values of reflection control language, but actual controlled device can only be accepted an output quantity, therefore will be with the Fuzzy set transform to accurate output quantity de-fuzzy, we can use fuzzy judgment, namely by principles such as method of weighted mean or the maximum method of degree of membership or center of gravity methods, obtain corresponding output quantity, adopt gravity model appoach to ask for the degree of accuracy of output quantity;
Draw the clear amount C (k) behind the fuzzy judgment, draw at last control output summary table.
5. the method for designing of fuzzy controller as claimed in claim 1 is characterized in that, the method for designing of described fuzzy controller comprises the algorithm of fuzzy controller:
At first to being input to the parameter initialization of PID controller;
Obtain current sampled value;
e(k)=r-y(k);
ee(k)=e(k)-e(k-1);
e(k-1)=e(k);
E (k), ec (k) obfuscation;
Through fuzzy reasoning and computing, de-fuzzy obtains Δ K
p, Δ K
i, Δ K
d
Calculate current K
p, K
i, K
d
Carry out the PID computing, amplitude limit output.
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