CN108536016B - Networked control method based on fuzzy inverse model - Google Patents
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- G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
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- G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
- G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
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- G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance
Abstract
The invention discloses a networked control method based on a fuzzy inverse model, which can obtain future control action by solving an inverse system of the fuzzy single-point model and adopting an iteration mode to compensate the influence of network time delay on the performance of a control system. By utilizing the method and the device, the mechanism of the controlled process does not need to be deeply understood, and the method and the device can be applied to a linear system and a nonlinear system.
Description
Technical Field
The invention relates to a networked control method based on a fuzzy inverse model, which can obtain future control action by solving an inverse system of a fuzzy single-point model and adopting an iteration mode to compensate the influence of network delay on the performance of a control system, and belongs to the technical field of automatic control.
Background
Advances in network technology have driven the development of control theory. In a network environment, the control structure is not a point-to-point manner in the traditional sense, but a distributed structure. The sensor, the controller and the actuator under the structure form a closed loop through network media to form a networked feedback control system. The device has the characteristics of simple structure, low cost, easy maintenance and the like. However, due to the characteristics of the network shared medium, phenomena such as time delay, data packet loss and the like inevitably exist in the network, which provides a new challenge for the traditional control theory.
Meanwhile, in practical application, mechanisms of some controlled processes are unclear, and it is difficult to directly establish a mechanism mathematical model, while existing networked control methods are mostly model-based methods, and development of some data-based control methods is urgently needed. The invention applies fuzzy clustering modeling technology, can directly establish a fuzzy clustering model of the system according to the input and output data of the controlled object, then convert the system into a fuzzy single-point model, and obtain a series of future control actions through iteration and inversion modes, thereby compensating the influence of network time delay, data packet loss and the like on the performance of the control system by selecting a proper control sequence mode at a process end. The method is based on data, so that the method has wide application space.
Disclosure of Invention
Technical problem to be solved
In view of the above problems in the prior art, a primary object of the present invention is to provide a networked control method based on a fuzzy inverse model, so as to fully improve the control performance of a networked control system.
(II) technical scheme
In order to achieve the purpose, the technical scheme of the invention is realized as follows:
a networked control method based on a fuzzy inverse model comprises the following steps:
A. according to the input and the output of the controlled process, a dynamic mathematical model of the system is obtained by a modeling method of fuzzy clustering;
B. converting a mathematical model of fuzzy clustering into an equivalent fuzzy single-point model;
C. according to the past process output and the past control action, a series of future process outputs can be obtained in an iterative mode on the basis of a fuzzy single-point model;
D. and judging whether an inverse system of the fuzzy single-point model exists or not, and if so, continuing to execute downwards. If not, the fuzzy single-point model is required to be segmented, and the step B is returned;
E. according to the given value and the future process output, a series of future control actions can be obtained by solving the inverse system of the fuzzy single-point model;
F. the control actions are packaged and transmitted to a process end from a controller end through a network, and a proper control sequence is selected to act on a controlled process through a network delay compensator at the process end so as to compensate the delay of a forward network channel;
G. and in the next execution cycle, repeatedly executing the steps E and F.
Preferably, the prediction model in the step a can be obtained only according to input and output data fully excited by the system, wherein the membership degree of the front part variable is obtained by a G-K algorithm, and the parameter of the back part variable is obtained by a least square method.
Preferably, the front part variable of the fuzzy single-point model in the step B is a piecewise triangular membership function, the division of the front part variable is more than that of the fuzzy clustering model, and the single-point parameter of the back part variable is obtained by a least square method, so that the fuzzy single-point model and the fuzzy clustering model are equivalent.
Preferably, the error accumulation is easily caused after the step C is iterated for a plurality of times, and an internal model control structure is adopted in practical application to increase feedback control.
Preferably, the time delay of the forward path is a fixed time delay or a random time delay.
Preferably, a maximum allowable delay is taken, and if a control sequence exceeds the maximum allowable delay, the control sequence at the maximum allowable delay can be used for calculation.
(III) advantageous effects
According to the technical scheme, the invention has the following beneficial effects:
1. the invention is applicable to occasions with unclear process mechanisms by adopting a fuzzy clustering method for modeling, and can obtain a prediction model in a fuzzy modeling mode as long as fully-excited process input and output data can be provided.
2. By using the method, the fuzzy single-point model is a nonlinear model in nature, so that the method can be applied to the networked control of the reversible nonlinear system.
3. By using the method and the device, when the inverse of the fuzzy single-point model does not exist, the inverse model can be obtained in a monotonous segmented mode by re-segmenting the discourse domain, so that the method and the device have wider application prospect.
4. By using the invention, a proper control sequence is selected at the process end through the network delay compensator to act on the controlled process, so that the time delay existing in the forward network channel can be compensated.
5. By utilizing the method, the control action is obtained by directly solving the inverse of the fuzzy single-point model when the controller is designed, and the method has the advantages of simple program, small calculated amount and convenient industrial application.
Drawings
FIG. 1 is a flowchart illustrating an implementation of a general technical solution of a networked control method based on a fuzzy inverse model according to the present invention;
FIG. 2 is a schematic diagram of a control structure of a fuzzy inverse model-based networked control method provided by the present invention;
FIG. 3 is a diagram of an internal model control structure of a networked control method based on a fuzzy inverse model;
FIG. 4 is a membership function of a antecedent variable obtained by fuzzy clustering modeling in an exemplary embodiment
FIG. 5 is a graph comparing the control effect of the fuzzy inverse model-based networked control method with the conventional PID control method under the condition that 10 steps of random time delay exist in the forward network channel;
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to specific embodiments and the accompanying drawings.
As shown in fig. 1,2 and 3, the present invention provides a networked control method based on a fuzzy inverse model, which includes:
A. according to the input and the output of the controlled process, a dynamic mathematical model of the system is obtained by a modeling method of fuzzy clustering;
B. converting a mathematical model of fuzzy clustering into an equivalent fuzzy single-point model;
C. according to the past process output and the past control action, a series of future process outputs can be obtained in an iterative mode on the basis of a fuzzy single-point model;
D. and judging whether an inverse system of the fuzzy single-point model exists or not, and if so, continuing to execute downwards. If not, the fuzzy single-point model is required to be segmented, and the step B is returned;
E. according to the given value and the future process output, a series of future control actions can be obtained by solving the inverse system of the fuzzy single-point model;
F. the control actions are packaged and transmitted to a process end from a controller end through a network, and a proper control sequence is selected to act on a controlled process through a network delay compensator at the process end so as to compensate the delay of a forward network channel;
G. and in the next execution cycle, repeatedly executing the steps E and F.
Preferably, the prediction model in the step a can be obtained only according to input and output data fully excited by the system, wherein the membership degree of the front part variable is obtained by a G-K algorithm, and the parameter of the back part variable is obtained by a least square method.
Preferably, the front part variable of the fuzzy single-point model in the step B is a piecewise triangular membership function, the division of the front part variable is more than that of the fuzzy clustering model, and the single-point parameter of the back part variable is obtained by a least square method, so that the fuzzy single-point model and the fuzzy clustering model are equivalent.
Preferably, the error accumulation is easily caused after the step C is iterated for a plurality of times, and an internal model control structure is adopted in practical application to increase feedback control.
Preferably, the time delay of the forward path is a fixed time delay or a random time delay.
Preferably, a maximum allowable delay is taken, and if a control sequence exceeds the maximum allowable delay, the control sequence at the maximum allowable delay can be used for calculation.
The step A, assuming that the data set Z contains input and output data of the controlled process, y (k), y (k-1), …, y (k-n)y+1 is the output of the system, u (k), u (k-1), …, u (k-n)u+1) is the input to the system,
in order to output the fuzzy sets,
for the input fuzzy set, the controlled process can be represented by a T-S fuzzy structure model:
Riif y (k) belongs to Ai1And y (k-1) belongs to Ai2And … and
y(k-ny+1) belong to
And u (k) belongs to Bi1And is
u (k-1) belongs to Bi2And … and u (k-n)u+1) belong to
Then
According to the input and the output of the system, a mathematical model of a controlled process is established by adopting a fuzzy clustering modeling technology, and the mathematical model comprises the following steps:
c clusters are selected, c is more than 1 and less than N (N is an integer), the fuzzification parameter m is more than 1, the convergence criterion epsilon is more than 0, and the partition matrix is initialized randomly.
Let l be 1,2, …, calculated as follows:
s1) calculating fuzzy clustering center
Wherein v is a fuzzy clustering center, μ is a membership function, z is an observed value of a fuzzification matrix, k is an integer and represents a kth fuzzy subset in the ith fuzzy cluster, and other symbols are as shown above.
S2) calculating a fuzzy clustering variance matrix F
Where T represents the transpose of a matrix or vector and the other symbols are as previously indicated.
S3) calculating the norm of the distance D
Wherein A isiNorm matrix for the ith cluster, ρiFor its constraint values, det represents the value of the determinant of the solution matrix, n is an integer, and the other symbols are as indicated previously.
S4) updating the partition matrix
If for 1. ltoreq. i.ltoreq.c, 1. ltoreq. k.ltoreq.N,
then
And others:
Repeating the above steps until | U(l)-U(l-1)I < ε, where U represents the membership function matrix, ε is the convergence criterion, and other symbols are as previously shown.
S5) identifying the back-part variable a by using a least square methodij,bij
S6) obtaining the output y (k +1) of the system
The step B comprises the following steps: and B, converting the fuzzy clustering model in the step A into a fuzzy single-point model in the following form:
Riif y (k) belongs to A'i1And y (k-1) is A'i2And … and
y (k-p +1) is of A'ipAnd u (k) is of type B'i1And is
u (k-1) belongs to B'i2And … and u (k-q +1) belongs to B'iq
Then y (k +1) ═ Ci (7)
The state vector x (k) is introduced to contain p-1 past outputs, q-1 past inputs and the current output, i.e. x (k) ═ y (k), …, y (k-p +1), u (k-1), …, u (k-q +1)]TIf X is equal to A1×…×Ap×B2×…×BqSimplified representation, replacement of B with B1Then the rule in the fuzzy single point model can be expressed as follows:
if X (k) belongs to X and u (k) belongs to B, then y (k +1) belongs to C (8)
Let M be the fuzzy set XiN is the fuzzy set BjThe total number of (2) is K-M.N, as shown in Table 1
TABLE 1 fuzzy single-point model rule base
By using the t-norm operator, the membership of the antecedent rule is
The output of the model y (k +1) may be normalized by the degree of membership βijWeighted average of the background cijTo obtain
The step C comprises the following steps: and obtaining a series of future process outputs y (k +2), …, y (k + P +1) and y (k) in an iterative manner on the basis of the fuzzy single-point model in the step B.
The step D comprises the following steps: and D, judging whether an inverse system of the fuzzy single-point model exists according to the following theorem, and if so, continuing to execute the step E downwards. If not, the fuzzy single-point model is required to be segmented, and the step B is returned to.
Theorem 1: let bj＝core(Bj) Is BjThe fuzzy one-point model described in step B is invertible when and only when the following conditions are met.
1) Each BjAll of the kernels of (1) are single points, and | B j1, j 1,2, …, N, and
2)b1<b2<…<bN→ci1<ci2<…<ciNor b is1<b2<…<bN→ci1>ci2>…>ciN,i＝1,2,…,M
The step E comprises the following steps: the rule-based model (8) is equivalent to the following regression model
y(k+1)＝f(x(k),u(k)) (11)
The inputs to the model are the current state x (k) ═ y (k), …, y (k-p +1), u (k-1), …, u (k-q +1)]TAnd the current input u (k), the output being the one-step predicted value y (k +1) of the process. The purpose of the control algorithm is to calculate the control input u (k) so that the system output at the next sampling instant equals the desired output r (k + 1). If the current state x (k) and the reference value r (k +1) are known, this can be done by model inversion, the control input being given by:
u(k)＝f-1(x(k),r(k+1)) (12)
in general, it is difficult to find the inverse model f-1. With the haplotype structure, however, the multivariate map (11) can be simplified to a univariate map for each particular state x (k),
y(k+1)＝fx(u(k)) (13)
thus, if the model is invertible, the inverse mapping can be easily found
A series of future control actions can then be obtained according to the following theorem and procedure.
Theorem 2: assuming that the controlled process can be represented by a reversible fuzzy single-point model as in step B, taking x arbitrarily, and satisfying
Arbitrarily take u to satisfy
For a given state x (k), the control law based on the inverse of the single-point model is given by the following rule:
if r (k +1) belongs to Cj(k) Then u (k) belongs to Bj,j＝1,2,…,N (14)
Wherein, Cj:Y→[0 1]And is a fuzzy set represented by a trigonometric membership function.
Wherein, the core cjObtained by the formula (16)
And c is1≤c2≤…≤cNFuzzy set BjAlso in sequence. Then
Wherein, bjIs BjThe core of (1). The fuzzy single point model can then be inverted as follows.
Step 1: the current system state is measured or estimated. For the input-output model, this means that the state x (k) is updated according to the output y (k), see equation (8).
Step 2: computing core cj，
And 3, step 3: reversibility was checked. If non-monotonic is detected, the rule base (14) is divided into two or more rule bases containing only monotonic rules.
And 4, step 4: the membership function is calculated using equation (15). If multiple rule bases are generated by step 3, a separate membership function is constructed for each rule base.
And 5: the control action u (k) is calculated using equation (17). If multiple rule bases are generated by step 3, a control action needs to be calculated for each rule base and selected according to additional criteria. Shown by the formula (12)
Then u (k +1), u (k +2), …, u (k + P) can be obtained in an iterative manner, i.e.:
in fact, the single point fuzzy model cannot fully describe the dynamics of the actual control process. Differences between the model and the process are inevitable due to process model mismatch, interference or noise, which will result in steady state errors in the open loop control. Fortunately, compensation can be made by an internal model control strategy.
The step E comprises the following steps: it is assumed that the delay of the forward channel is not greater than the control time domain. Due to the "packet transmission" nature of the internet, a series of future control actions u (k), u (k +1), …, u (k + P) are sent from the controller side to the process side packed together at sampling time k. At the process end, an appropriate control action can be selected from the latest control sequence to compensate for the network delay. For example, the latest control sequence obtained at the process end is
The control signal selected will be
u(k)＝u(k|k-t) (20)
The core idea of the invention is as follows: 1) establishing a T-S fuzzy model of a controlled object by adopting a fuzzy clustering modeling technology; 2) converting the fuzzy clustering model into an equivalent reversible fuzzy single-point model; 3) obtaining a series of future process outputs in an iterative manner on the basis of a fuzzy single-point model; 4) obtaining a series of future control actions in an inversion mode according to the process output and the future given value, packaging the control actions, and sending the control actions to the process end through a network by the controller end; 5) the network delay of the forward path can be compensated at the process end by selecting an appropriate control sequence. Realizing the networked control of the controlled process; 6) in order to reduce errors in practical application, an internal mold control structure is required.
The following describes a specific embodiment by taking a servo motor control system as an example. The system consists of a direct current motor, a rotary disc and an angle sensor, and the control target is to drive the rotary disc to a given angle through the motor. The discrete model between the system control input (voltage) and the angular position (degree) can be obtained by the least square method, and the sampling time is 0.04 second.
The controlled process and the controller are placed at different physical locations, respectively called a process end and a control end, and the two form a closed loop structure through a network, as shown in fig. 2. There are 10 steps of random time delay in the forward channel and no time delay in the reverse channel.
Three sinusoidal superimposed signals with amplitude of 0.4, frequency of 0.06 pi, 0.012 pi, 0.03 pi radians/sec were selected as excitation sources to generate a data set for fuzzy clustering modeling. The data is divided in half. Half was used for fuzzy clustering modeling and the other half was used for verification. The number c of clusters is 3, the blurring parameter m is 2, and the termination condition is 0.01. Membership functions of the antecedent variables y (k) and u (k) obtained by the fuzzy clustering algorithm are shown in FIG. 4. Then, a piecewise triangular membership function of the front-piece variable in the fuzzy single-point model can be designed:
the back-piece parameters of the fuzzy single-point model can then be obtained using the least squares method, as shown in table 2.
Table 2 fuzzy single-point model rule base in embodiment
According to the reversibility condition, the established fuzzy single-point model is reversible. Thus, control is achieved by following the foregoing steps. In order to verify the control effect, the method of the present invention is compared with the conventional PID control effect (the parameters of the PID controller are P ═ 0.01, I ═ 0.001, and D ═ 0.008), and fig. 5 is a comparison of the control effects of the two control methods in the embodiment, from which it can be seen that the control method of the present invention has a very good control effect.
The above-mentioned embodiments are intended to illustrate the objects, technical solutions and advantages of the present invention in further detail, and it should be understood that the above-mentioned embodiments are only exemplary embodiments of the present invention, and are not intended to limit the present invention, and any modifications, equivalents, improvements and the like made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (5)
1. An inverse model-based networked control method, the method comprising:
1) obtaining a dynamic mathematical model of the system by a modeling method of fuzzy clustering according to the input and the output of the controlled process;
assume that data set Z contains input and output data of the process being controlled, y (k), y (k-1), …, y (k-n)y+1 is the output of the system, u (k), u (k-1), …, u (k-n)u+1) is the input to the system,
in order to output the fuzzy sets,
for the input fuzzy set, the controlled process can be represented by a T-S fuzzy structure model:
Riif y (k) belongs to Ai1And y (k-1) belongs to Ai2And … and
y(k-ny+1) belong to
And u (k) belongs to Bi1And is
u (k-1) belongs to Bi2And … and u (k-n)u+1) belong to
Then
2) Converting the mathematical model of the fuzzy clustering into an equivalent fuzzy single-point model;
Riif y (k) belongs to A'i1And y (k-1) is A'i2And … and
y (k-p +1) is of A'ipAnd u (k) is of type B'i1And is
u (k-1) belongs to B'i2And … and u (k-q +1) belongs to B'iq
Then y (k +1) ═ Ci (7)
The state vector x (k) is introduced to contain p-1 past outputs, q-1 past inputs and the current output, i.e. x (k) ═ y (k), …, y (k-p +1), u (k-1), …, u (k-q +1)]TAnd then X is A'1×…×A′p×B′2×…×B′qSimply expressed, B is replaced by B'1Then the rule in the fuzzy single point model can be expressed as follows:
if X (k) belongs to X and u (k) belongs to B, then y (k +1) belongs to C (8)
Let M be the fuzzy set XiN is the fuzzy set BjThe total number of (2) is K ═ M.N, using cijExpressing that the membership degree of the front piece rule is as follows by using a t-norm operator:
the output of the model y (k +1) is normalized by the degree of membership βijWeighted average of the background cijTo obtain
3) Based on the past process output and the past control action, a series of future process outputs can be obtained in an iterative mode on the basis of a fuzzy single-point model;
4) judging whether an inverse system of the fuzzy single-point model exists or not, and if so, continuing to execute downwards; if not, the fuzzy single-point model needs to be segmented, and the step 2) is returned;
5) according to the given value and the future process output, a series of future control actions can be obtained by solving the inverse system of the fuzzy single-point model;
6) the control actions are packaged and transmitted to a process end from a controller end through a network, and a proper control sequence is selected to act on a controlled process through a network delay compensator at the process end so as to compensate the delay of a forward network channel;
7) in the next execution cycle, the steps 1), 2), 3), 4), 5) and 6) are repeatedly executed.
2. The method according to claim 1, wherein the prediction model in step 1) is obtained only according to input and output data fully excited by the system, wherein the membership degree of the front-part variable is obtained by a G-K algorithm, and the parameter of the back-part variable is obtained by a least square method; the front part variable of the fuzzy single-point model in the step 2) adopts a piecewise triangle membership function, the division of the front part variable is more than that of the fuzzy clustering model, and the single-point parameter of the back part is obtained by a least square method, so that the fuzzy single-point model and the fuzzy clustering model are equivalent.
3. The method according to claim 1, wherein error accumulation is easily caused after multiple iterations in step 3), and an internal model control structure is adopted in practical application to increase feedback control.
4. The method of claim 1, wherein the delay of the forward network path is a fixed delay or a random delay.
5. A method according to claim 1, characterized by taking a maximum allowed delay, and if a control sequence exceeds the maximum allowed delay, calculating with the control sequence at the maximum allowed delay.
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