A PID control method and system under fractional-order stochastic optimal control model

Abstract

The present invention belongs to the field of control technology. The present invention discloses a PID control method and system under a fractional-order random optimal control model, including: building a PID control environment, determining the transfer function of a PID control system; building a discrete random optimal control model driven by a fractional-order noise with a time lag and a performance functional of the optimal control model; obtaining an expression of an optimal control variable according to the optimal control model, and the optimal control variable makes the performance functional take an extreme value; substituting the actual input value and output value in the PID control system into the expression of the optimal control variable to obtain the actual value of the optimal control variable; substituting the actual value of the optimal control variable into the transfer function of the PID control system to obtain the optimal parameters of the PID control system. The optimal control model constructed by the present invention solves the disturbance of PID control by introducing fractional-order noise, and solves the delay of PID control by introducing a discrete random control system with a time lag, thereby effectively improving the accuracy of automatic control in engineering.

Description

Technical Field

[0001] The present invention relates to the technical field of PID control, and in particular to a PID control method and system under a fractional-order random optimal control model. Background Art

[0002] PID control system (Proportional-Integral-Derivative Control) is a typical application of classical control theory in practical engineering control. The advantages of PID controller include simple principle, strong robustness and wide application range. Although it is a linear controller in theory, it may encounter problems such as nonlinearity, time-varying, strong interference, etc. in practical application, which may affect the control effect.

[0003] The traditional method of adjusting the accuracy of the control system often uses trial and error, critical proportion method, etc., or adjusts the parameters of the PID controller based on a deterministic model. Due to the shortcomings of control such as delay and disturbance, there is a certain degree of error in the control effect. Summary of the invention

[0004] The purpose of the present invention is to provide a PID control method and system under a fractional-order stochastic optimal control model, which can solve at least one of the technical problems mentioned above. The specific solution is as follows:

[0005] According to the specific implementation mode disclosed in the present invention, the first aspect of the present invention provides a PID control method under a fractional-order stochastic optimal control model, comprising:

[0006] Build a PID control environment and determine the transfer function of the PID control system;

[0007] Constructing a discrete stochastic optimal control model driven by fractional-order noise with time lag and a performance functional of the optimal control model;

[0008] Obtaining an expression of an optimal control variable according to the optimal control model, wherein the optimal control variable makes the performance functional take an extreme value;

[0009] Substituting the actual input value and output value in the PID control system into the expression of the optimal control variable to obtain the actual value of the optimal control variable;

[0010] Substitute the actual value of the optimal control variable into the transfer function of the PID control system to obtain the optimal parameters of the PID control system.

[0011] Preferably, the optimal control model is:

[0012] ,

[0013] in, x is the state variable, u is the control variable, k are discrete points, is fractional-order noise;

[0014] , , , , , , , To determine the matrix;

[0015] and is the time lag term; , N is a positive integer, and ;

[0016] The performance functional expression of the optimal control model is:

[0017] ,

[0018] in, To determine the matrix; E Express expectations.

[0019] Preferably, before the step of constructing a discrete stochastic optimal control model driven by fractional-order noise with time lag, the method comprises:

[0020] Define fractional-order noise: ;

[0021] Define the admission control domain:

[0022] ,

[0023] in, ;

[0024] H for Hurst function, and ;

[0025] For discrete points K Fractional Brownian motion of

[0026] u is the control variable, is a family of continuously measurable random processes;

[0027] is a measurable space, is a non-empty set, for a non-empty subset of ;

[0028] for n dimensional real vector space.

[0029] Preferably, the expression of the optimal control variable is obtained according to the optimal control model, including:

[0030] Obtaining a variational equation of a state variable and a variational equation of a time-delay term of the state variable according to the optimal control model;

[0031] Calculating the explicit solution of the variational equation of the state variable and the explicit solution of the variational equation of the time delay term and substituting them into the variational inequality of the performance functional to obtain the expression of the optimal control variable;

[0032] The variational inequality of the performance functional is:

[0033] ,

[0034] in, ; represents the Kronecker function; m∈[1, N-1] is a positive integer;

[0035] represents the optimal state variable, represents the optimal control variable;

[0036] Explicit solutions to variational equations representing optimal state variables;

[0037] Explicit solutions to variational equations representing optimal state variables with time delay terms;

[0038] is a positive real number approaching zero, , To allow control domain.

[0039] Preferably, the expression for the explicit solution of the variational equation for calculating the state variable is:

[0040] ;

[0041] in, .

[0042] Preferably, the calculating of the state variable xThe explicit solution of the variational equation and the explicit solution of the time-delay variational equation are brought into the variational inequality of the performance functional to obtain the expression of the optimal control variable, including:

[0043] use Malliavin The fractional-order noise term in the variational inequality of the performance functional is processed by derivative, and the expression of the optimal control variable is obtained as follows:

[0044] ;

[0045] in, represents the Malliavin derivative; ;

[0046] , , , To determine the matrix.

[0047] Preferably, determining the transfer function of the PID control system according to the control environment includes:

[0048] The control variable is established according to the deviation value composed of the actual input value and the output value, and the expression is:

[0049] ,

[0050] After Laplace transformation of the control variable, we get:

[0051] ,

[0052] The transfer function is obtained as:

[0053] ;

[0054] in, s , t Represents time;

[0055] is the control variable, is the deviation, is the proportionality coefficient;

[0056] Integration time constant; is the integration coefficient;

[0057] is the integration coefficient; For the differential system.

[0058] Preferably, after determining the transfer function of the PID control system according to the control environment, the method further comprises:

[0059] The PID control system is preliminarily debugged to determine the proportional gain, integral time constant and differential time constant of the PID control system.

[0060] According to the specific embodiments disclosed in the present invention, the second aspect of the present invention discloses a PID control system under a fractional-order stochastic optimal control model, comprising: a data acquisition unit for acquiring actual input values ​​and output values ​​of a PID controller;

[0061] The optimal control model unit is used to implement the above method and obtain the actual value of the optimal control variable;

[0062] An adjustment unit adjusts the PID controller according to an actual value of the optimal control variable.

[0063] Compared with the prior art, the above solution disclosed in the present invention has at least the following beneficial effects:

[0064] The present invention uses a discrete random optimal control model driven by fractional-order noise with time lag to adjust the control accuracy of the PID control system. The expression of the optimal control variable is obtained by solving the model, and then the actual input value and output value in the PID control are brought into the expression of the optimal control variable to determine the actual value of the optimal control variable, thereby combining the transfer function to obtain the optimal parameters of the PID control system. K p , K i and K d The optimal control model constructed by the present invention solves the disturbance of PID control by introducing fractional-order noise, solves the delay problem of PID control by introducing a discrete random control system with time lag, and forms a discrete random optimal control model driven by fractional-order noise with time lag, thereby effectively improving the accuracy of automatic control in engineering and avoiding the situation in which the traditional method of adjusting PID control variables by trial and error method leads to errors in control results. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] The drawings herein are incorporated into the specification and constitute a part of the specification, showing embodiments consistent with the disclosure of the present invention, and together with the specification, are used to explain the principles disclosed in the present invention. Obviously, the drawings described below are only some embodiments disclosed in the present invention, and for ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work. In the drawings:

[0066] Figure 1is a flow chart of a PID control method according to a first embodiment of the present invention;

[0067] Figure 2 This is the principle block diagram of the PID controller;

[0068] Figure 3 It is a schematic diagram of a PID control system according to the third embodiment of the present invention. DETAILED DESCRIPTION

[0069] In order to make the purpose, technical scheme and advantages disclosed in the present invention clearer, the present invention will be further described in detail below in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments disclosed in the present invention, rather than all the embodiments. Based on the embodiments disclosed in the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection disclosed in the present invention.

[0070] The terms used in the embodiments disclosed in the present invention are only for the purpose of describing specific embodiments, and are not intended to limit the disclosure of the present invention. The singular forms "a", "said" and "the" used in the embodiments disclosed in the present invention and the appended claims are also intended to include plural forms, unless the context clearly indicates other meanings, and "multiple" generally includes at least two.

[0071] As used herein, the words "if" and "if" may be interpreted as "at the time of" or "when" or "in response to determining" or "in response to detecting", depending on the context. Similarly, the phrases "if it is determined" or "if (stated condition or event) is detected" may be interpreted as "when it is determined" or "in response to determining" or "when detecting (stated condition or event)" or "in response to detecting (stated condition or event)", depending on the context.

[0072] It should also be noted that the term "includes", "comprising" or any other variation thereof is intended to cover non-exclusive inclusion, so that a commodity or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such commodity or device. In the absence of more restrictions, the elements defined by the sentence "comprising a ..." do not exclude the existence of other identical elements in the commodity or device including the elements.

[0073] The optional embodiments disclosed in the present invention are described in detail below with reference to the accompanying drawings. Example 1

[0074] PID control is to use the proportional, integral and derivative of the deviation to form a control quantity through linear combination, control the controlled object, and finally provide feedback through the sensor. Figure 2 As shown in the block diagram, the actual input value The actual output value Composition deviation: The present invention obtains the expression of the optimal control variable by constructing a discrete random optimal control model driven by fractional-order noise with time lag, and uses the actual input value The actual output value Obtain the actual value of the optimal control variable to minimize the deviation of PID control, thereby improving the regulation accuracy.

[0075] Therefore, if Figure 1 As shown, the first embodiment of the present invention provides a PID control method, comprising the following steps:

[0076] Step S1, building a PID control environment and determining the transfer function of the PID control system;

[0077] Step S2, constructing a discrete stochastic optimal control model driven by fractional-order noise with time lag, and a performance functional of the optimal control model;

[0078] Step S3, obtaining an expression of an optimal control variable according to the optimal control model, wherein the optimal control variable makes the performance functional take an extreme value;

[0079] Step S4, substituting the actual input value and output value in the PID control system into the expression of the optimal control variable to obtain the actual value of the optimal control variable;

[0080] Step S5: Substitute the actual value of the optimal control variable into the transfer function of the PID control system to obtain the optimal parameters of the PID control system.

[0081] Specifically, in step S1, a control variable is established according to the deviation value composed of the actual input value and the output value. u ( t ) is:

[0082] ,

[0083] For the control variables u ( t ) is transformed by Laplace to obtain:

[0084] ,

[0085] Therefore, the transfer function Represents the relationship between the control amount and the deviation value:

[0086] ,

[0087] in, s , t Represents time;

[0088] is the control variable, is the deviation, is the proportionality coefficient;

[0089] Integration time constant; is the integration coefficient;

[0090] is the integration coefficient; is the differential coefficient.

[0091] Furthermore, after completing the construction of the PID control system and determining the transfer function of the PID control system in step S1, the following steps are also included:

[0092] Step S12: Perform preliminary debugging on the PID control system to determine the proportional gain of the PID control system. P , integration time constant and the differential time constant .

[0093] Specifically, they include:

[0094] Step S12.1, determine the proportional gain P .

[0095] Remove the integral and differential terms of PID and let , making PID pure proportional regulation;

[0096] The input is set to about 60%~70% of the maximum value allowed by the system, and the proportional gain P is gradually increased from 0 until the system oscillates;

[0097] Then gradually decrease the value from this point until the oscillation disappears, record the value of the proportional gain P, and set the proportional gain P of PID to 60%~70% of the current value.

[0098] Step S12.2: Determine the integral time constant .

[0099] After the proportional gain P is set, set a larger integral time constant The initial value of , then gradually decreases until oscillation occurs;

[0100] Then gradually increase the value from this point until the oscillation disappears, and set the integral time constant 150%~180% of the current value.

[0101] Step S12.3, determine the differential time constant .

[0102] Set a larger derivative time constant The initial value of , then gradually decreases until oscillation occurs;

[0103] Then gradually increase the value from this point until the oscillation disappears, and set the differential time constant 30% of the non-oscillating state.

[0104] At this point, the initial construction of the PID control system is completed. Next, the discrete random optimal control model driven by fractional-order noise with time lag is used to obtain the optimal parameters of the PID control system through the optimal control model, that is, the proportional coefficient , integral coefficient and the differential coefficient .

[0105] Specifically, step S2 includes:

[0106] Step S21: define fractional order noise and Admission Control Domain .

[0107] Fractional Order Noise : ,

[0108] in, ; H is the Hurst function and ; For discrete points k Fractional Brownian motion of .

[0109] Permission control domain : .

[0110] in, u is the control variable, is a family of continuously measurable random processes;

[0111] is a measurable space, is a non-empty set, for a non-empty subset of ;

[0112] for n dimensional real vector space.

[0113] Step S22: construct an optimal control model.

[0114] Take N discrete points in the PID control system and establish the following discrete stochastic optimal control model driven by fractional-order noise with time lag:

[0115] ,

[0116] in, x is the state variable, u is the control variable, k are discrete points;

[0117] , , , , , , , To determine the matrix;

[0118] and is the time lag term; is a positive integer, and ;

[0119] Performance functional of the optimal control model J ( u ) is:

[0120] ,

[0121] in, To determine the matrix; E Express expectations.

[0122] And determine the matrix , , , , , , , , The specific value of can be calculated from the subsequent steps.

[0123] In this embodiment, the optimal control variable to be found within the allowable control domain is , at this time, the performance functional of the optimal control model takes the extreme value, that is:

[0124] .

[0125] Step S3, obtaining an expression of an optimal control variable according to the optimal control model, comprising the following steps:

[0126] Step S31: Obtain state variables according to the optimal control model x The variational equation of and the variational equation of the time delay term of the state variable.

[0127] Step S32: Calculate the state variable x The explicit solution of the variational equation and the explicit solution of the variational equation with the time delay term are substituted into the variational inequality of the performance functional of the optimal control model to obtain the expression of the optimal control variable.

[0128] Specifically, step S31, in the optimal control model, different time lag terms and have different variational equations. Therefore, assuming ( ) are the optimal state variables and control variables, ( ) are non-optimal state variables and control variables, and , is a positive real number approaching zero, .

[0129] The optimal control variable is the control of the state variable. The variational equation of the state variable and its time-delay term can be derived as follows by differentiating the optimal control model:

[0130] ,

[0131] in, is the variational equation of the optimal state variables, k are discrete points;

[0132] , , , , , , , To determine the matrix;

[0133] is the variational equation of the optimal state variable of the time-delay term;

[0134] is a positive integer, and ;

[0135] is the Kronecker function. When k=m, ;

[0136] When k≠m, 0, m∈[1, N-1] is a positive integer.

[0137] Then, the expression for the explicit solution of the variational equation for the optimal state variable is:

[0138] ;

[0139] ;

[0140] The solution expression of the variational equation for the optimal state variable of the time-delay term is:

[0141] ,

[0142] In step S32, the explicit solution of the variational equation Substituting into the variational inequality of the performance functional of the optimal control model, using Malliavin The dual formula and the classical variational method are used to obtain the expression of the optimal control variable.

[0143] Among them, the variational inequality of the performance functional is:

[0144] ,

[0145] In this embodiment, using Malliavin The fractional-order noise term in the variational inequality of the performance functional is processed by derivative, and the expression of the optimal control variable is obtained as follows:

[0146] .

[0147] in, represents the Malliavin derivative;

[0148] ;

[0149] , , , To determine the matrix.

[0150] In step S4, the actual input and output values ​​in the PID control are substituted into the optimal control variable expression in step S3 to obtain the actual value of the optimal control variable, that is, the control variable of the PID control system in step 2. .

[0151] Specifically, in this embodiment, the actual input value is the non-optimal control state variable in step S3. x , the output value is the performance functional in step S2 , multiple sets of equations and multiple sets of unknowns can determine the matrix , , , , , , , , The specific value of In The value of .

[0152] In step S5, due to the deviation value in PID control It is known that the actual value of the optimal control variable obtained in step S4 is calculated based on the relationship between the proportional coefficient, the integral coefficient and the differential coefficient. , Combined with the transfer function between the control variable and the deviation in step S1 , the optimal proportionality coefficient can be solved K p , optimal integral coefficient K i and the optimal differential coefficient K d .

[0153] Example 2

[0154] The second embodiment of the present invention provides a PID control system under a fractional-order stochastic optimal control model, such as Figure 3 As shown, including:

[0155] The data acquisition unit 101 is used to acquire the actual input value and output value of the PID controller;

[0156] The optimal control model unit 102 is used to implement the method in the first embodiment to obtain the actual value of the optimal control variable; the adjustment unit 103 is used to adjust the PID controller according to the actual value of the optimal control variable.

[0157] It should be noted that the flowcharts and block diagrams in the accompanying drawings illustrate the possible implementation architecture, functions and operations of the system, method and computer program product according to the various embodiments disclosed in the present invention. In this regard, each box in the flowchart or block diagram can represent a module, a program segment, or a part of a code, and the module, program segment, or a part of a code contains one or more executable instructions for implementing the specified logical function. It should also be noted that in some alternative implementations, the functions marked in the box can also occur in a different order from the order marked in the accompanying drawings. For example, two boxes represented in succession can actually be executed substantially in parallel, and they can sometimes be executed in the opposite order, depending on the functions involved. It should also be noted that each box in the block diagram and / or flowchart, and the combination of boxes in the block diagram and / or flowchart can be implemented with a dedicated hardware-based system that performs a specified function or operation, or can be implemented with a combination of dedicated hardware and computer instructions.

[0158] The units involved in the embodiments disclosed in the present invention may be implemented by software or hardware, wherein the name of a unit does not limit the unit itself in some cases.

Claims

1. A PID control method under a fractional-order stochastic optimal control model, characterized in that: include: Build a PID control environment and determine the transfer function of the PID control system; Constructing a discrete stochastic optimal control model driven by fractional-order noise with time lag and a performance functional of the optimal control model; Obtaining an expression of an optimal control variable according to the optimal control model, wherein the optimal control variable makes the performance functional take an extreme value; Substituting the actual input value and output value in the PID control system into the expression of the optimal control variable to obtain the actual value of the optimal control variable; Substituting the actual value of the optimal control variable into the transfer function of the PID control system to obtain the optimal parameters of the PID control system; The expression of the optimal control variable is obtained according to the optimal control model, including: Obtaining a variational equation of a state variable and a variational equation of a time-delay term of the state variable according to the optimal control model; Calculating the explicit solution of the variational equation of the state variable and the explicit solution of the variational equation of the time delay term and substituting them into the variational inequality of the performance functional to obtain the expression of the optimal control variable; The variational inequality of the performance functional is: in, represents the Kronecker function; m∈[1, N-1] is a positive integer; represents the optimal state variable, represents the optimal control variable, represents the optimal state variable of the time lag term; Explicit solutions to variational equations representing optimal state variables; Explicit solutions to variational equations representing optimal state variables with time delay terms; ε is a positive real number approaching zero, v∈U ad , U ad To allow control domain; E represents expectation, δ and N are positive integers, and 0<δ <N-1;M k , R k , Z N To determine the matrix; The expression for the explicit solution of the variational equation for calculating the state variable is: in, A j , C i , To determine the matrix; E stands for expectation. is fractional-order noise; The explicit solution of the variational equation of the state variable x and the explicit solution of the variational equation of the time-delay term are calculated and brought into the variational inequality of the performance functional to obtain the expression of the optimal control variable, including: The Malliavin derivative is used to process the fractional noise term in the variational inequality of the performance functional, and the expression of the optimal control variable is obtained as follows: in, represents the Malliavin derivative; R m , C m , D m , To determine the matrix; M k , A j , Z N To determine the matrix.

2. The method according to claim 1, characterized in that The optimal control model is: Among them, x is the state variable, u is the control variable, k is the discrete point, is fractional-order noise; A k , B k , C k , D k , To determine the matrix; x k-δ and u k-δ is the time lag term; δ and N are positive integers, and 0<δ <N-1; The performance functional expression of the optimal control model is: Among them, M k , R k , Z k is the determination matrix; E represents expectation.

3. The method according to claim 1, characterized in that Before the step of constructing a discrete stochastic optimal control model driven by fractional-order noise with time lag, the method includes: Define fractional-order noise: Define the admission control domain: Where k = 0, 1, …, N, N < + ∞; H is the Hurst function, and 1 / 2 <H<1; is the fractional Brownian motion of discrete point K; u is the control variable, is a family of continuously measurable random processes; is a measurable space, Ω is a non-empty set, is a non-empty subset of Ω; is an n-dimensional real vector space.

4. The method according to claim 1, characterized in that The step of building a PID control environment and determining a transfer function of a PID control system includes: The control variable is established according to the deviation value composed of the actual input value and the output value, and the expression is: After Laplace transformation of the control variable, we get: The transfer function is obtained as: Among them, s and t represent time; u(·) is the control variable, e(·) is the deviation, K p is the proportionality coefficient; T i is the integration time constant; T d is the integration coefficient; K i =K p / T i is the integral coefficient; K d =K p *T d is the differential coefficient.

5. The method according to claim 1, characterized in that After the PID control environment is built and the transfer function of the PID control system is determined, the following steps are further included: The PID control system is preliminarily debugged to determine the proportional gain, integral time constant and differential time constant of the PID control system.

6. A PID control system under a fractional-order stochastic optimal control model, characterized in that: include: A data acquisition unit is used to collect the actual input value and output value of the PID controller; An optimal control model unit, used to implement the method according to any one of claims 1 to 5 to obtain an actual value of an optimal control variable; An adjustment unit adjusts the PID controller according to an actual value of the optimal control variable.

Images