An online identification method for double-integrating ball-bar objects

Abstract

The present invention provides an online identification method for a double-integral ball-bar object. The identification method for the double-integral ball-bar object to be identified in a closed-loop control system adopts the online identification method for the double-integral ball-bar object described by double integral plus pure delay based on step response and known time lag or the closed-loop identification method for the double-integral ball-bar object described by double integral plus pure delay with filter based on step response and known time lag. The identification method of the present invention can identify the double-integral ball-bar object as a continuous double-integral system of double integral plus pure delay or double integral plus pure delay with filter based on the position setting value data set and position output data set of the closed-loop system, the parameters of the feedback controller and the feedforward controller, and the delay time constant of the system to be identified, can effectively avoid the system from performing open-loop identification operations, can be directly applied to the control strategy design and parameter optimization of the double-integral ball-bar object, and provide an identification model basis for the implementation of advanced control methods such as dynamic characteristic analysis and controller design optimization of the double-integral ball-bar object, and has strong industrial application value and application prospects.

Description

Technical Field

[0001] The invention relates to the field of industrial control, and in particular to an online identification method for a double-integrating ball-bar object. Background Art

[0002] The current identification is mainly open-loop identification, which is an identification model that dynamically changes the system output by disturbing the control quantity without adding a controller. However, this method is not applicable to the double-integral ball-bar object, because the double-integral ball-bar object is an unstable double-integral object. When disturbed without adding a controller, the system output will diverge and become unstable, which is extremely unfavorable for maintaining the stable operation of the double-integral ball-bar object.

[0003] Some scholars have studied the identification of closed-loop systems. Since the closed-loop identification method for discrete systems is a discrete system, it will make the system characteristics analysis and controller optimization design difficult. In addition, the closed-loop identification method based on discrete systems is very sensitive to the sampling period of the system. The unreasonable sampling period will cause the operation of the identification algorithm to be ill-conditioned, which will cause the optimization and improvement of the control strategy and the implementation of advanced control methods based on the identified discrete system to fail. Therefore, it is very necessary to identify the continuous system based on the closed-loop system. However, most of the research on closed-loop systems is aimed at stable objects, and the research on the closed-loop identification method for a type of double-integral ball-bar object continuous system is still relatively lacking. In addition, since the ball-bar control system can have a feedforward effect, and since the set value change often adopts a step change, it is very necessary to propose a method for considering feedforward for the double-integral ball-bar system and identifying the double integral plus pure delay or double integral plus pure delay with filter based on the step data of the closed-loop system position set value and the system position output value data, so as to further provide a basis for the dynamic system characteristics analysis, control strategy optimization and advanced control method implementation. Summary of the invention

[0004] The purpose of the present invention is to overcome the shortcomings of the prior art in solving the closed-loop identification problem of a double-integral ball-bar object, and to propose an online identification method for a double-integral ball-bar object, which converts a closed-loop system consisting of a PID, a feedforward controller, and a double-integral plus pure delay or a double-integral plus pure delay with a filter into a least square form containing parameters to be identified, and identifies the parameters to be identified based on step data of a position setting value of the closed-loop system and position output value data.

[0005] The first aspect of the present invention provides an online identification method for a double-integral ball-bar object based on a double-integral plus pure delay description of a step response and a known time lag, comprising the following steps:

[0006] 1) The transfer function of double integration plus pure delay is used to describe the double integration ball-bar object to be identified. The double integration ball-bar object is:

[0007] Where G(s) is the transfer function of the double-integrating ball-bar plant, s and τ are the differential operator and the known delay constant of the double-integrating ball-bar plant, respectively, and a 1 The parameters that need to be identified for the double integrating ball bar object;

[0008] 2) Collect the position setting value data set R of the closed-loop system in the same time period under the step response 0 and position output dataset Y 0 , data length is n, sampling period is ΔT; position setting value data set R 0 and position output dataset Y 0 The form is as follows:

[0009] R 0 =[r 0 (1),…,r 0 (i),…,r 0 (n)] Y 0 =[y 0 (1),…,y 0 (i),…,y 0 (n)]

[0010] Among them, i represents the position of the data in the data set, 1≤i≤n; r 0 (1) r 0 (i) and r 0 (n) are the first data, the i-th data and the n-th data of the position setting value data set respectively; y 0 (1) y 0 (i) and y 0 (n) are the first data, the i-th data and the n-th data of the position output data set respectively;

[0011] 3) Assume that the position steady-state value of the closed-loop system at the beginning of the acquisition is r σ , the position setting value data set R in step 2) 0 and position output dataset Y 0 The data in the table are all deducted from the steady-state value r σ get:

[0012] Corresponding data in the available position setting value data set R: r(1) = r 0 (1)-r σ , r(i)=r 0 (i)-r σ , r(n)=r 0 (n)-rσ ;

[0013] The available position setting value data set R is in the form of: R = [r(1), ..., r(i), ..., r(n)];

[0014] The corresponding data in the available position output data set Y: y(1) = y 0 (1)-r σ , y(i)=y 0 (i)-r σ , y(n)=y 0 (n)-r σ ;

[0015] The available position output data set Y is in the form of: Y = [y(1),…,y(i),…,y(n)];

[0016] Wherein, r(1), r(i) and r(n) are respectively the first data, the i-th data and the n-th data of the available position setting value data set R; y(1), y(i) and y(n) are respectively the first data, the i-th data and the n-th data of the available position output data set Y;

[0017] 4) Assume that the amplitude of the step input of the closed-loop system is l, and the maximum positive integer not exceeding τ / ΔT is m; perform algebraic operations on all the data in the available position setting value data set R in step 3) to obtain the processed position setting value data set R 11 , R 21 and R 31 The data in:

[0018]

[0019] Processing position setting value data set R 11 , R 21 and R 31 In the form of:

[0020] R 11 =[r 11 (1),…,r 11 (i),…,r 11 (n)],R 21 =[r 21 (1),…,r 21 (i),…,r 21 (n)],

[0021] R 31 =[r 31 (1),…,r 31 (i),…,r 31 (n)];

[0022] Among them, r 11 (i) r 21 (i) and r 31 (i) are the processing position setting value data set R 11 , R 21 and R 31 The i-th data in ;

[0023] 5) Perform algebraic transformation on all the data in the available position output data set Y obtained in step 3) to obtain the processed position output data set Y 11 , Y 21 and Y 31 The data in:

[0024]

[0025]

[0026] Where j is the position of the data that cannot exceed i in the processing position data set, 1≤j≤i; y 11 (i) y 21 (i) and y 31 (i) are the processing position output data set Y 11 , Y 21 and Y 31 The i-th data in the processing position output data set Y 11 , Y 21 and Y 31 The forms are as follows:

[0027] Y 11 =[y 11 (1),…,y 11 (i),…,y 11 (n)],Y 21 =[y 21 (1),…,y 21 (i),…,y 21 (n)],

[0028] Y 31 =[y 31 (1),…,y 31 (i),…,y 31 (n)];

[0029] 6) Let the feedback controller in the closed-loop system be C(s) and the feedforward controller be C f (s), their mathematical expressions are:

[0030]

[0031] Among them, kp , k i and k d k is the proportional gain coefficient, integral gain coefficient and differential gain coefficient of the dual-integral ball-bar object feedback controller C(s); pf , k if and k df The feedforward controller for the double-integral ball-bar plant is C f The known parameters of (s) are proportional gain coefficient, integral gain coefficient and differential gain coefficient respectively;

[0032] For the processing position setting value data set R in step 4) 11 , R 21 and R 31 The data in step 5) and the processed position output dataset Y 11 , Y 21 and Y 31 The data in is transformed to get the final data set θ 1 The mathematical formula for the data in is as follows:

[0033] θ 1 (i)=(k d +k df )r 11 (i)+(k p +k pf )r 21 (i)+(k i +k if )r 31 (i)-k d y 11 (i)-k p y 21 (i)-k i y 31 (i) Among them, θ 1 (i) is the final data set θ 1 The i-th data in ;

[0034] The final dataset θ 1 The form: θ 1 =[θ 1 (1),…,θ 1 (i),…,θ 1 (n)];

[0035] 7) Define the coefficient a of the double-integrating ball-bar object to be identified 1 The parameter vector And finally the large dataset in is the final data set θ 1 The transpose of

[0036] The coefficient to be identified a of the double-integrating ball-bar object 1 The parameter vector Calculated by the available position output data set Y in step 3) and the final large data set θ:

[0037] in, θ T and Y T The parameter vectors are The transpose of the final large dataset θ and the transpose of the available position output dataset Y, (θ T θ) -1 is θ T Matrix inversion of θ;

[0038] The second aspect of the present invention proposes a closed-loop identification method for a double-integral ball-bar object based on step response and known time lag with filter double-integral plus pure delay description, the method comprising the following steps:

[0039] 1) The transfer function of first-order integral plus pure delay is used to describe the double-integral ball-bar object to be identified. The mathematical expression of the double-integral ball-bar object is:

[0040] Where G(s) is the transfer function of the double-integrating ball-bar plant, s and τ are the differential operator and the known delay constant of the double-integrating ball-bar plant, respectively, and a 1 and a 2 The parameters that need to be identified for the double integrating ball-bar object;

[0041] 2) Collect the position set value data set R in the same time period when the closed-loop system responds to the set value step 0 and position output dataset Y 0 , data length is n, sampling period is ΔT; position setting value data set R 0 and position output dataset Y 0 The form is as follows:

[0042] R 0 =[r 0 (1),…,r 0 (i),…,r 0 (n)],Y 0 =[y 0 (1),…,y 0 (i),…,y 0 (n)];

[0043] Among them, i represents the position of the data in the data set, 1≤i≤n; r 0 (1) r 0 (i) and r 0(n) are the first data, the i-th data and the n-th data of the position setting value data set respectively; y 0 (1) y 0 (i) and y 0 (n) are the first data, the i-th data and the n-th data of the position output data set respectively;

[0044] 3) The position steady-state value of the closed-loop system at the beginning of the acquisition is r σ , the position setting value data set R in step 2) 0 and position output dataset Y 0 The data in the table are all deducted from the steady-state value r σ , obtain the corresponding data in the available position setting value data set R and the available position output data set Y;

[0045] The mathematical calculation formulas for the data in the available position setting value data set R and the available position output data set Y are as follows:

[0046] r(1)=r 0 (1)-r σ , r(i)=r 0 (i)-r σ , r(n)=r 0 (n)-r σ ;

[0047] y(1)=y 0 (1)-r σ , y(i)=y 0 (i)-r σ , y(n)=y 0 (n)-r σ ;

[0048] Wherein, r(1), r(i) and r(n) are respectively the first data, the i-th data and the n-th data of the available position setting value data set R; y(1), y(i) and y(n) are respectively the first data, the i-th data and the n-th data of the available position output data set Y;

[0049] The available position setting value data set R and the available position output data set Y are in the following forms:

[0050] R=[r(1),…,r(i),…,r(n)], Y=[y(1),…,y(i),…,y(n)];

[0051] 4) The amplitude of the step response of the closed-loop system is l, and the maximum integer not exceeding τ / ΔT is m; performing algebraic operations on all the data in the available position setting value data set R in step 3) to obtain the processed position setting value data set R 11 , R21 and R 31 Data in

[0052] Processing position setting value data set R 11 , R 21 and R 31 The mathematical formulas for the data in are as follows:

[0053]

[0054]

[0055] Among them, r 11 (i) r 21 (i) and r 31 (i) are the processing position setting value data set R 11 , R 21 and R 31 The i-th data in ;

[0056] Processing position setting value data set R 11 , R 21 and R 31 The forms are as follows:

[0057] R 11 =[r 11 (1),…,r 11 (i),…,r 11 (n)],R 21 =[r 21 (1),…,r 21 (i),…,r 21 (n)],

[0058] R 31 =[r 31 (1),…,r 31 (i),…,r 31 (n)];

[0059] 5) Perform algebraic transformation on all the data in the available position output data set Y obtained in step 3) to obtain the processed position output data set Y 10 , Y 11 , Y 21 and Y 31 Data in

[0060] Processing location output dataset Y 10 , Y 11 , Y 21 and Y 31 The mathematical calculation formulas for the data are as follows:

[0061]

[0062] Where j is the position of the data that cannot exceed i in the data set, 1≤j≤i; y 10 (i) y 11 (i) y 21 (i) and y 31 (i) are the processing position output data set Y 10 , Y 11 , Y 21 and Y 31 The i-th data in ;

[0063] Processing location output dataset Y 10 , Y 11 , Y 21 and Y 31 The forms are as follows:

[0064] Y 10 =[y 10 (1),…,y 10 (i),…,y 10 (n)],Y 11 =[y 11 (1),…,y 11 (i),…,y 11 (n)],

[0065] Y 21 =[y 21 (1),…,y 21 (i),…,y 21 (n)],Y 31 =[y 31 (1),…,y 31 (i),…,y 31 (n)];

[0066] 6) Let the feedback controller in the closed-loop system be C(s) and the feedforward controller be C f (s), their mathematical expressions are as follows:

[0067]

[0068] Among them, k p , k i and k d k is the proportional gain coefficient, integral gain coefficient and differential gain coefficient of the dual-integral ball-bar object feedback controller C(s); pf , k if and k df The feedforward controller for the double-integral ball-bar plant is C fThe known parameters of (s) are proportional gain coefficient, integral gain coefficient and differential gain coefficient respectively;

[0069] For the processing position setting value data set R in step 4) 11 , R 21 and R 31 The data in step 5) and the processed position output dataset Y 10 , Y 11 , Y 21 and Y 31 The data in is transformed to get the final data set θ 1 and θ 2 Data in

[0070] The final dataset θ 1 and θ 2 The mathematical calculation formulas for the data are as follows:

[0071] θ 1 (i)=(k d +k df )r 11 (i)+(k p +k pf )r 21 (i)+(k i +k if )r 31 (i)-k d y 11 (i)-k p y 21 (i)-k i y 31 (i);

[0072] θ 2 (i) = -y 10 (i);

[0073] Among them, θ 1 (i) and θ 2 (i) is the final data set θ 1 and θ 2 The i-th data in ;

[0074] The final dataset θ 1 and θ 2 The forms are as follows:

[0075] θ 1 =[θ 1 (1),…,θ 1 (i),…,θ 1 (n)];

[0076] θ 2 =[θ2 (1),…,θ 2 (i),…,θ 2 (n)];

[0077] 7) Define the coefficient a of the double-integrating ball-bar object to be identified 1 and a 2 The parameter vector And finally the large dataset in and is the final data set θ 1 The transposed and final dataset θ 2 The transpose of the double integral ball-bar object to be identified 1 and a 2 The parameter vector Calculated by the available position output data set Y in step 3) and the final large data set θ:

[0078]

[0079] in, θ T and Y T The parameter vectors are The transpose of the final large dataset θ and the transpose of the available position output dataset Y, (θ T θ) -1 is θ T Matrix inversion of θ.

[0080] The third aspect of the present invention proposes a closed-loop control system for a double-integral ball-bar object, including a double-integral ball-bar object and a controller. The identification method of the double-integral ball-bar object to be identified in the closed-loop control system is the online identification method of the double-integral ball-bar object described by double integral plus pure delay based on step response and known time lag, or the closed-loop identification method of the double-integral ball-bar object described by double integral plus pure delay containing filter based on step response and known time lag.

[0081] The characteristics and beneficial effects of the present invention are:

[0082] The present invention can identify a double-integral ball-bar object as a continuous double-integral system of double integral plus pure delay or double integral plus pure delay containing a filter based on a position set value data set and a position output data set of a closed-loop system, parameters of a feedback controller and a feedforward controller, and a delay time constant of a system to be identified. The present invention can effectively avoid the operation of open-loop identification of the system, can be directly applied to the control strategy design and parameter optimization of the double-integral ball-bar object, and provides an identification model basis for the implementation of advanced control methods such as dynamic characteristic analysis of the double-integral ball-bar object and controller design optimization. The invention has strong industrial application value and application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0083] Figure 1 This is a closed-loop structure block diagram of the closed-loop control system in Example 2 of the present invention.

[0084] Figure 2 This is a trend change diagram of the position setting value data set, the position output data set and the identification model output in Example 2 of the present invention. DETAILED DESCRIPTION

[0085] Various exemplary embodiments of the present invention will be described in detail below in conjunction with specific embodiments. The description of the exemplary embodiments is merely illustrative and is not intended to be any limitation on the present invention and its application or use. The present invention can be implemented in many different forms and is not limited to the embodiments described herein. These embodiments are provided to make the present invention thorough and complete and to fully express the scope of the present invention to those skilled in the art. It should be noted that unless otherwise specifically stated, the relative arrangement of the components and steps described in these embodiments should be interpreted as being merely exemplary and not as a limitation.

[0086] All terms (including technical terms or scientific terms) used in the present invention have the same meanings as those understood by ordinary technicians in the field to which the present invention belongs, unless otherwise specifically defined. It should also be understood that terms defined in general dictionaries should be interpreted as having meanings consistent with their meanings in the context of the relevant technology, and should not be interpreted in an idealized or extremely formal sense, unless explicitly defined herein.

[0087] Technologies, methods, and equipment known to ordinary technicians in the relevant art may not be discussed in detail, but where appropriate, the technologies, methods, and equipment should be considered as part of the specification.

[0088] The following is further described in detail with reference to the accompanying drawings and specific embodiments.

[0089] Example 1

[0090] like Figure 1 As shown, this embodiment provides a closed-loop control system for a dual-integral ball-bar object, including a dual-integral ball-bar object and a controller. The identification method of the dual-integral ball-bar object to be identified in the closed-loop control system adopts the following online identification method of the dual-integral ball-bar object described by dual integration plus pure delay based on step response and known time lag.

[0091] The online identification method of the double-integral ball-bar object based on the double-integral plus pure delay description of the step response and the known time lag is implemented by the following steps:

[0092] 1) The transfer function of double integration plus pure delay is used to describe the double-integral ball-bar object to be identified. The mathematical expression of the double-integral ball-bar object is:

[0093] Where G(s) is the transfer function of the double-integrating ball-bar plant, s and τ are the differential operator and the known delay constant of the double-integrating ball-bar plant, respectively, and a 1 It is the parameter that needs to be identified by the double-integrating ball-bar object; the delay constant of the double-integrating ball-bar object is generally 0≤τ≤100;

[0094] 2) Collect the position setting value data set R of the closed-loop system in the same time period under the step response 0 and position output dataset Y 0 , data length is n, sampling period is ΔT; position setting value data set R 0 and position output dataset Y 0 The form is as follows:

[0095] R 0 =[r 0 (1),…,r 0 (i),…,r 0 (n)],Y 0 =[y 0 (1),…,y 0 (i),…,y 0 (n)];

[0096] Among them, i represents the position of the data in the data set, 1≤i≤n; r 0 (1) r 0 (i) and r 0 (n) are the first data, the i-th data and the n-th data of the position setting value data set respectively; y 0 (1) y 0 (i) and y 0 (n) are the first data, the i-th data and the n-th data of the position output data set respectively; the length of the collected data is generally 100≤n≤100000, and the sampling period of the double-integral ball-bar object is generally 0.002s≤ΔT≤0.5s;

[0097] 3) Assume that the position steady-state value of the closed-loop system at the beginning of the acquisition is r σ , the position setting value data set R in step 2) 0 and position output dataset Y 0 The data in the table are all deducted from the steady-state value r σ , the corresponding data in the available position setting value data set R and the available position output data set Y can be obtained; the position steady-state value of the double-integral ball-bar object is generally -100≤r σ ≤100;

[0098] The mathematical formula for the data in the available position setting value data set R is as follows:

[0099] r(1)=r 0 (1)-r σ , r(i)=r 0 (i)-r σ , r(n)=r 0 (n)-r σ ;

[0100] The mathematical formula for the data in the available position output dataset Y is as follows:

[0101] y(1)=y 0 (1)-r σ , y(i)=y 0 (i)-r σ , y(n)=y 0 (n)-r σ ;

[0102] Wherein, r(1), r(i) and r(n) are respectively the first data, the i-th data and the n-th data of the available position setting value data set R; y(1), y(i) and y(n) are respectively the first data, the i-th data and the n-th data of the available position output data set Y;

[0103] The available position setting value data set R and the available position output data set Y are in the following forms:

[0104] R=[r(1),…,r(i),…,r(n)], Y=[y(1),…,y(i),…,y(n)];

[0105] 4) Assume that the amplitude of the step input of the closed-loop system is l, and the maximum positive integer not exceeding τ / ΔT is m; perform algebraic operations on all the data in the available position setting value data set R in step 3) to obtain the processed position setting value data set R 11 , R 21 and R 31 The data in; The amplitude of the closed-loop system step response is generally -50≤l≤50 and 200≤m≤20000;

[0106] Processing position setting value data set R 11 , R 21 and R 31 The mathematical formulas for the data in are as follows:

[0107]

[0108] Among them, r 11(i) r 21 (i) and r 31 (i) are the processing position setting value data set R 11 , R 21 and R 31 The i-th data in ;

[0109] Processing position setting value data set R 11 , R 21 and R 31 The forms are as follows:

[0110] R 11 =[r 11 (1),…,r 11 (i),…,r 11 (n)],R 21 =[r 21 (1),…,r 21 (i),…,r 21 (n)],

[0111] R 31 =[r 31 (1),…,r 31 (i),…,r 31 (n)];

[0112] 5) Perform algebraic transformation on all the data in the available position output data set Y obtained in step 3) to obtain the processed position output data set Y 11 , Y 21 and Y 31 Data in

[0113] Processing location output dataset Y 11 , Y 21 and Y 31 The mathematical calculation formulas for the data are as follows:

[0114]

[0115] Where j is the position of the data that cannot exceed i in the processing position data set, 1≤j≤i; y 11 (i) y 21 (i) and y 31 (i) are the processing position output data set Y 11 , Y 21 and Y 31 The i-th data in ;

[0116] Processing location output dataset Y 11 , Y 21 and Y 31 The forms are as follows: 11 =[y11 (1),…,y 11 (i),…,y 11 (n)],Y 21 =[y 21 (1),…,y 21 (i),…,y 21 (n)],Y 31 =[y 31 (1),…,y 31 (i),…,y 31 (n)];

[0117] 6) The feedback controller in the closed-loop system is C(s), and the feedforward controller is C f (s), their mathematical expressions are:

[0118]

[0119] Among them, k p , k i and k d The proportional gain coefficient, integral gain coefficient and differential gain coefficient of the double-integral ball-bar object feedback controller are C(s); the double-integral ball-bar object feedback controller generally has -100≤k p ≤100, -100≤k i ≤100 and -100 ≤ k d ≤100; k pf , k if and k df The feedforward controller for the double-integral ball-bar plant is C f The known parameters of (s) are proportional gain coefficient, integral gain coefficient and differential gain coefficient respectively; the double-integral ball-bar object feedforward controller generally has -100≤k pf ≤100, -1000≤k if ≤1000 and -1000≤k df ≤1000;

[0120] For the processing position setting value data set R in step 4) 11 , R 21 and R 31 The data in step 5) and the processed position output dataset Y 11 , Y 21 and Y 31 The data in is transformed to get the final data set θ 1 Data in

[0121] The final dataset θ 1 The mathematical calculation formulas for the data are as follows:

[0122] θ1 (i)=(k d +k df )r 11 (i)+(k p +k pf )r 21 (i)+(k i +k if )r 31 (i)-k d y 11 (i)-k p y 21 (i)-k i y 31 (i)

[0123] Among them, θ 1 (i) is the final data set θ 1 The i-th data in ;

[0124] The final dataset θ 1 The forms are as follows: 1 =[θ 1 (1),…,θ 1 (i),…,θ 1 (n)];

[0125] 7) Define the coefficient a of the double-integrating ball-bar object to be identified 1 The parameter vector And finally the large dataset in is the final data set θ 1 The transpose of

[0126] The coefficient to be identified a of the double-integrating ball-bar object 1 The parameter vector It can be calculated by the available position output data set Y in step 3) and the final large data set θ:

[0127] in θ T and Y T The parameter vectors are The transpose of the final large dataset θ and the transpose of the available position output dataset Y, (θ T θ) -1 is θ T Matrix inversion of θ.

[0128] Example 2

[0129] The difference between this embodiment and embodiment 1 is that the identification method of the double-integral ball-bar object to be identified in the closed-loop control system adopts a closed-loop identification method of the double-integral ball-bar object with filter double-integral plus pure delay description based on step response and known time lag.

[0130] In this embodiment, the actual double integral ball rod is exclusive The position setting value data and position output data obtained when the step amplitude is 5 and there is output white noise are explained as follows:

[0131] 1) The transfer function of first-order integral plus pure delay is used to describe the double-integral ball-bar object to be identified. The mathematical expression of the double-integral ball-bar object is as follows: The delay constant of the double-integrating ball-bar object in this embodiment is τ = 0.1;

[0132] Where G(s) is the transfer function of the double-integrating ball-bar plant, s and τ are the differential operator and the known delay constant of the double-integrating ball-bar plant, respectively, and a 1 and a 2 The parameters that need to be identified for the double integrating ball-bar object;

[0133] 2) Collect the position set value data set R in the same time period when the closed-loop system responds to the set value step 0 and position output dataset Y 0 , data length is n, sampling period is ΔT; position setting value data set R 0 and position output dataset Y 0 The form is as follows:

[0134] R 0 =[r 0 (1),…,r 0 (i),…,r 0 (n)],Y 0 =[y 0 (1),…,y 0 (i),…,y 0 (n)];

[0135] Among them, i represents the position of the data in the data set, 1≤i≤n; r 0 (1) r 0 (i) and r 0 (n) are the first data, the i-th data and the n-th data of the position setting value data set respectively; y 0 (1) y 0 (i) and y 0 (n) are the first data, the i-th data and the n-th data of the position output data set respectively; the length of the collected data in this embodiment is n=7000, and the sampling period is ΔT=0.02s;

[0136] 3) The position steady-state value of the closed-loop system at the beginning of the acquisition is r σ , the position setting value data set R in step 2) 0 and position output dataset Y 0 The data in the table are all deducted from the steady-state value r σ , the corresponding data in the available position setting value data set R and the available position output data set Y can be obtained; in this embodiment, the position steady-state value of the closed-loop system at the beginning of data acquisition is r σ =3;

[0137] The mathematical formula for the data in the available position setting value data set R is as follows:

[0138] r(1)=r 0 (1)-r σ , r(i)=r 0 (i)-r σ , r(n)=r 0 (n)-r σ ;

[0139] The mathematical formula for the data in the available position output dataset Y is as follows:

[0140] y(1)=y 0 (1)-r σ , y(i)=y 0 (i)-r σ , y(n)=y 0 (n)-r σ ;

[0141] Wherein, r(1), r(i) and r(n) are respectively the first data, the i-th data and the n-th data of the available position setting value data set R; y(1), y(i) and y(n) are respectively the first data, the i-th data and the n-th data of the available position output data set Y;

[0142] The available position setting value data set R and the available position output data set Y are in the following forms:

[0143] R=[r(1),…,r(i),…,r(n)], Y=[y(1),…,y(i),…,y(n)];

[0144] 4) The amplitude of the step response of the closed-loop system is l, and the maximum integer not exceeding τ / ΔT is m; performing algebraic operations on all the data in the available position setting value data set R in step 3) to obtain the processed position setting value data set R 11 , R 21 and R 31In this embodiment, the amplitude of the step input of the closed-loop system is l=5, and the maximum positive integer not exceeding τ / ΔT is m=5;

[0145] Processing position setting value data set R 11 , R 21 and R 31 The mathematical formulas for the data in are as follows:

[0146]

[0147] Among them, r 11 (i) r 21 (i) and r 31 (i) are the processing position setting value data set R 11 , R 21 and R 31 The i-th data in the processing position setting value data set R 11 , R 21 and R 31 The forms are as follows:

[0148] R 11 =[r 11 (1),…,r 11 (i),…,r 11 (n)],R 21 =[r 21 (1),…,r 21 (i),…,r 21 (n)],R 31 =[r 31 (1),…,r 31 (i),…,r 31 (n)];

[0149] 5) Perform algebraic transformation on all the data in the available position output data set Y obtained in step 3) to obtain the processed position output data set Y 10 , Y 11 , Y 21 and Y 31 Data in

[0150] Processing location output dataset Y 10 , Y 11 , Y 21 and Y 31 The mathematical calculation formulas for the data are as follows:

[0151]

[0152] Where j is the position of the data that cannot exceed i in the data set, 1≤j≤i; y10 (i) y 11 (i) y 21 (i) and y 31 (i) are the processing position output data set Y 10 , Y 11 , Y 21 and Y 31 The i-th data in ;

[0153] Processing location output dataset Y 10 , Y 11 , Y 21 and Y 31 The forms are as follows:

[0154] Y 10 =[y 10 (1),…,y 10 (i),…,y 10 (n)],Y 11 =[y 11 (1),…,y 11 (i),…,y 11 (n)],Y 21 =[y 21 (1),…,y 21 (i),…,y 21 (n)],Y 31 =[y 31 (1),…,y 31 (i),…,y 31 (n)];

[0155] 6) The feedback controller in the closed-loop system is C(s), and the mathematical expressions of the feedback controller C(s) are as follows:

[0156]

[0157] Among them, k p , k i and k d is the proportional gain coefficient, integral gain coefficient and differential gain coefficient of the dual-integral ball-bar object feedback controller C(s); in this embodiment, the dual-integral ball-bar object feedback controller has k p =1, k i = 0.5 and k d =4;

[0158] The feedforward controller in the closed-loop system is C f (s), feedforward controller C f The mathematical expressions of (s) are as follows:

[0159]

[0160] Among them, k pf , k if and k df The feedforward controller for the double-integral ball-bar plant is C f The known parameters of (s) are proportional gain coefficient, integral gain coefficient and differential gain coefficient respectively; the double-integral ball-bar object feedforward controller of this embodiment is k pf =0, k if = 0 and k df =0;

[0161] For the processing position setting value data set R in step 4) 11 , R 21 and R 31 The data in step 5) and the processed position output dataset Y 10 , Y 11 , Y 21 and Y 31 The data in is transformed to get the final data set θ 1 and θ 2 Data in

[0162] The final dataset θ 1 and θ 2 The mathematical calculation formulas for the data are as follows:

[0163] θ 1 (i)=(k d +k df )r 11 (i)+(k p +k pf )r 21 (i)+(k i +k if )r 31 (i)-k d y 11 (i)-k p y 21 (i)-k i y 31 (i), θ 2 (i) = -y 10 (i);

[0164] Among them, θ 1 (i) and θ 2 (i) is the final data set θ 1 and θ 2 The i-th data in ;

[0165] The final dataset θ 1 and θ 2 The forms are as follows:

[0166] θ 1 =[θ 1 (1),…,θ 1 (i),…,θ 1 (n)],θ 2 =[θ 2 (1),…,θ 2 (i),…,θ 2 (n)];

[0167] 7) Define the coefficient a of the double-integrating ball-bar object to be identified 1 and a 2 The parameter vector And finally the large dataset in and is the final data set θ 1 The transposed and final dataset θ 2 The transpose of the double integral ball-bar object to be identified 1 and a 2 The parameter vector It can be calculated by the available position output data set Y in step 3) and the final large data set θ:

[0168] in θ T and Y T The parameter vectors are The transpose of the final large dataset θ and the transpose of the available position output dataset Y, (θ T θ) -1 is θ T Matrix inversion of θ;

[0169] The parameters to be identified of the double-integrating ball-bar object in this embodiment are a 1 =0.3126 and a 2 =1.308.

[0170] Simulation test

[0171] Figure 2 : is a trend change diagram of the position setting value data set, the position output data set and the identification model output in this embodiment. The dotted line is the trend of the setting value data set, the dotted line is the trend of the position output data set, and the thick solid line is the trend of the identification method in this embodiment. Figure 1 The output trend of the closed-loop structure under the stimulation of the available position set value data set. From the trend results, it can be seen that although there is a certain deviation in the delay time constant of the system, the identification method can still fit the position output data set well and can more accurately reflect the dynamic characteristics of the closed-loop system, which illustrates the effectiveness of the method of this embodiment.

Claims

1. An online identification method for a double-integral ball-bar object based on a double-integral plus pure delay description of a step response and a known time lag, characterized in that: The following steps are involved: 1) The transfer function of double integration plus pure delay is used to describe the double integration ball-bar object to be identified. The double integration ball-bar object is: Wherein, G(s) is the transfer function of the double-integrating ball-bar object, s and τ are the differential operator and the known delay constant of the double-integrating ball-bar object respectively, and a1 is the parameter to be identified by the double-integrating ball-bar object; 2) Collect the position setting value data set R0 and the position output data set Y0 in the same time period of the closed-loop system under the step response, the data length is n, and the sampling period is ΔT; the position setting value data set R0 and the position output data set Y0 are in the following form: R0=[r0(1),…,r0(i),…,r0(n)], Y0=[y0(1),…,y0(i),…,y0(n)]; Wherein, i represents the position of the data in the data set, 1≤i≤n; r0(1), r0(i) and r0(n) are the first data, the i-th data and the n-th data of the position setting value data set respectively; y0(1), y0(i) and y0(n) are the first data, the i-th data and the n-th data of the position output data set respectively; 3) Assume that the position steady-state value of the closed-loop system at the beginning of the acquisition is r σ , subtract the position steady-state value r from the data in the position setting value data set R0 and the position output data set Y0 in step 2) σ get: Corresponding data in the available position setting value data set R: r(1) = r0(1) - r σ , r(i)=r0(i)-r σ , r(n)=r0(n)-r σ ; The available position setting value data set R is in the form of: R = [r(1), ..., r(i), ..., r(n)]; The corresponding data in the available position output data set Y: y(1) = y0(1) - r σ , y(i)=y0(i)-r σ , y(n)=y0(n)-r σ ; The available position output data set Y is in the form of: Y = [y(1),…,y(i),…,y(n)]; Wherein, r(1), r(i) and r(n) are respectively the first data, the i-th data and the n-th data of the available position setting value data set R; y(1), y(i) and y(n) are respectively the first data, the i-th data and the n-th data of the available position output data set Y; 4) Assume that the amplitude of the step input of the closed-loop system is l, and the maximum positive integer not exceeding τ / ΔT is m; perform algebraic operations on all the data in the available position setting value data set R in step 3) to obtain the processed position setting value data set R 11 , R 21 and R 31 The data in: Processing position setting value data set R 11 , R 21 and R 31 In the form of: R 11 =[r 11 (1),…,r 11 (i),…,r 11 (n)],R 21 =[r 21 (1),…,r 21 (i),…,r 21 (n)], R 31 =[r 31 (1),…,r 31 (i),…,r 31 (n)]; Among them, r 11 (i) r 21 (i) and r 31 (i) are the processing position setting value data set R 11 , R 21 and R 31 The i-th data in ; 5) Perform algebraic transformation on all the data in the available position output data set Y obtained in step 3) to obtain the processed position output data set Y 11 , Y 21 and Y 31 The data in: Where j is the position of the data that cannot exceed i in the processing position data set, 1≤j≤i; y 11 (i) y 21 (i) and y 31 (i) are the processing position output data set Y 11 , Y 21 and Y 31 The i-th data in the processing position output data set Y 11 , Y 21 and Y 31 The forms are as follows: AND 11 =[and 11 (1),…,and 11 (i),…,and 11 (n)],And 21 =[and 21 (1),…,and 21 (i),…,and 21 (n)], AND 31 =[and 31 (1),…,and 31 (i),…,and 31 (n)]; 6) Let the feedback controller in the closed-loop system be C(s) and the feedforward controller be C f (s), their mathematical expressions are: Among them, k p , k i and k d k is the proportional gain coefficient, integral gain coefficient and differential gain coefficient of the dual-integral ball-bar object feedback controller C(s); pf , k if and k df The feedforward controller for the double-integral ball-bar plant is C f The known parameters of (s) are proportional gain coefficient, integral gain coefficient and differential gain coefficient respectively; For the processing position setting value data set R in step 4) 11 , R 21 and R 31 The data in step 5) and the processed position output dataset Y 11 , Y 21 and Y 31 The data in the final data set θ1 is transformed by the data in the data set, and the mathematical calculation formula is as follows: θ1(i)=(k d +k df )r 11 (i)+(k p +k pf )r 21 (i)+(k i +k if )r 31 (i)-k d y 11 (i)-k p y 21 (i)-k i y 31 (i) Among them, θ1(i) is the i-th data in the final data set θ1; The final data set θ1 is in the form of: θ1 = [θ1(1),…,θ1(i),…,θ1(n)]; 7) Define the parameter vector composed of the coefficients a1 to be identified for the double-integral ball-bar object And finally the large dataset in is the transpose of the final data set θ1; The parameter vector composed of the coefficients a1 to be identified for the double-integrating ball-bar object Calculated by the available position output data set Y in step 3) and the final large data set θ: in, θ T and Y T The parameter vectors are The transpose of the final large dataset θ and the transpose of the available position output dataset Y, (θ T θ) -1 is θ T Matrix inversion of θ.

2. A closed-loop identification method for a double-integral ball-bar object based on step response and known time lag with filter double-integral plus pure delay description, characterized in that: The method comprises the following steps: 1) The transfer function of first-order integral plus pure delay is used to describe the double-integral ball-bar object to be identified. The mathematical expression of the double-integral ball-bar object is: Wherein, G(s) is the transfer function of the double-integrating ball-bar object, s and τ are the differential operator and the known delay constant of the double-integrating ball-bar object, respectively, and a1 and a2 are the parameters that need to be identified for the double-integrating ball-bar object; 2) Collect the position set value data set R0 and the position output data set Y0 in the same time period when the closed-loop system responds to the set value step. The data length is n and the sampling period is ΔT. The position set value data set R0 and the position output data set Y0 are in the following form: R0=[r0(1),…,r0(i),…,r0(n)], Y0=[y0(1),…,y0(i),…,y0(n)]; Wherein, i represents the position of the data in the data set, 1≤i≤n; r0(1), r0(i) and r0(n) are the first data, the i-th data and the n-th data of the position setting value data set respectively; y0(1), y0(i) and y0(n) are the first data, the i-th data and the n-th data of the position output data set respectively; 3) The position steady-state value of the closed-loop system at the beginning of the acquisition is r σ , subtract the position steady-state value r from the data in the position setting value data set R0 and the position output data set Y0 in step 2) σ , obtain the corresponding data in the available position setting value data set R and the available position output data set Y; The mathematical calculation formulas for the data in the available position setting value data set R and the available position output data set Y are as follows: r(1)=r0(1)-r σ ,r(i)=r0(i)-r σ ,r(n)=r0(n)-r σ ; y(1)=y0(1)-r σ ,y(i)=y0(i)-r σ ,y(n)=y0(n)-r σ ; Wherein, r(1), r(i) and r(n) are respectively the first data, the i-th data and the n-th data of the available position setting value data set R; y(1), y(i) and y(n) are respectively the first data, the i-th data and the n-th data of the available position output data set Y; The available position setting value data set R and the available position output data set Y are in the following forms: R=[r(1),…,r(i),…,r(n)], Y=[y(1),…,y(i),…,y(n)]; 4) The amplitude of the step response of the closed-loop system is l, and the maximum integer not exceeding τ / ΔT is m; performing algebraic operations on all the data in the available position setting value data set R in step 3) to obtain the processed position setting value data set R 11 , R 21 and R 31 Data in Processing position setting value data set R 11 , R 21 and R 31 The mathematical formulas for the data in are as follows: Among them, r 11 (i) r 21 (i) and r 31 (i) are the processing position setting value data set R 11 , R 21 and R 31 The i-th data in ; Processing position setting value data set R 11 , R 21 and R 31 The forms are as follows: R 11 =[r 11 (1),…,r 11 (i),…,r 11 (n)],R 21 =[r 21 (1),…,r 21 (i),…,r 21 (n)], R 31 =[r 31 (1),…,r 31 (i),…,r 31 (n)]; 5) Perform algebraic transformation on all the data in the available position output data set Y obtained in step 3) to obtain the processed position output data set Y 10 , Y 11 , Y 21 and Y 31 Data in Processing location output dataset Y 10 , Y 11 , Y 21 and Y 31 The mathematical calculation formulas for the data are as follows: Where j is the position of the data that cannot exceed i in the data set, 1≤j≤i; y 10 (i) y 11 (i) y 21 (i) and y 31 (i) are the processing position output data set Y 10 , Y 11 , Y 21 and Y 31 The i-th data in ; Processing location output dataset Y 10 , Y 11 , Y 21 and Y 31 The forms are as follows: AND 10 =[and 10 (1),…,and 10 (i),…,and 10 (n)],And 11 =[and 11 (1),…,and 11 (i),…,and 11 (n)], AND 21 =[and 21 (1),…,and 21 (i),…,and 21 (n)],And 31 =[and 31 (1),…,and 31 (i),…,and 31 (n)]; 6) Let the feedback controller in the closed-loop system be C(s) and the feedforward controller be C f (s), their mathematical expressions are as follows: Among them, k p , k i and k d k is the proportional gain coefficient, integral gain coefficient and differential gain coefficient of the dual-integral ball-bar object feedback controller C(s); pf , k if and k df The feedforward controller for the double-integral ball-bar plant is C f The known parameters of (s) are proportional gain coefficient, integral gain coefficient and differential gain coefficient respectively; For the processing position setting value data set R in step 4) 11 , R 21 and R 31 The data in step 5) and the processed position output dataset Y 10 , Y 11 , Y 21 and Y 31 The data in is transformed to obtain the data in the final data sets θ1 and θ2; Finally, the mathematical calculation formulas for the data in the data sets θ1 and θ2 are as follows: θ1(i)=(k d +k df )r 11 (i)+(k p +k pf )r 21 (i)+(k i +k if )r 31 (i)-k d y 11 (i)-k p y 21 (i)-k i y 31 (i); θ2(i)=-y 10 (i); Among them, θ1(i) and θ2(i) are the i-th data in the final data sets θ1 and θ2; The final data sets θ1 and θ2 are in the following forms: θ1=[θ1(1),…,θ1(i),…,θ1(n)]; θ2=[θ2(1),…,θ2(i),…,θ2(n)]; 7) Define the parameter vector consisting of the coefficients a1 and a2 to be identified for the double-integrating ball-bar object And finally the large dataset in and is the transpose of the last data set θ1 and the transpose of the last data set θ2; the parameter vector consisting of the coefficients a1 and a2 to be identified of the double-integrating ball-bar object Calculated by the available position output data set Y in step 3) and the final large data set θ: in, θ T and Y T The parameter vectors are The transpose of the final large dataset θ and the transpose of the available position output dataset Y, (θ T θ) -1 is θ T Matrix inversion of θ.

3. A closed-loop control system for a double-integrating ball-bar object, comprising a double-integrating ball-bar object and a controller, characterized in that: The identification method of the double-integral ball-bar object to be identified in the closed-loop control system adopts the online identification method of the double-integral ball-bar object described by double integral plus pure delay based on step response and known time lag as described in claim 1, or the closed-loop identification method of the double-integral ball-bar object described by double integral plus pure delay containing filter based on step response and known time lag as described in claim 2.

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