CN105388764A - Electro-hydraulic servo PID control method and system based on dynamic matrix feed-forward prediction - Google Patents

Abstract

The present invention provides an electro-hydraulic servo PID control method and system based on dynamic matrix feedforward prediction, wherein the method includes: optimizing the input volume of the electro-hydraulic servo system by combining a DMC feedforward controller and a PID negative feedback controller, The specific steps are as follows: establish a DMC feed-forward controller; optimize the performance index of the electro-hydraulic servo system through the DMC feed-forward controller, and optimize the control input value of the electro-hydraulic servo system by rolling; establish a PID negative feedback controller to obtain the optimized electro-hydraulic servo The control input value of the system; the optimized control input value of the electro-hydraulic servo system obtained by the DMC feed-forward controller and the optimized control input value of the electro-hydraulic servo system obtained by the PID negative feedback controller are obtained to obtain the electro-hydraulic servo system Total optimized control input values. The above invention can solve the problem of not relying on the mathematical model of the object and the interference caused by the outside world.

Description

Electro-hydraulic servo PID control method and system based on dynamic matrix feedforward prediction

technical field

The present invention relates to the technical field of PID control, and more specifically, relates to an electro-hydraulic servo PID control method and system based on dynamic matrix feedforward prediction.

Background technique

At present, electro-hydraulic servo systems are widely used in aviation, aerospace, weapons, large machinery, metallurgy and other industrial sectors. The function of the electro-hydraulic servo control system is to control the parameters of the system load within a certain range according to the pre-set parameters to prevent the load from malfunctioning. Therefore, the accuracy of the electro-hydraulic servo system is closely related to the parameters that determine the normal operation of the load. With the development of modern industry, higher requirements are put forward for the performance of the electro-hydraulic servo system, and at the same time, the system is required to have a strong adaptability to harsh environments.

The electro-hydraulic servo system is a typical electro-hydraulic coupling system, which is characterized by nonlinearity, uncertainty, time-varying, external interference and cross-coupling interference. In addition, the hydraulic servo system is also affected by various factors such as oil viscosity, temperature, and field conditions. Due to the influence of "soft" parameter factors, it is difficult to establish an accurate mathematical model of the system. At present, the electro-hydraulic servo system is usually controlled by PID (Proportion, Integration, and Differentiation). The PID control principle is simple, easy to tune, easy to use, and the adjustment performance index is not very sensitive to slight changes in the controlled object. However, the PID controller can only achieve satisfactory results if the parameters are well tuned. In order to meet the requirements of electro-hydraulic servo system control performance, it is necessary to seek a new control strategy combined with PID control. The Smith predictive control method can make the regulator act in advance, thereby offsetting the influence caused by the time-lag characteristic, reducing the overshoot, improving the stability of the system, accelerating the adjustment process, and improving the rapidity of the system; but the Smith predictive control has Two main drawbacks: (1) the robustness to changes in object characteristics cannot be guaranteed; (2) it cannot be well overcome when there are external disturbances.

Therefore, in order to solve the above problems, it is necessary to provide a new electro-hydraulic servo PID control technology.

Contents of the invention

In view of the above problems, the object of the present invention is to provide an electro-hydraulic servo PID control method and system based on dynamic matrix feedforward prediction, so as to solve the problem of not relying on the mathematical model of the object and the interference caused by the outside world.

The present invention provides an electro-hydraulic servo PID control method based on dynamic matrix feed-forward prediction, including: optimizing the input volume of the electro-hydraulic servo system by combining a DMC feed-forward controller and a PID negative feedback controller, and the specific steps are as follows:

Set up the DMC feed-forward controller;

Optimizing the performance index of the electro-hydraulic servo system through the DMC feedforward controller, and scrolling optimizing the control input value of the electro-hydraulic servo system;

Establishing the PID negative feedback controller, obtaining and optimizing the control input value of the electro-hydraulic servo system; wherein, tuning the parameters of the PID negative feedback controller;

According to the rolling optimized control input value of the electro-hydraulic servo system obtained by the DMC feedforward controller and the optimized control input value of the electro-hydraulic servo system obtained by the PID negative feedback controller, the Overall optimized control input values for electro-hydraulic servo systems.

The present invention also provides another electro-hydraulic servo PID control system based on dynamic matrix feedforward prediction, including:

DMC feedforward controller establishment unit, for establishing described DMC feedforward controller;

A performance index optimization unit is used to optimize the performance index of the electro-hydraulic servo system through the DMC feedforward controller;

A control input value rolling optimization unit is used to scroll and optimize the control input value of the electro-hydraulic servo system through the DMC feedforward controller;

A PID negative feedback controller establishment unit is used to establish the PID negative feedback controller to obtain and optimize the control input value of the electro-hydraulic servo system;

A parameter tuning unit of the PID negative feedback controller, used for tuning the parameters of the PID negative feedback controller;

The overall optimized control input value acquisition unit is used for the rolling optimized control input value of the electro-hydraulic servo system obtained according to the DMC feedforward controller and the electro-hydraulic servo system obtained according to the PID negative feedback controller. The optimized control input value of the servo system is used to obtain the overall optimized control input value of the electro-hydraulic servo system.

It can be seen from the above technical scheme that the present invention provides an electro-hydraulic servo PID control method and system based on dynamic matrix feedforward prediction, and adopts a PID controller based on feedforward DMC (dynamic matrix control) to carry out control design and analysis on the electro-hydraulic servo system . The DMC algorithm uses the unit step response coefficient of the object to establish a prediction model, does not rely on the precise mathematical model of the object, and can use the control output sequence in a small time domain to realize the optimization of the control input at the current moment through rolling optimization. On the other hand, the DMC algorithm can effectively suppress the interference brought by the outside world by introducing a regularization term in the optimized performance index, so that the entire electro-hydraulic servo system has better speed, accuracy and stability.

To the accomplishment of the above and related ends, one or more aspects of the invention comprise the features hereinafter described in detail and particularly pointed out in the claims. The following description and accompanying drawings detail certain exemplary aspects of the invention. These aspects are indicative, however, of but a few of the various ways in which the principles of the invention may be employed. Furthermore, the invention is intended to include all such aspects and their equivalents.

Description of drawings

By referring to the following description combined with the accompanying drawings and the contents of the claims, and with a more comprehensive understanding of the present invention, other objectives and results of the present invention will be more clear and easy to understand. In the attached picture:

Fig. 1 is a schematic flow chart of an electro-hydraulic servo PID control method based on dynamic matrix feedforward prediction according to an embodiment of the present invention;

2 is a block diagram of a control structure of an electro-hydraulic servo system according to an embodiment of the present invention;

Fig. 3 is a structural block diagram of an electro-hydraulic servo PID control system based on dynamic matrix feedforward prediction according to an embodiment of the present invention.

The same reference numerals indicate similar or corresponding features or functions throughout the drawings.

detailed description

In the following description, for purposes of explanation, numerous specific details are set forth in order to provide a thorough understanding of one or more embodiments. It may be evident, however, that these embodiments may be practiced without these specific details.

Aiming at the above-mentioned problems that the robustness with the change of object characteristics cannot be guaranteed, and when there is external interference, it cannot be well overcome. The present invention proposes an electro-hydraulic servo servo system based on dynamic matrix feedforward prediction. A PID control method and system, the present invention adopts a feed-forward DMC-based PID controller to carry out control design and analysis on an electro-hydraulic servo system to solve the above problems.

Specific embodiments of the present invention will be described in detail below in conjunction with the accompanying drawings.

In order to illustrate the electrohydraulic servo PID control method based on dynamic matrix feedforward prediction provided by the present invention, FIG. 1 shows the flow of the electrohydraulic servo PID control method based on dynamic matrix feedforward prediction according to an embodiment of the present invention.

As shown in Figure 1, the electro-hydraulic servo PID control method based on dynamic matrix feed-forward prediction provided by the present invention includes: optimizing the input quantity of the electro-hydraulic servo system by combining a DMC feed-forward controller and a PID negative feedback controller, specifically Proceed as follows:

S110: establishing a DMC feedforward controller;

S120: optimize the performance index of the electro-hydraulic servo system through the DMC feed-forward controller, and optimize the control input value of the electro-hydraulic servo system by scrolling;

S130: Establishing a PID negative feedback controller to obtain control input values for optimizing the electro-hydraulic servo system; wherein, tuning parameters of the PID negative feedback controller;

S140: According to the optimized control input value of the rolling of the electro-hydraulic servo system obtained by the DMC feedforward controller and the optimized control input value of the electro-hydraulic servo system obtained by the PID negative feedback controller, obtain the total optimized value of the electro-hydraulic servo system Control input value.

In the present invention, a PID controller based on feed-forward DMC is used to control design and analysis of the electro-hydraulic servo system, wherein DMC (Dynamic Matrix Control) is an advanced predictive control algorithm, and the DMC algorithm uses the unit step of the object The prediction model established by the response coefficient does not depend on the precise mathematical model of the object, and can use the control output sequence in a small time domain to realize the optimization of the control input at the current moment through rolling optimization.

That is to say, in the present invention, DMC is used as the feed-forward controller of the system, and is combined with the PID negative feedback controller to optimize the input value in the electro-hydraulic servo system in advance.

In step S110, a DMC feed-forward controller is established, that is, a prediction model of the DMC algorithm is established.

The DMC algorithm uses the unit step response coefficient of the object to establish a prediction model. After adding a unit step signal to the input end of the electro-hydraulic servo system, the dynamic step response coefficients at each sampling time are respectively a _i = a(iT) , i=1,2,..., N, N is the time domain length of the model;

According to the proportional and superposition properties of the linear system, after applying M input control increments Δu(k+j) to the system from time k, j=0,1,...M-1, the prediction of the system at p times in the future The output is equal to the superposition of the output of the system when no control increment is applied and the system output caused by applying these M input control increments alone, that is:

y _M (k+1|k)＝y ₀ (k+1|k)+a ₁ Δu(k)(1a)

y _M (k+2|k)＝y ₀ (k+2|k)+a ₂ Δu(k)+a ₁ Δu(k+1)(1b)

.

.

.

y _M (k+P|k)＝y ₀ (k+P|k)+a _P Δu(k)+…+a _P-M+1 Δu(k+M-1) (1c) to formula (1a ) to (1c) are written in vector form as:

Y _M (k+1)=Y ₀ (k+1)+AΔU(k)(2)

Among them, ΔU(k)=[Δu(k),Δu(k+1),…,Δu(k+M-1)] ^T , P is the length of the rolling optimization time domain, M is the length of the control time domain (M≤ P≤N), A is a P×M matrix composed of step response coefficients, as follows:

In step S12, the performance index of the electro-hydraulic servo system is optimized by the DMC feedforward controller, and the input quantity of the electro-hydraulic servo system is optimized for scrolling, that is, the optimized performance index and the input of the scroll optimization controller.

Among them, DMC adopts the rolling optimization objective function, selects the control increment sequence in the future control time domain M, so that the predicted output value in the future optimization time domain P of the system under its influence is as close as possible to the expected output value, and the optimal control law is given by The following quadratic performance metrics are determined:

$\mathrm{<span\; class="notranslate">\; min</span>}\mathrm{<span\; class="notranslate">\; J</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; P</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; q</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&rsqb;</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; m</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}{\mathrm{<span\; class="notranslate">\; \&Delta;u</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

Among them, q _i and r _j are weight coefficients, which respectively represent the suppression of tracking error and control variable change;

The vector form of formula (4) is:

$\mathrm{<span\; class="notranslate">\; min</span>}\mathrm{<span\; class="notranslate">\; J</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span>{<span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; Q</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span>{<span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; R</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

Among them, Y _r (k+1)=[y _r (k+1),...,y _r (k+P)] ^T is the expected output value of the system at P sampling moments in the future; Q is the error coefficient matrix, R is the control right matrix, expressed as:

Q=diag[q ₁ ,q ₂ ,...,q _P ], R=diag[r ₁ ,r ₂ ,...,r _M ]

Bring formula (2) into formula (5), set dJ(k)/dΔU(k)=0, and obtain the optimal control law as follows:

ΔU(k)＝(A ^T QA+R) ^-1 A ^T Q[Y _r (k+1)-Y ₀ (k+1)](6)

Formula (6) provides the optimal solution of ΔU(k)=[Δu(k), Δu(k+1),...,Δu(k+M-1)] ^T , and the DMC feedforward control The controller uses the real-time control increment Δu(k) to act on the object as actual control:

u(k)=u(k-1)+Δu(k)(7)

Among them, in formula (7),

Δu(k)=[1,0,…,0](A ^T QA+R) ^-1 A ^T Q[Y _r (k+1)-Y ₀ (k+1)](8)

In the above step S130, a PID negative feedback controller is established.

The present invention uses an incremental PID controller to control the electro-hydraulic servo system online, and its control law can be described as the following form:

u _PID (k)＝u _PID (k-1)+K _p (e(k)-e(k-1))+K _i e(k)

(9)

+K _d (e(k)-2e(k-1)+e(k-2))

Among them, K _p , K _i and K _d are proportional coefficients, integral time constants and differential time constants respectively; e(k) is the difference between the actual output value of the system at time k and the given expected value.

In the process of establishing the PID negative feedback controller, it is necessary to tune the parameters of the PID controller. Among them, the meaning of PID controller parameter tuning is actually to adjust the three parameters of K _p , _KI and K _D to match the characteristics of the controller with the characteristics of the controlled object to meet the control effect to be achieved by the control system. For pure lag industrial process control, the commonly used industrial tuning method of PID parameters is: stable boundary (critical proportional band method). Among them, its line of sight is to remove the integral and differential effects in the case of a closed-loop system, so that the system can generate equal-amplitude oscillations under the action of a pure proportioner. Using the critical gain K _p and the critical oscillation period T at this time, according to Ziegler and The empirical formula and correction type proposed by Nichols are shown in the following table, and the three parameters of PID are obtained by looking up Table 1.

Table 1 Parameter tuning formula of critical proportional band method

As can be seen from the above, by combining the feed-forward DMC algorithm and the PID negative feedback controller, the control structure of the electro-hydraulic servo system according to the embodiment of the present invention as shown in Figure 2 is established. Then, the total optimal control input of the system at time k value is

u _sum (k) = u _PID (k) + u(k) (10)

Among them, u _PID (k) is the control law obtained by the PID negative feedback controller; u(k) is the control law obtained by the DMC feedforward controller.

Corresponding to the above method, the present invention also provides an electro-hydraulic servo PID control system based on dynamic matrix feed-forward prediction, and Fig. 3 shows an electro-hydraulic servo PID control system based on dynamic matrix feed-forward prediction according to an embodiment of the present invention logical structure.

As shown in Figure 3, an electro-hydraulic servo PID control system 300 based on dynamic matrix feedforward prediction provided by the present invention includes: a DMC feedforward controller establishment unit 310, a performance index optimization unit 320, and a control input value rolling optimization unit 330 , a PID negative feedback controller establishment unit 340 , a parameter tuning unit 350 of the PID negative feedback controller and an overall optimized control input value acquisition unit 360 .

Wherein, the DMC feedforward controller establishment unit 310 is used to establish the DMC feedforward controller;

The performance index optimization unit 320 is used to optimize the performance index of the electro-hydraulic servo system through the DMC feedforward controller;

The control input value rolling optimization unit 330 is used to scroll and optimize the control input value of the electro-hydraulic servo system through the DMC feedforward controller;

The PID negative feedback controller establishment unit 340 is used to establish the PID negative feedback controller to obtain the control input value of the optimized electro-hydraulic servo system;

The parameter tuning unit 350 of the PID negative feedback controller is used for tuning the parameters of the PID negative feedback controller;

The total optimized control input value acquisition unit 360 is used to obtain the optimized control input value of the electro-hydraulic servo system obtained according to the DMC feedforward controller and the optimized control input value of the electro-hydraulic servo system obtained according to the PID negative feedback controller , to obtain the total optimized control input value of the electro-hydraulic servo system.

Wherein, in the process of establishing the DMC feedforward controller by the DMC feedforward controller establishment unit 310, the DMC algorithm adopts the unit step response coefficient of the object to establish a prediction model, and adds a unit step response coefficient at the input end of the electro-hydraulic servo system After the jump signal, the dynamic step response coefficient a _i =a(iT) at each sampling time, i=1,2,...,N, N is the time domain length of the model;

According to the proportional and superposition properties of the linear system, after applying M input control increments Δu(k+j) to the system from time k, j=0,1,...M-1, the prediction of the system at p times in the future The output is equal to the superposition of the output of the system when no control increment is applied and the system output caused by applying these M input control increments alone, that is:

y _M (k+1|k)＝y ₀ (k+1|k)+a ₁ Δu(k)(1a)

y _M (k+2|k)＝y ₀ (k+2|k)+a ₂ Δu(k)+a ₁ Δu(k+1)(1b)

.

.

.

y _M (k+P|k)＝y ₀ (k+P|k)+a _P Δu(k)+…+a _P-M+1 Δu(k+M-1) (1c) to formula (1a ) to (1c) are written in vector form as:

Y _M (k+1)=Y ₀ (k+1)+AΔU(k)(2)

Among them, ΔU(k)=[Δu(k),Δu(k+1),…,Δu(k+M-1)] ^T , P is the length of the rolling optimization time domain, M is the length of the control time domain (M≤ P≤N), A is a P×M matrix composed of step response coefficients, as follows:

Wherein, the performance index optimization unit 320 and the control input value rolling optimization unit 330 optimize the performance index of the electro-hydraulic servo system through the DMC feedforward controller, and in the process of optimizing the input quantity of the electro-hydraulic servo system,

The DMC feedforward controller scrolls to optimize the objective function, selects the control increment sequence in the future control time domain M, and makes the predicted output value of the system in the future optimization time domain P as close as possible to the expected output value under its action, the optimal control law Determined by the following quadratic performance metrics:

$\mathrm{<span\; class="notranslate">\; min</span>}\mathrm{<span\; class="notranslate">\; J</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; P</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; q</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&rsqb;</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; m</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}{\mathrm{<span\; class="notranslate">\; \&Delta;u</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

Among them, q _i and r _j are weight coefficients, which respectively represent the suppression of tracking error and control variable change;

The vector form of formula (4) is:

$\mathrm{<span\; class="notranslate">\; min</span>}\mathrm{<span\; class="notranslate">\; J</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span>{<span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; Q</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span>{<span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; R</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

Among them, Y _r (k+1)=[y _r (k+1),...,y _r (k+P)] ^T is the expected output value of the system at P sampling moments in the future; Q is the error coefficient matrix, R is the control right matrix, expressed as:

Q=diag[q ₁ ,q ₂ ,...,q _P ], R=diag[r ₁ ,r ₂ ,...,r _M ]

Bring formula (2) into formula (5), set dJ(k)/dΔU(k)=0, and obtain the optimal control law as follows:

ΔU(k)＝(A ^T QA+R) ^-1 A ^T Q[Y _r (k+1)-Y ₀ (k+1)](6)

Formula (6) provides the optimal solution of ΔU(k)=[Δu(k), Δu(k+1),...,Δu(k+M-1)] ^T , and the DMC feedforward control The controller uses the real-time control increment Δu(k) to act on the object as actual control:

u(k)=u(k-1)+Δu(k)(7)

Among them, in formula (7),

Δu(k)=[1,0,…,0](A ^T QA+R) ^-1 A ^T Q[Y _r (k+1)-Y ₀ (k+1)](8)

Wherein, the PID negative feedback controller establishment unit 340 is in the process of establishing the PID negative feedback controller, and the PID controller performs online control on the electro-hydraulic servo system, and its control law is:

u _PID (k)＝u _PID (k-1)+K _p (e(k)-e(k-1))+K _i e(k)

(9)

+K _d (e(k)-2e(k-1)+e(k-2))

Among them, K _p , K _i and K _d are proportional coefficient, integral time constant and differential time constant respectively;

e(k) is the difference between the actual output value of the system at time k and the given expected value.

Wherein, the overall optimized control input value acquisition unit 360 is in the process of acquiring the overall optimized control input value of the electro-hydraulic servo system, the DMC feedforward controller and the PID negative feedback controller are combined, and at K time the overall optimization of the system is The control input values for are:

u _sum (k) = u _PID (k) + u(k) (10)

Among them, u _PID (k) is the control law obtained by the PID negative feedback controller; u(k) is the control law obtained by the DMC feedforward controller.

It can be seen from the above embodiments that in the electro-hydraulic servo PID control method and system based on dynamic matrix feedforward prediction provided by the present invention, the DMC algorithm uses the unit step response coefficient of the object to establish a prediction model, and does not rely on the precise mathematical model of the object. The control output sequence in a small time domain can be used to realize the optimization of the control input quantity at the current moment through rolling optimization. On the other hand, the DMC algorithm can effectively suppress the interference brought by the outside world by introducing a regularization term in the optimized performance index, so that the entire electro-hydraulic servo system has better speed, accuracy and stability.

The electro-hydraulic servo PID control method and system based on dynamic matrix feed-forward prediction according to the present invention have been described by way of example with reference to the accompanying drawings. However, those skilled in the art should understand that for the electro-hydraulic servo PID control method and system based on dynamic matrix feedforward prediction proposed by the present invention, various improvements can be made without departing from the content of the present invention. Therefore, the protection scope of the present invention should be determined by the contents of the appended claims.

Claims (10)

1. An electrohydraulic servo PID control method based on dynamic matrix feedforward prediction, comprising: combining the input quantity of electrohydraulic servo system by DMC feedforward controller and PID negative feedback controller, concrete steps are as follows: Set up the DMC feed-forward controller; Optimizing the performance index of the electro-hydraulic servo system through the DMC feedforward controller, and scrolling optimizing the control input value of the electro-hydraulic servo system; Establishing the PID negative feedback controller, obtaining and optimizing the control input value of the electro-hydraulic servo system; wherein, tuning the parameters of the PID negative feedback controller; According to the rolling optimized control input value of the electro-hydraulic servo system obtained by the DMC feedforward controller and the optimized control input value of the electro-hydraulic servo system obtained by the PID negative feedback controller, the Overall optimized control input values for electro-hydraulic servo systems. 2. the electrohydraulic servo PID control method based on dynamic matrix feedforward prediction as claimed in claim 1, wherein, in the process of setting up described DMC feedforward controller, The DMC algorithm adopts the unit step response coefficient of the object to carry out the establishment of the prediction model, after adding the unit step signal to the input end of the electro-hydraulic servo system, the dynamic step response coefficients at each sampling time are respectively a _i =a (iT), i=1,2,...,N, N is the time domain length of the model; According to the proportional and superposition properties of the linear system, after applying M input control increments Δu(k+j) to the system from time k, j=0,1,...M-1, the prediction of the system at p times in the future The output is equal to the superposition of the output of the system when no control increment is applied and the system output caused by applying these M input control increments alone, that is: y _M (k+1|k)＝y ₀ (k+1|k)+a ₁ Δu(k)(1a) y _M (k+2|k)＝y ₀ (k+2|k)+a ₂ Δu(k)+a ₁ Δu(k+1)(1b) · · · y _M (k+P|k)＝y ₀ (k+P|k)+a _P Δu(k)+…+a _P-M+1 Δu(k+M-1)(1c) Write formulas (1a) to (1c) in vector form as: Y _M (k+1)=Y ₀ (k+1)+AΔU(k)(2) Among them, ΔU(k)=[Δu(k),Δu(k+1),…,Δu(k+M-1)] ^T , P is the length of the rolling optimization time domain, M is the length of the control time domain (M≤ P≤N), A is a P×M matrix composed of step response coefficients, as follows: . 3. the electrohydraulic servo PID control method based on dynamic matrix feedforward prediction as claimed in claim 1, wherein, optimize the performance index of electrohydraulic servo system by described DMC feedforward controller, and scroll optimization described electrohydraulic During the input volume of the servo system, The DMC feedforward controller scrolls to optimize the objective function, and selects the control increment sequence in the future control time domain M, so that the predicted output value in the future optimization time domain P of the system under its action is as close as possible to the expected output value, and the optimal The control law is determined by the following quadratic performance metrics: Among them, q _i and r _j are weight coefficients, which respectively represent the suppression of tracking error and control variable change; The vector form of formula (4) is: Among them, Y _r (k+1)=[y _r (k+1),...,y _r (k+P)] ^T is the expected output value of the system at P sampling moments in the future; Q is the error coefficient matrix, R is the control right matrix, expressed as: Q=diag[q ₁ ,q ₂ ,...,q _P ], R=diag[r ₁ ,r ₂ ,...,r _M ] Bring formula (2) into formula (5), set dJ(k)/dΔU(k)=0, and obtain the optimal control law as follows: ΔU(k)＝(A ^T QA+R) ^-1 A ^T Q[Y _r (k+1)-Y ₀ (k+1)](6) Formula (6) provides the optimal solution of ΔU(k)=[Δu(k), Δu(k+1),...,Δu(k+M-1)] ^T , and the DMC feedforward control The controller uses the real-time control increment Δu(k) to act on the object as actual control: u(k)=u(k-1)+Δu(k)(7) Among them, in formula (7), Δu(k)=[1,0,...,0]( ^AT QA+R) ^{-1 AT} Q[Y _r (k+1)-Y ₀ (k+1)] (8). 4. the electrohydraulic servo PID control method based on dynamic matrix feedforward prediction as claimed in claim 1, wherein, in the process of setting up described PID negative feedback controller, The PID controller performs online control on the electro-hydraulic servo system, and its control law is: Among them, K _p , K _i and K _d are proportional coefficient, integral time constant and differential time constant respectively; e(k) is the difference between the actual output value of the system at time k and the given expected value. 5. the electro-hydraulic servo PID control method based on dynamic matrix feed-forward prediction as claimed in claim 1, wherein, in the process of obtaining the total control input value of the electro-hydraulic servo system, The DMC feedforward controller is combined with the PID negative feedback controller, and the total optimal control input value of the system at K moment is: u _sum (k) = u _PID (k) + u(k) (10) Among them, u _PID (k) is the control law obtained by the PID negative feedback controller; u(k) is the control law obtained by the DMC feedforward controller. 6. An electro-hydraulic servo PID control system based on dynamic matrix feedforward prediction, comprising: DMC feedforward controller establishment unit, for establishing described DMC feedforward controller; A performance index optimization unit is used to optimize the performance index of the electro-hydraulic servo system through the DMC feedforward controller; A control input value rolling optimization unit is used to scroll and optimize the control input value of the electro-hydraulic servo system through the DMC feedforward controller; A PID negative feedback controller establishment unit is used to establish the PID negative feedback controller to obtain and optimize the control input value of the electro-hydraulic servo system; A parameter tuning unit of the PID negative feedback controller, used for tuning the parameters of the PID negative feedback controller; The overall optimized control input value acquisition unit is used for the rolling optimized control input value of the electro-hydraulic servo system obtained according to the DMC feedforward controller and the electro-hydraulic servo system obtained according to the PID negative feedback controller. The optimized control input value of the servo system is used to obtain the overall optimized control input value of the electro-hydraulic servo system. 7. the electrohydraulic servo PID control system based on dynamic matrix feedforward prediction as claimed in claim 6, wherein, described DMC feedforward controller establishment unit is in the process of setting up described DMC feedforward controller, The DMC algorithm adopts the unit step response coefficient of the object to carry out the establishment of the prediction model, after adding the unit step signal to the input end of the electro-hydraulic servo system, the dynamic step response coefficients at each sampling time are respectively a _i =a (iT), i=1,2,...,N, N is the time domain length of the model; According to the proportional and superposition properties of the linear system, after applying M input control increments Δu(k+j) to the system from time k, j=0,1,...M-1, the prediction of the system at p times in the future The output is equal to the superposition of the output of the system when no control increment is applied and the system output caused by applying these M input control increments alone, that is: y _M (k+1|k)＝y ₀ (k+1|k)+a ₁ Δu(k)(1a) y _M (k+2|k)＝y ₀ (k+2|k)+a ₂ Δu(k)+a ₁ Δu(k+1)(1b) · · · y _M (k+P|k)＝y ₀ (k+P|k)+a _P Δu(k)+…+a _P-M+1 Δu(k+M-1)(1c) Write formulas (1a) to (1c) in vector form as: Y _M (k+1)=Y ₀ (k+1)+AΔU(k)(2) Among them, ΔU(k)=[Δu(k),Δu(k+1),…,Δu(k+M-1)] ^T , P is the length of the rolling optimization time domain, M is the length of the control time domain (M≤ P≤N), A is a P×M matrix composed of step response coefficients, as follows: . 8. The electro-hydraulic servo PID control system based on dynamic matrix feedforward prediction as claimed in claim 6, wherein, said performance index optimization unit and said control input value rolling optimization unit are optimized by said DMC feedforward controller The performance index of the electro-hydraulic servo system, and in the process of optimizing the input volume of said electro-hydraulic servo system, The DMC feed-forward controller scrolls to optimize the objective function, and selects the control increment sequence in the future control time domain M, so that the predicted output value in the future optimization time domain P of the system under its action is as close as possible to the expected output value, and the optimal The control law is determined by the following quadratic performance metrics: Among them, q _i and r _j are weight coefficients, which respectively represent the suppression of tracking error and control variable change; The vector form of formula (4) is: Among them, Y _r (k+1)=[y _r (k+1),...,y _r (k+P)] ^T is the expected output value of the system at P sampling moments in the future; Q is the error coefficient matrix, R is the control right matrix, expressed as: Q=diag[q ₁ ,q ₂ ,...,q _P ], R=diag[r ₁ ,r ₂ ,...,r _M ] Bring formula (2) into formula (5), set dJ(k)/dΔU(k)=0, and obtain the optimal control law as follows: ΔU(k)＝(A ^T QA+R) ^-1 A ^T Q[Y _r (k+1)-Y ₀ (k+1)](6) Formula (6) provides the optimal solution of ΔU(k)=[Δu(k), Δu(k+1),...,Δu(k+M-1)] ^T , and the DMC feedforward control The controller uses the real-time control increment Δu(k) to act on the object as actual control: u(k)=u(k-1)+Δu(k)(7) Among them, in formula (7), Δu(k)=[1,0,...,0]( ^AT QA+R) ^{-1 AT} Q[Y _r (k+1)-Y ₀ (k+1)] (8). 9. The electro-hydraulic servo PID control system based on dynamic matrix feed-forward prediction as claimed in claim 6, wherein, said PID negative feedback controller establishment unit described in the process of establishing said PID negative feedback controller, The PID controller performs online control on the electro-hydraulic servo system, and its control law is: Among them, K _p , K _i and K _d are proportional coefficient, integral time constant and differential time constant respectively; e(k) is the difference between the actual output value of the system at time k and the given expected value. 10. The electro-hydraulic servo PID control system based on dynamic matrix feed-forward prediction as claimed in claim 6, wherein, the control input value acquisition unit of the overall optimization obtains the overall optimized control input of the electro-hydraulic servo system During the value process, The DMC feedforward controller is combined with the PID negative feedback controller, and the total optimized control input value of the system at K time is: u _sum (k) = u _PID (k) + u(k) (10) Among them, u _PID (k) is the control law obtained by the PID negative feedback controller; u(k) is the control law obtained by the DMC feedforward controller.