CN111077766A - Control algorithm of random moving target tracking trolley based on nonlinear PID - Google Patents

Control algorithm of random moving target tracking trolley based on nonlinear PID Download PDF

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CN111077766A
CN111077766A CN201911414933.4A CN201911414933A CN111077766A CN 111077766 A CN111077766 A CN 111077766A CN 201911414933 A CN201911414933 A CN 201911414933A CN 111077766 A CN111077766 A CN 111077766A
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link
trolley
algorithm
value
slope
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林程
李瑞峰
蒋清山
蔡章辉
林雅峰
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Fujian Quanzhou HIT Research Institute of Engineering and Technology
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    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B11/00—Automatic controllers
    • G05B11/01—Automatic controllers electric
    • G05B11/36—Automatic controllers electric with provision for obtaining particular characteristics, e.g. proportional, integral, differential
    • G05B11/42—Automatic controllers electric with provision for obtaining particular characteristics, e.g. proportional, integral, differential for obtaining a characteristic which is both proportional and time-dependent, e.g. P. I., P. I. D.

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Abstract

The invention discloses a control algorithm of a random moving target tracking trolley based on nonlinear PID, which comprises an algorithm for controlling the running speed U (t) of the trolley, wherein the algorithm of U (t) is a nonlinear combination of three links of a proportional link P, an integral link I and a differential link D. The algorithm can select proper elementary functions to construct the coefficients of the nonlinear PID according to the motion characteristics and the system characteristics of the random motion target tracking trolley, namely, the defects of the nonlinear combination of three links of a proportional link P, an integral link I and a differential link D controlled by the PID are overcome.

Description

Control algorithm of random moving target tracking trolley based on nonlinear PID
Technical Field
The invention relates to the field of equipment for tracking a random moving target, in particular to a control method of a random moving target tracking trolley.
Background
In the control theory of motion, there are two very different ways of thinking: model theory and control theory. The design of a proper control law based on a mathematical model of a controlled object is a main characteristic of a model theory and is the basis of a modern control theory. However, for tracking a random moving target, the modern control theory is difficult to be used for armed because a mathematical model is difficult to establish. While a PID (proportional, integral, derivative) controller, as a standard model-free control method, seems to have good effects on the control of target tracking. However, the conventional PID control faces the contradiction between 'overshoot' (overshoot: overshoot or maximum deviation, which is one of the dynamic performance indexes of the control system, and is an index value of the dynamic performance of the response process curve, i.e. step response curve analysis, of the linear control system under the input of the step signal) and 'response'.
A conventional PID controller, which is a controller based on deviation of a set value from a target value, has a conventional PID time-domain function as follows,
Figure BDA0002350938060000011
wherein the three items on the right of the equal sign are P, I, D links respectively, and the left of the equal sign is system output for controlling the speed of the trolley. However, the system faces the contradiction of overshoot and precision, and particularly for a trolley moving at a high speed, in order to realize target tracking for random high-speed movement, the moving state of a target needs to be pre-judged in advance, and a response is made quickly, which is a great challenge for a traditional PID controller.
Disclosure of Invention
The invention aims to provide a control algorithm of a random moving target tracking trolley based on a nonlinear PID, which solves the defects through nonlinear combination of three links of a proportional link P, an integral link I and a differential link D controlled by the PID and has good control effect on the target tracking trolley.
In order to achieve the purpose, the technical scheme of the invention is as follows: a control algorithm of a random moving target tracking trolley based on nonlinear PID comprises an algorithm for controlling the running speed U (t) of the trolley, wherein the algorithm of U (t) is a nonlinear combination of three links of a proportional link P, an integral link I and a differential link D, and a time domain function is as follows,
Figure BDA0002350938060000021
wherein e (t) is the deviation of the trolley position and the target position at the moment t;
kp is a proportional link P, Kp is a gain coefficient of the proportional link P, and a linear function is selected for calculation, wherein the formula is that Kp is mpe(t)+npWherein n ispIs an initial value, mpThe slope is calculated, and the initial value n is adjusted according to the running condition of a trolley control systempAnd slope mpA value of (d);
Figure BDA0002350938060000022
the integral element I is represented by Ki, the gain coefficient of the integral element I is represented by a linear function of negative slope, and the formula is represented by Ki mie(t)+niAnd its value range is Ki ≧ 0, where niInitial value, miThe slope is calculated according to the running condition of the trolley control system, and the initial value n is adjustediAnd slope miA value of (d);
Figure BDA0002350938060000023
the differential element D is defined as Kd is the gain coefficient of the differential element D, and the reciprocal function is selected for calculation, and the formula is
Figure BDA0002350938060000024
And the value range is Kd more than or equal to 0, and m is adjusted according to the running condition of a trolley control system during calculationd、ndAnd ldThe value of (c).
By adopting the technical scheme, the invention has the beneficial effects that: the control algorithm is compared with the prior PID control algorithm, and the prior algorithm adjusts three parameters of Kp, Ki and Kd in PID, while the invention expands the algorithm and adjusts mp、np、ni、mi、md、ndAnd ldSeven parameters in total, thereby being more flexible, eliminating the defects of the original algorithm and realizing the purpose of randomly moving the targetThe motion characteristic and the system characteristic of the tracking trolley are tracked, and a proper elementary function is selected to construct the coefficient of the nonlinear PID, so that the weight ratio of the proportional link P, the integral link I and the differential link D can be adjusted in real time according to the motion state of the system, the contradiction between PID control 'overshoot' and 'response' is eliminated, the control effect on the target tracking trolley is good, and the tracking efficiency, precision and stability of the trolley on the target are improved.
Drawings
FIG. 1 is a functional curve diagram of a gain coefficient in a proportional link P in a control algorithm of a random moving target tracking trolley based on a nonlinear PID (proportion integration differentiation);
FIG. 2 is a functional curve diagram of a gain coefficient in an integral element I in a control algorithm of a random moving target tracking trolley based on a nonlinear PID (proportion integration differentiation);
FIG. 3 is a functional curve diagram of a gain coefficient in a differential link D in a control algorithm of a random moving target tracking trolley based on a nonlinear PID.
Detailed Description
In order to further explain the technical solution of the present invention, the present invention is explained in detail by the following specific examples.
A control algorithm of a random moving target tracking trolley based on nonlinear PID comprises an algorithm for controlling the running speed U (t) of the trolley, wherein the algorithm of U (t) is a nonlinear combination of three links of a proportional link P, an integral link I and a differential link D, and a time domain function is as follows,
Figure BDA0002350938060000031
where e (t) is the deviation of the cart position from the target position at time t, the objective of the control method is to adjust the value of u (t) so that the value of e (t) is stabilized around 0.
Kp[e(t)]The proportional link P is provided, Kp is the gain coefficient of the proportional link P, and the gain coefficient is a function of the relative e (t), and the proportional link has the fastest response speed and the most effectObviously, the Kp parameter is affecting the responsiveness of the system, which is one of the most major causes of overshoot; an overshoot is caused by an excessive Kp parameter, and if the overshoot is caused, the slope mp is appropriately reduced, and if the response is totally insufficient, np is appropriately increased; therefore, after e (t) is close to 0, the weight of the proportional loop is reduced, and when e (t) is still larger, the proportional loop plays a main role, and the Kp is calculated by a linear function, wherein the formula is that Kp is mpe(t)+npWherein n ispIs an initial value, mpIs a slope, so the initial value n is adjusted according to the running condition of a trolley control system during calculationpAnd slope mpTo meet the operating requirements, and specifically, manually inputting and adjusting the initial value n according to the operating condition of the trolley control systempAnd slope mpThe curve chart of the proportional link is finally obtained by calculation and is shown in figure 1.
Figure BDA0002350938060000041
For the integration element I, Ki is the gain factor of the integration element I, which itself is also a function of e (t). The Ki parameter is mainly used for improving the steady-state characteristic of the system, but is also overshot when the Ki parameter is too large, and the Ki parameter is improved by improving the slope miThe absolute value of the sum of the absolute valuesiTo control the scope of the integration element. The integral link is mainly used for eliminating the steady-state error of the system, because the proportional link is a link based on the error magnitude, the action of the proportional link is in direct proportion to the error magnitude, when e (t) is close to 0, the action is very weak, the integral link is introduced to eliminate the steady-state error, the integral link only acts when e (t) is close to 0, a linear function of a negative slope (also called a linear function of a negative number) is selected for calculation, and the formula is that Ki is mie(t)+niAnd its value range is Ki ≧ 0, where niInitial value, miThe slope is calculated according to the running condition of the trolley control system, and the initial value n is adjustediAnd slope miTo meet operational requirements; specifically, an initial value n is manually input and adjusted according to the running condition of a trolley control systemiAnd slope miValue of (A)Finally, a curve graph of the integral link is obtained through calculation and is shown in figure 2;
Figure BDA0002350938060000042
for the differential element D, Kd is the gain factor of the differential element D, which itself is also a function of the relative e (t). The differentiation link is used for analyzing the deviation e (t) of the current moment and the deviation e (t-1) of the previous moment to pre-judge the motion state of a target, and has two main functions:
1) when the target suddenly accelerates and moves away from the position where e (t) is close to 0, the action of the proportional link is limited because e (t) is very small at the moment, and the response of the integral link is not timely enough. Therefore, it is necessary to amplify the action of the differential element at this time so that the output increases rapidly following the increase in e (t).
2) When the trolley rapidly approaches the target, i.e. e (t) rapidly approaches a certain threshold value towards the 0 direction, the system is required to rapidly decelerate the trolley so as to reduce overshoot, and when the speed of the trolley is reduced to a certain threshold value, the effect of a differential link is required to be rapidly eliminated, because the trolley generates a pause phenomenon due to the fact that the differential link is too large. Therefore, the calculation selects the calculation of reciprocal function (also called power function with negative exponent) with the formula of
Figure BDA0002350938060000051
And its value range is Kd greater than or equal to 0, mdIs the magnitude of the influence function, and m can be increased when the effect of differential action needs to be improveddNumerical values, however mdToo large, can cause jerking of the car, ndIs the slope of the influence function, ndThe larger the curve is, the steeper the curve is, when the trolley approaches the target, the action of the differential link can be rapidly promoted, otherwise, when the target is far away from the trolley, the action of the integral link can be rapidly eliminated, and the proportional loop plays a main role. Meanwhile, as the Kd value range is more than or equal to 0, l can pass throughdThe scope of the differential link is adjusted by manually inputting and adjusting m according to the running condition of the trolley control systemd、ndAnd ldThe calculated graph is shown in fig. 3.
The inventionIn, np、mp、ni、mi、md、ndAnd ldThe values of (A) are adjusted adaptively according to the tested data, and each manual input adjustment is carried out on the seven values np、mp、ni、mi、md、ndAnd ldA joint re-entry adjustment is made.
The above embodiments and drawings are not intended to limit the form and style of the present invention, and any suitable changes or modifications thereof by those skilled in the art should be considered as not departing from the scope of the present invention.

Claims (1)

1. A control algorithm of a random moving target tracking trolley based on nonlinear PID is characterized by comprising an algorithm for controlling the running speed U (t) of the trolley, wherein the algorithm of U (t) is a nonlinear combination of three links of a proportional link P, an integral link I and a differential link D, and a time domain function is as follows,
Figure FDA0002350938050000011
wherein e (t) is the deviation of the trolley position and the target position at the moment t;
Kpis a proportional link P, KpThe gain coefficient of the proportional element P is calculated by selecting a linear function with the formula of Kp＝mpe(t)+ηpWherein n ispIs an initial value, mpThe slope is calculated, and the initial value n is adjusted according to the running condition of a trolley control systempAnd slope mpA value of (d);
Figure FDA0002350938050000012
the integral element I is represented by Ki, the gain coefficient of the integral element I is represented by a linear function of negative slope, and the formula is represented by Ki mie(t)+niAnd its value range is Ki ≧ 0, where niInitial value, miSlope, calculated according to the operating conditions of the car control systemAdjusting the initial value niAnd slope miA value of (d);
Figure FDA0002350938050000013
the differential element D is defined as Kd is the gain coefficient of the differential element D, and the reciprocal function is selected for calculation, and the formula is
Figure FDA0002350938050000014
And the value range is Kd more than or equal to 0, and m is adjusted according to the running condition of a trolley control system during calculationd、ndAnd ldThe value of (c).
CN201911414933.4A 2019-12-31 2019-12-31 Control algorithm of random moving target tracking trolley based on nonlinear PID Pending CN111077766A (en)

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Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20160011571A1 (en) * 2013-02-28 2016-01-14 Avl List Gmbh Method for Designing a Non-Linear Controller for Non-Linear Processes
CN105929683A (en) * 2016-06-23 2016-09-07 东南大学 Differential adjustable PID controller parameter project adjusting method

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20160011571A1 (en) * 2013-02-28 2016-01-14 Avl List Gmbh Method for Designing a Non-Linear Controller for Non-Linear Processes
CN105929683A (en) * 2016-06-23 2016-09-07 东南大学 Differential adjustable PID controller parameter project adjusting method

Non-Patent Citations (3)

* Cited by examiner, † Cited by third party
Title
文建平等: "无速度传感器的内嵌式永磁同步电机自抗扰控制调速系统", 《中国电机工程学报》 *
李瑞峰等: "两轮驱动移动机器人控制系统的研制", 《机械设计与制造》 *
石振华: "PID的自整定控制及其研究", 《中国优秀博硕士学位论文全文数据库（硕士） 信息科技辑》 *

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Application publication date: 20200428