CN107656527A - The gain switching nonlinear control method of agri-vehicle path trace - Google Patents

The gain switching nonlinear control method of agri-vehicle path trace Download PDF

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CN107656527A
CN107656527A CN201710958763.0A CN201710958763A CN107656527A CN 107656527 A CN107656527 A CN 107656527A CN 201710958763 A CN201710958763 A CN 201710958763A CN 107656527 A CN107656527 A CN 107656527A
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mrow
agri
vehicle
mfrac
msup
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林相泽
耿晶
王祥
黄帅婷
薛金林
郑恩来
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Nanjing Agricultural University
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Nanjing Agricultural University
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course or altitude of land, water, air, or space vehicles, e.g. automatic pilot
    • G05D1/02—Control of position or course in two dimensions
    • G05D1/021—Control of position or course in two dimensions specially adapted to land vehicles
    • G05D1/0231—Control of position or course in two dimensions specially adapted to land vehicles using optical position detecting means
    • G05D1/0246—Control of position or course in two dimensions specially adapted to land vehicles using optical position detecting means using a video camera in combination with image processing means

Abstract

The invention discloses a kind of gain of agri-vehicle path trace to switch nonlinear control method, agri-vehicle working environment is extremely complex, it is required that the controller of design will not only meet that track path is steady, it is accurate, it hurry up, also to possess stronger robustness, the gain switching nonlinear control method of particularly a kind of agri-vehicle path trace, this method is by the way of nonlinear Control, the expected path of the vehicle pose of output and input is compared, correct decisions are carried out by gamma controller, control executing agency drives the process of vehicle tracking expected path, so as to realize accurate tracking.Complicated and changeable due to agri-vehicle motion model, the control device taken is also relatively more flexible, and the present invention realizes the tracking accuracy of vehicle route by the way of gain switching and anticipatory control, the control effect that the gamma controller used reaches for：Overshoot is less than 5%, and regulating time is less than 3s, has reached the effect of accurate tracking.

Description

The gain switching nonlinear control method of agri-vehicle path trace
Technical field
The present invention relates to a kind of gain of agri-vehicle path trace to switch nonlinear control method, belongs to agri-vehicle Navigation Control technical field.
Background technology
Agri-vehicle autonomous navigation technology mainly includes：Navigation sensor, path planning, the foundation of auto model and road Design of footpath tracking control unit etc., wherein path following control are one of key factors for determining navigation accuracy.
Agricultural vehicle farm work environment is very high to the structure and performance requirement of system, therefore the design of tracking control unit Increasing scholar is just being attracted to be studied.
Research shows that agri-vehicle working environment is extremely complex both at home and abroad, and it moves by natural environment, edaphic condition, born The influence of many non-linear factors such as lotus change, this requires the controller of design not only to meet that track path is steady, accurate, fast, Also to possess stronger robustness.Path tracking control method mainly includes PID control, optimum control, fuzzy control and nerve Network control etc..In control strategy, PID control effect realizes relatively easy, technology maturation, as long as being had according to Vehicular turn Body situation, after rational control decision and effective parameter tuning, it is possible to obtain satisfied control effect, therefore PID control is all applied in the course changing control of a variety of agri-vehicles.
But the PID/feedback controller of linear time invariant has basic performance limitation, such as rise time and overshoot The limitation in the time field such as amount and the limitation of the frequency range such as gain and phase, this control strategy for agri-vehicle from The high accuracy that main navigation control system increasingly requires, robust stability are obvious deficiencies.This background is based on, is found New control method and prioritization scheme is necessary and urgent.
The content of the invention
Purpose：In order to overcome the deficiencies in the prior art, the present invention provides a kind of increasing of agri-vehicle path trace Benefit switching nonlinear control method.Using agri-vehicle as control object, design path tracking nonlinear pid controller.Pass through two The method design PID controller parameter of secondary anticipatory control, the linear control method then switched by gain, to improve system Response time and change the adjustable extent of frequency, realize the intelligent precision navigation of agri-vehicle.The control method of design can To realize DAZ gene, for adjustment time in the range of 3s, overshoot reaches what high precision tracking gave within 5% Path.
Technical scheme：In order to solve the above technical problems, the technical solution adopted by the present invention is：
A kind of gain switching nonlinear control method of agri-vehicle path trace, comprises the following steps：
Step 1：Agri-vehicle path following control system is built, by PID controller C (s), agri-vehicle system model G (s) forms the closed loop transfer function, of agri-vehicle path following control system, and wherein agri-vehicle system model is by steering system Unite model G0And agri-vehicle motion model G (s)1(s) form；
Step 2：According to the actual demand of vehicle movement, the input of setting agri-vehicle path following control system schedules to last Path u is hoped, exports as Actual path tracking effect y, now sets desired throughput as y=u=1；
Step 3：It is tractor to determine the specific research object of agri-vehicle, and the motion model of agri-vehicle chooses O ' The linear model that Connor is proposed, is easy to the research to model；
Step 4：The linear model of agri-vehicle is proposed based on step 3, the Dongfanghong X- for recycling Luo Xiwen to propose The closed-loop identification result of the DGPS automatic navigation control systems of 804 tractors, draw steering model G0(s), so as to drawing Agri-vehicle system model G (s)；
Step 5：Agri-vehicle system model is proposed based on step 4, agri-vehicle is designed using the mode of anticipatory control The controller C of path following control system1(s), make system on the premise of keeping stable, accelerate response speed, then to control Device C1(s) the controller C of agri-vehicle path following control system is designed using the mode of secondary anticipatory control2(s), further The response speed of quickening system；
Step 6：In the controller C that step 5 provides2(s) on the basis of, to controller plus proportional control factor, control Device C3(s)=KC2(s), K ＜ 1, C3(s) effect is in order to preferably reduce overshoot, while to passband mid-band frequency Selective power is stronger, plays a part of removing high-frequency noise；
Step 7：Controller C3(s) to agricultural vehicle system model G (s) control, relative controller C2(s) control comes Say, can not only reach reduction overshoot, while noise can also be reduced, but the numerical value of additional proportion part is actually Less than 1, therefore the response speed of system is slack-off, so in order to solve linear controller to agri-vehicle path following control system Existing for system the time field limitation, such as regulating time and rise time, therefore in agri-vehicle path following control system In, gain switching nonlinear Control is introduced, after adding gain switching control, forms nonlinear pid controller C4(s) it is, that this is non- Linear controller is acted in agri-vehicle system model, optimizes the dynamic property of agri-vehicle path following control system.
Further, in the step 1, agricultural Vehicular system model is by turning in agri-vehicle path following control system System model and agri-vehicle motion model composition, the Actual path now exported in agri-vehicle path following control system Tracking effect y and input variable u derivation relation is as follows：
Wherein：The input variable expected path u and output variable Actual path of agri-vehicle path following control system with Track effect y relation is the relationship of signal transfer function, and controller function C (s) determines input and exported specific Relation.
Further, it is described Step 3: in four, it is assumed that do not consider tire and ground lateral sliding, ground even, speed of advancing Spend constant and slow, be two-wheeled vehicle model by tractor model simplification, expression formula is as follows：
In formula, ψ is course angle, unit for °, VxFor tractor direction of advance speed, unit m/s, L are wheelbase, unit For m, δ is deflecting roller drift angle, unit for °, x is the vehicle movement along path direction, and unit m, y are Actual path tracking effect Fruit, unit m；It is further assumed that ψ and δ is intended to 0 in line tracking, tractor model decouple and linear Change, establish following expression：
In formula, u is control input variable expected path, after Laplace transformation, with deflecting roller drift angle rate of changeFor agriculture With vehicle movement model G1(s) input, Actual path tracking effect y are output；
Agri-vehicle motion model G1(s) expression formula is as follows, wherein, car speed Vx1m/s, wheelbase L is taken to take 2.314m；s Represent the frequency domain variable of time；
The controller of design is used for agri-vehicle motion model G1(s) in adjusting；
It is expected deflecting roller drift angle δu(s) it is steering model G0(s) input, it is then right(s) integrated, obtained To δ (s), and with the output that actual steering wheel drift angle δ (s) is steering, transmission function steering model G0(s) it is：
It is by (4) formula and (5) Shi Ke get, open-loop transfer function agri-vehicle system model G (s)：
Further, in the step 5, based on agri-vehicle system model G (s), designed using the mode of anticipatory control The controller of system, make closed-loop system on the premise of the requirement of stability is met, further speed up response speed, now need Judge whether the dynamic performance index of closed-loop system meets the requirement of system, the controller of this secondary design is from signal analysis Angle set out, i.e., using the method for frequency analysis, with the interval angles that 5 ° are phase advanced argument, with 65 ° for maximum phase Advanced argument, 25 ° are minimum phase advanced argument, and an anticipatory control, process once advanced school are carried out to agri-vehicle system model After positive control, on the premise of response speed is ensured, dynamic performance index is considered, it is control to choose 65 ° of leading phase amount The phase advance angle of device processed, the controller C of agri-vehicle path following control system1And open-loop transfer function C (s)1(s)G(s) Respectively：
Now, agri-vehicle system model is in controller C1(s) the agri-vehicle path following control system under adjusting is moved State performance indications are：
σ %=54.5%, ts=5.66s, tr=0.67s (9)
Wherein, overshoot σ %, regulating time ts, rise time tr；And provide agri-vehicle path following control system Dynamic performance index requires as follows：
σ % ＜ 5%, ts＜ 3s, tr＜ 3s (10)
Wherein：Regulating time tsRefer to reach and be maintained at the shortest time required in the error of final value ± 5%；During rising Between trRefer to that response curve rises to the time needed for the 90% of steady-state value from the 10% of steady-state value；
Because system is unsatisfactory for dynamic performance index requirement after an anticipatory control, in order to further speed up system Response speed, secondary anticipatory control link is designed, on the basis of 65 ° of a leading phase, with 5 ° for phase advanced argument Interval angles, with 65 ° for maximum phase advanced argument, 25 ° are minimum phase advanced argument, and agri-vehicle system model is entered respectively The secondary anticipatory control of row, on the premise of overshoot is ensured, considers dynamic performance index, chooses secondary leading phase 65 ° of leading phase angles for controller, after secondary anticipatory control control, the controller C of system2And open loop transmission (s) Function C2(s) G (s) is respectively：
Now, agri-vehicle system model is in controller C2(s) the agri-vehicle path following control system under adjusting is moved State performance indications are：
σ %=44.8%, ts=12.95s, tr=0.36s (13)
Further, in the step 6, the controller C based on step 5 design2(s) to agri-vehicle system model Dynamic performance index can be seen that overshoot is larger by (13) formula, so additional proportion is adjusted here, it is to increase phase Nargin, reduce the overshoot of closed-loop system, while serve the effect for removing high-frequency noise, the system of additional proportion regulation here Number K, K value are according to controller C2(s) Bode diagram of agri-vehicle system model is acted on, when K meets K ＜ 1, is reached Reduce the effect of overshoot, by many experiments, it is determined that as 0.1 ＜ K ＜ 0.7, C3(s)=KC2(s) agri-vehicle is acted on The phase margin numerical value of the Bode diagram of system model is more than C1And C (s)2(s) to the phase of the Bode diagram of agri-vehicle system model Position nargin numerical value, can preferably adjust overshoot.
Further, in the step 7, therefore in agri-vehicle path following control system, cut using turn off gain Nonlinear control method is changed, by controller C3(s) non-linearity PID controller C is become4(s), determine, corresponded to most through many experiments Open-loop transfer function under excellent dynamic performance index is that K here takes 0.3.
Now, agri-vehicle system model is in controller C4(s) the agri-vehicle path following control system under adjusting is moved State performance indications are：
σ %=4.44%, ts=2.79s, tr=1.90s (15)
After non-linear gain switches link, the overshoot of the optimal closed-loop system unit-step response finally obtained is 4.44% rise time be the 1.90s times be 2.79s, it is seen then that gain switch nonlinear Control in the case of, agri-vehicle road Footpath tracking system can obtain more satisfied tracking effect.
Beneficial effect：The gain switching nonlinear control method of agri-vehicle path trace provided by the invention, using agriculture It is the three rank linear vehicle mathematical modelings determined based on O ' connor et al. with Vehicular system model buildings method, passes through It is effective that lot of experimental data and emulation, which demonstrate this three ranks linear vehicle model, is suitable as the object of the analysis of system Model.For agri-vehicle system model, by the way of secondary anticipatory control, the design to controller is realized, so as to System is reached stable, the advantages of switching nonlinear Control followed by gain, overcome the PID/feedback control of linear time invariant Device processed it is basic to closed-loop system time field limitation, such as the limitation of rise time and overshoot, and frequency range, such as Gain and phase, further to improve the dynamic property of system.The method design system that comprehensive analysis passes through secondary anticipatory control Controller and using gain switching nonlinear control method come further to improve the dynamic performance index of system be this hair Bright key point.
Compared with prior art, the present invention has the following advantages：(1) using gain switching nonlinear control method, agriculture is designed With the controller of vehicle route tracking control system, further improve dynamic performance index, by anticipatory control twice, make to close On the premise of loop system meets the requirement of stability, accelerate response speed, with reference to the excellent of gain switching nonlinear control method Point, overcome the PID/feedback controller of the linear time invariant performance practice field basic to closed-loop system and frequency range Limitation.(2) nonlinear pid controller of this secondary design and integer rank PID and Fractional Order PID Controller are to identical systems model Optimal control results be compared, find after nonlinear PID controller, the dynamic performance index of system is more excellent, overshoot No more than 5%, regulating time is less than 3s.(3) closed-loop control is used, cumulative errors can be eliminated, reaches the dynamic of system Energy index request, realizes DAZ gene.
Brief description of the drawings
Fig. 1 is control method flow chart of the present invention；
Fig. 2 is simplified two-wheeled vehicle model；
Fig. 3 is agri-vehicle path following control system control principle drawing；
Fig. 4 is the Bode diagram of agri-vehicle system model open cycle system；
Fig. 5 is the Bode diagram of open-loop transfer function after an anticipatory control, and partial enlarged drawing；
Fig. 6 is the analogous diagram of a leading angle；
Fig. 7 is the later analogous diagram of secondary anticipatory control；
Fig. 8 is the later emulation enlarged drawing of secondary anticipatory control；
Fig. 9 is linear Feedback Control figure；
Figure 10 is nonlinear Feedback Control figure；
Figure 11 is the picture specification based on variable gain control；
Figure 12 is that the quadrant based on variable gain control is explained；
Figure 13 is secondary correction later plus gain switches the simulation curve of link；
Figure 14 is that nonlinear PID controller and optimum PID control and the simulated effect of fractional order control compare.
Embodiment
The present invention is further described below in conjunction with the accompanying drawings.
As shown in figure 1, a kind of gain switching nonlinear control method of agri-vehicle path trace, including step are as follows：
Step 1：Agri-vehicle path following control system is built, by PID controller C (s), agri-vehicle system model G (s) forms the closed loop transfer function, of agri-vehicle path following control system, and wherein agri-vehicle system model is by steering system Unite model G0And agri-vehicle motion model G (s)1(s) form；
Step 2：According to the actual demand of vehicle movement, the input of setting agri-vehicle path following control system schedules to last Path u is hoped, exports as Actual path tracking effect y, now sets desired throughput as y=u=1；
Step 3：It is tractor to determine the specific research object of agri-vehicle, and the motion model of agri-vehicle chooses O ' The linear model that Connor is proposed, is easy to the research to model；
Step 4：The linear model of agri-vehicle is proposed based on step 3, the Dongfanghong X- for recycling Luo Xiwen to propose The closed-loop identification result of the DGPS automatic navigation control systems of 804 tractors, draw steering model G0(s), so as to drawing Agri-vehicle system model G (s)；
Step 5：Agri-vehicle system model is proposed based on step 4, agri-vehicle is designed using the mode of anticipatory control The controller C of path following control system1(s), make system on the premise of keeping stable, accelerate response speed, then to control Device C1(s) the controller C of agri-vehicle path following control system is designed using the mode of secondary anticipatory control2(s), further The response speed of quickening system；
Step 6：In the controller C that step 5 provides2(s) on the basis of, to controller plus proportional control factor, control Device C3(s)=KC2(s), K ＜ 1, C3(s) effect is in order to preferably reduce overshoot, while to passband mid-band frequency Selective power is stronger, plays a part of removing high-frequency noise；
Step 7：Controller C3(s) to agricultural vehicle system model G (s) control, relative controller C2(s) control comes Say, can not only reach reduction overshoot, while noise can also be reduced, but the numerical value of additional proportion part is actually Less than 1, therefore the response speed of system is slack-off, so in order to solve linear controller to agri-vehicle path following control system Existing for system the time field limitation, such as regulating time and rise time, therefore in agri-vehicle path following control system In, gain switching nonlinear Control is introduced, after adding gain switching control, forms nonlinear pid controller C4(s) it is, that this is non- Linear controller is acted in agri-vehicle system model, optimizes the dynamic property of agri-vehicle path following control system.
As shown in Fig. 2 it is specific research object to select representative tractor, because agri-vehicle working environment Complexity, therefore agricultural vehicle farm work environment is very high to the structure and performance requirement of system, therefore the design of tracking control unit Increasing scholar is just being attracted to be studied.Assuming that not considering tire and ground lateral sliding, ground even, speed of advancing Spend it is constant and slowly under the premise of, the motion model of tractor can be reduced to two-wheeled vehicle model, expression formula is：
Further, it is assumed that ψ and δ is intended to 0 in line tracking, and tractor model is decoupled and linearized, is built Vertical following expression：
As shown in figure 3, agri-vehicle path following control is the vehicle pose and expected path for obtaining related sensor Compare, correct decisions are made by controller, control executing agency drives the process of vehicle tracking expected path, at this During, in order to improve the performance of closed-loop system, the design adds the nonlinear element of gain switching, quotes gain switching Nonlinear system model.
The open-loop transfer function agri-vehicle system model of this secondary design is：
As shown in figure 4, the system of this open-loop transfer function is a minimum phase system, the amplitude of open cycle system is drawn Nargin GmTo bear infinite (Inf dB), Phase margin is -12.2 °, and the system of drawing is unstable.
From system compensation principle, anticipatory control link is sealed in forward path, the stability of system can be improved, The effect of anticipatory control is in order to which on the premise of the stability of a system is ensured, quickening response speed in theory can be to agricultural vehicle The increased phase advanced argument of system model is 90 °, and the phase margin of system is r*=70 ° after correction, and in physical instrument only Highest phase advanced argument can be increased as 65 °, r*=47 ° of the phase margin of system after correction.With 5 ° between phase advanced argument It it is respectively 25 °, 30 °, 35 °, 40 °, 45 °, 50 °, 55 °, 60 °, 65 ° to the increased phase advanced argument of system, through one every angle After secondary anticipatory control, the Bode diagram and analogous diagram of the open-loop transfer function of agri-vehicle path following control system, such as Fig. 5 Shown in Fig. 6.The minimum curve of overshoot is the simulation curve after advanced 65 ° of phase in Fig. 6, response speed near Slow is the curve after 25 °, 30 °, 35 °, 40 °, 45 °, 50 °, 55 °, 60 °, 65 ° of leading phase successively.Through an anticipatory control with The open-loop transfer function of agri-vehicle path following control system and overshoot and rise time are respectively such as Tables 1 and 2 institute afterwards Show：
Open-loop transfer function after 1 anticipatory controls of table
Dynamic performance index of the table 2 through an anticipatory control
After an anticipatory control, overshoot is between 54.5%-89.7%, and the overshoot of system is general in engineering 1.5%-25.4% is chosen, overshoot is not met by the actual requirement of engineering, and the response time is longer, so in phase Secondary anticipatory control is carried out on the basis of advanced 65 °.
Analogous diagram after secondary anticipatory control, as shown in FIG. 7 and 8.On the basis of 65 degree of a leading phase, With 5 ° be phase advanced argument interval angles, respectively to system increase by 25 ° of phase advance angle, 30 °, 35 °, 40 °, 45 °, 50 °, 55 °, 60 °, 65 °, so that the phase margin increase of system, overshoot decline, response speed is accelerated.In Fig. 8 response speed from Near being secondary 65 ° of leading phase, 60 °, 55 °, 50 °, 45 °, 40 °, 35 °, 30 °, 25 ° of curve successively slowly, through secondary super The open-loop transfer function of agri-vehicle path following control system and overshoot and rise time are respectively such as table after preceding correction 3 and table 4 shown in：
Open-loop transfer function after 3 two anticipatory controls of table
Dynamic performance index of the table 4 through secondary anticipatory control
In Fig. 8 and Fig. 9 analogous diagrams, be successively from left to right secondary 65 ° of anticipatory control, 60 °, 55 °, 50 °, 45 °, 40 °, 35 °, 30 °, 25 ° of simulation waveform are secondary super in conjunction with table 4 as can be seen that system is on the basis of 65 ° of leading phase The simulation curve of preceding 65 ° of phase is compared to being that overshoot is smaller, the rise time is most short for other secondary anticipatory control phases Comparatively curve, dynamic property are optimized.For compared to one time anticipatory control, after secondary anticipatory control, Overshoot reduces, and the rise time also shortens accordingly.After secondary anticipatory control, overshoot 39.5%-46.1% it Between, the overshoot of system typically chooses 1.5%-25.4% in engineering, therefore overshoot is not met by wanting for engineering reality The reason for asking, and can be seen that regulating time is relatively long from analogous diagram, produce this phenomenon is linear time invariant Be present basic dynamic property limitation, including the limitation in time field and the limitation of frequency range in controller, cut using gain The dynamic performance index more excellent than linear system can be obtained by changing the method for nonlinear Control, be switched with reference to gain non-linear Control method advantage, the design is using agri-vehicle as control object, using gain switching control, to improve the sound of closed-loop system Between seasonable and frequency-adjustable scope, more excellent dynamic performance index is obtained with this.
It is to further improve the response of closed-loop system as shown in figure 9, being to add the closed-loop control figure before gain switching Time and frequency-adjustable scope, more excellent dynamic performance index is obtained with this.
As shown in Figure 10, u is the input of agri-vehicle path following control system, and e inputs for error, and y is Actual path Tracking effect, C3(s) it is the controller function after secondary anticipatory control, G (s) is the transmission letter of agri-vehicle motion model Number.Be by e andRelation adjust variable gain, the general principle of variable gain control is as follows：
1. e is away from 0There is gamma controller, controlled quentity controlled variable can be increased, so as to reduce error e, Vehicle route tracking effect is become apparent from, meets dynamic performance index requirement.
2. e is close to 0There is no the effect of gamma controller.
As shown in figure 11, only there is a gain switching in dash area, gain function is as follows：
As shown in figure 12, the explanation of quadrant is given, forFunction acts on the diagram in section, and figure illustrates non- Linear controller only works in one or three quadrants.
Add the analogous diagram of gain switching link as shown in figure 13, by controller C3(s) nonlinear pid controller C is become4 (s), determined through many experiments, the open-loop transfer function under corresponding optimal dynamic performance index is：
Here proportional control factor K takes 0.3, and the determination of numerical value is the optimal solution determined by many experiments.
The optimal controller function that this secondary design determines is after gain switches nonlinear Control, the emulation that can reach Effect acts on the analogous diagram of identical systems model with optimum PID control effect and optimal fractional order control device action effect Compare as shown in figure 14.Dynamic corresponding to non-linearity PID and optimal PID and optimal Fractional Order PID Controller action effect Energy index is as follows：
Overshoot and regulating time of the table 5 after non-linearity PID and optimum PID control
Note：Regulating time in table refers to reach and is maintained at the shortest time required in the error of final value ± 5%, rises Time refers to that response curve rises to the time needed for the 90% of steady-state value from the 10% of steady-state value.
Analogous diagram 14 and analytical table 5, compare and draw, after nonlinear pid controller acts on model, the dynamic of acquisition Can index it is more excellent, the overshoot finally determined is 4.44%, rise time 1.90s, regulating time 2.79s, now closed loop System has more satisfied agri-vehicle path trace effect.
Described above is only the preferred embodiment of the present invention, it should be pointed out that：For the ordinary skill people of the art For member, under the premise without departing from the principles of the invention, some improvements and modifications can also be made, these improvements and modifications It should be regarded as protection scope of the present invention.

Claims (6)

  1. A kind of 1. gain switching nonlinear control method of agri-vehicle path trace, it is characterised in that：It is as follows including step：
    Step 1：Agri-vehicle path following control system is built, by PID controller C (s), agri-vehicle system model G (s) The closed loop transfer function, of agri-vehicle path following control system is formed, wherein agri-vehicle system model is by steering model G0And agri-vehicle motion model G (s)1(s) form；
    Step 2：According to the actual demand of vehicle movement, the input of agri-vehicle path following control system is set it is expected road Footpath u, export as Actual path tracking effect y, now set desired throughput as y=u=1；
    Step 3：It is tractor to determine the specific research object of agri-vehicle, and the motion model of agri-vehicle chooses O ' Connor The linear model of proposition, it is easy to the research to model；
    Step 4：The linear model of agri-vehicle is proposed based on step 3, the Dongfanghong X-804 for recycling Luo Xiwen to propose is drawn The closed-loop identification result of the DGPS automatic navigation control systems of machine, draw steering model G0(s), so as to drawing agri-vehicle System model G (s)；
    Step 5：Agri-vehicle system model is proposed based on step 4, agri-vehicle path is designed using the mode of anticipatory control The controller C of tracking control system1(s) system, is made to accelerate response speed on the premise of keeping stable, then to controller C1 (s) the controller C of agri-vehicle path following control system is designed using the mode of secondary anticipatory control2(s), further speed up The response speed of system；
    Step 6：In the controller C that step 5 provides2(s) on the basis of, to controller plus proportional control factor, controller C3 (s)=KC2(s), K ＜ 1, C3(s) effect is in order to preferably reduce overshoot, while to the selection of passband mid-band frequency Ability is stronger, plays a part of removing high-frequency noise；
    Step 7：In order to solve linear controller to existing for agri-vehicle path following control system the time field limitation, Such as regulating time and rise time, therefore in agri-vehicle path following control system, gain switching nonlinear Control is introduced, After adding gain switching control, nonlinear pid controller C is formed4(s) this gamma controller, is acted on into agri-vehicle system In system model, optimize the dynamic property of agri-vehicle path following control system.
  2. 2. the gain switching nonlinear control method of agri-vehicle path trace according to claim 1, it is characterised in that： In the step 1, the Actual path tracking effect y and input variable u that are now exported in agri-vehicle path following control system Derivation relation it is as follows：
    <mrow> <mi>y</mi> <mo>=</mo> <mfrac> <mrow> <mi>C</mi> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mi>G</mi> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <mi>C</mi> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mi>G</mi> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mi>u</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow>
    Wherein：Input variable expected path u and output variable Actual path the tracking effect of agri-vehicle path following control system Fruit y relation is the relationship of signal transfer function, and controller function C (s) determines the physical relationship of input and output.
  3. 3. the gain switching nonlinear control method of agri-vehicle path trace according to claim 1, it is characterised in that： It is described Step 3: in four, it is assumed that do not consider that tire and ground lateral sliding, ground even, pace are constant and slow, will drag Machine drawing model simplification is two-wheeled vehicle model, and expression formula is as follows：
    <mrow> <mtable> <mtr> <mtd> <mrow> <mi>&amp;psi;</mi> <mo>=</mo> <mfrac> <msub> <mi>V</mi> <mi>x</mi> </msub> <mi>L</mi> </mfrac> <mi>t</mi> <mi>a</mi> <mi>n</mi> <mrow> <mo>(</mo> <mi>&amp;delta;</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mover> <mi>x</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>=</mo> <msub> <mi>V</mi> <mi>x</mi> </msub> <mi>cos</mi> <mrow> <mo>(</mo> <mi>&amp;psi;</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mover> <mi>y</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>=</mo> <msub> <mi>V</mi> <mi>x</mi> </msub> <mi>sin</mi> <mrow> <mo>(</mo> <mi>&amp;psi;</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow>
    In formula, ψ is course angle, unit for °, VxFor tractor direction of advance speed, unit m/s, L are wheelbase, unit m, δ For deflecting roller drift angle, unit for °, x is the vehicle movement along path direction, and unit m, y are Actual path tracking effect, unit For m；It is further assumed that ψ and δ is intended to 0 in line tracking, tractor model is decoupled and linearized, established as follows Expression formula：
    <mrow> <mtable> <mtr> <mtd> <mrow> <mover> <mi>y</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>=</mo> <msub> <mi>V</mi> <mi>x</mi> </msub> <mi>&amp;psi;</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mover> <mi>&amp;psi;</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>=</mo> <mfrac> <msub> <mi>V</mi> <mi>x</mi> </msub> <mi>L</mi> </mfrac> <mi>&amp;delta;</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mover> <mi>&amp;delta;</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>=</mo> <mi>u</mi> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow>
    In formula, u is control input variable expected path, after Laplace transformation, with deflecting roller drift angle rate of changeFor agri-vehicle Motion model G1(s) input, Actual path tracking effect y are output；
    Agri-vehicle motion model G1(s) expression formula is as follows, wherein, car speed Vx1m/s, wheelbase L is taken to take 2.314m；S is represented The frequency domain variable of time；
    <mrow> <msub> <mi>G</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mi>y</mi> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mover> <mi>&amp;delta;</mi> <mo>&amp;CenterDot;</mo> </mover> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <msubsup> <mi>V</mi> <mi>x</mi> <mn>2</mn> </msubsup> <mo>/</mo> <mi>L</mi> </mrow> <msup> <mi>s</mi> <mn>3</mn> </msup> </mfrac> <mo>=</mo> <mfrac> <mn>0.432</mn> <msup> <mi>s</mi> <mn>3</mn> </msup> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>
    The controller of design is used for agri-vehicle motion model G1(s) in adjusting；
    It is expected deflecting roller drift angle δu(s) it is steering model G0(s) input, it is then rightIntegrated, obtain δ (s), and with the output that actual steering wheel drift angle δ (s) is steering, transmission function steering model G0(s) it is：
    <mrow> <msub> <mi>G</mi> <mn>0</mn> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mi>&amp;delta;</mi> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> <mrow> <msub> <mi>&amp;delta;</mi> <mi>u</mi> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>=</mo> <mfrac> <mn>11.36</mn> <mrow> <msup> <mi>s</mi> <mn>2</mn> </msup> <mo>+</mo> <mn>3.57</mn> <mi>s</mi> <mo>+</mo> <mn>11.36</mn> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow>
    It is by (4) formula and (5) Shi Ke get, open-loop transfer function agri-vehicle system model G (s)：
    <mrow> <mi>G</mi> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mi>y</mi> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> <mrow> <msub> <mi>&amp;delta;</mi> <mi>u</mi> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>=</mo> <mfrac> <mn>4.9</mn> <mrow> <msup> <mi>s</mi> <mn>2</mn> </msup> <mrow> <mo>(</mo> <msup> <mi>s</mi> <mn>2</mn> </msup> <mo>+</mo> <mn>3.57</mn> <mi>s</mi> <mo>+</mo> <mn>11.36</mn> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> <mo>.</mo> </mrow>
  4. 4. the gain switching nonlinear control method of agri-vehicle path trace according to claim 1, it is characterised in that： In the step 5, based on agri-vehicle system model G (s), using the controller of the mode design system of anticipatory control, make to close Loop system further speeds up response speed on the premise of the requirement of stability is met, now needs to judge the dynamic of closed-loop system Whether state performance indications meet the requirement of system, and the controller of this secondary design is the angle from signal analysis, i.e., using frequency The method of rate analysis, with the interval angles that 5 ° are phase advanced argument, with 65 ° for maximum phase advanced argument, 25 ° surpass for minimum phase Preceding amount, an anticipatory control is carried out to agri-vehicle system model, after anticipatory control control, ensureing response speed On the premise of degree, dynamic performance index is considered, choose the phase advance angle that 65 ° of leading phase amount is controller, agricultural vehicle The controller C of path following control system1And open-loop transfer function C (s)1(s) G (s) is respectively：
    <mrow> <msub> <mi>C</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mn>1</mn> <mo>+</mo> <mn>3.18</mn> <mi>s</mi> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <mn>0.15</mn> <mi>s</mi> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow>
    <mrow> <msub> <mi>C</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mi>G</mi> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mo>(</mo> <mn>1</mn> <mo>+</mo> <mn>3.18</mn> <mi>s</mi> <mo>)</mo> <mo>&amp;times;</mo> <mn>4.9</mn> </mrow> <mrow> <mo>(</mo> <mn>1</mn> <mo>+</mo> <mn>0.15</mn> <mi>s</mi> <mo>)</mo> <mo>(</mo> <msup> <mi>s</mi> <mn>4</mn> </msup> <mo>+</mo> <mn>3.57</mn> <msup> <mi>s</mi> <mn>3</mn> </msup> <mo>+</mo> <mn>11.36</mn> <msup> <mi>s</mi> <mn>2</mn> </msup> <mo>)</mo> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> </mrow>
    Now, agri-vehicle system model is in controller C1(s) the agri-vehicle path following control dynamic performance under adjusting Index is：
    σ %=54.5%, ts=5.66s, tr=0.67s (9)
    Wherein, overshoot σ %, regulating time ts, rise time tr；And provide agri-vehicle path following control system dynamic Performance indications require as follows：
    σ % ＜ 5%, ts＜ 3s, tr＜ 3s (10)
    Wherein：Regulating time tsRefer to reach and be maintained at the shortest time required in the error of final value ± 5%；Rise time trIt is Finger response curve rises to the time needed for the 90% of steady-state value from the 10% of steady-state value；
    Because system is unsatisfactory for dynamic performance index requirement after an anticipatory control, in order to further speed up the response of system Speed, secondary anticipatory control link is designed, on the basis of 65 ° of a leading phase, with the angular interval that 5 ° are phase advanced argument Degree, with 65 ° for maximum phase advanced argument, 25 ° are minimum phase advanced argument, agri-vehicle system model are carried out respectively secondary super Preceding correction, on the premise of overshoot is ensured, consider dynamic performance index, it is controller to choose secondary 65 ° of leading phase Leading phase angle, by secondary anticipatory control control after, the controller C of system2And open-loop transfer function C (s)2(s)G(s) Respectively：
    <mrow> <msub> <mi>C</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mo>(</mo> <mn>1</mn> <mo>+</mo> <mn>3.18</mn> <mi>s</mi> <mo>)</mo> <mo>(</mo> <mn>1</mn> <mo>+</mo> <mn>1.15</mn> <mi>s</mi> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mn>1</mn> <mo>+</mo> <mn>0.15</mn> <mi>s</mi> <mo>)</mo> <mo>(</mo> <mn>1</mn> <mo>+</mo> <mn>0.054</mn> <mi>s</mi> <mo>)</mo> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>11</mn> <mo>)</mo> </mrow> </mrow>
    <mrow> <msub> <mi>C</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mi>G</mi> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mo>(</mo> <mn>1</mn> <mo>+</mo> <mn>3.18</mn> <mi>s</mi> <mo>)</mo> <mo>(</mo> <mn>1</mn> <mo>+</mo> <mn>1.15</mn> <mi>s</mi> <mo>)</mo> <mo>&amp;times;</mo> <mn>4.9</mn> </mrow> <mrow> <mo>(</mo> <mn>1</mn> <mo>+</mo> <mn>0.15</mn> <mi>s</mi> <mo>)</mo> <mo>(</mo> <mn>1</mn> <mo>+</mo> <mn>0.054</mn> <mi>s</mi> <mo>)</mo> <mo>(</mo> <msup> <mi>s</mi> <mn>4</mn> </msup> <mo>+</mo> <mn>3.57</mn> <msup> <mi>s</mi> <mn>3</mn> </msup> <mo>+</mo> <mn>11.36</mn> <msup> <mi>s</mi> <mn>2</mn> </msup> <mo>)</mo> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>12</mn> <mo>)</mo> </mrow> </mrow>
    Now, agri-vehicle system model is in controller C2(s) the agri-vehicle path following control dynamic performance under adjusting Index is：
    σ %=44.8%, ts=12.95s, tr=0.36s (13).
  5. A kind of 5. transformer station process layer anti-misoperation locking logic testing device according to claim 1, it is characterised in that： In the step 6, by many experiments, it is determined that as 0.1 ＜ K ＜ 0.7, C3(s)=KC2(s) agri-vehicle system is acted on The phase margin numerical value of the Bode diagram of model is more than C1And C (s)2(s) to the phase margin of the Bode diagram of agri-vehicle system model Numerical value, it can preferably adjust overshoot.
  6. 6. the gain switching nonlinear control method of agri-vehicle path trace according to claim 1, it is characterised in that： In the step 7, in agri-vehicle path following control system, nonlinear control method is switched using turn off gain, will be controlled Device C processed3(s) nonlinear pid controller C is become4(s), determined through many experiments, the open loop under corresponding optimal dynamic performance index Transmission function is that K here takes 0.3：
    <mrow> <msub> <mi>C</mi> <mn>4</mn> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mi>G</mi> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mo>(</mo> <mn>1</mn> <mo>+</mo> <mn>3.18</mn> <mi>s</mi> <mo>)</mo> <mo>(</mo> <mn>1</mn> <mo>+</mo> <mn>1.15</mn> <mi>s</mi> <mo>)</mo> <mo>&amp;times;</mo> <mn>4.9</mn> <mo>&amp;times;</mo> <mi>K</mi> </mrow> <mrow> <mo>(</mo> <mn>1</mn> <mo>+</mo> <mn>0.15</mn> <mi>s</mi> <mo>)</mo> <mo>(</mo> <mn>1</mn> <mo>+</mo> <mn>0.054</mn> <mi>s</mi> <mo>)</mo> <mo>(</mo> <msup> <mi>s</mi> <mn>4</mn> </msup> <mo>+</mo> <mn>3.57</mn> <msup> <mi>s</mi> <mn>3</mn> </msup> <mo>+</mo> <mn>11.36</mn> <msup> <mi>s</mi> <mn>2</mn> </msup> <mo>)</mo> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>14</mn> <mo>)</mo> </mrow> </mrow>
    Now, agri-vehicle system model is in controller C4(s) the agri-vehicle path following control dynamic performance under adjusting Index is：
    σ %=4.44%, ts=2.79s, tr=1.90s (15).
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