CN110971152B - Multi-motor anti-saturation sliding mode tracking control method based on total quantity consistency - Google Patents

Multi-motor anti-saturation sliding mode tracking control method based on total quantity consistency Download PDF

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CN110971152B
CN110971152B CN201911175334.1A CN201911175334A CN110971152B CN 110971152 B CN110971152 B CN 110971152B CN 201911175334 A CN201911175334 A CN 201911175334A CN 110971152 B CN110971152 B CN 110971152B
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motor
saturation
sliding mode
total amount
torque
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张昌凡
张乾
何静
刘建华
杨醒醒
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Hunan University of Technology
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P6/00—Arrangements for controlling synchronous motors or other dynamo-electric motors using electronic commutation dependent on the rotor position; Electronic commutators therefor
    • H02P6/04—Arrangements for controlling or regulating the speed or torque of more than one motor
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T10/00—Road transport of goods or passengers
    • Y02T10/60—Other road transportation technologies with climate change mitigation effect
    • Y02T10/72—Electric energy management in electromobility

Abstract

The invention discloses a multi-motor anti-saturation sliding mode tracking control method based on total amount consistency. Firstly, the method comprises the following steps: according to a voltage and torque balance equation of the permanent magnet brushless motor, parameter perturbation and load torque disturbance are considered, and a mathematical model of the multi-motor traction system is established; secondly, the method comprises the following steps: designing a sliding mode interference observer according to a mathematical model of a multi-motor traction system, and observing an unknown composite interference value formed by combining parameter perturbation and load torque disturbance; thirdly, the method comprises the following steps: designing an auxiliary anti-saturation system according to relevant parameters of a mathematical model of the multi-motor traction system; fourthly: combining a sliding mode variable structure theory, introducing an interference observation value and an auxiliary system state, and designing a total amount cooperative tracking controller; the invention adopts a multi-motor anti-saturation sliding mode tracking control method based on total amount consistency, and makes up for performance reduction caused by saturation constraint in the existing total amount consistency theory; meanwhile, the method is also suitable for the condition that a plurality of motors in a multi-motor system are saturated.

Description

Multi-motor anti-saturation sliding mode tracking control method based on total quantity consistency
Technical Field
The invention relates to the field of traction torque total amount cooperative control, in particular to a multi-motor traction total amount cooperative anti-saturation control method based on a sliding mode variable structure.
Background
The saturation limitation is a nonlinear problem which often occurs in practical engineering, and the input saturation in the transportation control technology or the flow saturation in a traffic network can affect the whole transportation efficiency and even cause traffic accidents in severe cases. The term saturation originates from the integrator in PI control, kothare proposes a unified framework for traditional anti-saturation, and then combines with modern control techniques, tarbouriech and Turner to further develop modern anti-saturation techniques. In recent years, with the development of mathematical theories, saturated ones are treated with a combination of Nussbaum functions, smooth functions or mean theorem; the anti-saturation compensator is also divided into a static type and a dynamic type, and the saturated type is processed by using a compensation idea: hussain et al have studied a static antisaturation compensator, have reduced the conservatism and realized simply; subsequently, hussain and Turner et al propose a robust nonlinear dynamic anti-saturation compensator, which makes saturation decay faster; meanwhile, parameters of the anti-saturation compensator are solved by using a Linear Matrix Inequality (LMI), and estimation of an attraction domain can be expanded. Recently, direct compensation of control inputs using an auxiliary anti-saturation system has been studied more extensively. In summary, the technology of anti-saturation is becoming more and more perfect, but with large-scale transportation and highly complicated industrial networks, multi-motor traction systems are widely used, especially in the fields of rail transit, air transportation, robots and the like. Therefore, in combination with modern anti-saturation technology, solving the saturation problem in a complex multi-motor traction system is extremely challenging and of practical engineering significance.
For a heavy-load locomotive which is towed by multiple motors in actual engineering, parameter perturbation and load torque disturbance caused by a complex and severe environment necessarily exist, a method for increasing sliding mode switching gain is often adopted to counteract the disturbance based on a control strategy of a sliding mode variable structure, but the problem of input saturation caused by increasing control input is also solved; meanwhile, when the locomotive normally runs or a certain wheel pair idles or slides, the problem of input saturation of the traction motor is very likely to be caused in the current total amount cooperative control, which affects the total amount traction performance of the locomotive and even causes accidents in severe cases. Input saturation is a nonlinear problem often occurring in practical engineering, and linearization processing cannot be performed, which brings great difficulty to the design of a control strategy.
Disclosure of Invention
The invention provides a multi-motor anti-saturation sliding mode tracking control method based on total amount consistency, aiming at the problem that the input saturation problem of multiple motors under the total amount consistency theory in the prior art is nonlinear in practical engineering and cannot be subjected to linearization processing.
In order to achieve the purpose, the invention adopts the following technical scheme:
the multi-motor anti-saturation sliding mode tracking control method based on total amount consistency comprises the following steps:
s1, according to a voltage and torque balance equation of a permanent magnet brushless motor, considering parameter perturbation and load torque disturbance, and establishing a mathematical model of a multi-motor traction system; the voltage and torque balance equation of the permanent magnet brushless motor is as follows:
Figure BDA0002289809230000021
wherein: r is j ，L j Respectively representing the resistance and inductance of the armature circuit, i j As armature current, ω j Is the output angular velocity, u, of the motor gearbox j Voltage at input port of armature circuit, k ej Is a back electromotive force constant, k tj To the gear ratio of the gearbox, J 0j And J 1j Representing the moment of inertia of the motor and gear head, respectively, b 0j And b 1j Respectively representing the viscous friction coefficients, k, of the motor and the gear head mj Is the motor torque constant, T Lj For load torque, T ej And outputting the torque for the motor.
The mathematical model of the multi-motor traction system is as follows:
Figure BDA0002289809230000022
in the formula (I), the compound is shown in the specification,
Figure BDA0002289809230000023
wherein x is 1j Is the output angular velocity, x, of the motor gearbox 2j Is angular acceleration, x 3j In order to output the torque to the motor,
Figure BDA0002289809230000029
in order to achieve an equivalent moment of inertia,
Figure BDA0002289809230000025
is an equivalent viscous damping constant, d 1j ＝Δa 0j x 1j +Δa 1j x 2j +Δb j u j +f j (t)，
Figure BDA0002289809230000026
S2, designing a sliding mode interference observer according to a mathematical model of the multi-motor traction system, and observing an unknown composite interference value formed by combining parameter perturbation and load torque disturbance; designing a sliding mode disturbance observer as follows:
Figure BDA0002289809230000027
in the formula:
Figure BDA0002289809230000028
is an estimate of the corresponding state, w j ＝[k 1 sgn(e 1 )0 k 3 sgn(e 3 )] T Sgn () is a sign function, k 1 And k 3 Is the normal number to be designed.
The parameter satisfies k 1 ＞|e 2 | max +η 1 ，k 3 ＞|d 2j | max +η 3 Wherein eta 1 And η 3 Is an arbitrary normal number, the observer error will be in a finite time T 1 Converging inwardly to the slip-form face, i.e.
Figure BDA0002289809230000031
If t > t 1 Then, there are:
Figure BDA0002289809230000032
the observed values of the unknown composite interference are:
Figure BDA0002289809230000033
in the formula (I), the compound is shown in the specification,
Figure BDA0002289809230000034
is an estimate of the unknown complex interference.
S3, designing an auxiliary anti-saturation system according to relevant parameters of a mathematical model of the multi-motor traction system; the auxiliary anti-saturation system is as follows:
Figure BDA0002289809230000035
in the formula: x is the number of aj To assist the system state, y aj To assist system output, A aj For the coefficients to be designed, τ is a small positive constant, Δ u = u j -v j ，s 2 Is a slip form surface, constant
Figure BDA0002289809230000036
S4, combining a sliding mode variable structure theory, introducing an interference observation value and an auxiliary system state, and designing a total amount cooperative tracking controller; the total amount cooperative tracking controller comprises:
Figure BDA0002289809230000037
wherein, c 2j And ε j To design the parameters, j =1,2, ·, m.
Designing parameters of a total amount cooperative anti-saturation sliding mode tracking controller, and when the design parameters meet the condition that c is more than 0 2j ＜2A aj -1 and ε j ＞ζ j The total output torque of each motor can track the upper reference state T in a limited time * 。
And (3) proving that: defining a computation matrix as Z = [ s ] 2 x a1 x a2 ...x am ] T ，
Selecting a positive definite Lyapunov function as follows:
Figure BDA0002289809230000038
obtaining a derivative:
Figure BDA0002289809230000041
using xy ≤ 0.5x 2 +0.5y 2 The inequality of the model is:
Figure BDA0002289809230000042
therefore, the first and second electrodes are formed on the substrate,
Figure BDA0002289809230000043
if it is true, i.e. the global asymptotic is stable, the switching plane is reached and maintained for a finite time T, i.e. T > T, s 2 →0，x aj → 0; the selected slip form surface is s 2 = e, e → 0, when T > T can be obtained; and the cooperative tracking error by design is ^ 4>
Figure BDA0002289809230000044
Then->
Figure BDA0002289809230000045
The total amount is consistent.
The invention has the beneficial effects that:
1. the multi-motor cooperative control is expanded from individual consistency to total consistency.
2. By introducing the observed value of unknown composite interference into the design of the controller, the phenomenon that the control input is increased due to the fact that the disturbance is offset by increasing the sliding mode switching gain in the sliding mode control is avoided.
3. The state of the auxiliary anti-saturation system is introduced into the design of the controller, and the influence of input saturation on the total amount cooperative tracking performance under the total amount consistency theory is reduced.
4. The method is not only suitable for the single-motor input saturation problem, but also suitable for the condition that a plurality of motors in a multi-motor traction system are all input saturated.
Drawings
FIG. 1 is a control system framework diagram of a multi-motor anti-saturation sliding mode tracking control method based on total quantity consistency;
FIG. 2 is a view of a sudden change disturbance observation curve of the sliding mode disturbance observer motor 1;
FIG. 3 is a slowly varying disturbance observation curve diagram of the sliding mode disturbance observer motor 2;
FIG. 4 is a high-frequency noise observation curve diagram of the sliding mode disturbance observer motor 3;
FIG. 5 is a graph of a sliding mode disturbance observer motor 4 uniform noise observation;
FIG. 6 is a graph of control input without clipping;
fig. 7 is a control curve input diagram for clipping 220;
FIG. 8 is a graph of the effect of total synergistic tracking without anti-saturation;
FIG. 9 is a graph of the effect of co-tracking of total amount with anti-saturation;
FIG. 10 is a plot of total cooperative tracking error without anti-saturation;
FIG. 11 is a plot of total cooperative tracking error with anti-saturation;
FIG. 12 is a graph of a saturated input error curve;
fig. 13 is a saturated output torque curve.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to specific embodiments. It should be understood that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the invention.
The heavy-duty locomotive is a complex electromechanical system, the embodiment takes a multi-motor traction system consisting of 4 motors with different parameters as an object to verify the effectiveness of the method, the parameters of each motor are shown in the following table, and the initial torque of each motor is assumed to be 0.1.
Figure BDA0002289809230000051
The traction characteristic curve given consists of a piecewise function: simulating a motor starting stage at 0 → 0.3 s; simulating the constant-speed running stage of the motor in 0.3 → 0.7 s; simulating the deceleration stop stage of the motor in 0.7-1s as follows:
Figure BDA0002289809230000052
sliding mode disturbance observer performance simulation
In order to effectively verify the excellent performance of the sliding mode interference observer, 4 different interference signals of sudden change interference, slowly changing interference, high-frequency noise and uniform noise are respectively applied to 4 motors. In the designed sliding mode disturbance observer type, a parameter k is set 1 ＝1，k 3 =10, observation graphs of the four disturbances shown in fig. 2-5 can be obtained, observation curves of the four disturbance signals can be analyzed, the maximum tracking time of the observer is about 0.00007s, and although there is an error for the abrupt disturbance shown in fig. 2, it can be seen that the tracking is completed within the maximum tracking time. Therefore, the sliding mode disturbance observer designed by the method has good observation performance and meets the design requirements of an actual controller.
Total amount synergy-based performance simulation of anti-saturation sliding mode tracking controller
The control algorithm provided by the part is verified to greatly improve the total cooperative tracking performance through the comparative simulation of total cooperative tracking control with or without anti-saturation, and meanwhile, the complex problem that a plurality of motors are saturated in input can be solved. It can be seen from fig. 6 that the sum-coordinated tracking control without regard to saturation would cause motors 1 and 3 to exceed the rated voltage by 220V, so the simulation sets the limit to ± 220; the parameters are set in the auxiliary anti-saturation system and the controller formula as follows: a. The aj ＝2×10 6 ,B aj ＝1500,c 2j ＝1.6×10 5 τ =0.00001. It can be seen from the graph of fig. 7 that the control inputs of the motors are effectively controlled at the rated voltage, and meanwhile, the problem of saturation of the four motors at 0.535s,0.894s,0.608s and 0.871s can be solved.
Analyzing the simulation diagram to obtain: as can be seen from the curves of fig. 8 and fig. 10, the total amount without anti-saturation cooperative tracking control has a large deviation when the motor is saturated, which seriously affects the overall tracking performance; FIG. 9 and FIG. 11 show that the total amount of anti-saturation coordinated tracking control designed herein can greatly improve the impact of input saturation on overall tracking performance; meanwhile, the integral tracking performance can be well ensured under the condition that two motors are saturated at the constant speed and the deceleration stage. The saturation input error curve of fig. 12 shows the saturation time and the anti-saturation timeliness of each motor; the saturated output torque curve of fig. 13 may show that the multi-motor system ensures consistent total by coordinating the tractive effort of each motor before and after saturation.
The above-mentioned embodiments are merely preferred embodiments for fully illustrating the present invention, and the scope of the present invention is not limited thereto. The equivalent substitutions or changes made by the person skilled in the art on the basis of the present invention are all within the protection scope of the present invention.

Claims (5)

1. The multi-motor anti-saturation sliding mode tracking control method based on total quantity consistency is characterized by comprising the following steps of:
s1, according to a voltage and torque balance equation of a permanent magnet brushless motor, considering parameter perturbation and load torque disturbance, and establishing a mathematical model of a multi-motor traction system; the mathematical model of the multi-motor traction system is as follows:
Figure 739273DEST_PATH_IMAGE001
in the formula (I), the compound is shown in the specification,
Figure 390834DEST_PATH_IMAGE002
Figure 373834DEST_PATH_IMAGE003
Figure 769043DEST_PATH_IMAGE004
Figure 255519DEST_PATH_IMAGE005
Figure 343561DEST_PATH_IMAGE006
wherein the content of the first and second substances,
Figure 610594DEST_PATH_IMAGE007
is the output angular velocity of the motor gearbox,
Figure 747178DEST_PATH_IMAGE008
in the case of an angular acceleration,
Figure 150477DEST_PATH_IMAGE009
in order to output the torque to the motor,
Figure 845638DEST_PATH_IMAGE010
，
Figure 599968DEST_PATH_IMAGE011
，
Figure 274663DEST_PATH_IMAGE012
，
Figure 798048DEST_PATH_IMAGE013
in order to be equivalent to the moment of inertia,
Figure 227892DEST_PATH_IMAGE014
in order to be an equivalent viscous damping constant,
Figure 141622DEST_PATH_IMAGE015
，
Figure 682324DEST_PATH_IMAGE016
，
Figure 263478DEST_PATH_IMAGE017
and
Figure 598645DEST_PATH_IMAGE018
respectively representing the resistance and inductance of the armature circuit,
Figure 763785DEST_PATH_IMAGE019
in order to be a constant of the back electromotive force,
Figure 842599DEST_PATH_IMAGE020
is the transmission ratio of the gear box,
Figure 340577DEST_PATH_IMAGE021
and
Figure 784327DEST_PATH_IMAGE022
respectively representing the rotational inertia of the motor and the gear head,
Figure 545DEST_PATH_IMAGE023
and
Figure 820734DEST_PATH_IMAGE024
respectively representing the viscous friction coefficients of the motor and the gear head,
Figure 173217DEST_PATH_IMAGE025
is the motor torque constant;
s2, designing a sliding mode interference observer according to a mathematical model of the multi-motor traction system, and observing an unknown composite interference value formed by combining parameter perturbation and load torque disturbance; the sliding mode disturbance observer is as follows:
Figure 115766DEST_PATH_IMAGE026
in the formula:
Figure 491383DEST_PATH_IMAGE027
is an estimate of the corresponding state of the state,
Figure 912000DEST_PATH_IMAGE028
，
Figure 820788DEST_PATH_IMAGE029
in the form of a function of the sign,
Figure 668659DEST_PATH_IMAGE030
and
Figure 593889DEST_PATH_IMAGE031
is a normal number to be designed;
s3, designing an auxiliary anti-saturation system according to relevant parameters of a mathematical model of the multi-motor traction system; the auxiliary anti-saturation system is as follows:
Figure 755880DEST_PATH_IMAGE032
in the formula:
Figure 82956DEST_PATH_IMAGE033
in order to assist in the state of the system,
Figure 304990DEST_PATH_IMAGE034
in order to assist in the output of the system,
Figure 717517DEST_PATH_IMAGE035
for the coefficients to be designed, the coefficients are,
Figure 417620DEST_PATH_IMAGE036
is a small positive constant number of bits which,
Figure 599203DEST_PATH_IMAGE037
，
Figure 54455DEST_PATH_IMAGE038
is a slip form surface, constant
Figure 390496DEST_PATH_IMAGE039
；
S4, combining a sliding mode variable structure theory, introducing an interference observation value and an auxiliary system state, and designing a total amount cooperative tracking controller; the total amount cooperative tracking controller is designed as follows:
Figure 956606DEST_PATH_IMAGE040
wherein the content of the first and second substances,
Figure 930379DEST_PATH_IMAGE041
and
Figure 556532DEST_PATH_IMAGE042
in order to be able to design the parameters,
Figure 943651DEST_PATH_IMAGE043
。
2. the multi-motor anti-saturation sliding-mode tracking control method based on total quantity consistency according to claim 1, wherein in the step S1, the voltage and torque balance equation of the permanent magnet brushless motor is as follows:
Figure 985556DEST_PATH_IMAGE044
wherein:
Figure 141731DEST_PATH_IMAGE017
，
Figure 876469DEST_PATH_IMAGE018
respectively represent electricityThe resistance and inductance of the pivot circuit,
Figure 485305DEST_PATH_IMAGE045
in order to be the armature current,
Figure 658797DEST_PATH_IMAGE046
is the output angular velocity of the motor gearbox,
Figure 105697DEST_PATH_IMAGE047
is the voltage at the input port of the armature circuit,
Figure 73653DEST_PATH_IMAGE019
in order to be a constant of the back electromotive force,
Figure 107468DEST_PATH_IMAGE020
is the transmission ratio of the gear box,
Figure 553493DEST_PATH_IMAGE021
and
Figure 621943DEST_PATH_IMAGE022
respectively representing the rotational inertia of the motor and the gear head,
Figure 760800DEST_PATH_IMAGE023
and
Figure 344228DEST_PATH_IMAGE024
respectively representing the viscous friction coefficients of the motor and the gear head,
Figure 531627DEST_PATH_IMAGE025
is a constant of the torque of the motor,
Figure 516901DEST_PATH_IMAGE048
in order to be the load torque,
Figure 262878DEST_PATH_IMAGE049
and outputting the torque for the motor.
3. The multi-motor anti-saturation sliding mode tracking control method based on total amount consistency according to claim 1, wherein the observed value of unknown composite interference in step S2 is as follows:
Figure 333602DEST_PATH_IMAGE050
，
in the formula (I), the compound is shown in the specification,
Figure 324692DEST_PATH_IMAGE051
is an estimate of the unknown composite interference.
4. The multi-motor anti-saturation sliding mode tracking control method based on total quantity consistency according to claim 1 is not only suitable for the single-motor input saturation problem, but also suitable for the condition that a plurality of motors in a multi-motor traction system are all input saturated.
5. The multi-motor anti-saturation sliding mode tracking control method based on total amount consistency according to claim 1, characterized in that the control targets are: the multi-motor system coordinates the torque output of each motor through a total amount cooperative control protocol to ensure that the torque output of each motor is the sum of the torques in a limited time
Figure 164472DEST_PATH_IMAGE052
The inner and set traction characteristic curves tend to be consistent, namely:
Figure 645131DEST_PATH_IMAGE053
in the formula (I), the compound is shown in the specification,
Figure 875256DEST_PATH_IMAGE054
for a given traction curve, the traction curve is,
Figure 732353DEST_PATH_IMAGE055
a finite time for the sliding mode to converge to the origin.
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