CN110971152A - 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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CN110971152A
CN110971152A CN201911175334.1A CN201911175334A CN110971152A CN 110971152 A CN110971152 A CN 110971152A CN 201911175334 A CN201911175334 A CN 201911175334A CN 110971152 A CN110971152 A CN 110971152A
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motor
saturation
sliding mode
total amount
torque
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张昌凡
张乾
何静
***
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
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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 a plurality of motors under the total amount consistency theory in the prior art has nonlinear condition in practical engineering and can not carry out linearization treatment,
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 quantity consistency comprises the following steps:
s1, according to a voltage and torque balance equation of the permanent magnet brushless motor, considering parameter perturbation and load torque disturbance, and establishing a mathematical model of the multi-motor traction system; the voltage and torque balance equation of the permanent magnet brushless motor is as follows:
Figure BDA0002289809230000021
wherein: rj，LjRepresenting the resistance and inductance, i, of the armature circuit, respectivelyjIs armature current, ωjIs the output angular velocity, u, of the motor gearboxjIs the voltage at the input port of the armature circuit, kejIs a back electromotive force constant, ktjIs the gear ratio of the gearbox, J0jAnd J1jRepresenting the moment of inertia of the motor and gear head, respectively, b0jAnd b1jRespectively representing the viscous friction coefficients, k, of the motor and the gear headmjIs the motor torque constant, TLjFor load torque, TejAnd 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 is1jIs the output angular velocity, x, of the motor gearbox2jIs angular acceleration, x3jIn order to output the torque to the motor,
Figure BDA0002289809230000029
in order to be equivalent to the moment of inertia,
Figure BDA0002289809230000025
is an equivalent viscous damping constant, d1j＝Δa0jx1j+Δa1jx2j+Δbjuj+fj(t)，
Figure BDA0002289809230000026
S2, designing a sliding mode disturbance observer according to a mathematical model of the multi-motor traction system, and observing an unknown composite disturbance 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, wj＝[k1sgn(e1)0 k3sgn(e3)]TSgn () is the sign function, k1And k3Is the normal number to be designed.
The parameter satisfies k1＞|e2|max+η1，k3＞|d2j|max+η3Wherein η1And η3Is any normal number, the observer error will be in a finite time T1Converging inwardly to the slip-form face, i.e.
Figure BDA0002289809230000031
If t > t1Then, 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 composite 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 ofajTo assist the system state, yajTo assist system output, AajFor the coefficients to be designed, τ is a small positive constant, Δ u ═ uj-vj，s2Is a slip form surface, constant
Figure BDA0002289809230000036
S4, introducing an interference observation value and an auxiliary system state by combining a sliding mode variable structure theory, and designing a total amount cooperative tracking controller; the total amount cooperative tracking controller comprises:
Figure BDA0002289809230000037
wherein, c2jAnd εjTo 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 02j＜2Aaj-1 and εj＞ζjThe 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 ═ s2xa1xa2...xam]T，
Selecting a positive definite Lyapunov function as follows:
Figure BDA0002289809230000038
and (5) obtaining a derivative:
Figure BDA0002289809230000041
using xy ≤ 0.5x2+0.5y2The 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, s2→0，xaj→ 0; the selected slip form surface is s2E, when T > T can be obtained, e → 0; and by the designed cooperative tracking error of
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 further described in detail with reference to the following 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 set1＝1，k3As 10, observation graphs of the four disturbances shown in fig. 2 to 5 can be obtained, and the maximum tracking time of the observer is about 0.00007s when the observation curves of the four disturbance signals are analyzed, although there is an error in 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 total amount coordinated tracking control without taking saturation into account would cause motors 1 and 3 to exceed the rated voltage of 220V, so the simulation sets the limit to ± 220; in the auxiliary anti-saturation system and controller typeThe setting parameters are as follows: a. theaj＝2×106,Baj＝1500,c2j＝1.6×105τ is 0.00001. As can be seen from the graph of fig. 7, 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 substitution or change made by the technical personnel in the technical field on the basis of the invention is all within the protection scope of the 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 the permanent magnet brushless motor, considering parameter perturbation and load torque disturbance, and establishing a mathematical model of the multi-motor traction system; the mathematical model of the multi-motor traction system is as follows:
Figure FDA0002289809220000011
in the formula (I), the compound is shown in the specification,
Figure FDA0002289809220000012
wherein x is1jIs the output angular velocity, x, of the motor gearbox2jIs angular acceleration, x3jIn order to output the torque to the motor,
Figure FDA0002289809220000013
in order to be equivalent to the moment of inertia,
Figure FDA0002289809220000014
is an equivalent viscous damping constant, d1j＝Δa0jx1j+Δa1jx2j+Δbjuj+fj(t)，
Figure FDA0002289809220000015
S2, designing a sliding mode disturbance observer according to a mathematical model of the multi-motor traction system, and observing an unknown composite disturbance value formed by combining parameter perturbation and load torque disturbance; the sliding mode disturbance observer is as follows:
Figure FDA0002289809220000016
in the formula:
Figure FDA0002289809220000017
is an estimate of the corresponding state, wj＝[k1sgn(e1) 0 k3sgn(e3)]TSgn () is the sign function, k1And k3Is the 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 FDA0002289809220000018
in the formula: x is the number ofajTo assist the system state, yajTo assist system output, AajFor the coefficients to be designed, the coefficients are,τ is a small normal number, Δ u ═ uj-vj，s2Is a slip form surface, constant
Figure FDA0002289809220000019
S4, introducing an interference observation value and an auxiliary system state by combining a sliding mode variable structure theory, and designing a total amount cooperative tracking controller; the total amount cooperative tracking controller is designed as follows:
Figure FDA0002289809220000021
wherein, c2jAnd εjFor the parameter to be designed, j is 1,2, …, m.
2. The multi-motor anti-saturation sliding-mode tracking control method based on total quantity consistency according to claim 1, wherein in step S1, the voltage and torque balance equation of the permanent magnet brushless motor is as follows:
Figure FDA0002289809220000022
wherein: rj，LjRepresenting the resistance and inductance, i, of the armature circuit, respectivelyjIs armature current, ωjIs the output angular velocity, u, of the motor gearboxjIs the voltage at the input port of the armature circuit, kejIs a back electromotive force constant, ktjIs the gear ratio of the gearbox, J0jAnd J1jRepresenting the moment of inertia of the motor and gear head, respectively, b0jAnd b1jRespectively representing the viscous friction coefficients, k, of the motor and the gear headmjIs the motor torque constant, TLjFor load torque, TejAnd 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 disturbance in step S2 is as follows:
Figure FDA0002289809220000023
in the formula (I), the compound is shown in the specification,
Figure FDA0002289809220000024
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 summed up and is in limited time tsThe inner and set traction characteristic curves tend to be consistent, namely:
Figure FDA0002289809220000025
in the formula, T*For a given traction curve, tsThe finite time for the sliding mode to converge to the origin.
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CN113391616A (en) * 2021-05-13 2021-09-14 中国矿业大学 Mining trolley bus safety state estimation method based on event trigger mechanism
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CN113885314A (en) * 2021-10-22 2022-01-04 电子科技大学 Nonlinear system tracking control method with unknown gain and interference
CN113885314B (en) * 2021-10-22 2023-05-23 电子科技大学 Nonlinear system tracking control method with unknown gain and interference
CN114114925A (en) * 2021-11-29 2022-03-01 江南大学 Cooperative self-adaptive sliding mode constraint control method and system based on data driving
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