CN114844405A - Integration sliding mode control system of permanent magnet synchronous motor - Google Patents

Integration sliding mode control system of permanent magnet synchronous motor Download PDF

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Publication number
CN114844405A
CN114844405A CN202210291754.1A CN202210291754A CN114844405A CN 114844405 A CN114844405 A CN 114844405A CN 202210291754 A CN202210291754 A CN 202210291754A CN 114844405 A CN114844405 A CN 114844405A
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load torque
value
sliding mode
feedback gain
torque
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刘颖慧
凌云
张晓虎
黄云章
周建华
汤彩珍
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Hunan University of Technology
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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
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/0003—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control
    • H02P21/0007—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control using sliding mode control
    • 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
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/13—Observer control, e.g. using Luenberger observers or Kalman filters
    • 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
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/14—Estimation or adaptation of machine parameters, e.g. flux, current or voltage
    • H02P21/18—Estimation of position or speed
    • 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
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/14—Estimation or adaptation of machine parameters, e.g. flux, current or voltage
    • H02P21/20—Estimation of torque
    • 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
    • H02P25/00—Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details
    • H02P25/02—Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details characterised by the kind of motor
    • H02P25/022—Synchronous motors
    • 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
    • H02P27/00—Arrangements or methods for the control of AC motors characterised by the kind of supply voltage
    • H02P27/04—Arrangements or methods for the control of AC motors characterised by the kind of supply voltage using variable-frequency supply voltage, e.g. inverter or converter supply voltage
    • H02P27/06—Arrangements or methods for the control of AC motors characterised by the kind of supply voltage using variable-frequency supply voltage, e.g. inverter or converter supply voltage using dc to ac converters or inverters
    • H02P27/08—Arrangements or methods for the control of AC motors characterised by the kind of supply voltage using variable-frequency supply voltage, e.g. inverter or converter supply voltage using dc to ac converters or inverters with pulse width modulation
    • 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
    • H02P2207/00—Indexing scheme relating to controlling arrangements characterised by the type of motor
    • H02P2207/05—Synchronous machines, e.g. with permanent magnets or DC excitation
    • 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

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  • Engineering & Computer Science (AREA)
  • Power Engineering (AREA)
  • Control Of Ac Motors In General (AREA)
  • Control Of Motors That Do Not Use Commutators (AREA)

Abstract

The invention discloses an integral sliding mode control system of a permanent magnet synchronous motor, wherein a load torque observer adjusts feedback gain according to the change of a load torque given value output by a sliding mode speed controller, observes the load torque according to the angular speed and the current of a rotor to obtain a load torque observed value and sends the load torque observed value to the sliding mode speed controller, the load torque observed value can not change greatly, but the given subentry part in the load torque given value changes due to the change of the rotor angular speed given value or/and the change of the rotor angular speed actual value, or the given subentry part in the load torque given value changes due to the change of system model parameters, so that the load torque observed value has large fluctuation, the feedback gain is adjusted in advance, and when the load torque observed value really generates an observation error, the response speed of the observer is accelerated, the observation error of the load torque observation value is quickly reduced, and the rapidity and the accuracy of the motor speed control are further improved.

Description

Integration sliding mode control system of permanent magnet synchronous motor
The invention discloses a driving control method of a mining traction permanent magnet synchronous motor, which is a divisional application with an original application number of 202010918598.8 and an application date of 09-04 in 2020.
Technical Field
The invention relates to the technical field of permanent magnet synchronous motors, in particular to an integral sliding mode control system of a permanent magnet synchronous motor.
Background
The permanent magnet synchronous motor has the advantages of high efficiency, large torque, good rotating speed performance and the like, and is widely applied to the fields of manufacturing, electric automobiles, industrial production and the like. The mining traction motor has complex and changeable working environment, large load torque change and wide speed regulation range, can be started by large torque, is inferior to a sliding mode control method in robustness of a permanent magnet synchronous motor vector control method based on a PI controller, but can generate obvious buffeting of the motor speed when load disturbance or internal parameter perturbation occurs in the sliding mode control method.
Disclosure of Invention
The invention aims to provide a permanent magnet synchronous motor integral sliding mode control system for improving load torque observation response speed and reducing torque observation fluctuation aiming at the conditions of large load torque change and wide speed regulation range.
The sliding mode speed controller adopts an integral sliding mode control mode; the load torque observer adjusts the feedback gain according to the change of the load torque given value output by the sliding mode speed controller, and the feedback gain is adjusted according to the rotor angular speed omega and the current i q Observing the load torque to obtain a load torque observed value
Figure BDA0003561850200000011
Load torque observation value output by load torque observer
Figure BDA0003561850200000012
Is sent to a sliding mode speed controller.
Defining a state variable of the sliding mode speed controller as
Figure BDA0003561850200000013
Where ω is the rotor angular velocity, ω * Is a given rotor angular velocity; the sliding mode surface of the sliding mode speed controller is s y ＝c y y 1 +y 2 Wherein c is y Is a slip form face parameter, and c y Is greater than 0. Given value of load torque output by sliding mode speed controller
Figure BDA0003561850200000014
And q-axis torque current setpoint
Figure BDA0003561850200000015
Is composed of
Figure BDA0003561850200000021
Wherein J is the moment of inertia, p is the motor pole pair number, psi f Is a permanent magnet flux linkage, B is the coefficient of friction; coefficient μ 1, coefficient μ 2 Coefficient of μ 3 Coefficient of μ 4 Exponential rate of approach coefficient for speed sliding mode control, and mu 1 ＞0，μ 2 ＞0，μ 4 ＞0，0＜μ 3 ＜1。
The load torque observer is
Figure BDA0003561850200000022
Wherein the content of the first and second substances,
Figure BDA0003561850200000023
k W is the proportional gain of the load torque observer and requires k w ＜0；
Figure BDA0003561850200000024
Is an estimate of the rotor angular velocity, g is the feedback gain of the load torque observer and g < 0.
The load torque observer is used for setting a load torque according to the load torque output by the sliding mode speed controller
Figure BDA0003561850200000025
The method of adjusting the feedback gain g by the change of (2) is:
step (one), calculating
Figure BDA0003561850200000026
Step (2), judgment
Figure BDA0003561850200000027
Whether or not greater than epsilon 2 (ii) a When in use
Figure BDA0003561850200000028
Greater than epsilon 2 Taking feedback gain g equal to g min And entering the step (5); when DeltaT is less than or equal to epsilon 2 Then, entering the step (3);
step (3), judgment
Figure BDA0003561850200000029
Whether or not less than epsilon 1 (ii) a When in use
Figure BDA00035618502000000210
Less than epsilon 1 Taking feedback gain g equal to g max And entering the step (5); when in use
Figure BDA00035618502000000211
Is greater than or equal to epsilon 1 If yes, entering the step (IV);
step (IV), the feedback gain g is according to
Figure BDA00035618502000000212
After calculation, entering step (5);
and (5) observing the load torque by the load torque observer according to the value of the feedback gain g to obtain a load torque observed value
Figure BDA00035618502000000213
The sliding mode speed controller carries out control operation to obtain a load torque set value
Figure BDA00035618502000000214
Wherein epsilon 1 Comparing thresholds, e, for lower limits of torque variation 2 Comparing threshold values for upper limits of torque variation, and 0 & ltepsilon 1 ＜ε 2 ；g max For high value of feedback gain, g min Is a low value of feedback gain, and g min ＜g max ＜0。
Selecting g min 、g max 、ε 1 、ε 2 The method of the value is:
step 1), a load torque observer and a sliding mode speed controller are both in a stable state, and the angular speed of a given rotor and the load torque are kept unchanged;
step 2), the feedback gain g is gradually reduced from a larger value, for example, the feedback gain g is gradually reduced from-0.01, when the steady-state error observed by the load torque reaches the steady-state error limit value observed by the load torque, the feedback gain g at the moment is determined to be g max ；
Step 3) keeping the given rotor angular speed and the load torque constant and making the feedback gain g equal to g max Continuously carrying out n times
Figure BDA0003561850200000031
Measuring the value and dividing n times
Figure BDA0003561850200000032
Maximum m in the measurement
Figure BDA0003561850200000033
The average value of the measured values is used as a torque variation comparison threshold epsilon;
step 4), finely adjusting and changing the feedback gain g, keeping the angular speed of the given rotor unchanged and enabling the load torque to be suddenly changed when the load torque observer and the sliding mode speed controller are both in a stable state, and measuring the tracking and adjusting time of the load torque observer on the premise of ensuring that the torque observation tracking overshoot of the load torque observer output observation value is within the torque observation tracking overshoot limit;
step 5), repeating the step 4), and selecting the feedback gain g with the shortest tracking and adjusting time as g min A value;
step 6), keeping the given rotor angular speed and the load torque unchanged again and making the feedback gain g equal to g min Continuously carrying out n times
Figure BDA0003561850200000034
Measuring the value, and measuring the maximum m of n measurements
Figure BDA0003561850200000035
The average value of the sum of the values is used as a torque variation upper limit comparison threshold epsilon 2 。
N is an integer of 20 or more, and m is an integer of 5 or more and 0.5n or less.
Proportional gain k W According to
Figure BDA0003561850200000036
Selecting; wherein, T N Is the rated torque of the motor, beta is more than 0; further, 1. ltoreq. beta.ltoreq.20 is required.
The sliding mode speed controller has the advantages that the output item of the sliding mode speed controller comprises the compensation subentry load torque observed value, namely the load torque observed value is fed forward to the given value of the current regulator, under the condition that the given current part output by the sliding mode speed controller does not need to be adjusted greatly, the load disturbance or the related influence caused by the change of system parameters can be counteracted, and the buffeting of the system is effectively weakened. The algorithm for automatically adjusting the feedback gain according to the variable quantity of the given value of the load torque avoids the problems that the torque observation fluctuation is large due to the fact that a load torque observer selects a fixed small feedback gain, and the convergence time is long due to the fact that a fixed large feedback gain is selected. The feedback gain is automatically adjusted when the load torque given value changes, the load torque observed value can not change greatly, but the load torque observed value is caused to have large fluctuation because the given value of the rotor angular speed or/and the actual value of the rotor angular speed changes to change the given subentry part in the given value of the load torque or because the system model parameters change to change the given subentry part in the given value of the load torque, the feedback gain is adjusted in advance, when the load torque observed value really generates an observation error, the response speed of an observer is accelerated, the observation error of the load torque observed value is quickly reduced, and the rapidity and the accuracy of the motor speed control are further improved.
Drawings
FIG. 1 is a block diagram of an embodiment 1 of a permanent magnet synchronous motor speed control system;
FIG. 2 is a flowchart of an embodiment 1 of a method for automatically adjusting feedback gain;
FIG. 3 is a block diagram of an embodiment 2 of a permanent magnet synchronous motor speed control system;
fig. 4 is a flowchart of an embodiment 2 of a method for automatically adjusting feedback gain.
Detailed Description
The present invention will be described in further detail below with reference to the accompanying drawings and examples.
Fig. 1 is a block diagram of an embodiment 1 of a permanent magnet synchronous motor speed control system. In fig. 1, a Clarke conversion module inputs three-phase current i of a permanent magnet synchronous motor (i.e., PMSM) a 、i b And i c And outputs the current i under the two-phase static alpha-beta axis coordinate system α 、i β (ii) a A position sensor in the position and speed detection module detects the position theta of the rotor of the permanent magnet synchronous motor and converts the position theta into the angular speed omega of the rotor for output; park conversion module input current i α 、i β And rotor position theta, and outputs current i under a rotating d-q axis coordinate system d 、i q (ii) a Input rotor given angular speed omega of sliding mode speed controller SMC * And rotor angular velocity omega, output load torque set value T L * And torque current given component i' q (ii) a Input load torque set value T of load torque observer L * Rotor angular velocity ω and current i q The output torque current compensation component i ″) q (ii) a Torque current given component i' q And a torque current compensation component i ″) q After addition, the sum is used as a given value i of q-axis torque current q (ii) a q-axis current PI controller inputs q-axis torque current given value i q And current i d And outputting a control voltage U under a q-axis coordinate system q (ii) a A q-axis torque current given value i is input into a d-axis current PI controller d And current i d And outputting control voltage U under d-axis coordinate system d D-axis torque current setpoint i d Equal to 0; the Park inverse transformation module inputs a control voltage U under a d-q axis coordinate system d 、U q And outputs the control voltage U under an alpha-beta axis coordinate system α 、U β (ii) a Input control voltage U of SVPWM module (space vector pulse width modulation module) α 、U β To output pulsesA signal is sent to a three-phase inverter, and the three-phase inverter converts a direct current voltage U dc Converting into three-phase AC power supply U a 、U b 、U c Thereby driving the permanent magnet synchronous motor to operate.
Neglecting the influence of core eddy current and hysteresis loss, etc., adopting i d The method comprises the following steps of (1) performing directional control on a PMSM rotor magnetic field, establishing a mathematical model of the PMSM under a d-q axis rotation coordinate system, wherein a voltage equation is as follows:
Figure BDA0003561850200000041
for adopting i d The salient pole type PMSM vector control system adopts a control mode of 0, and an electromagnetic torque equation is as follows:
Figure BDA0003561850200000042
the PMSM equation of motion is:
Figure BDA0003561850200000043
in the formulae (1), (2) and (3), u d 、u q Voltages of d-q axes, respectively; i.e. i d 、i q Currents of d-q axes, respectively; l is a radical of an alcohol d 、L q Inductances of the d-q axes, respectively; t is e Is an electromagnetic torque; t is a unit of L Is the load torque; r is the resistance of the stator; p is the number of pole pairs of the motor; omega e Is the rotor electrical angular velocity, i.e. angular frequency; ω is the rotor angular velocity, i.e. the mechanical angular velocity of the rotor of the electrical machine; psi f Is a permanent magnet flux linkage; j is the moment of inertia; b is the coefficient of friction; t is time.
Let the angular speed error e of the rotor of the motor be omega * -ω，ω * Is a given rotor angular speed of the motor. The state variables defining the permanent magnet synchronous motor speed control system embodiment 1 are:
Figure BDA0003561850200000051
obtained by the following formulas (2), (3) and (4):
Figure BDA0003561850200000052
equation (5) is simplified to 1.5p ψ f /J，u＝i q The system state space equation of the embodiment 1 can be obtained as follows:
Figure BDA0003561850200000053
selecting a sliding mode surface function as follows:
s＝cx 1 +x 2 (7)
in the formula (7), s is a sliding mode surface, c is a parameter of the sliding mode surface, and c is more than 0. In equation (7), c is a coefficient of the rotor angular velocity error term, and its influence on the control action is mainly similar to a proportional coefficient in PID control, and the value of c also balances the rotor angular velocity error and the rate of change of the rotor angular velocity error, and is usually selected within a range of greater than 0 and less than 1000, for example, c is 60. The derivation of equation (7) can be:
Figure BDA0003561850200000054
the expression of the conventional exponential approximation law is:
Figure BDA0003561850200000055
in the formula (9), sgn () is a sign function, -k 1 sgn(s) is the constant velocity approach term, -k 2 s is an exponential approach term, k 1 、k 2 Two coefficients respectively determine the buffeting of the slip form surface and the motion quality of the approaching process, and k 1 、k 2 Are all greater than 0. In order to improve the response speed of the system, the constant-speed approach term is improved on the basis of the traditional exponential approach rateChanging into a variable speed approach term, the improved approach law is as follows:
Figure BDA0003561850200000056
wherein k is 1 ＞0，k 2 ＞0，1＜k 3 ＜2，k 4 Is greater than 0. When the value of | s | is large,
Figure BDA0003561850200000057
the approach speed of the variable speed approach item is higher, and the approach movement speed of the slip form can be accelerated; when the value of | s | is small,
Figure BDA0003561850200000058
the approach speed of the variable speed approach term is smaller, and the buffeting can be weakened. k is a radical of 4 The value can be selected near the rotor angular speed change rate by referring to the rotor angular speed change rate when the permanent magnet synchronous motor is started under rated load, and further, the value is taken within the range of 80% to 120% of the rotor angular speed change rate; for example, the time taken for starting a permanent magnet synchronous motor from a rated load to a rated rotating speed of 1500r/min is set to be 0.21s, and the average rotor angular speed change rate is 750rad/s 2 It is recommended that k be at this time 4 The value is within the range of 600-900. k is a radical of 3 The larger the shift, the larger k 3 Generally, the value is in the range of 1.05-1.3. In general, the coefficient k 1 And coefficient k 2 The values of (A) are all less than 2000; coefficient k 2 The larger the system state can approach the sliding mode at a greater speed; coefficient k 1 Determining the speed, k, of arrival at the switching plane 1 The smaller the distance across the switching plane and the smaller the jitter. k is a radical of 1 And k 2 Respectively, a variable speed approach term coefficient and an exponential approach term coefficient, because
Figure BDA0003561850200000061
The value of (b) varies around 1, and therefore the coefficient k of the shift approach term in the equation (10) 1 And exponential approximation term coefficient k 2 The setting can be performed according to a method for adjusting the medium-speed approaching term coefficient and the exponential approaching term coefficient in the traditional exponential approaching rate. k is a radical of 3 The speed change coefficient is the speed change coefficient, and the speed change speed is changed according to the size of the speed change coefficient; k is a radical of 4 Is the mobility coefficient, the magnitude of which changes the shift critical point.
Combining formulas (8) and (10), and taking the calculated q-axis given current as the torque current given component i' q Obtaining the given value T of the load torque output by the sliding mode speed controller L * And torque current given component i' q Comprises the following steps:
Figure BDA0003561850200000062
the output of the sliding mode speed controller of the permanent magnet synchronous motor speed control system in the embodiment 1 contains an integral term, and filtering is carried out on the control quantity, so that the buffeting of a system can be weakened, and the steady-state error of the system can be reduced. Defining the Lyapunov function as:
Figure BDA0003561850200000063
from formulas (10) and (12):
Figure BDA0003561850200000064
in formula (13), k 1 ＞0，k 2 ＞0，s·sgn(s)≥0，
Figure BDA0003561850200000065
Therefore, it is
Figure BDA0003561850200000066
The system tracking error can be converged to zero in a limited time, and the system can stably run.
Setting parameters c, k in designing sliding mode speed controller 1 、k 2 、k 3 、k 4 By first determining k 3 、k 4 A value of (d); given value i of q-axis torque current * q Comprising only a given component i 'of the input torque current' q (i.e. theWithout load torque compensation control), and then adjusting the sliding mode surface parameter c and the variable speed approaching term coefficient k from small to large in the sliding mode of the system 1 Until the system generates obvious buffeting, the buffeting suppression and the system state convergence speed are considered on the basis, and the sliding mode surface parameter c and the variable speed approaching term coefficient k are properly reduced 1 A value of (d); finally, the exponential approximation term coefficient k is adjusted primarily based on the rapidity of the system reach segment (e.g., motor start-up phase of step response) while simultaneously suppressing slip mode buffeting 2 And to make appropriate fine adjustments to other parameter values of the sliding mode speed controller.
According to the PMSM electromagnetic torque and the motion equation, the constant value can be regarded as a constant value in a change period for constant step load, namely
Figure BDA0003561850200000071
The angular speed and the load torque of the motor rotor are used as state variables to form a PMSM state equation as follows:
Figure BDA0003561850200000072
based on equation (14), a load torque observer embodiment 1 is established with load torque and motor rotor angular velocity as objects to be observed:
Figure BDA0003561850200000073
in the formula (15), the reaction mixture is,
Figure BDA0003561850200000074
is an observed value of the load torque,
Figure BDA0003561850200000075
is an estimate of the angular velocity of the rotor, g is the feedback gain of the load torque observer,
Figure BDA0003561850200000076
k g is the sliding mode gain of the load torque observer embodiment 1, and the load torque observer embodiment 1 is a sliding mode observer. Motor friction is smaller in specific weight than load torque, and if B is 0 and the influence of friction is ignored, load torque observer embodiment 1 of equation (15) becomes:
Figure BDA0003561850200000077
from (14) and equation (16) when B is 0, the error equation of load torque observer embodiment 1 is obtained as:
Figure BDA0003561850200000078
in the formula (17), the compound represented by the formula (I),
Figure BDA0003561850200000079
for the estimation error of the angular velocity of the rotor,
Figure BDA00035618502000000710
for the observation error of the load torque, and defining the sliding mode surface of the observer as
Figure BDA00035618502000000711
According to the accessibility condition of the sliding mode, the system stability condition of the observer with the formula (16) is k g ≤-|e 2 And g is less than 0.
Based on equation (14), with the load torque and the motor rotor angular velocity as the observation targets, a load torque observer embodiment 2 can be established as follows:
Figure BDA00035618502000000712
motor friction is smaller in specific weight than load torque, and if B is 0 and the influence of friction is ignored, load torque observer embodiment 2 of equation (18) becomes:
Figure BDA00035618502000000713
in the formulae (18) and (19),
Figure BDA00035618502000000714
is an observed value of the load torque,
Figure BDA00035618502000000715
is an estimate of the angular velocity of the rotor, g is the feedback gain of the load torque observer,
Figure BDA0003561850200000081
k W is the proportional gain of load torque observer embodiment 2, load torque observer embodiment 2 being a state observer. According to the formula (14) and the formula (19) when B is 0, the error equation of the load torque observer embodiment 2 is obtained as follows:
Figure BDA0003561850200000082
in the formula (20), the reaction mixture is,
Figure BDA0003561850200000083
for the estimation error of the angular velocity of the rotor,
Figure BDA0003561850200000084
is the load torque observation error. The state observer of equation (19) is an autonomous linear system, at k W < 0, and g < 0, the observer is asymptotically stable. Formula (15) of load torque observer embodiment 1 and formula (18) of load torque observer embodiment 2 both take into account friction factors of the motor, and the addition of small friction damping adversely affects the rapidity of the system response, but can increase the stability on the basis of formula (16) and formula (19), respectively.
In observer embodiment 1 in which expressions (15) and (16) are selected, sliding mode gain k g Is set according to
Figure BDA0003561850200000085
Selection is performed. In the formula (21), alpha is more than or equal to 1; typically, the value of α is selected in the range of 1 to 5, for example, α is selected to be equal to 1.5. Load torque observer embodiment 1 in observing load torque, k g Is too small as | e 2 The observer cannot enter a sliding mode state when l is larger; k is a radical of formula B The absolute value of the load torque is selected to be large enough to ensure that the observer enters a sliding mode state, but the steady-state observation fluctuation of the load torque is increased; k is a radical of g The value of (c) is changed along with the change of the load torque observation error, and the observer stability can be improved and the steady state observation fluctuation of the load torque can be reduced simultaneously.
When observer example 2 of expressions (18) and (19) is selected, proportional gain k W Is set according to
Figure BDA0003561850200000086
A selection is made. In the formula (22), T N Is the rated torque of the motor, beta is more than 0; the value β is generally selected within the range of 1 to 20, and for example, β is 10. When the selection of beta is increased, the steady state fluctuation observed by the load torque is increased, but the tracking overshoot of the torque observation is reduced; when the beta selection is decreased, the steady state fluctuation of the load torque observation becomes small, but the torque observation overshoot amount becomes large.
In the observers represented by equations (15) and (16) or equations (18) and (19), the magnitude of the feedback gain g greatly affects the load torque observation result. The larger the feedback gain g is, the smaller the fluctuation of the observed torque is, but the slower the identification speed of the observed torque is; the smaller the feedback gain g, the faster the observed torque speed, but the greater the observed torque ripple. In consideration of this problem, in the conventional load torque observer, the observation speed and the fluctuation of the load torque are considered together, and the feedback gain g is taken as a median, but this abandons the advantages of small fluctuation when the feedback gain is large and fast observation speed when the feedback gain is small.
The motor sliding mode speed control mainly inhibits the influence of parameter change and external load disturbance on a system by increasing the amplitude of discontinuous terms in a controller, but the increase of the amplitude can cause the inherent buffeting of the sliding mode. In order to solve the contradiction between the buffeting and the disturbance resistance of the sliding mode control system, the observer is used for observing the load disturbance change in real time, and the load torque observed value is subjected to feedforward compensation to the current regulator, so that the amplitude of a discontinuous item in the sliding mode control is reduced, the given torque change caused by the parameter change is weakened, or the system buffeting is caused by the load disturbance. In order to fully utilize the advantages of the feedback gain g in high and low values, according to the load torque set value observed values at two adjacent moments and the magnitude of the load torque set value variable quantity, the feedback gain g is given when the load torque set value changes little and the load torque observed value changes little; when the change of the set value of the load torque is large or the change of the observed value of the load torque is large, a smaller value of the feedback gain g is given to accelerate the observation speed, and finally, the comprehensive result of high observation speed, small fluctuation and stronger stability is obtained by adjusting the feedback gain g.
When the embodiment 1 of the load torque observer or the embodiment 2 of the load torque observer is used in the embodiment 1 of the speed control system of the permanent magnet synchronous motor in the figure 1, the load torque observer sets a given value according to the load torque
Figure BDA0003561850200000091
And load torque observed value
Figure BDA0003561850200000092
Is adjusted in dependence on the rotor angular velocity omega and the current i q Observing the load torque to obtain a new load torque observed value
Figure BDA0003561850200000093
Fig. 2 is a flowchart of an embodiment 1 of a feedback gain automatic adjustment method, and when an embodiment 1 of a load torque observer or an embodiment 2 of the load torque observer is used in an embodiment 1 of a speed control system of a permanent magnet synchronous motor in fig. 1, the feedback gain automatic adjustment is performed. During the periodic control of the primary motor speed, the adjustment of the feedback gain g shown in fig. 2 (b) is later than the load torque observation and the output calculation of the sliding mode speed controller, as follows:
firstly, a load torque observer carries out load torque T according to the value of the existing feedback gain g L Observing to obtain the observed value of the load torque
Figure BDA0003561850200000094
The sliding mode speed controller carries out control operation to obtain a load torque set value
Figure BDA0003561850200000095
At this time
Figure BDA0003561850200000096
Is composed of
Figure BDA0003561850200000097
Figure BDA0003561850200000098
Is composed of
Figure BDA0003561850200000099
Until the next adjustment of the feedback gain g, that time
Figure BDA00035618502000000910
Become into
Figure BDA00035618502000000911
Become into
Figure BDA00035618502000000912
Step two, calculating
Figure BDA00035618502000000913
Figure BDA00035618502000000914
Step III, judging whether delta T is larger than epsilon 2 (ii) a When Δ T is greater than ε 2 Taking feedback gain g equal to g min And withdrawing; when Δ T is equal to or less than ε 2 Then, the step IV is carried out;
step four, judging whether delta T is smaller than epsilon 1 (ii) a When Δ T is less than ε 1 Taking feedback gain g equal to g max And withdrawing; when DeltaT is greater than or equal to epsilon 1 Then the process goes to the fifth step;
step five, the feedback gain g is according to
Figure BDA00035618502000000915
And (6) performing calculation.
Wherein epsilon 1 Comparing thresholds, e, for lower limits of torque variation 2 Comparing threshold values for upper limits of torque variation, and 0 & ltepsilon 1 ＜ε 2 ；g max For high value of feedback gain, g min Is a low value of feedback gain, and g min ＜g max ＜0。
In the periodic control process of the primary motor speed, the adjustment of the feedback gain g shown in (a) of fig. 2 is prior to the observation of the load torque and the output calculation of the sliding mode speed controller, the feedback gain g adjusting method changes the steps from the first step to the fifth step, and changes the steps from the second step to the fourth step, the quitting of the steps is changed into the entering step, and the exiting of the steps is changed into the entering step
Figure BDA0003561850200000101
Figure BDA0003561850200000102
In fig. 2, the sum of the amount of change in the given value of load torque and the amount of change in the observed value of load torque has been obtained 2 times recently
Figure BDA0003561850200000103
Figure BDA0003561850200000104
ΔT L * For the difference between the last 2 load torque setpoints,
Figure BDA0003561850200000105
the difference between the last 2 load torque observations. When Δ T is greater than ε 2 When the feedback gain g is equal to g, the feedback gain g is selected to indicate that the observed value of the load torque has large fluctuation or the observed value of the load torque has large fluctuation due to the change of system model parameters, the change of the set value of the rotor angular speed and the change of the actual value of the rotor angular speed, so that the change of the set value of the load torque is large and the observed value of the load torque has large fluctuation min Carrying out rapid identification and observation on the load torque; when Δ T is less than ε 1 When the feedback gain g is selected to be equal to g, the load torque set value changes little and the state load torque observed value fluctuates little, and the feedback gain g is selected to be equal to g max Carrying out load torque identification and observation mainly based on stability; when DeltaT is greater than or equal to epsilon 1 And is less than or equal to epsilon 2 And then, the feedback gain g is calculated according to the formula (23), so that the feedback gain g is reduced along with the increase of the delta T in the interval, and the adverse effect on the working stability of the torque observer, which is caused by the fact that the feedback gain g is changed violently due to small change of the delta T, is avoided. In FIG. 2,. epsilon 1 、ε 2 The specific value of (a) is related to the sampling control period (cycle time) of the sliding mode speed controller, the permanent magnet synchronous motor and the load condition thereof, and epsilon 2 The value is generally set in a range of less than 5% of the rated torque, for example, 22 N.m for the rated torque, ε 1 ＝0.1N·m，ε 2 0.6N · m. The value of the feedback gain g satisfies g min ＜g max < 0, in general, g min ≥-5000。g min When the value is suddenly changed, the torque observation tracking overshoot of the load torque observer is within the torque observation tracking overshoot limit value; g max The value should be that when the load torque is unchanged and the load torque observer and the sliding mode speed controller are both in a steady state, the sum Delta T of the variation of the given value of the load torque and the variation of the observed value of the load torque is less than epsilon for the last 2 times 1 (ii) a For example, the feedback gain g is selected max ＝-0.5，g min -10. Selecting g min 、g max 、ε 1 、ε 2 The specific method of the value is:
step (1), a load torque observer and a sliding mode speed controller are both in a stable state, and the angular speed of a given rotor and the load torque are kept unchanged;
step (2), the feedback gain g is gradually reduced from a larger value, for example, the feedback gain g is gradually reduced from-0.01, when the steady-state error observed by the load torque reaches the load torque observation steady-state error limit value, the feedback gain g at the moment is determined to be g max ；
Step (3), keeping the given rotor angular speed and the load torque unchanged, and making the feedback gain g equal to g max Continuously measuring the Δ T values n times, and using the average value of the sum of m Δ T values in the n times as the torque variation lower limit comparison threshold ε 1 ；
Step (4), fine-tuning and changing the feedback gain g, keeping the angular speed of the given rotor unchanged and enabling the load torque to be suddenly changed when the load torque observer and the sliding mode speed controller are both in a stable state, and measuring the tracking and adjusting time of the load torque observer on the premise of ensuring that the torque observation tracking overshoot of the load torque observer output observation value is within the torque observation tracking overshoot limit;
and (5) repeating the step (4), and selecting the feedback gain g with the shortest tracking and adjusting time as g min A value; under the normal condition, when the torque observation tracking overshoot is close to the torque observation tracking overshoot limit value, the tracking adjustment time of the load torque observer is short;
and (6) keeping the given rotor angular speed and the load torque unchanged again and enabling the feedback gain g to be equal to g min Continuously measuring the Δ T values n times, and taking the average value of the sum of the m Δ T values in the n times as the torque variation upper limit comparison threshold value ε 2 。
Observing to obtain a load torque observed value
Figure BDA0003561850200000111
Then, the observed value of the load torque is measured
Figure BDA0003561850200000112
Converted into a torque current compensation component i ″) q Feedforward compensation is carried out to the input of a q-axis current PI controller, and a component i 'is given to a torque current output by a sliding mode speed controller' q Compensation is performed. q-axis torque current given value i of q-axis current PI controller * q Comprises the following steps:
Figure BDA0003561850200000113
in formula (24), k q ＝1/(1.5pψ f ) The compensation factor is observed for torque. Comparing the equation (11) with the equation (24), when the load is disturbed or the system parameter is changed, the load torque compensation is not added in the equation (11), and a larger k needs to be selected 1 、k 2 The value is used for providing enough large given current variation to counteract the disturbance of the load or the related influence of the variation of the system parameters so as to ensure that the rotating speed of the motor can be quickly constant; equation (24) feed-forward compensates the load torque observations into the current regulator without requiring a large k 1 、k 2 Under the condition of the value, when the load is disturbed or the system parameter is changed, a given current variable quantity which is large enough is provided to offset the relevant influence of the disturbance of the load or the change of the system parameter, the output pressure of the sliding mode speed controller and the amplitude of a discontinuous term are reduced, and the buffeting of the system is effectively weakened.
When the feedback gain value is fixed, the smaller the feedback gain g is, the larger the oscillation amplitude observed by the load torque is, and the stronger the fluctuation is; the larger the feedback gain g is, the smaller the oscillation amplitude observed by the load torque is, and the higher the observation accuracy is. The automatic gain adjustment algorithm solves the problems that small feedback gains in a load torque observer cause large torque observation fluctuation and large feedback gains are long in convergence time, convergence time and fluctuation amplitude indexes are superior to those of a compromise gain algorithm, a load torque change value can be tracked quickly, observation errors caused by given changes or parameter changes can be reduced quickly, the oscillation amplitude is small, observation precision is high, and a good observation effect is achieved.
When a given rotation speed is changed at a rated load torque, although the actual load torque is not changed, as can be seen from the load torque observer constructed by equations (15), (16) or equations (18), (19), when the rotor angular velocity ω is changed, the observed torque observed value changes even if the load torque is not changed, resulting in an observation error. When the given rotating speed is changed under the rated load torque, the control and regulation process of the sliding mode control system of the permanent magnet synchronous motor is that firstly, the sliding mode speed controller changes according to the given speed to ensure that the output load torque given value T is changed L * Is changed so that the torque current is set to a value i * q Is changed, so that the electromagnetic torque T of the permanent magnet synchronous motor is further changed e The change drives the motor to change the angular speed omega of the rotor; if the feedback gain g is only based on the variation of the observed value of the load torque
Figure BDA0003561850200000114
Automatic adjustment is carried out, and only when the angular speed omega of the rotor changes, the observed value of the load torque is enabled to be
Figure BDA0003561850200000115
After the change, the feedback gain g is adjusted; feedback gain g variation Δ T according to given value of load torque L * And amount of change in observed value of load torque
Figure BDA0003561850200000116
Is automatically adjusted, when the given rotation speed is changed, the given value T of the load torque is caused to be changed L * Change, load torque observed value
Figure BDA0003561850200000117
If no change has occurred, the feedback gain g is adjusted in advance, and the observed value of the load torque is adjusted
Figure BDA0003561850200000121
When the observation error is really generated, the response speed of the observer can be accelerated, and the load rotation can be eliminated (reduced) as soon as possibleObserved value of moment
Figure BDA0003561850200000122
The observation error of the motor speed control is further improved, and the rapidity and the accuracy of the motor speed control are further improved. Similarly, when the system model parameter changes, the given value T of the load torque is caused to change L * Anticipating load torque observations
Figure BDA0003561850200000123
When the feedback gain g changes, the feedback gain g changes according to the variable quantity delta T of the given value of the load torque L * And amount of change in observed value of load torque
Figure BDA0003561850200000124
The feedback gain g can be adjusted in advance by automatic adjustment, the response speed of the observer is accelerated, and the observed value of the load torque is eliminated (reduced) as soon as possible
Figure BDA0003561850200000125
The speed control method and the device can further improve the rapidity and the accuracy of the speed control of the motor. Of course, the observed value is caused if the load is disturbed
Figure BDA0003561850200000126
When the change is made, the user can select the desired mode,
Figure BDA0003561850200000127
when a large change occurs, as can be seen from fig. 2, the feedback gain g can also be automatically adjusted to eliminate (reduce) the load torque observed value as soon as possible
Figure BDA0003561850200000128
Making the load torque observed value
Figure BDA0003561850200000129
Follow up on load torque T as soon as possible L A change in (c).
In the periodic control process of the permanent magnet synchronous motor speed control system embodiment 1, the current k time (or the k step) is calculatedGiven value of load torque T L * Is marked as T L * (k) Observed value of load torque
Figure BDA00035618502000001210
Is marked as
Figure BDA00035618502000001211
The moment k-1 is the previous periodic control process moment of the moment k, and the given value T of the load torque L * Is marked as T L * (k-1), load torque observed value
Figure BDA00035618502000001212
Is marked as
Figure BDA00035618502000001213
The moment k-2 is the previous periodic control process moment of the moment k-1, and the given value T of the load torque L * Is marked as T L * (k-2), load torque observed value
Figure BDA00035618502000001214
Is marked as
Figure BDA00035618502000001215
In fig. 2, (b) load torque observation and speed control are performed first, and then feedback gain automatic adjustment is performed, where the periodic control process of the motor speed is as follows:
step one, detecting the rotor position theta, the rotor angular speed omega and the three-phase current i of the permanent magnet synchronous motor a 、i b And i c ；
Step two, according to three-phase current i a 、i b And i c Clark conversion is carried out on the permanent magnet synchronous motor to obtain current i under an alpha-beta axis coordinate system α 、i β According to the current i α 、i β Carrying out Park conversion on the rotor position theta to obtain a current i under a d-q axis coordinate system d 、i q ；
Thirdly, the load torque observer depends on the rotor angular speed omega and the current i q Observing the load torque to obtain a load torque observed value
Figure BDA00035618502000001216
And a torque current compensation component i ″) q ；
Step four, the sliding mode speed controller gives the angular speed omega according to the input rotor * And the rotor angular speed omega is subjected to control calculation to obtain a load torque set value
Figure BDA00035618502000001217
And torque current given component i' q ；
Step five, feedback gain g of the load torque observer is set according to the load torque L * And load torque observed value
Figure BDA00035618502000001218
Is adjusted;
step six, giving component i 'according to torque current' q And a torque current compensation component i ″) q Calculating to obtain a given value i of q-axis torque current q * (ii) a d-axis current controller according to d-axis torque current set value i d * And the current i under the d-axis coordinate system d PI control operation is carried out on the difference value between the two to obtain a control voltage U under a d-axis coordinate system d (ii) a The q-axis current controller sets a value i according to the q-axis torque current q * And the current i under a q-axis coordinate system q The difference value between the two is subjected to PI control operation to obtain a control voltage U under a q-axis coordinate system q (ii) a According to the control voltage U under a d-q axis coordinate system d 、U q Carrying out Park inverse transformation to obtain a control voltage U under an alpha-beta axis coordinate system α 、U β (ii) a d-axis torque current set value i d * Equal to 0;
step seven, controlling the voltage U under the alpha-beta axis coordinate system α 、U β As input of the SVPWM module, the SVPWM module controls a three-phase inverter to generate a three-phase alternating current power supply U a 、U b 、U c Thereby driving the permanent magnet synchronous motor to operateAnd (7) turning.
In fig. 2, (a) the feedback gain is automatically adjusted first, and then the load torque observation and the speed control are performed, in the above steps, the order of the step five and the steps three and four should be interchanged, that is, the step five is performed first, and the step three and four are performed later.
Fig. 3 is a block diagram of an embodiment 2 of a speed control system of a permanent magnet synchronous motor, specifically, an integral sliding mode control system of a permanent magnet synchronous motor. The difference between the embodiment 2 in fig. 3 and the embodiment 1 in fig. 1 is that the sliding mode speed controller adopts an integral sliding mode control mode, and the observed value of a load torque observer
Figure BDA0003561850200000131
Sent to a sliding mode speed controller, and a load torque observed value is already included in a given q-axis current (a given torque current component) output by the sliding mode speed controller
Figure BDA0003561850200000132
Therefore, the q-axis given current (given torque current component) output by the sliding mode speed controller in embodiment 2 can be directly used as the q-axis given torque current value, and can also play a role in load torque compensation; given value T of load torque output by sliding mode speed controller L Δ Also already including load torque observations
Figure BDA0003561850200000133
The load torque observer directly follows the load torque set value T L Δ The function of the feedback gain automatic adjustment is the same as that of the feedback gain automatic adjustment performed by the feedback gain automatic adjustment method embodiment 1 according to the sum delta T of the variation of the load torque set value and the variation of the load torque observed value in the last 2 times;
Figure BDA0003561850200000134
the state variables defining the permanent magnet synchronous motor speed control system embodiment 2 are:
Figure BDA0003561850200000135
selecting a sliding mode surface function as follows:
s y ＝c y y 1 +y 2 (26)
in the formula (26), c y Is a slip form face parameter, and c y Is greater than 0. C in formula (26) y The coefficient of the rotor angular velocity error integral term, the influence of the size of the coefficient on the control action is mainly similar to the proportional coefficient in PID control, c y The value of (c) is also taken into account for balancing the rotor angular velocity error integral term and the rotor angular velocity error term, under the normal condition y Selected within a range of greater than 0 and less than 100. The derivation of equation (26) can be:
Figure BDA0003561850200000136
on the basis of the traditional exponential approximation law, a new approximation law is adopted as follows:
Figure BDA0003561850200000137
μ 1 、μ 2 、μ 3 、μ 4 exponential rate coefficient for speed sliding mode control, where 1 ＞0，μ 2 ＞0，0＜μ 3 ＜1，μ 4 Is greater than 0. When s y When the l is large, the ratio,
Figure BDA0003561850200000138
the approach speed of the variable speed approach item is higher, and the approach movement speed of the slip form can be accelerated; when s y When the l is small, the ratio of l,
Figure BDA0003561850200000139
the approach speed of the variable speed approach term is smaller, and the buffeting can be weakened. Mu.s 4 The value can refer to the allowable steady-state error, mu, of the rotor angular speed when the permanent magnet synchronous motor stably runs 4 Taking a value not greater than a reciprocal value of the allowable steady state error, and further taking a value within a range of 50% to 100% of the reciprocal value; for example, let the allowable steady-state error of the rotor angular speed of the PMSM be 5rad/s (radian/second), μ 4 The suggested value is not more than 0.2, further, mu 4 And ranges from 0.1 to 0.2. Mu.s 3 Generally around 0.5, and further, mu 3 Typically in the range of 0.4 to 0.6. Generally, the coefficient μ 1 Coefficient of sum μ 2 Are all less than 5000. Mu.s 1 And mu 2 Respectively, a variable speed approaching term coefficient and an exponential approaching term coefficient, because
Figure BDA0003561850200000149
Is changed in the vicinity of 1, and therefore, the coefficient μ of the shift approach term in the equation (28) 1 Coefficient of sum exponential approximation term mu 2 The setting can be performed according to a method for adjusting the medium-speed approaching term coefficient and the exponential approaching term coefficient in the traditional exponential approaching rate. Mu.s 3 Is the migration coefficient, the magnitude of which changes the shift critical point; mu.s 4 The magnitude of the variable speed coefficient changes the variable speed. E in the formula (28) is a natural exponent, i.e., a base of a natural logarithm.
Combining formulas (2), (3) and (27) to obtain:
Figure BDA0003561850200000141
combining formulas (28) and (29), and taking the calculated q-axis given current as a q-axis torque current given value i directly Δ q The given value i of the q-axis torque current output by the controller can be obtained Δ q And a given value T of load torque L Δ Comprises the following steps:
Figure BDA0003561850200000142
in equation (30), the load torque value T L Using the output value of a load torque observer
Figure BDA0003561850200000143
Instead of this. Defining the Lyapunov function as:
Figure BDA0003561850200000144
from formulas (26) and (28):
Figure BDA0003561850200000145
in the formula (32), mu 1 ＞0，μ 2 ＞0，
Figure BDA0003561850200000146
s y ·sgn(s y ) Not less than 0, so
Figure BDA0003561850200000147
The tracking error of the observer can be converged to zero in a limited time, and the system can stably run.
Setting parameter c in designing sliding mode speed controller y 、μ 1 、μ 2 、μ 3 、μ 4 Is carried out by first determining mu 3 、μ 4 A value of (d); let the output value of the load torque observer in equation (30)
Figure BDA0003561850200000148
(i.e., without load torque compensation control), and then adjusting the sliding mode surface parameter c from small to large in the sliding mode of the system y And the variable speed approaching term coefficient mu 1 till the system generates obvious buffeting, and on the basis, the buffeting suppression and the system state convergence speed are considered, and the sliding mode surface parameter c is properly reduced y And a coefficient mu of a shift approximation term 1 A value of (d); finally, the exponential approximation term coefficient μ is adjusted primarily based on the rapidity of the system reach segment (e.g., the motor start-up phase of the step response) while simultaneously suppressing slip mode buffeting 2 And adapting other parameter values of the sliding mode speed controllerWhen fine tuning is performed.
The load torque observer in the permanent magnet synchronous motor speed control system embodiment 2 in fig. 3 still adopts the aforementioned load torque observer embodiment 1, or adopts the aforementioned load torque observer embodiment 2; at the moment, the load torque observer is used for setting the load torque according to the load torque output by the sliding mode speed controller
Figure BDA0003561850200000151
Is adjusted in dependence on the rotor angular velocity omega and the current i q For load torque T L Observing to obtain the observed value of the load torque
Figure BDA0003561850200000152
Fig. 4 is a flowchart of an embodiment 2 of a feedback gain automatic adjustment method, and when the embodiment 1 of the load torque observer or the embodiment 2 of the load torque observer is used in the embodiment 2 of the speed control system of the permanent magnet synchronous motor in fig. 3, the feedback gain automatic adjustment is performed. In FIG. 4,. epsilon 1 The torque change lower limit comparison threshold value is set, epsilon 2 is the torque change upper limit comparison threshold value, and 0 & ltepsilon 1 ＜ε 2 ；g max For high value of feedback gain, g min Is a low value of feedback gain, and g min ＜g max ＜0；ΔT L Δ The difference between the load torque set points for the last 2 times. During the periodic control of the primary motor speed, the adjustment of the feedback gain g shown in fig. 4 (a) precedes the observation of the load torque and the calculation of the output of the sliding mode speed controller by:
step (one), calculating
Figure BDA0003561850200000153
Step (2), judgment
Figure BDA0003561850200000154
Whether or not greater than epsilon 2 (ii) a When in use
Figure BDA0003561850200000155
Greater than epsilon 2 Taking feedback gain g equal to g min And entering the step (5); when DeltaT is less than or equal to epsilon 2 Then, entering the step (3);
step (3), judgment
Figure BDA0003561850200000156
Whether or not less than epsilon 1 (ii) a When in use
Figure BDA0003561850200000157
Less than epsilon 1 Taking feedback gain g equal to g max And entering the step (5); when in use
Figure BDA0003561850200000158
Is greater than or equal to epsilon 1 Entering the step (IV);
step (IV), the feedback gain g is according to
Figure BDA0003561850200000159
Entering step (5) after calculation;
step (5) of the load torque observer to the load torque T L Observing to obtain the observed value of the load torque
Figure BDA00035618502000001510
The sliding mode speed controller carries out control operation to obtain
Figure BDA00035618502000001511
At this time
Figure BDA00035618502000001512
Is composed of
Figure BDA00035618502000001513
Becomes during the next periodic control of motor speed
Figure BDA00035618502000001514
In the periodic control process of the primary motor speed, the adjustment of the feedback gain g shown in (b) of fig. 4 is later than the load torque observation and the output calculation of the sliding mode speed controller, and the specific method is as follows:
step A, a load torque observer measures load torque T L Observing to obtain the observed value of the load torque
Figure BDA00035618502000001515
The sliding mode speed controller carries out control operation to obtain
Figure BDA00035618502000001516
At this time
Figure BDA00035618502000001517
Is composed of
Figure BDA00035618502000001518
Becomes during the next periodic control of motor speed
Figure BDA00035618502000001519
Step B, calculating
Figure BDA00035618502000001520
Step C, judgment
Figure BDA00035618502000001521
Whether or not greater than epsilon 2 (ii) a When in use
Figure BDA00035618502000001522
Greater than epsilon 2 Taking feedback gain g equal to g min And withdrawing; when DeltaT is less than or equal to epsilon 2 Entering the step D;
step D, judgment
Figure BDA00035618502000001523
Whether or not less than epsilon 1 (ii) a When in use
Figure BDA00035618502000001524
Less than epsilon 1 Taking feedback gain g equal to g max And withdrawing; when in use
Figure BDA0003561850200000161
Is greater than or equal to epsilon 1 Entering the step E;
and E, calculating the feedback gain g according to the formula (33) and then quitting.
T L Δ The output items of (1) include given sub-items in a changing state due to the change of system parameters, the change of a given value of the angular speed of the rotor, or the change of an actual value of the angular speed of the rotor
Figure BDA0003561850200000162
Also includes compensating for the fractional load torque observations
Figure BDA0003561850200000163
When | Δ T L Δ | is greater than epsilon 2 In time, the observed value of the load torque shows large fluctuation, or T is caused by the change of system model parameters, the change of a set value of the rotor angular speed and the change of an actual value of the rotor angular speed L Δ Will cause large fluctuations in the load torque observations, the feedback gain g is chosen to be equal to g min Carrying out rapid identification and observation on the load torque; when | Δ T L Δ | is less than epsilon 1 A factor (i.e., T) that indicates that the load torque observation is fluctuating little and will cause the load torque observation to fluctuate significantly L Δ Given partial term in) is small, the feedback gain g is chosen to be equal to g max Carrying out load torque identification and observation mainly based on stability; when | Δ T L Δ | is greater than or equal to epsilon 1 And is less than or equal to epsilon 2 Then, the feedback gain g is calculated according to equation (33) so that the feedback gain g follows | Δ T in this interval L Δ Decrease with increasing | Δ T to avoid the decrease due to | Δ T L Δ The small change of | causes the feedback gain g to generate a severe change, which brings adverse effect on the working stability of the torque observer. In FIG. 4，ε 1 、ε 2 The specific value of (a) is related to the sampling control period (cycle time) of the sliding mode speed controller, the permanent magnet synchronous motor and the load condition thereof, and epsilon 2 The value is generally set in a range of less than 5% of the rated torque, for example, 22 N.m for the rated torque, ε 1 ＝0.1N·m，ε 2 0.6N · m. The value of the feedback gain g satisfies g min ＜g max < 0, in general, g min ≥-5000。g min When the value is suddenly changed, the torque observation tracking overshoot of the load torque observer output observation value is within the torque observation tracking overshoot limit value; g max The value should be taken when the load torque is unchanged, the load torque observer and the sliding mode speed controller are both in a steady state, and the difference value | delta T between the load torque set values for the last 2 times L Δ | is less than epsilon 1 (ii) a For example, the feedback gain g is selected max ＝-0.5，g min ＝-10。
Selecting g min 、g max 、ε 1 、ε 2 The specific method of the value is:
step 1), a load torque observer and a sliding mode speed controller are both in a stable state, and the angular speed of a given rotor and the load torque are kept unchanged;
step 2), the feedback gain g is gradually reduced from a larger value, for example, the feedback gain g is gradually reduced from-0.01, when the steady-state error observed by the load torque reaches the steady-state error limit value observed by the load torque, the feedback gain g at the moment is determined to be g max ；
Step 3) keeping the given rotor angular speed and the load torque constant and making the feedback gain g equal to g max Continuously carrying out n times
Figure BDA0003561850200000164
Measuring the value and dividing n times
Figure BDA0003561850200000165
Maximum m in the measurement
Figure BDA0003561850200000166
The average value of the measured values is used as a torque variation comparison threshold epsilon;
step 4), finely adjusting and changing the feedback gain g, keeping the angular speed of the given rotor unchanged and enabling the load torque to be suddenly changed when the load torque observer and the sliding mode speed controller are both in a stable state, and measuring the tracking and adjusting time of the load torque observer on the premise of ensuring that the torque observation tracking overshoot of the load torque observer output observation value is within the torque observation tracking overshoot limit;
step 5), repeating the step 4), and selecting the feedback gain g value with the shortest tracking and adjusting time as g min A value; under the normal condition, when the torque observation tracking overshoot is close to the torque observation tracking overshoot limit value, the tracking adjustment time of the load torque observer is short;
step 6), keeping the given rotor angular speed and the load torque unchanged again and making the feedback gain g equal to g min Continuously carrying out n times
Figure BDA0003561850200000171
Measuring the value, and measuring the maximum m of n measurements
Figure BDA0003561850200000172
The average value of the sum of the values is used as a torque variation upper limit comparison threshold epsilon 2 。
G is selected from the above min 、g max Value and comparison threshold ε 1 、ε 2 In the specific method, the parameters in the sliding mode speed controller are set and are realized under the condition of load torque compensation control; it is recommended that n is an integer of 20 or more and m is an integer of 5 or more and 0.5n or less.
The output term of the sliding mode speed controller of equation (30) includes the observed value of the compensation polynomial load torque
Figure BDA0003561850200000173
Equivalent to feeding forward the observed value of the load torque to the given value of the current regulator in the formula (24), the observed value of the load torque is generated in the part of the given current which does not need to be output by the sliding mode speed controllerUnder the condition of large adjustment, the related influence caused by the disturbance of the load or the change of system parameters can be counteracted, and the buffeting of the system is effectively weakened. Variation delta T of feedback gain g according to given value of load torque L Δ The algorithm for automatic adjustment avoids the problems of large torque observation fluctuation caused by selecting a fixed small feedback gain and long convergence time caused by selecting a fixed large feedback gain of a load torque observer, can quickly reduce the observation error of the load torque when the given subentry part in the load torque set value is changed or/and the load torque observed value part is changed due to the change of control parameters, model parameters and the like of a system or the disturbance of the load, and improves the observation effect and the rapidity and the accuracy of the motor speed control. The feedback gain g is automatically adjusted when the load torque given value changes, the load torque observed value can not change greatly, but the load torque observed value is caused to have large fluctuation due to the change of the rotor angular speed given value or/and the change of the rotor angular speed actual value to change the given subentry part in the load torque given value or the change of the given subentry part in the load torque given value due to the change of system model parameters, the feedback gain g is adjusted in advance, when the load torque observed value really generates an observation error, the response speed of an observer is accelerated, the observation error of the load torque observed value is quickly reduced, and the rapidity and the accuracy of the motor speed control are further improved.
Embodiment 2 of a system for controlling the speed of a permanent magnet synchronous motor with a sliding mode speed controller in an integral sliding mode control mode, wherein the feedback gain of the system is set according to the load torque L Δ The algorithm for automatically adjusting the variation is applied to the embodiment 1 of the speed control system of the permanent magnet synchronous motor, and the feedback gain is based on the sum of the variation of the given value of the load torque and the variation of the observed value of the load torque for the last 2 times
Figure BDA0003561850200000174
The algorithms for automatic adjustment are the same, so that the phenomenon that the load torque observer selects a fixed small feedback gain to cause large torque observation fluctuation is avoided, and the load torque observer selects a fixed large feedback gainThe feedback gain causes the problem of long convergence time, and can change in control parameters, model parameters and the like of a system or cause disturbance of a load to cause a load torque given value T L Δ When the change (including the change of the given component or/and the change of the compensation component) occurs, the observation error of the load torque is quickly reduced, and the observation effect and the rapidity and the accuracy of the motor speed control are improved. The feedback gain g varies in accordance with the load torque set value T L Δ Automatically adjust to load torque observed value
Figure BDA0003561850200000175
If the observed value of load torque has large fluctuation due to the change of the set value of rotor angular speed or/and the change of the actual value of rotor angular speed, the feedback gain g is adjusted in advance, and if the observed value of load torque has large fluctuation due to the change of the set component of the set value of load torque caused by the change of the system model parameters, the feedback gain g is adjusted in advance, and if the observed value of load torque has large fluctuation, the feedback gain g is adjusted in advance
Figure BDA0003561850200000181
When the observation error is really generated, the response speed of the observer is accelerated, and the observed value of the load torque is quickly reduced
Figure BDA0003561850200000182
The speed control method and the device can further improve the rapidity and the accuracy of the speed control of the motor.
In the periodic control process of the permanent magnet synchronous motor speed control system embodiment 2, the load torque set value calculated at the current k time (or the k step) is set
Figure BDA0003561850200000183
Is marked as
Figure BDA0003561850200000184
Observed value of load torque
Figure BDA0003561850200000185
Is marked as
Figure BDA0003561850200000186
The moment k-1 is the previous periodic control process moment of the moment k, the given value of the load torque
Figure BDA0003561850200000187
Is marked as
Figure BDA0003561850200000188
Observed value of load torque
Figure BDA0003561850200000189
Is marked as
Figure BDA00035618502000001810
The moment k-2 is the previous periodic control process moment of the moment k-1, and the given value of the load torque
Figure BDA00035618502000001811
Is marked as
Figure BDA00035618502000001812
Observed value of load torque
Figure BDA00035618502000001813
Is marked as
Figure BDA00035618502000001814
When the feedback gain g is adjusted according to (a) in fig. 4, the control process includes the following steps:
step one, detecting the rotor position theta, the rotor angular speed omega and the three-phase current i of the permanent magnet synchronous motor a 、i b And i c ；
Step two, according to three-phase current i a 、i b And i c Clark conversion is carried out on the permanent magnet synchronous motor to obtain current i under an alpha-beta axis coordinate system α 、i β According to the current i α 、i β Carrying out Park conversion on the rotor position theta to obtain a current i under a d-q axis coordinate system d 、i q ；
Thirdly, setting the feedback gain g of the load torque observer according to the load torque
Figure BDA00035618502000001815
Is adjusted;
step four, the load torque observer is used for observing the rotor angular speed omega and the current i q Observing the load torque to obtain a load torque observed value
Figure BDA00035618502000001816
Step five, the sliding mode speed controller gives the angular speed omega according to the input rotor * Rotor angular velocity ω and load torque observed values
Figure BDA00035618502000001817
Control calculation is carried out to obtain a given value of load torque
Figure BDA00035618502000001818
Given value of torque current of sum q axis
Figure BDA00035618502000001819
Step six, the d-axis current controller sets a value i according to the d-axis torque current d * And the current i under the d-axis coordinate system d The difference value between the two is subjected to PI control operation to obtain a control voltage U under a d-axis coordinate system d (ii) a The q-axis current controller sets the value according to the q-axis torque current
Figure BDA00035618502000001820
And the current i under a q-axis coordinate system q The difference value between the two is subjected to PI control operation to obtain a control voltage U under a q-axis coordinate system q (ii) a According to the control voltage U under a d-q axis coordinate system d 、U q Carrying out Park inverse transformation to obtain a control voltage U under an alpha-beta axis coordinate system α 、U β ；
Step seven, controlling the voltage U under the alpha-beta axis coordinate system α 、U β As SVThe input of the PWM module is controlled by the SVPWM module to generate a three-phase AC power supply U a 、U b 、U c Thereby driving the permanent magnet synchronous motor to operate.
When the feedback gain g is adjusted according to (b) in fig. 4, in the step of the control process, the contents of the step four and the step five are performed first, and the content of the step three is performed later.
In each of the above embodiments, the torque observation tracking overshoot limit is typically 1% to 10% of the rated torque of the motor, specifically, the torque observation tracking overshoot limit is 2% of the rated torque, or 5% of the rated torque, or 10% of the rated torque, and so on. The load torque is suddenly changed from one fixed value to another fixed value, the moment when the sudden change starts to the moment when the load torque observer outputs the observation value and stably enters the range of the load torque observation steady-state error limit value is a torque observation transition process, and the tracking adjustment time refers to the time of the transition process; the load torque observation steady-state error refers to an error between an observation torque instantaneous value and a load torque when the load torque is unchanged and the load torque observer is in a steady state, and the error comprises an observation error caused by buffeting of the sliding mode observer and an observation error caused by interference reasons other than load fluctuation, or an observation error caused by the observation error caused by buffeting of the rotor angular speed and the observation error caused by interference reasons other than the load fluctuation of the state observer; the load torque observation steady-state error limit value is the maximum absolute value of the load torque observation steady-state error allowed by the load torque observer; the observed load torque steady state error limit is typically 1% to 5% of the rated torque of the motor, specifically, the observed load torque steady state error limit is 1% of the rated torque, or 2% of the rated torque, or 5% of the rated torque, and so on. The torque observation tracking overshoot refers to that the load torque is suddenly changed from one constant value to another constant value, and the observed value output by the load torque observer exceeds the maximum deviation value of the load torque after sudden change. When the observed steady state error of the load torque is within a range proximate to the observed steady state error limit of the load torque, for example, within a range of 95% to 105%, or within a range of 98% to 102%, the observed steady state error of the load torque is considered to increase to the observed steady state error limit of the load torque. The sliding mode speed controller is in a stable state, namely the sliding mode speed controller is stably in a sliding mode; the rotor angular speed steady-state error refers to a difference value between an instantaneous value and a steady-state value of the motor rotor angular speed in a steady state, and the rotor angular speed steady-state error limit value is a maximum absolute value of the rotor angular speed steady-state error allowed by a system. In the load torque observer, the sliding mode observer of the embodiment 1 being in a stable state means that the sliding mode observer is stably in a sliding mode; the state observer of embodiment 2 being in a steady state means that the state observer is in an operating state after the torque observation transient. The rotor angular speed steady-state error refers to a difference value between an instantaneous value and a steady-state value of the motor rotor angular speed in a steady state, and the rotor angular speed steady-state error limit value is a maximum absolute value of the rotor angular speed steady-state error allowed by a system.
The permanent magnet synchronous motor speed control system comprising the permanent magnet synchronous motor integral sliding mode control system can be used for controlling a mining traction motor and can also be used for other permanent magnet synchronous motor application occasions.
In addition to the technical features described in the specification, other technical features related to the invention are the conventional technical skill which is mastered by a person skilled in the art. For example, the q-axis current controller and the d-axis current controller adopt PI controllers for control and selection of controller parameters, the sliding mode speed controller for selection of control parameters, the position and speed detection module uses a rotary transformer or a photoelectric encoder for detection of the rotation angle and the rotation speed of the rotor of the permanent magnet synchronous motor, and the Clarke transformation module, the Park inverse transformation module, the SVPWM module, and the transformation method and the application method of the three-phase inverter, etc., all of which are conventional techniques grasped by those skilled in the art.

Claims (6)

1. An integral sliding mode control system of a permanent magnet synchronous motor comprises a sliding mode speed controller and a load torque observer, and is characterized in that the sliding mode speed controller adopts an integral sliding mode control mode; the load torque observer adjusts the feedback gain according to the change of the load torque given value output by the sliding mode speed controller, and adjusts the feedback gain according to the change of the load torque given value output by the sliding mode speed controllerSub angular velocity ω and current i q Observing the load torque to obtain a load torque observed value
Figure FDA0003561850190000011
Load torque observation value output by load torque observer
Figure FDA0003561850190000012
Is sent to a sliding mode speed controller;
defining a state variable of the sliding mode speed controller as
Figure FDA0003561850190000013
Where ω is the rotor angular velocity, ω * Is a given rotor angular velocity; the sliding mode surface of the sliding mode speed controller is s y ＝c y y 1 +y 2 Wherein c is y Is a slip form surface parameter, and c y Is greater than 0; given value of load torque output by sliding mode speed controller
Figure FDA0003561850190000014
And q-axis torque current setpoint
Figure FDA0003561850190000015
Is composed of
Figure FDA0003561850190000016
Wherein J is the moment of inertia, p is the motor pole pair number, psi f Is a permanent magnet flux linkage, B is the coefficient of friction; coefficient mu 1 Coefficient of μ 2 Coefficient of μ 3 Coefficient of μ 4 Exponential rate of approach coefficient for speed sliding mode control, and mu 1 ＞0，μ 2 ＞0，μ 4 ＞0，0＜μ 3 ＜1；
The load torque observer is
Figure FDA0003561850190000017
Wherein the content of the first and second substances,
Figure FDA0003561850190000018
k W is the proportional gain of the load torque observer and requires k W ＜0；
Figure FDA0003561850190000019
Is an estimate of the rotor angular velocity, g is the feedback gain of the load torque observer and g < 0.
2. The permanent magnet synchronous motor integration sliding-mode control system of claim 1, wherein the load torque observer is used for setting a value according to load torque output by the sliding-mode speed controller
Figure FDA00035618501900000110
The method of adjusting the feedback gain g by the change of (2) is:
step (1), calculating
Figure FDA00035618501900000111
Step (2), judgment
Figure FDA00035618501900000112
Whether or not greater than epsilon 2 (ii) a When in use
Figure FDA00035618501900000113
Greater than epsilon 2 Taking feedback gain g equal to g min And entering the step (5); when DeltaT is less than or equal to epsilon 2 Then, entering the step (3);
step (3), judgment
Figure FDA00035618501900000114
Whether it is small or notIn epsilon 1 (ii) a When in use
Figure FDA00035618501900000115
Less than epsilon 1 Taking feedback gain g equal to g max And entering the step (5); when in use
Figure FDA0003561850190000021
Is greater than or equal to epsilon 1 Then, entering the step (4);
step (4), the feedback gain g is according to
Figure FDA0003561850190000022
Entering step (5) after calculation;
and (5) observing the load torque by the load torque observer according to the value of the feedback gain g to obtain a load torque observed value
Figure FDA0003561850190000023
The sliding mode speed controller carries out control operation to obtain a load torque set value
Figure FDA0003561850190000024
Wherein epsilon 1 Comparing thresholds, e, for lower limits of torque variation 2 Comparing threshold values for upper limits of torque variation, and 0 & ltepsilon 1 ＜ε 2 ；g max For high value of feedback gain, g min Is a low value of feedback gain, and g min ＜g max ＜0。
3. The PMSM integral sliding mode control system of claim 2, wherein g is selected min 、g max 、ε 1 、ε 2 The method of the value is:
step 1), a load torque observer and a sliding mode speed controller are both in a stable state, and the angular speed of a given rotor and the load torque are kept unchanged;
step 2), the feedback gain g is gradually reduced from a larger value, for example, the feedback gain g is gradually reduced from-0.01, when the steady-state error observed by the load torque reaches the steady-state error limit value observed by the load torque, the feedback gain g at the moment is determined to be g max ；
Step 3) keeping the given rotor angular speed and the load torque constant and making the feedback gain g equal to g max Continuously carrying out n times
Figure FDA0003561850190000025
Measuring the value and dividing n times
Figure FDA0003561850190000026
Maximum m in the measurement
Figure FDA0003561850190000027
The average value of the measured values is used as a torque variation comparison threshold epsilon;
step 4), finely adjusting and changing the feedback gain g, keeping the given rotor angular velocity unchanged and making the load torque suddenly change when the load torque observer and the sliding mode speed controller are both in a stable state, and measuring the tracking and adjusting time of the load torque observer on the premise of ensuring that the torque observation tracking overshoot of the output observed value of the load torque observer is within the torque observation tracking overshoot limit;
step 5), repeating the step 4), and selecting the feedback gain g value with the shortest tracking and adjusting time as g min A value;
step 6), keeping the given rotor angular speed and the load torque unchanged again and making the feedback gain g equal to g min Continuously carrying out n times
Figure FDA0003561850190000028
Measuring the value, and measuring the maximum m of n measurements
Figure FDA0003561850190000029
The average value of the sum of the values is used as torque variation upper limit comparisonThreshold value epsilon 2 ；
N is an integer of 20 or more, and m is an integer of 5 or more and 0.5n or less.
4. The PMSM integral sliding mode control system of claim 1, wherein the proportional gain k W According to the following
Figure FDA00035618501900000210
Selecting; wherein, T N Is the rated torque of the motor, beta is more than 0.
5. The integral sliding-mode control system of the permanent magnet synchronous motor according to claim 4, wherein β is more than or equal to 1 and less than or equal to 20.
6. The permanent magnet synchronous motor integral sliding-mode control system according to claim 1, further comprising a q-axis current controller, a d-axis current controller, a Clarke transformation module, a position and speed detection module, a Park transformation module, a Park inverse transformation module, an SVPWM module and a three-phase inverter.
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