CN110752806B - Sliding mode rotating speed control method of built-in permanent magnet synchronous motor with improved approach law - Google Patents
Sliding mode rotating speed control method of built-in permanent magnet synchronous motor with improved approach law Download PDFInfo
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- H—ELECTRICITY
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- H02P6/00—Arrangements for controlling synchronous motors or other dynamo-electric motors using electronic commutation dependent on the rotor position; Electronic commutators therefor
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Abstract
The invention discloses a sliding mode rotating speed control method of a built-in permanent magnet synchronous motor with an improved approach law, which adopts a sliding mode rotating speed controller with the improved approach law as a speed ring, takes the difference value of a given rotor angular speed and an actual rotor angular speed as input, and outputs electromagnetic torque; obtaining d and q axis current set values through maximum torque current ratio control; then acquiring three-phase stator current, and obtaining d-axis and q-axis current actual values through clarke conversion and park conversion; the current loop is controlled by PI, and
the voltage signal is input as a current loop and output as a voltage signal, and the voltage under a static coordinate system is obtained through park inverse transformation; and then, the voltage input voltage space vector pulse width is modulated to obtain a switching signal of the inverter, so that the three-phase stator voltage is output after passing through the inverter and is used for controlling the rotating speed and the torque of the motor to realize speed regulation. The invention can improve the robustness, dynamic response and external load resistance of the speed regulating system, and further weaken the buffeting problem caused by sliding mode control.
Description
Technical Field
The invention relates to a sliding mode rotating speed control method of a built-in permanent magnet synchronous motor with an improved approach law, in particular to sliding mode variable structure control of a speed ring of the built-in permanent magnet synchronous motor, and belongs to the field of motor control.
Background
The built-in permanent magnet synchronous motor has the advantages of small volume, light weight, high efficiency, stable operation, wide speed regulation range and the like, thereby having wide application in various fields such as electric automobiles, trains, aerospace and the like. However, the mathematical model of the interior permanent magnet synchronous motor is a high-order, nonlinear and strongly coupled multivariable system, the high-performance interior permanent magnet synchronous motor needs a speed loop controller to realize quick response, accurate tracking, small overshoot and strong anti-interference capability, the current linear control method of PI is widely applied to the speed loop controller of the interior permanent magnet synchronous motor, but when the internal parameters of the system change or are interfered by the outside, the traditional control method is difficult to meet the dynamic response performance and the anti-interference capability of the interior permanent magnet synchronous motor in corresponding occasions.
In order to solve the problems in the existing rotating speed loop PI control technology, methods such as sliding mode control, self-adaptive control, neural network control and the like are proposed by domestic and foreign people. The sliding mode control is insensitive to parameter change, has strong anti-interference capability, good robustness and other advantages, and is widely applied to speed loop control of the built-in permanent magnet synchronous motor. However, the sliding mode control has an inherent buffeting phenomenon, and for the problem, some researchers use an integral sliding mode surface, a terminal sliding mode surface, a fractional order sliding mode surface and the like to reduce the buffeting problem, and other researchers use conventional approach laws such as an exponential approach law, a variable speed approach law, a power approach law and the like to weaken buffeting to a certain extent, but the buffeting is still large, and the robustness of a motor speed regulating system is influenced.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a sliding mode rotating speed control method of a built-in permanent magnet synchronous motor with an improved approach law, so that the robustness, the dynamic response and the external load resistance of a speed regulating system of the built-in permanent magnet synchronous motor are improved, and the buffeting problem caused by sliding mode control is further weakened.
In order to achieve the purpose, the invention adopts the technical scheme that:
the invention relates to a sliding mode rotating speed control method of a built-in permanent magnet synchronous motor for improving the approach law, which is characterized by being applied to a system consisting of the built-in permanent magnet synchronous motor, an inverter and a coder and being carried out according to the following steps:
step one, detecting the actual rotor angular speed omega of the built-in permanent magnet synchronous motor through an encodermAnd rotor angle information θ;
step two, collecting three-phase alternating current signals i under an abc three-phase static coordinate systema,ib,icAnd obtaining the current i under the two-phase static coordinate system through clarke transformationα,iβApplying the current iα,iβFurther obtaining the actual value i of the current under the rotating coordinate system through park transformationd,iq；
Step three, adopting a sliding mode rotating speed controller with an improved approach law as a speed ring, and setting a given rotor angular speed omegarefAnd said actual rotor angular velocity ωmAs an input, the electromagnetic torque T of the motor is output via the speed loope；
Step four, electromagnetic torque T of the motoreAs input of the maximum torque current ratio control, the given value of the output current is controlled through the maximum torque current ratio control strategy
Step five, mixing
As an input to the q-axis current loop PI controller, will
As input to a d-axis current loop PI controller, to output a voltage signal ud,uq；
The voltage signal u is converted into a voltage signald,uqObtaining the voltage u under the static coordinate system through park inverse transformationα,uβApplying said voltage uα,uβAs input of voltage space vector pulse width modulation, thereby obtaining a switching signal of the inverter;
the switching signal outputs three-phase stator voltage u after passing through the invertera,ub,ucAnd the control device is used for controlling the rotating speed and the torque of the built-in permanent magnet synchronous motor so as to realize speed regulation.
The sliding mode rotating speed control method is also characterized in that: establishing the approximation rule in the third step by using the formula (1):
in formula (1): x is the number of1Is a state variable of the system, and x1＝ωref-ωm(ii) a Delta is a state variable x1The compensation coefficient of (2); s is a slip form surface; alpha is a power coefficient of the absolute value of the sliding mode surface;
is the derivative of the slip form face; k is a radical ofmTo switch gain; μ is the switching gain kmThe amplification factor of (a); k is a radical of1Is a linear gain; k is a radical of2|x1I is a linear compensation gain; sgn (·) is a sign function; k is a radical of1,k2,k0,kn>0，0<μ,α,δ<1。
Electromagnetic torque T in the third stepeIs obtained by the following steps:
step 3.1, designing an integral sliding mode surface s by using the formula (2):
in the formula (2), c0,c1Is a slip formTwo design parameters of a face; and c is0,c1>0；
3.2, establishing an electromagnetic torque equation and a motor motion equation of the motor by using the formula (3):
in formula (3): l isd、LqIs d, q-axis inductance and Ld≠Lq(ii) a p is the number of pole pairs;
is a permanent magnet flux linkage; i.e. idIs a component of the d-axis of the current; i.e. iqIs a component of the current q-axis; j. the design is a squaremThe moment of inertia of the shaft end of the motor; b is a viscous friction coefficient; t isLIs the load torque.
Step 3.3, establishing two state variables x of the system by using the formula (4)1And x2：
In formula (4):
is x1A derivative of (a);
is omegamA derivative of (a);
step 3.4, two state variables x according to the motor motion equation and the system1And x2The state space equation is established using equation (5):
in formula (5): d (t) is a disturbance term of the system; u is a control law; a is a state variable x1The coefficient of (a); b is the coefficient of the control law u,
u＝Te，
and 3.5, selecting a saturation function shown as the formula (6) to replace the sign function:
and 3.6, obtaining the electromagnetic torque T of the motor by using the formula (7) by combining the derivation of the sliding mode surface s, the motor motion equation, the saturation function and the approximation lawe：
Compared with the prior art, the invention has the beneficial effects that:
1. the invention adopts a sliding mode rotating speed control method of a built-in permanent magnet synchronous motor with an improved approach law, and the designed approach law introduces a state variable x1And a slip form surface s, which can be based on the state variable x1The distance between the slip form surface s and the slip form surface is adaptively adjusted to approach the slip form surface, so that the given rotating speed signal can be tracked quickly, buffeting of the system is weakened, and dynamic and static response and robustness of the system are improved.
2. Compared with the traditional PI control method, the method can better and faster track the given rotating speed signal, can better resist external interference when the external load changes, and increases the robustness of the system; compared with the sliding mode rotating speed control method of the traditional approach law, the method overcomes the defect that the state variable x of the traditional approach law is in the approach stage1Can not approach the sliding mode surface quickly, and in the sliding mode stage, the state variable x1The sliding mode surface is repeatedly switched, and finally the sliding mode surface cannot be stabilized at the original point and the like, so that the speed of approaching the sliding mode surface is increased, and the sliding mode surface is fastThe given rotating speed signal is tracked, the buffeting of the system is reduced, and the dynamic and static response performance of the speed regulating system of the built-in permanent magnet synchronous motor is improved.
Drawings
FIG. 1 is a block diagram of a sliding mode rotation speed control system of an interior permanent magnet synchronous motor of the improved approach law of the present invention;
FIG. 2 is a simulation diagram of the sliding mode rotating speed control of the improved approach law and the sliding mode rotating speed control approach sliding mode surface of the traditional approach law, which is provided by the invention;
FIG. 3 is a simulation diagram of sliding mode rotation speed control of improved approach law and sliding mode rotation speed control of traditional PI control and traditional approach law when the invention is in no-load and the initial speed is 1000 rad/min;
FIG. 4 is a simulation diagram of sliding mode rotation speed control of improved approach law and conventional PI control when the load is added at 0.6s and the initial speed is 1000 rad/min;
FIG. 5 is a flow chart of the design of the sliding mode rotational speed controller of the improved approach law of the present invention.
Detailed Description
In this embodiment, as shown in fig. 1, a sliding mode rotation speed control method of a built-in permanent magnet synchronous motor with an improved approach law includes the following specific steps:
step one, detecting the actual rotor angular speed omega of the built-in permanent magnet synchronous motor through an encodermAnd rotor angle information θ;
step two, collecting three-phase alternating current signals i under an abc three-phase static coordinate system by using a current sensora,ib,icAnd obtaining the current i under the two-phase static coordinate system through clarke transformation shown as the formula (1)α,iβWill current iα,iβFurther obtaining the actual value i of the current under the rotating coordinate system through park transformation shown in the formula (2)d,iq；
In formulae (1) and (2): i.e. ia,ib,icIs the three-phase stator winding current id,iqIs the current in two-phase rotation coordinate, iα,iβIs the stator current in a two-phase stationary reference.
Step three, adopting a sliding mode rotating speed controller with an improved approach law as a speed ring, and setting a given rotor angular speed omegarefAnd said actual rotor angular velocity ωmAs an input, the electromagnetic torque T of the motor is output via the speed loopeThe sliding mode rotating speed controller with the improved approach law is specifically designed as follows:
step 3.1, two state variables x of the system are defined by using the formula (3)1And x2：
In formula (3):
is x1Derivative of, ωrefFor a given angular speed of the rotor, ωmFor the actual angular speed of the rotor to be,
is omegamThe derivative of (c).
And 3.2, utilizing a motor motion equation and an electromagnetic torque equation in the formula (4):
in formula (4): l isd、LqIs d, q-axis inductance and Ld≠Lq(ii) a p is the number of pole pairs;
is a permanent magnet flux linkage; i.e. idIs a component of the d-axis of the current; i.e. iqIs a component of the current q-axis; j. the design is a squaremThe moment of inertia of the shaft end of the motor; b is a viscous friction coefficient; t isLIs the load torque.
Step 3.3, obtaining formula (5) from formula (3) and formula (4):
formula (6) is derived from formula (5):
in formula (6): d (t) is a disturbance term of the system; u is a control law; a is a state variable x1The coefficient of (a); b is the coefficient of the control law u,
u＝Te，
step 3.4, designing an integral sliding mode surface s by using the formula (7):
in the formula (7), c0,c1Two design parameters for the slip form face; and c is0,c1>0；
Formula (8) can be derived from formula (7):
and 3.5, introducing the power term technology into the power approximation law to reduce the approaching speed when the system state approaches the sliding mode surface, and finally stabilizing the system state at the origin to be beneficial to weakening buffeting of the system. The expression of the power approximation law is shown in formula (9):
in formula (9): alpha and beta are power approximation law design parameters.
Step 3.6, the exponential approaching law mainly approaches by an exponential term in an approaching movement stage, the approaching speed is high, the dynamic quality is improved, but in a sliding mode stage, a switching band is in a band shape and is switched back and forth on a sliding mode surface, the switching band cannot approach to an original point but approaches to a buffeting of the original point, so that the system is possibly excited without considering a high-frequency part in the modeling process, and the stability of the system is seriously influenced. The expression of the exponential approximation law is shown in formula (10):
in formula (10): epsilon and eta are design parameters of exponential approximation law.
And 3.7, designing an improved approximation law by using a formula (11) according to the advantages of the exponential approximation law and the power approximation law:
in formula (11): x is the number of1Is a state variable of the system, and x1＝ωref-ωm(ii) a Delta is a state variable x1The compensation coefficient of (2); s is a slip form surface; alpha is a power coefficient of the absolute value of the sliding mode surface;
is the derivative of the slip form face; k is a radical ofmTo switch gain; μ is the switching gain kmThe amplification factor of (a); k is a radical of1Is a linear gain; k is a radical of2|x1Is a line |A linear compensation gain; sgn (·) is a sign function; k is a radical of1,k2,k0,kn>0，0<μ,α,δ<1。
And 3.8, selecting a saturation function shown as the formula (12) to replace a sign function:
step 3.9, the control law of the sliding mode rotating speed controller obtained by the formula (6), the formula (11) and the formula (12) is shown as the formula (13):
step 3.10, in order to prove the stability of the sliding mode rotating speed controller for improving the approach law, a Lyapunov function shown in the formula (14) is selected:
formula (15) can be obtained by deriving formula (14):
the sliding mode rotation speed controller of the approximation rule is stable according to the formula (15).
In summary, in the specific implementation process, the sliding mode rotation speed controller of the present invention sets the rotor angular speed ω to a given valuerefAnd the actual rotor angular velocity ωmAs an input signal, the speed loop outputs the electromagnetic torque T of the motore. Introducing a state variable x in the design of sliding mode surface1The requirement on an acceleration signal in the control quantity is avoided, and the steady-state error of the system is reduced; the advantages of exponential approximation law and power approximation law are used for reference in the design of approximation law, and a state variable x is introduced1And a slip form surface s, which can be based on the state variable x1Is smooth and slipperyThe distance between the die surfaces s is adaptively adjusted to approach the speed, and finally, the original point is stabilized, and the buffeting of the system is reduced, so that the robustness of the system is improved; meanwhile, a continuous saturation function sat(s) is adopted to replace a sign function sgn(s) in a conventional approach law, and buffeting of the system is further reduced. The design steps of the sliding mode rotating speed controller with the improved approach law are shown in fig. 5.
Step four, electromagnetic torque T of the motoreAs input of the maximum torque current ratio control, the given value of the output current is controlled through the maximum torque current ratio control strategy
Wherein,
can be calculated from equations (16) and (17):
step five, mixing
As an input to the q-axis current loop PI controller, will
As input to a d-axis current loop PI controller, to output a voltage signal ud,uq；
Will voltage signal ud,uqObtaining the voltage u under the static coordinate system through the park inverse transformation shown in the formula (18)α,uβVoltage u toα,uβAs input of voltage space vector pulse width modulation, thereby obtaining a switching signal of the inverter;
the switching signal passes through the inversePost-inverter output three-phase stator voltage ua,ub,ucAnd the control device is used for controlling the rotating speed and the torque of the built-in permanent magnet synchronous motor so as to realize speed regulation.
Fig. 2 is a simulation diagram of the sliding mode rotating speed control of the improved approach law provided by the present invention and the sliding mode rotating speed control of the conventional approach law approaching the sliding mode surface, and it can be seen that the sliding mode rotating speed control of the improved approach law provided by the present invention has a higher speed approaching the sliding mode surface than the sliding mode rotating speed control of the conventional approach law, and can be stabilized at the origin to reduce the buffeting of the system.
Fig. 3 is a simulation diagram of sliding mode rotating speed control of the improved approximation rule and sliding mode rotating speed control of the traditional PI control and the traditional approximation rule when the initial speed is 1000rad/min, which shows that the sliding mode rotating speed control of the improved approximation rule of the invention has less overshoot, faster dynamic response, can quickly reach stable rotating speed and has better rotating speed tracking performance.
FIG. 4 is a simulation diagram of sliding mode rotation speed control of the improved approximation rule and traditional PI control when the initial speed of the sliding mode rotation speed control is 1000rad/min and a load is 10 N.m after 0.6s is added, and shows that the sliding mode rotation speed control of the improved approximation rule can better resist external load interference.
Claims (2)
1. A sliding mode rotating speed control method of a built-in permanent magnet synchronous motor for improving the approach law is characterized by being applied to a system consisting of the built-in permanent magnet synchronous motor, an inverter and an encoder and comprising the following steps:
step one, detecting the actual rotor angular speed omega of the built-in permanent magnet synchronous motor through an encodermAnd rotor angle information θ;
step two, collecting three-phase alternating current signals i under an abc three-phase static coordinate systema,ib,icAnd obtaining the current i under the two-phase static coordinate system through clarke transformationα,iβApplying the current iα,iβFurther obtaining the actual value i of the current under the rotating coordinate system through park transformationd,iq；
Step three, adopting a sliding mode rotating speed controller with an improved approach law as a speed ring, and setting a given rotor angular speed omegarefAnd said actual rotor angular velocity ωmAs an input, the electromagnetic torque T of the motor is output via the speed loope；
Establishing the approximation rule in the third step by using the formula (1):
in formula (1): x is the number of1Is a state variable of the system, and x1＝ωref-ωm(ii) a Delta is a state variable x1The compensation coefficient of (2); s is a slip form surface; alpha is a power coefficient of the absolute value of the sliding mode surface;
is the derivative of the slip form face; k is a radical ofmTo switch gain; μ is the switching gain kmThe amplification factor of (a); k is a radical of1Is a linear gain; k is a radical of2|x1I is a linear compensation gain; sgn (·) is a sign function; k is a radical of1,k2,k0,kn>0，0<μ,α,δ<1；
Step four, electromagnetic torque T of the motoreAs input of the maximum torque current ratio control, the given value of the output current is controlled through the maximum torque current ratio control strategy
Step five, mixing
As an input to the q-axis current loop PI controller, will
As input to a d-axis current loop PI controller, to output a voltage signal ud,uq；
The voltage signal u is converted into a voltage signald,uqObtaining the voltage u under the static coordinate system through park inverse transformationα,uβApplying said voltage uα,uβAs input of voltage space vector pulse width modulation, thereby obtaining a switching signal of the inverter;
the switching signal outputs three-phase stator voltage u after passing through the invertera,ub,ucAnd the control device is used for controlling the rotating speed and the torque of the built-in permanent magnet synchronous motor so as to realize speed regulation.
2. The sliding mode rotational speed control method according to claim 1, characterized in that the electromagnetic torque T in the third stepeIs obtained by the following steps:
step 3.1, designing an integral sliding mode surface s by using the formula (2):
in the formula (2), c0,c1Two design parameters for the slip form face; and c is0,c1>0；
3.2, establishing an electromagnetic torque equation and a motor motion equation of the motor by using the formula (3):
in formula (3): l isd、LqIs d, q-axis inductance and Ld≠Lq(ii) a p is the number of pole pairs;
is a permanent magnet flux linkage; i.e. idIs a component of the d-axis of the current;iqis a component of the current q-axis; j. the design is a squaremThe moment of inertia of the shaft end of the motor; b is a viscous friction coefficient; t isLIs the load torque;
step 3.3, establishing two state variables x of the system by using the formula (4)1And x2：
In formula (4):
is x1A derivative of (a);
is omegamA derivative of (a);
step 3.4, two state variables x according to the motor motion equation and the system1And x2The state space equation is established using equation (5):
in formula (5): d (t) is a disturbance term of the system; u is a control law; a is a state variable x1The coefficient of (a); b is the coefficient of the control law u,
u＝Te，
and 3.5, selecting a saturation function shown as the formula (6) to replace the sign function:
and 3.6, obtaining the electromagnetic torque T of the motor by using the formula (7) by combining the derivation of the sliding mode surface s, the motor motion equation, the saturation function and the approximation lawe：
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