CN111181468B - Method for determining control parameter stability domain of finite time control BBMC speed regulation system - Google Patents

Method for determining control parameter stability domain of finite time control BBMC speed regulation system Download PDF

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CN111181468B
CN111181468B CN202010064506.4A CN202010064506A CN111181468B CN 111181468 B CN111181468 B CN 111181468B CN 202010064506 A CN202010064506 A CN 202010064506A CN 111181468 B CN111181468 B CN 111181468B
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CN111181468A (en
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张瑞瑞
肖华根
陈娟
姜海鹏
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Hunan University of Science and 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
    • H02P23/00—Arrangements or methods for the control of AC motors characterised by a control method other than vector control
    • H02P23/0004—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust 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
    • 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
    • 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
    • H02P2207/01—Asynchronous machines

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Abstract

The invention discloses a method for determining a control parameter stability domain of a finite time control BBMC speed regulation system, which comprises the following steps: establishing a state differential equation of the BBMC speed regulation system by taking inductive current, capacitor voltage and output current in the BBMC as state variables; obtaining a dynamic equation of the system according to the state differential equation; designing a control function of the BBMC speed regulating system according to the dynamic equation of the system; obtaining the duty ratio of a power switch tube in the BBMC according to a control function and a finite time control principle; obtaining a discrete iteration mapping model of the BBMC inverter stage according to the duty ratio; establishing a discrete iteration mapping model of the three-phase asynchronous motor; obtaining a discrete iteration mapping model of the BBMC speed regulating system based on finite time control according to the discrete iteration mapping model of the BBMC inverter stage and the discrete iteration mapping model of the three-phase asynchronous motor; and obtaining the value range of the control parameter when the BBMC speed regulation system stably operates through numerical simulation according to the obtained discrete iterative mapping model.

Description

Method for determining control parameter stability domain of finite time control BBMC speed regulation system
Technical Field
The invention relates to the field of asynchronous motor speed regulation, in particular to a method for determining a control parameter stability region of a finite time control BBMC speed regulation system.
Background
The Buck-Boost matrix converter (BBMC) is a novel power converter with high voltage transmission ratio and capable of directly outputting high-quality sine waves, and is suitable for being applied to an asynchronous motor speed regulating system as a power converter.
However, to realize high-performance speed regulation control of the BBMC-based asynchronous motor speed regulation system, an effective control strategy must be adopted for the research. The finite time control is a control method which can make a closed-loop control system converge in finite time, has extremely strong dynamic stability and disturbance resistance, and is very suitable for being used in the control of an asynchronous motor speed regulating system based on BBMC. When the speed regulating system is controlled by adopting limited time control, the value taking problem of a plurality of control parameters is involved, and if the control parameters are not selected properly, the expected control effect is difficult to achieve.
Disclosure of Invention
In order to solve the technical problem, the invention provides a method for determining a control parameter stability region of a limited time control BBMC speed regulation system, and the value range of relevant control parameters can be determined when the system stably operates.
The technical scheme for solving the technical problems comprises the following steps:
step (1): establishing a state differential equation of the BBMC speed regulation system by taking inductive current, capacitor voltage and output current in the BBMC as state variables;
step (2): obtaining a dynamic equation of the BBMC speed regulating system according to the state differential equation obtained in the step (1);
and (3): designing a control function of the BBMC speed regulating system according to the dynamic equation of the BBMC speed regulating system obtained in the step (2);
and (4): obtaining the duty ratio of a power switching tube in the BBMC according to the control function of the BBMC speed regulation system obtained in the step (3) and a finite time control principle;
and (5): obtaining a discrete iteration mapping model of the BBMC inverter stage according to the duty ratio of the power switch tube in the BBMC obtained in the step (4);
and (6): establishing a discrete iteration mapping model of the three-phase asynchronous motor;
and (7): obtaining a discrete iteration mapping model of the BBMC speed regulating system based on finite time control according to the discrete iteration mapping model of the BBMC inverter stage obtained in the step (5) and the discrete iteration mapping model of the three-phase asynchronous motor obtained in the step (6);
and (8): and (4) obtaining the value range of the control parameter when the BBMC speed regulation system stably operates through numerical simulation according to the discrete iterative mapping model of the BBMC speed regulation system based on the finite time control obtained in the step (7).
Preferably, in the step (1), the inductive current, the capacitor voltage and the output current in the BBMC are used as state variables, and a state differential equation of the asynchronous motor speed regulating system based on the BBMC is established, specifically:
Figure BDA0002375543290000021
wherein: i.e. iL、uCAnd ioRespectively representing inductive current, capacitor voltage and output current in BBMC, E is input voltage of BBMC inverter stage, u is output voltage of BBMC inverter stageDFor the common terminal voltage of three-phase stator winding of asynchronous motor, L is BBMC main circuit inductance, C is BBMC main circuit capacitance, R is1And L1Respectively is the equivalent resistance and the equivalent inductance of the single-phase winding of the asynchronous motor, d is the duty ratio of a power switch in the BBMC, and d belongs to [0,1 ]]。
Preferably, step (2) is to obtain a dynamic equation of the system according to the state differential equation obtained in step (1), specifically:
let the reference output voltage of BBMC be urefThe error of the output voltage of the BBMC is obtained as follows:
x1＝uC-uref (2)
according to the formula (1) and the formula (2), the dynamic equation of the system is obtained as follows:
Figure BDA0002375543290000031
wherein: x is the number of1、x2、x3、iL、uCAnd ioAre all variables of time t.
Preferably, the step (3) designs a control function of the BBMC speed regulation system according to the dynamic equation of the system obtained in the step (2), specifically:
step (3-1): defining a time scale coordinate transformation as:
Figure BDA0002375543290000032
wherein: and t is Ks, and K is a coordinate transformation coefficient.
Step (3-2): and (3) according to the time scale coordinate transformation formula shown in the formula (4), transforming the formula (3) to obtain:
Figure BDA0002375543290000041
step (3-3): the control function of the BBMC governor system obtained according to equation (5) is:
Figure BDA0002375543290000042
preferably, the step (4) obtains the duty ratio of the power switching tube in the BBMC according to the control function and the finite time control principle of the BBMC speed control system obtained in the step (3), and specifically comprises:
firstly, according to the finite time control principle, a system control function f(s) is determined as follows:
Figure BDA0002375543290000043
wherein: satαAs a function of saturation, k1、k2、k3、α1、α2And alpha3Are control parameters.
Then, it is obtained from equations (6) and (7):
Figure BDA0002375543290000044
finally, according to the formula (4) and the formula (8), the duty ratio of the power switch tube in the BBMC is obtained as follows:
Figure BDA0002375543290000045
wherein:
Figure BDA0002375543290000046
preferably, the step (5) obtains a discrete iterative mapping model of the BBMC inverter stage according to the duty ratio of the power switching tube in the BBMC obtained in the step (4), specifically:
the method comprises the following steps of establishing a differential equation of state by taking inductive current and capacitor voltage in BBMC as state variables:
Figure BDA0002375543290000051
according to the formula (9), the on-time T of the power switch tube in the nth switching period T can be obtainedonAnd off time toffRespectively is as follows:
Figure BDA0002375543290000052
wherein: dnAnd represents the duty ratio of the power switch tube in the BBMC in the nth switching period T.
According to equations (10) and (11), the discrete iterative mapping model for the BBMC inversion stage is obtained as follows:
Figure BDA0002375543290000053
wherein: u. ofC(n+1)And iL(n+1)Respectively representing the capacitor voltage and the inductor current i in the (n +1) T moment BBMCo(n)Denotes the output current of BBMC at time nT, M, N and ω are intermediate variables, and
Figure BDA0002375543290000054
uC(n)and iL(n)Respectively representing the capacitor voltage and the inductor current at time nT BBMC.
Preferably, the step (6) of establishing a discrete iterative mapping model of the three-phase asynchronous motor specifically comprises:
establishing a state differential equation of the three-phase asynchronous motor on a two-phase static coordinate system as follows:
Figure BDA0002375543290000061
wherein: u. ofsαAnd usβRepresenting the stator voltage, i, of the motor in two-phase stationary coordinates, respectivelysαAnd isβRepresenting the stator currents of the motor in two stationary phases, ΨrαAnd ΨrβRespectively representing the rotor flux, T, of the motor in two-phase stationary coordinatesLRepresenting motor load torque, ωrRepresenting the angular velocity, L, of the rotor of the machines、Lr、Lm、Rs、Rr、npAnd J respectively represent the self inductance of the stator, the self inductance of the rotor, the mutual inductance of the stator and the rotor, the resistance of the stator, the resistance of the rotor, the pole pair number and the moment of inertia of the motor,
Figure BDA0002375543290000062
representing the leakage coefficient, T, of the motorr＝Lr/RrRepresenting the rotor electromagnetic time constant.
Discretizing the state differential equation shown in the formula (13) by a Runge-Kutta method to obtain:
Figure BDA0002375543290000063
wherein:
Figure BDA0002375543290000064
is the state vector at time (n +1) T,
Figure BDA0002375543290000065
is the state vector at time nT, K1、K2、K3And K4Are all intermediate variables, and K1＝f(xn,yn)，
Figure BDA0002375543290000066
K4＝f(xn+TK0,yn+TK3)，
Figure BDA0002375543290000071
usα(n)And usβ(n)Respectively representing the stator voltage i of the motor at the moment nT on the two-phase stationary coordinatesα(n)And isβ(n)Representing the stator currents of the machine at the moment nT in two-phase stationary coordinates, Ψrα(n)And Ψrβ(n)Respectively representing the rotor flux linkage, omega, at time nT on the two-phase stationary coordinater(n)Representing the angular velocity of the rotor of the machine at time nT.
Preferably, the step (7) obtains a discrete iteration mapping model of the BBMC speed regulation system based on finite time control according to the discrete iteration mapping model of the BBMC inverter stage obtained in the step (5) and the discrete iteration mapping model of the three-phase asynchronous motor obtained in the step (6), and specifically comprises:
Figure BDA0002375543290000081
wherein:
Figure BDA0002375543290000082
and
Figure BDA0002375543290000083
respectively representing the three-phase capacitor voltages at time (n +1) T BBMC,
Figure BDA0002375543290000084
and
Figure BDA0002375543290000085
respectively represents three-phase inductive current in the BBMC at the (n +1) T moment,
Figure BDA0002375543290000086
Figure BDA0002375543290000087
and
Figure BDA0002375543290000088
respectively represents the conduction time of the three-phase power switch tube in the n-th switch period T,
Figure BDA0002375543290000089
and
Figure BDA00023755432900000810
respectively showing the turn-off time of the three-phase power switch tube in the BBMC in the nth switching period T,
Figure BDA00023755432900000811
and
Figure BDA00023755432900000812
respectively representing the duty ratio of three-phase power switching tubes in the BBMC in the nth switching period T, MA、MB、MC、NA、NBAnd NCAre all intermediate variables, and
Figure BDA00023755432900000813
Figure BDA00023755432900000814
Figure BDA00023755432900000815
Figure BDA00023755432900000816
preferably, the step (8) obtains the value range of the control parameter when the BBMC speed regulation system operates stably through numerical simulation according to the discrete iterative mapping model of the BBMC speed regulation system based on finite time control obtained in the step (7), specifically:
step (8-1): setting system parameters, including: BBMC main circuit inductance L, main circuit capacitance C, motor stator self-inductance LsSelf-inductance of rotor LrStator and rotor mutual inductance LmStator resistor RsRotor resistance RrN number of pole pairspMoment of inertia J, load torque TLPower, powerSwitching period T and maximum iteration number N of switching tubemaxThree-phase capacitor reference voltage in BBMC
Figure BDA0002375543290000091
Period T of reference voltage of capacitor0(and satisfy T)0kT, k being a positive integer), a control parameter k1、k2、k3、α1、α2And alpha3And increasing the change parameter delta X, and taking 1 as the initial value of the counting variable q.
Step (8-2): first order the controlled variable Y1～Y6Respectively representing control parameters k1、k2、k3、α1、α2And alpha3；
Step (8-3): let control variable YqThe initial value of the variable parameter X is set to be 0, and other control variables are kept unchanged;
step (8-4): calculating the state variable i at the time (n +1) T by equation (15)α(n+1)And iβ(n+1)；
Step (8-5): judgment of iα(n+1)And iβ(n+1)Whether or not to satisfy i simultaneouslyα(n+1)＝iα(n)And iβ(n+1)＝iβ(n)If yes, the system is in a stable state, and the step (8-8) is executed; otherwise, executing the step (8-6);
step (8-6): judging whether the iteration number N is more than NmaxIf yes, executing the step (8-7); otherwise, adding 1 to the iteration number n, and returning to the step (8-4);
step (8-7): adding delta X to the change parameter X, enabling the iteration number n to return to 1, and returning to the step (8-4);
step (8-8): let the corresponding change parameter value X at this time be the lower limit value of the parameter stability domain, that is: xmin＝X；
Step (8-9): adding delta X to the variation parameter X, and enabling the iteration number n to return to 1;
step (8-10): calculating the state variable i at the time (n +1) T by equation (15)α(n+1)And iβ(n+1)；
Step (8-11): judgment of iα(n+1)And iβ(n+1)Whether or not to satisfy i simultaneouslyα(n+1)＝iα(n)And iβ(n+1)＝iβ(n)If yes, the system is in a stable state, and the step (8-12) is executed; otherwise, executing the step (8-13);
step (8-12): let variable XmaxX, then returning to step (8-9);
step (8-13): judging whether the iteration number N is more than NmaxIf yes, executing the step (8-14); otherwise, adding 1 to the iteration number n, and returning to the step (8-10);
step (8-14): let Yqmin＝Xmin，Yqmax＝XmaxObtaining the control variable Y of the speed regulating system when the speed regulating system operates stablyqHas a value range of (Y)qmin，Yqmax)；
Step (8-15): judging whether the counting variable q is smaller than 6, if so, executing the step (8-16), otherwise, executing the step (8-17);
step (8-16): adding 1 to the counting variable q, and returning to the step (8-3);
step (8-17): the resulting controlled variable YqValue range (Y)qmin，Yqmax) (q 1, 2.. 6) corresponds to the control parameter k, respectively1、k2、k3、α1、α2And alpha3The specific value of each control parameter is determined according to the value range of each control parameter, and the stable operation of the BBMC speed regulating system based on the limited time control can be realized.
Compared with the prior art, the invention has the technical effects that: the method takes inductive current, capacitor voltage and output current in a Buck-Boost matrix converter (BBMC) as state variables, and establishes a state differential equation of an asynchronous motor speed regulating system based on the BBMC; obtaining a dynamic equation of the system according to the state differential equation; designing a control function of the BBMC speed regulating system according to the dynamic equation of the system; obtaining the duty ratio of a power switch tube in the BBMC according to the control function and the finite time control principle of the BBMC speed regulating system; obtaining a discrete iteration mapping model of a BBMC inverter stage according to the duty ratio of the power switch tube in the BBMC; establishing a discrete iteration mapping model of the three-phase asynchronous motor; obtaining a discrete iteration mapping model of the BBMC speed regulating system based on finite time control according to the discrete iteration mapping model of the BBMC inverter stage and the discrete iteration mapping model of the three-phase asynchronous motor; and obtaining the value range of the relevant control parameters when the BBMC speed regulating system based on the finite time control realizes stable operation through numerical simulation according to the discrete iterative mapping model of the BBMC speed regulating system based on the finite time control. The invention adopts a finite time control strategy aiming at an asynchronous motor speed regulating system taking BBMC as a power converter, determines the stable domain range of control parameters of the system on the premise of ensuring the stable operation of the system, and can ensure the stable operation of the BBMC speed regulating system.
Drawings
FIG. 1 is a topological structure diagram of a BBMC-based asynchronous motor speed regulation system of the present invention;
FIG. 2 is a flow chart of the present invention;
FIG. 3 is a flow chart of determining the value range of the control parameter of the BBMC speed control system discrete iterative mapping model based on finite time control in the present invention.
Detailed Description
Fig. 1 is a topology structure diagram of an asynchronous motor speed regulation system based on BBMC according to an embodiment of the present invention. The BBMC adopts the structural form of an AC-DC-AC two-stage converter, the rectifying stage of the BBMC is an 3/2-phase matrix converter, and the inverter stage adopts the structural form of a three-phase Buck-Boost inverter and consists of three Buck-Boost DC/DC converters with the same structure; and three-phase stator windings of the three-phase asynchronous motor are respectively connected to three output ends of the BBMC.
Referring to fig. 2, a flow chart of a method for determining a control parameter stability region of a finite time control BBMC speed control system provided by the invention is shown. The method comprises the following steps:
step (1): the method comprises the following steps of establishing a state differential equation of an asynchronous motor speed regulating system based on BBMC by taking inductive current, capacitor voltage and output current in BBMC as state variables, wherein the state differential equation specifically comprises the following steps:
Figure BDA0002375543290000111
wherein: i.e. iL、uCAnd ioRespectively representing inductive current, capacitor voltage and output current in BBMC, E is input voltage of BBMC inverter stage, u is output voltage of BBMC inverter stageDFor the common terminal voltage of three-phase stator winding of asynchronous motor, L is BBMC main circuit inductance, C is BBMC main circuit capacitance, R is1And L1Respectively is the equivalent resistance and the equivalent inductance of the single-phase winding of the asynchronous motor, d is the duty ratio of a power switch in the BBMC, and d belongs to [0,1 ]]。
Step (2): obtaining a dynamic equation of the system according to the state differential equation obtained in the step (1), specifically:
let the reference output voltage of BBMC be urefThe error of the output voltage of the BBMC is obtained as follows:
x1＝uC-uref (2)
according to the formula (1) and the formula (2), the dynamic equation of the BBMC speed regulating system is obtained as follows:
Figure BDA0002375543290000121
wherein: x is the number of1、x2、x3、iL、uCAnd ioAre all variables of time t.
And (3): designing a control function of the BBMC speed regulating system according to the dynamic equation of the BBMC speed regulating system obtained in the step (2), which specifically comprises the following steps:
step (3-1): defining a time scale coordinate transformation as:
Figure BDA0002375543290000122
wherein: and t is Ks, and K is a coordinate transformation coefficient.
Step (3-2): and (3) according to the time scale coordinate transformation formula shown in the formula (4), transforming the formula (3) to obtain:
Figure BDA0002375543290000131
step (3-3): the control function of the BBMC governor system obtained according to equation (5) is:
Figure BDA0002375543290000132
and (4): and (4) obtaining the duty ratio of a power switching tube in the BBMC according to the control function of the BBMC speed regulating system obtained in the step (3) and the finite time control principle, specifically:
firstly, according to the finite time control principle, a system control function f(s) is determined as follows:
Figure BDA0002375543290000133
wherein: satαAs a function of saturation, k1、k2、k3、α1、α2And alpha3Are control parameters.
Then, it is obtained from equations (6) and (7):
Figure BDA0002375543290000134
finally, according to the formula (4) and the formula (8), the duty ratio of the power switch tube in the BBMC is obtained as follows:
Figure BDA0002375543290000135
wherein:
Figure BDA0002375543290000136
and (5): obtaining a discrete iteration mapping model of the BBMC inverter stage according to the duty ratio of the power switching tube in the BBMC obtained in the step (4), specifically:
the method comprises the following steps of establishing a differential equation of state by taking inductive current and capacitor voltage in BBMC as state variables:
Figure BDA0002375543290000141
according to the formula (9), the on-time T of the power switch tube in the nth switching period T can be obtainedonAnd off time toffRespectively is as follows:
Figure BDA0002375543290000142
wherein: dnAnd represents the duty ratio of the power switch tube in the BBMC in the nth switching period T.
According to equations (10) and (11), the discrete iterative mapping model for the BBMC inversion stage is obtained as follows:
Figure BDA0002375543290000143
wherein: u. ofC(n+1)And iL(n+1)Respectively representing the capacitor voltage and the inductor current i in the (n +1) T moment BBMCo(n)Denotes the output current of BBMC at time nT, M, N and ω are intermediate variables, and
Figure BDA0002375543290000144
uC(n)and iL(n)Respectively representing the capacitor voltage and the inductor current at time nT BBMC.
And (6): establishing a discrete iteration mapping model of the three-phase asynchronous motor, specifically:
firstly, establishing a state differential equation of the three-phase asynchronous motor on a two-phase static coordinate system as follows:
Figure BDA0002375543290000151
wherein: u. ofsαAnd usβRespectively indicating that the motor is stationary in two phasesStator voltage at stop coordinate, isαAnd isβRepresenting the stator currents of the motor in two stationary phases, ΨrαAnd ΨrβRespectively representing the rotor flux, T, of the motor in two-phase stationary coordinatesLRepresenting motor load torque, ωrRepresenting the angular velocity, L, of the rotor of the machines、Lr、Lm、Rs、Rr、npAnd J respectively represent the self inductance of the stator, the self inductance of the rotor, the mutual inductance of the stator and the rotor, the resistance of the stator, the resistance of the rotor, the pole pair number and the moment of inertia of the motor,
Figure BDA0002375543290000152
representing the leakage coefficient, T, of the motorr＝Lrthe/R represents the rotor electromagnetic time constant.
Then, the differential equation of state shown in equation (13) is discretized by the Runge-Kutta method to obtain:
Figure BDA0002375543290000153
wherein:
Figure BDA0002375543290000154
is the state vector at time (n +1) T,
Figure BDA0002375543290000155
is the state vector at time nT, K1、K2、K3And K4Are all intermediate variables, and K1＝f(xn,yn)，
Figure BDA0002375543290000156
K4＝f(xn+TK0,yn+TK3)，
Figure BDA0002375543290000161
usα(n)And usβ(n)Respectively representing the stator voltage i of the motor at the moment nT on the two-phase stationary coordinatesα(n)And isβ(n)Representing the stator currents of the machine at the moment nT in two-phase stationary coordinates, Ψrα(n)And Ψrβ(n)Respectively representing the rotor flux linkage, omega, at time nT on the two-phase stationary coordinater(n)Representing the angular velocity of the rotor of the machine at time nT.
And (7): obtaining a discrete iteration mapping model of the BBMC speed regulating system based on finite time control according to the discrete iteration mapping model of the BBMC inverter stage obtained in the step (5) and the discrete iteration mapping model of the three-phase asynchronous motor obtained in the step (6), and specifically:
Figure BDA0002375543290000171
wherein:
Figure BDA0002375543290000172
and
Figure BDA0002375543290000173
respectively representing the three-phase capacitor voltages at time (n +1) T BBMC,
Figure BDA0002375543290000174
and
Figure BDA0002375543290000175
respectively represents three-phase inductive current in the BBMC at the (n +1) T moment,
Figure BDA0002375543290000176
Figure BDA0002375543290000177
and
Figure BDA0002375543290000178
respectively represents the conduction time of the three-phase power switch tube in the n-th switch period T,
Figure BDA0002375543290000179
and
Figure BDA00023755432900001710
respectively showing the turn-off time of the three-phase power switch tube in the BBMC in the nth switching period T,
Figure BDA00023755432900001711
and
Figure BDA00023755432900001712
respectively representing the duty ratio of three-phase power switching tubes in the BBMC in the nth switching period T, MA、MB、MC、NA、NBAnd NCAre all intermediate variables, and
Figure BDA00023755432900001713
Figure BDA00023755432900001714
Figure BDA00023755432900001715
Figure BDA00023755432900001716
and (8): and (4) obtaining the value range of the control parameter of the BBMC speed regulation system in stable operation through numerical simulation according to the discrete iterative mapping model of the BBMC speed regulation system based on the finite time control obtained in the step (7). Referring to fig. 3, a flowchart for determining a control parameter value range according to a finite time control-based BBMC speed regulation system discrete iteration mapping model according to an embodiment of the present invention includes the following specific steps:
step (8-1): setting system parameters, including: BBMC main circuit inductance L, main circuit capacitance C, motor stator self-inductance LsSelf-inductance of rotor LrStator and rotor mutual inductance LmStator resistor RsRotor resistance RrN number of pole pairspMoment of inertia J, load torque TLPower, powerSwitching period T and maximum iteration number N of switching tubemaxThree-phase capacitor reference voltage in BBMC
Figure BDA0002375543290000181
Period T of reference voltage of capacitor0(and satisfy T)0kT, k being a positive integer), a control parameter k1、k2、k3、α1、α2And alpha3And increasing the change parameter delta X, and taking 1 as the initial value of the counting variable q.
Step (8-2): first order the controlled variable Y1～Y6Respectively representing control parameters k1、k2、k3、α1、α2And alpha3；
Step (8-3): let control variable YqThe initial value of the variable parameter X is set to be 0, and other control variables are kept unchanged;
step (8-4): calculating the state variable i at the time (n +1) T by equation (15)α(n+1)And iβ(n+1)；
Step (8-5): judgment of iα(n+1)And iβ(n+1)Whether or not to satisfy i simultaneouslyα(n+1)＝iα(n)And iβ(n+1)＝iβ(n)If yes, the system is in a stable state, and the step (8-8) is executed; otherwise, executing the step (8-6);
step (8-6): judging whether the iteration number N is more than NmaxIf yes, executing the step (8-7); otherwise, adding 1 to the iteration number n, and returning to the step (8-4);
step (8-7): adding delta X to the change parameter X, enabling the iteration number n to return to 1, and returning to the step (8-4);
step (8-8): let the corresponding change parameter value X at this time be the lower limit value of the parameter stability domain, that is: xmin＝X；
Step (8-9): adding delta X to the variation parameter X, and enabling the iteration number n to return to 1;
step (8-10): calculating the state variable i at the time (n +1) T by equation (15)α(n+1)And iβ(n+1)；
Step (8-11): judgment of iα(n+1)And iβ(n+1)Whether or not to satisfy i simultaneouslyα(n+1)＝iα(n)And iβ(n+1)＝iβ(n)If yes, the system is in a stable state, and the step (8-12) is executed; otherwise, executing the step (8-13);
step (8-12): let an intermediate variable XmaxX, then returning to step (8-9);
step (8-13): judging whether the iteration number N is more than NmaxIf yes, executing the step (8-14); otherwise, adding 1 to the iteration number n, and returning to the step (8-10);
step (8-14): let Yqmin＝Xmin，Yqmax＝XmaxObtaining the control variable Y of the speed regulating system when the speed regulating system operates stablyqHas a value range of (Y)qmin，Yqmax)；
Step (8-15): judging whether the counting variable q is smaller than 6, if so, executing the step (8-16), otherwise, executing the step (8-17);
step (8-16): adding 1 to the counting variable q, and returning to the step (8-3);
step (8-17): the resulting controlled variable YqValue range (Y)qmin，Yqmax) (q 1, 2.. 6) corresponds to the control parameter k, respectively1、k2、k3、α1、α2And alpha3The specific value of each control parameter is determined according to the value range of each control parameter, and the stable operation of the BBMC speed regulating system based on the limited time control can be realized.

Claims (3)

1. A method for determining a control parameter stability region of a finite time control BBMC speed regulation system is characterized by comprising the following steps:
step (1): the method comprises the following steps of establishing a state differential equation of a BBMC speed regulation system by taking inductive current, capacitor voltage and output current in BBMC as state variables, and specifically comprising the following steps:
Figure FDA0003387003830000011
wherein: i.e. iL、uCAnd ioRespectively representing inductive current, capacitor voltage and output current in BBMC, E is input voltage of BBMC inverter stage, u is output voltage of BBMC inverter stageDFor the common terminal voltage of three-phase stator winding of asynchronous motor, L is BBMC main circuit inductance, C is BBMC main circuit capacitance, R is1And L1Respectively is the equivalent resistance and the equivalent inductance of the single-phase winding of the asynchronous motor, d is the duty ratio of a power switch in the BBMC, and d belongs to [0,1 ]]；
Step (2): obtaining a dynamic equation of the BBMC speed regulating system according to the state differential equation obtained in the step (1), wherein the specific steps are as follows:
let the reference output voltage of BBMC be urefThe error of the output voltage of the BBMC is obtained as follows:
x1＝uC-uref (2)
according to the formula (1) and the formula (2), the dynamic equation of the BBMC speed regulating system is obtained as follows:
Figure FDA0003387003830000012
wherein: x is the number of1、x2、x3、iL、uCAnd ioAre all variables of time t;
and (3): designing a control function of the BBMC speed regulating system according to the dynamic equation of the BBMC speed regulating system obtained in the step (2), and specifically comprising the following steps:
step (3-1): defining a time scale coordinate transformation as:
Figure FDA0003387003830000021
wherein: k is a coordinate transformation coefficient;
step (3-2): and (3) according to the time scale coordinate transformation formula shown in the formula (4), transforming the formula (3) to obtain:
Figure FDA0003387003830000022
step (3-3): the control function of the BBMC governor system obtained according to equation (5) is:
Figure FDA0003387003830000023
and (4): and (4) obtaining the duty ratio of a power switching tube in the BBMC according to the control function and the finite time control principle of the BBMC speed regulating system obtained in the step (3), and specifically comprising the following steps:
according to the finite time control principle, determining a system control function f(s) as follows:
Figure FDA0003387003830000024
wherein: satαAs a function of saturation, k1、k2、k3、α1、α2And alpha3Is a control parameter;
according to the formulae (6) and (7):
Figure FDA0003387003830000031
finally, according to equations (4) and (8), the duty ratio of the power switch tube in the BBMC can be obtained as follows:
Figure FDA0003387003830000032
wherein:
Figure FDA0003387003830000033
and (5): and (4) obtaining a discrete iteration mapping model of the BBMC inverter stage according to the duty ratio of the power switch tube in the BBMC obtained in the step (4), which comprises the following specific steps:
the method comprises the following steps of establishing a differential equation of state by taking inductive current and capacitor voltage in BBMC as state variables:
Figure FDA0003387003830000034
according to the formula (9), the on-time T of the power switch tube in the nth switching period T can be obtainedonAnd off time toffRespectively is as follows:
Figure FDA0003387003830000035
wherein: dnThe duty ratio of the power switch tube in the BBMC in the nth switching period T is represented;
according to the equations (10) and (11), the discrete iterative mapping model of the BBMC inverter stage is obtained as follows:
Figure FDA0003387003830000036
wherein: u. ofC(n+1)And iL(n+1)Respectively representing the capacitor voltage and the inductor current i in the (n +1) T moment BBMCo(n)Denotes the output current of BBMC at time nT, M, N and ω are intermediate variables, and
Figure FDA0003387003830000041
uC(n)and iL(n)Respectively representing the capacitor voltage and the inductor current at time nT BBMC,
and (6): the method comprises the following steps of establishing a discrete iteration mapping model of the three-phase asynchronous motor: establishing a state differential equation of the three-phase asynchronous motor on a two-phase static coordinate system as follows:
Figure FDA0003387003830000042
wherein:usαand usβRepresenting the stator voltage, i, of the motor in two-phase stationary coordinates, respectivelysαAnd isβRepresenting the stator currents of the motor in two stationary phases, ΨrαAnd ΨrβRespectively representing the rotor flux, T, of the motor in two-phase stationary coordinatesLRepresenting motor load torque, ωrRepresenting the angular velocity, L, of the rotor of the machines、Lr、Lm、Rs、Rr、npAnd J respectively represent the self inductance of the stator, the self inductance of the rotor, the mutual inductance of the stator and the rotor, the resistance of the stator, the resistance of the rotor, the pole pair number and the moment of inertia of the motor,
Figure FDA0003387003830000043
representing the leakage coefficient, T, of the motorr＝Lr/RrRepresents the rotor electromagnetic time constant;
discretization of formula (13) by Runge-Kutta method gives:
Figure FDA0003387003830000044
wherein:
Figure FDA0003387003830000051
is the state vector at time (n +1) T,
Figure FDA0003387003830000052
is the state vector at time nT, K1、K2、K3And K4Are all intermediate variables, and K1＝f(xn,yn)，
Figure FDA0003387003830000053
K4＝f(xn+TK0,yn+TK3)，
Figure FDA0003387003830000054
Figure FDA0003387003830000055
usα(n)And usβ(n)Respectively representing the stator voltage i of the motor at the moment nT on the two-phase stationary coordinatesα(n)And isβ(n)Representing the stator currents of the machine at the moment nT in two-phase stationary coordinates, Ψrα(n)And Ψrβ(n)Respectively representing the rotor flux linkage, omega, at time nT on the two-phase stationary coordinater(n)Representing the angular speed of the motor rotor at the moment nT;
and (7): obtaining a discrete iteration mapping model of the BBMC speed regulating system based on finite time control according to the discrete iteration mapping model of the BBMC inverter stage obtained in the step (5) and the discrete iteration mapping model of the three-phase asynchronous motor obtained in the step (6);
and (8): and (4) obtaining the value range of the control parameter when the BBMC speed regulation system stably operates through numerical simulation according to the discrete iterative mapping model of the BBMC speed regulation system based on the finite time control obtained in the step (7).
2. The finite time control BBMC speed regulating system control parameter stability domain determining method as claimed in claim 1, wherein: the specific steps of the step (7) are as follows:
Figure FDA0003387003830000061
wherein:
Figure FDA0003387003830000062
and
Figure FDA0003387003830000063
respectively representing the three-phase capacitor voltages at time (n +1) T BBMC,
Figure FDA0003387003830000064
and
Figure FDA0003387003830000065
respectively represents three-phase inductive current in the BBMC at the (n +1) T moment,
Figure FDA0003387003830000066
and
Figure FDA0003387003830000067
respectively represents the conduction time of the three-phase power switch tube in the n-th switch period T,
Figure FDA0003387003830000068
Figure FDA0003387003830000069
and
Figure FDA00033870038300000610
respectively showing the turn-off time of the three-phase power switch tube in the BBMC in the nth switching period T,
Figure FDA00033870038300000611
and
Figure FDA00033870038300000612
respectively representing the duty ratio of three-phase power switching tubes in the BBMC in the nth switching period T, MA、MB、MC、NA、NBAnd NCAre all intermediate variables, and
Figure FDA00033870038300000613
Figure FDA00033870038300000614
Figure FDA0003387003830000071
Figure FDA0003387003830000072
3. the finite time control BBMC speed regulating system control parameter stability domain determining method as claimed in claim 2, wherein: the specific steps of the step (8) are as follows:
step (8-1): setting system parameters, including: BBMC main circuit inductance L, main circuit capacitance C, motor stator self-inductance LsSelf-inductance of rotor LrStator and rotor mutual inductance LmStator resistor RsRotor resistance RrN number of pole pairspMoment of inertia J, load torque TLSwitching period T and maximum iteration number N of power switching tubemaxThree-phase capacitor reference voltage in BBMC
Figure FDA0003387003830000073
Period T of reference voltage of capacitor0And satisfy T0K is positive integer, control parameter k1、k2、k3、α1、α2And alpha3Changing parameter increment delta X, and taking 1 as the initial value of a counting variable q;
step (8-2): first order the controlled variable Y1～Y6Respectively representing control parameters k1、k2、k3、α1、α2And alpha3；
Step (8-3): let control variable YqThe initial value of the variable parameter X is set to be 0, and other control variables are kept unchanged;
step (8-4): calculating the state variable i at the time (n +1) T by equation (15)α(n+1)And iβ(n+1)；
Step (8-5): judgment of iα(n+1)And iβ(n+1)Whether or not to satisfy i simultaneouslyα(n+1)＝iα(n)And iβ(n+1)＝iβ(n)If yes, the system is in a stable state, and the step (8-8) is executed; otherwise, executing the step (8-6);
step (8-6): judging whether the iteration number N is more than NmaxIf yes, executing the step (8-7);otherwise, adding 1 to the iteration number n, and returning to the step (8-4);
step (8-7): adding delta X to the change parameter X, enabling the iteration number n to return to 1, and returning to the step (8-4);
step (8-8): let the corresponding change parameter value X at this time be the lower limit value of the parameter stability domain, that is: xmin＝X；
Step (8-9): adding delta X to the variation parameter X, and enabling the iteration number n to return to 1;
step (8-10): calculating the state variable i at the time (n +1) T by equation (15)α(n+1)And iβ(n+1)；
Step (8-11): judgment of iα(n+1)And iβ(n+1)Whether or not to satisfy i simultaneouslyα(n+1)＝iα(n)And iβ(n+1)＝iβ(n)If yes, the system is in a stable state, and the step (8-12) is executed; otherwise, executing the step (8-13);
step (8-12): let variable XmaxX, then returning to step (8-9);
step (8-13): judging whether the iteration number N is more than NmaxIf yes, executing the step (8-14); otherwise, adding 1 to the iteration number n, and returning to the step (8-10);
step (8-14): let Yqmin＝Xmin，Yqmax＝XmaxObtaining the control variable Y of the speed regulating system when the speed regulating system operates stablyqHas a value range of (Y)qmin，Yqmax)；
Step (8-15): judging whether the counting variable q is smaller than 6, if so, executing the step (8-16), otherwise, executing the step (8-17);
step (8-16): adding 1 to the counting variable q, and returning to the step (8-3);
step (8-17): the resulting controlled variable YqValue range (Y)qmin，Yqmax) Q is 1,2, 6, i.e. corresponding to the control parameter k, respectively1、k2、k3、α1、α2And alpha3And determining the specific value of each control parameter according to the value range of each control parameter.
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