METHOD FOR MODEL PREDICTIVE CURRENT CONTROL OF TWO-MOTOR TORQUE SYNCHRONIZATION SYSTEM

Abstract

A method for model predictive current control of a two-motor torque synchronization system, which belongs to the field of power electronics and motor control. The present disclosure takes an indirect matrix converter and a two-motor system which are coaxially and rigidly connected as a target, and takes two-motor torque synchronization performance and current tracking performance as main control objectives. A two-motor unified prediction model is established and a value function based on free components of error items is configured so as to solve the problems in which when model predictive current control is performed on a two-motor system, setting of a value function weighting coefficient needs to be performed manually, and consequently the setting process is complicated and an erroneous switch state combination is likely to be selected.

Claims

1. A method for model predictive current control for a two-motor torque synchronization system, wherein the method is suitable for a two-motor torque synchronization system driven by an indirect matrix converter and comprises: 1) generating a PWM control signal through a rectifier stage controller by a rectifier stage of the indirect matrix converter adopting a space vector modulation strategy without zero vector, and providing a stable and reliable DC output voltage for an inverter stage of the indirect matrix converter subsequently, 2) establishing a two-motor sunified prediction model by taking the two-motor torque synchronization system driven by two coaxially and rigidly connected motors with a same load as a subject, torque synchronization performance and current tracking performance between the motors as main control objectives, and a current value of each motor and a torque synchronization error ε between the motors as a state variable, 3) inputting the state variable and an input voltage of a previous moment, obtaining a predicted value of the state variable at a next moment as an output through the two-motor unified prediction model, analyzing a composition of each error item in a weighted sum value function in a value function evaluation unit for model predictive current control, normalizing each error value by focusing on an offset degree of a free component of each error to a fixed component, and proposing a value function based on the free component of the error item, and 4) proposing an adaptive weight coefficient without artificial iterative comparison and applying the adaptive weight coefficient to a model prediction current control of the two-motor torque synchronization system for selecting the weight coefficient in the value function based on the free component of the error item; adjusting the weight coefficient online and in real time by an adaptive factor according to a running state of the system, and meeting requirements of various working conditions with expected torque synchronization performance and current tracking performance of the system into account.

2. The method for model predictive current control for a two-motor torque synchronization system according to claim 1, wherein said rectifier stage of the indirect matrix converter adopting a space vector modulation strategy without zero vector in step 1) is as follows: the rectifier stage of the indirect matrix converter adopts an SVPWM modulation strategy without zero vector so that a voltage polarity of a DC link is positive, wherein the voltage utilization ratio is the highest, and the power grid side is controlled by a unit power factor, the rectifier stage of the indirect matrix converter only uses two effective space vectors in a unit switching cycle, that is, a phase current vector I.sub.ref of an average output at any moment is synthesized by two adjacent effective current effective vectors of a sector where the phase current vector I.sub.ref is located, where the SVPWM strategy of the rectifier stage without zero vector is denoted as t.sub..Math. and t.sub.v in two time periods of the unit switching cycle, the corresponding DC voltages are denoted as u.sub..Math. and u.sub.v, and the corresponding duty ratios are denoted as d.sub..Math. and d.sub.v, respectively, and an average voltage u.sub.dc_av of an intermediate DC link of the indirect matrix converter in the unit switching cycle is expressed as follows: $u_{\text{dc\_av}}=d_{\mu }\cdot u_{\mu }+d_{\nu }\cdot u_{\nu }=\frac{3u_{\text{im}}}{2\cos {\theta }_{\text{in}}}$ where cosθ.sub.in=max{|cosθ.sub.a|,|cosθ.sub.b|,|cosθ.sub.c|}; θ.sub.a,θ.sub.b,θ.sub.c and u.sub.im represent phase angles and amplitude of an input phase voltage of the indirect matrix converter, respectively.

3. The method for model predictive current control of a two-motor torque synchronization system according to claim 1, wherein the torque synchronization error ε between the motors in step 2) is defined as follows: $\epsilon ={{\rm T}}_{\text{el}}-T_{\text{e2}}$ where T.sub.e1 and T.sub.e2 are output torques of the two motors, respectively.

4. The method for model predictive current control of a two-motor torque synchronization system according to claim 1, wherein a discrete state equation of the two-motor unified prediction model in step 2) comprising time delay compensation is as follows: $X\left(k+2\right)=G\left(k+1\right)\cdot X\left(k+1\right)+F\cdot U\left(k+1\right)+K\cdot D\left(k+1\right)$ where X(k+1)=[i.sub.d1(k+1) i.sub.q1(k+1) i.sub.d2(k+1) i.sub.q2(k+1) ε(k+1)].sup.T; U(k+1)=(u.sub.d1(k+1) u.sub.q1(k+1) u.sub.d2(k+1) u.sub.q2(k+1)].sup.T; D(k+1)=(T.sub.sω.sub.r1(k+1)Ψ.sub.f1/L.sub.1T.sub.sω.sub.r2(k+1)Ψ.sub.f2/L.sub.2].sup.T, and where X(k+1) represents a state vector at (k+1)T.sub.s, U(k+1) represents an input vector at (k+1)T.sub.s, D(k+1) represents a transfer vector at (k+1)T.sub.s, G(k+1) represents a state matrix of the two-motor torque synchronization system at (k+1)T.sub.s; F represents an input matrix of the two-motor torque synchronization system; K represents a transfer matrix of the two-motor torque synchronization system; i.sub.di(k+1) and i.sub.qi(k+1) represent d-axis and q-axis components of a stator current of an i.sup.th motor at (k+1)T.sub.s, respectively, and i represents the ordinal number of the motor, i=1,2; ε(k+1) represents a torque synchronization error of the two motors at (k+1)T.sub.s, and k represents the ordinal number of a control cycle; u.sub.di(k+1) and u.sub.qi(k+1) represent d-axis and q-axis components of a stator voltage of the i.sup.th motor at (k+1)T.sub.s, respectively, T.sub.s is a control cycle of the two-motor torque synchronization system, and ω.sub.ri(k+1), Ψ.sub.fi and L.sub.i are a rotor angular velocity, a permanent magnet flux linkage and a stator inductance of the i.sup.th motor at k+1, respectively.

5. The method for model predictive current control of a two-motor torque synchronization system according to claim 4, wherein the weighted sum value function in step 3) is: $\begin{array}{l}CF={\lambda }_{\text{d}}\cdot g_{\text{d}}+{\lambda }_{\text{q}}\cdot g_{\text{q}}+{\lambda }_{\text{ε}}\cdot g_{\text{ε}}\\ \left\{\begin{array}{c}{g}_{\text{d}}=\left|i_{\text{d}}^{\text{ref}}-i_{\text{d1}}\left(k+2\right)\right|+\left|i_{\text{d}}^{\text{ref}}-i_{\text{d2}}\left(k+2\right)\right|=g_{\text{d1}}+g_{\text{d2}}\\ g_{\text{q}}=\left|i_{\text{q}}^{\text{ref}}-i_{\text{q1}}\left(k+2\right)\right|+\left|i_{\text{q}}^{\text{ref}}-i_{\text{q2}}\left(k+2\right)\right|=g_{\text{q1}}+g_{\text{q2}}\\ g_{\text{ε}}=\left|\epsilon \left(k+2\right)\right|=\left|1.5p_1{\psi }_{f1}{i}_{\text{q1}}\left(k+2\right)-1.5p_2{\psi }_{f2}{i}_{\text{q2}}\left(k+2\right)\right|\end{array}\right)\end{array}$ where g.sub.d, g.sub.q and g.sub.ε are d-axis and q-axis current tracking errors and the torque synchronization error of the two motors, respectively, λ.sub.d, λ.sub.q and λ.sub.ε are the weight coefficients of the corresponding errors in the value function obtained by an empirical setting method; i.sub.refd and i.sub.refq are the reference values of d-axis current and q-axis current of the motor, respectively, and p.sub.i is the number of pole-pairs of the motor i.

6. The method for model predictive current control of a two-motor torque synchronization system according to claim 1, wherein the value function based on the free component of the error item in step 3) is as follows: $\begin{array}{l}C{F}_{\text{new}}={\lambda }_{\text{d}}^{\raisebox{1ex}{$\text{o}$}\!\left/ \!\raisebox{-1ex}{$\text{o}$}\right.}\cdot g_{\text{d}}^{\raisebox{1ex}{$\text{o}$}\!\left/ \!\raisebox{-1ex}{$\text{o}$}\right.}+{\lambda }_{\text{q}}^{\raisebox{1ex}{$\text{o}$}\!\left/ \!\raisebox{-1ex}{$\text{o}$}\right.}\cdot g_{\text{q}}^{\raisebox{1ex}{$\text{o}$}\!\left/ \!\raisebox{-1ex}{$\text{o}$}\right.}+{\lambda }_{\text{ε}}^{\raisebox{1ex}{$\text{o}$}\!\left/ \!\raisebox{-1ex}{$\text{o}$}\right.}\cdot g_{\text{ε}}^{\raisebox{1ex}{$\text{o}$}\!\left/ \!\raisebox{-1ex}{$\text{o}$}\right.}\\ \left\{\begin{array}{l}{g}_{\text{d}}^{\raisebox{1ex}{$\text{o}$}\!\left/ \!\raisebox{-1ex}{$\text{o}$}\right.}=g_{\text{d1}}^{\raisebox{1ex}{$\text{o}$}\!\left/ \!\raisebox{-1ex}{$\text{o}$}\right.}+g_{\text{d2}}^{\raisebox{1ex}{$\text{o}$}\!\left/ \!\raisebox{-1ex}{$\text{o}$}\right.}={\displaystyle \underset{i-1}{\overset{2}{.Math.}}\left|\frac{{\rho }_{\text{d}i}^{\raisebox{1ex}{$\text{o}$}\!\left/ \!\raisebox{-1ex}{$\text{o}$}\right.}+{\tau }_{\text{d}i}}{2{\tau }_{\text{d}i\text{max}}}\right|}\hfill \\ g_{\text{q}}^{\raisebox{1ex}{$\text{o}$}\!\left/ \!\raisebox{-1ex}{$\text{o}$}\right.}=g_{\text{q1}}^{\raisebox{1ex}{$\text{o}$}\!\left/ \!\raisebox{-1ex}{$\text{o}$}\right.}+g_{\text{q2}}^{\raisebox{1ex}{$\text{o}$}\!\left/ \!\raisebox{-1ex}{$\text{o}$}\right.}={\displaystyle \underset{i=1}{\overset{2}{.Math.}}\left|\frac{{\rho }_{\text{q}i}^{\raisebox{1ex}{$\text{o}$}\!\left/ \!\raisebox{-1ex}{$\text{o}$}\right.}+{\tau }_{\text{q}i}}{2{\tau }_{\text{q}i\text{max}}}\right|}\hfill \\ g_{\text{ε}}^{\raisebox{1ex}{$\text{o}$}\!\left/ \!\raisebox{-1ex}{$\text{o}$}\right.}={\displaystyle \underset{i=1}{\overset{2}{.Math.}}\left|\frac{{\rho }_{\text{ε}}^{\raisebox{1ex}{$\text{o}$}\!\left/ \!\raisebox{-1ex}{$\text{o}$}\right.}+{\tau }_{\text{ε}}}{2{\tau }_{\text{ε}\text{max}}}\right|}\hfill \end{array}\right)\end{array}$ where ${\lambda }_{\text{ε}}^{\raisebox{1ex}{$\text{o}$}\!\left/ \!\raisebox{-1ex}{$\text{o}$}\right.},{\lambda }_{\text{d}}^{\raisebox{1ex}{$\text{o}$}\!\left/ \!\raisebox{-1ex}{$\text{o}$}\right.}\text{and}{\lambda }_{\text{q}}^{\raisebox{1ex}{$\text{o}$}\!\left/ \!\raisebox{-1ex}{$\text{o}$}\right.}$ are adaptive weight coefficients of the torque synchronization error, d-axis and q-axis current tracking errors, respectively; ρ̃.sub.ε and ρ̃.sub.qi are the simplified forms of the fixed components of the corresponding errors respectively; τ.sub.ε, τ.sub.di and τ.sub.qi are free components of the torque synchronization error and the d-axis and the q-axis current tracking errors, respectively.

7. The method for model predictive current control of a two-motor torque synchronization system according to claim 6, wherein the adaptive weight coefficient in step 4) is: a weight of the torque synchronization error is: ${\lambda }_{\text{ε}}^{\raisebox{1ex}{$\text{o}$}\!\left/ \!\raisebox{-1ex}{$\text{o}$}\right.}=G_{\text{ε}}\cdot \lambda$ where G.sub.ε and λ are the adaptive factor and the initial weight coefficient of the torque synchronization error, respectively; the adaptive factor is $\begin{array}{l}{G}_{\epsilon }=\left\{\begin{array}{l}\begin{array}{cc}1,& {\rho }_{\epsilon \text{}\_\text{pu}}\le {\rho }_{\lim }\end{array}\\ 1+\frac{h}{{\rho }_{\lim }}\cdot \left({\rho }_{\epsilon \text{}\_\text{pu}}-{\rho }_{\lim }\right),{\rho }_{\epsilon \text{}\_\text{pu}}>{\rho }_{\lim }\end{array}\right\}\\ {\rho }_{\epsilon \_\text{pu}}=\left|\frac{{\rho }_{\epsilon }}{T_{\text{N}}}\right|\end{array}$ where ρ.sub.lim and h are a fixed component limit value and a linear variation coefficient of the adaptive weight factor, respectively; ρ.sub.ε_pu and T.sub.N are a per-unit value of the fixed component of the torque synchronization error and the rated torque of the motor, respectively; and the definition and parameter selection of the adaptive weight coefficients λ.sub.d and λ.sub.d corresponding to the d-axis and the q-axis current tracking errors are the same with the adaptive weight coefficient of the torque synchronization error ${\lambda }_{\text{ε}}^{\raisebox{1ex}{$\text{o}$}\!\left/ \!\raisebox{-1ex}{$\text{o}$}\right.}\cdot$ .

8. The method for model predictive current control of a two-motor torque synchronization system according to claim 1, wherein in step 4), the step of applying the adaptive weight coefficient to the model predictive current control of the two-motor torque synchronization system comprises following online rolling optimization sub-steps: 4.1) obtaining current values of the two motors at kT.sub.s by sampling, substituting all switch state combinations into the two-motor unified prediction model and by considering the delay compensation, calculating fixed components ρ.sub.di, ρ.sub.qi, ρ.sub.ε, free components τ.sub.di, τ.sub.qi, τ.sub.ε and simplified forms ρ̃.sub.di, ρ̃.sub.qi, ρ̃.sub.ε(i=1,2) of the fixed components of d-axis q-axis current tracking errors and the torque synchronization error of the two motors at (k+2)T.sub.s; 4.2) substituting the adaptive weight coefficient of each error item and the error components of the two motors at (k+2)T.sub.s together into the value function based on the free component of the error item for online evaluation; 4.3) selecting a group of switch state feedbacks that is capable of minimizing the value of the value function based on the free component of the error item as output of the inverter stages of the two motors at (k+1)T.sub.s; and 4.4) moving sampling time back, k=k+1, and repeating above steps.

Description

BRIEF DESCRIPTION OF DRAWINGS

[0032] FIG. 1 is a block diagram of the control structure of an indirect matrix converter-two-motor system.

[0033] FIG. 2 is a schematic diagram of input voltage sector division.

[0034] FIG. 3 is a schematic diagram of the MPCC predictive control structure of the present disclosure.

DESCRIPTION OF EMBODIMENTS

[0035] The method for model predictive current control of a two-motor torque synchronization system driven by an indirect matrix converter according to the present disclosure will be described in detail with reference to the following embodiments and drawings.

[0036] An indirect matrix converter-two-motor system is mainly composed of a three-phase AC input power supply, an input filter, an indirect matrix converter rectifier stage, an inverter stage and two permanent magnet synchronous motors. Its topology is shown in FIG. 1. The rectifier stage consists of six bidirectional switches S.sub.mn(m=a,b,c respectively represent three-phase bridge arms; n=u,l represent the upper and lower bridge arms respectively); the two inverter stage converters are the same as the traditional voltage source inverters, each consisting of 6 IGBTs and a reverse recovery diode.

[0037] The rectifier DC bus connects two inverter stages, and each inverter stage drives a permanent magnet synchronous motor. The two motors are rigidly connected by coaxial connection, and are controlled by the double closed-loop control structure of speed and current. The control signal is input through the inverter stage to control the current tracking performance and torque synchronization performance of the motors. After the speed error of a motor 1 passes through the speed regulator, it provides the same torque reference signal for both motors. The current inner loop adopts vector control with i.sub.d=0. In order to realize the closed-loop control of the torque synchronization error of two motors, a common practice is that two motors adopt independent current loop controllers respectively, and then a coupling link is used to output torque synchronization signals to compensate the torque given values of each motor, and finally the output torque synchronization control is realized. By virtue of the advantages of the simple control structure and fast dynamic response capability of MPCC, the current controllers of two motors are integrated into one MPCC controller, the current inner loop control structure is simplified, and the multi-objective control of the two-motor torque synchronization system is realized.

[0038] In order to make the voltage polarity of the DC link positive, maximize the voltage utilization rate, and make the power grid side be controlled by unit power factor, a SVPWM modulation strategy without zero vector is usually adopted in the rectifier stage of the indirect matrix converter. Therefore, according to the method shown in FIG. 2, the input voltage intervals are equally divided according to the zero-crossing point of the input phase voltage, and each interval occupies π/3 electrical angle, and each interval is called a sector. In a unit switching cycle, the DC side of the rectifier stage outputs two relatively large line voltages with positive polarity according to a certain duty ratio. The switching state, output DC voltage and duty ratio of the six-sector rectifier stage are shown in Table 1.

TABLE-US-00001 Switching State and DC Voltage of Six Sector Rectifier Stage First section Second section Sector Switch on S.sub.mn DC voltage u.sub..Math. Duty ratio d.sub..Math. Switch on S.sub.mn DC voltage u.sub.v Duty ratio d.sub.v 1 S.sub.au S.sub.bl u.sub.ab -u.sub.b/u.sub.a S.sub.au S.sub.cl u.sub.ac -u.sub.c/u.sub.a 2 S.sub.bu S.sub.cl u.sub.bc -u.sub.b/u.sub.c S.sub.au S.sub.cl u.sub.ac -u.sub.a/u.sub.c 3 S.sub.bu S.sub.cl u.sub.bc -u.sub.c/u.sub.b S.sub.bu S.sub.al u.sub.ba - u.sub.a/u.sub.b 4 S.sub.cu S.sub.al u.sub.ca -u.sub.c/u.sub.a S.sub.bu S.sub.al u.sub.ba -u.sub.b/u.sub.a 5 S.sub.cu S.sub.al u.sub.ca -u.sub.a/u.sub.c S.sub.cu S.sub.bl u.sub.cb -u.sub.b/u.sub.c 6 S.sub.au S.sub.bl u.sub.ab - u.sub.a/u.sub.b S.sub.cu S.sub.bl u.sub.cb -u.sub.c/u.sub.b

[0039] The average voltage u.sub.dc_av of the intermediate DC link of the indirect matrix converter in unit switching cycle is expressed as follows

[00016]$u_{\text{dc\_av}}=d_{\mu }\cdot u_{\mu }+d_v\cdot u_v=\frac{3u_{im}}{2\text{cos}{\theta }_{in}}$

where cos cosθ.sub.in=max{|cosθ.sub.a|,|cosθ.sub.b|,|cosθ.sub.c|}; θ.sub.a, θ.sub.b, θ.sub.c and u.sub.im are the phase angles and amplitude of an input phase voltage of the indirect matrix converter, respectively.

[0040] Under the d-q axis rotating coordinate system, the voltage equation of the i.sup.th surface permanent magnet synchronous motor (SPMSM) is as follows:

[00017]$\left\{\begin{array}{l}\frac{d{i}_{di}}{dt}=-\frac{R_i}{L_i}{i}_{di}+{\omega }_{ri}{i}_{qi}+\frac{u_{di}}{L_i}\hfill \\ \frac{d{i}_{qi}}{dt}=-{\omega }_{ri}{i}_{di}-\frac{R_i}{L_i}{i}_{qi}+\frac{u_{qi}}{L_i}-\frac{{\psi }_{fi}{\omega }_{ri}}{L_i}\hfill \end{array}\right)$

where i.sub.di and i.sub.qi, u.sub.di and u.sub.qi are d-axis and q-axis components of the stator current and stator voltage, respectively; R.sub.i, L.sub.i, ψ.sub.fi and ω.sub.ri are stator resistance, stator inductance, permanent magnet flux linkage and rotor electrical angular velocity respectively, where ω.sub.ri=p.sub.iω.sub.i, ω.sub.i is the mechanical angular velocity of the rotor; p.sub.i is the number of pole-pairs of the motor; i represents the motor serial number, i=1,2.

[0041] Euler discretization of formula (2) is carried out, and the state values of the d-axis and q-axis components of the stator current of the i.sup.th motor at (k+1)T.sub.s are obtained as follows

[00018]$\left\{\begin{array}{l}{i}_{di}\left(k+1\right)=A_i{i}_{di}\left(k\right)+B_i\left(k\right)i_{qi}\left(k\right)+C_i{u}_{di}\left(k\right)\hfill \\ i_{qi}\left(k+1\right)=A_i{i}_{qi}\left(k\right)-B_i\left(k\right)i_{di}\left(k\right)+C_i{u}_{qi}\left(k\right)-D_i\left(k\right)\hfill \end{array}\right\}$

where A.sub.¡=1-T.sub.sRi/L.sub.¡; B¡(k)=T.sub.sω.sub.r¡(k); C.sub.i=T.sub.s/L.sub.i; D.sub.¡(k)=T.sub.sω.sub.r¡(k)ψ.sub.fi/L.sub.¡; T.sub.s is the control cycle of the system.

[0042] The electromagnetic torque equation of the i.sup.th motor is

[00019]$T_{ei}\left(k\right)=1.5p_i{\psi }_{fi}{i}_{qi}\left(k\right)$

[0043] The two-motor torque synchronization error is defined as

[00020]$\epsilon =T_{e1}-T_{e2}$

[0044] There are 64 switch combination states in the inverter stage of the two-motor torque synchronization system driven by an indirect matrix converter. The predicted values of d and q axis current and torque synchronization error at (k+2)T.sub.s can be obtained from the current value at kT.sub.s and the two-motor unified prediction model. Subsequently, the optimal switch combination state is selected as the output of the inverter stage at (k+1)T.sub.s by online evaluation of the value function.

[0045] The weighted sum value function is applied in MPCC of the two-motor torque synchronization system driven by an indirect matrix converter. The weighted sum value function has the following form:

[00021]$CF={\lambda }_d\cdot g_d+{\lambda }_q\cdot g_q+{\lambda }_{\in }\cdot g_{\in }$

[00022]$\left\{\begin{array}{l}{g}_{\text{d}}=\left|i_{\text{d}}^{\text{ref}}-i_{\text{d}1}\left(k+2\right)\right|+\left|i_{\text{d}}^{\text{ref}}-i_{\text{d}2}\left(k+2\right)\right|=g_{\text{d}1}+g_{\text{d}2}\hfill \\ g_{\text{q}}=\left|i_{\text{q}}^{\text{ref}}-i_{\text{q}1}\left(k+2\right)\right|+\left|i_{\text{q}}^{\text{ref}}-i_{\text{q}2}\left(k+2\right)\right|=g_{\text{q}1}+g_{\text{q}2}\hfill \\ g_{\text{ε}}=\left|\epsilon \left(k+2\right)\right|=\left|H_1{i}_{\text{q}1}\left(k+2\right)-H_2{i}_{\text{q}2}\left(k+2\right)\right|\hfill \end{array}\right)$

where g.sub.d, g.sub.q and g.sub.ε are the current tracking errors of d-axis and q-axis and torque synchronization error of the two motors, respectively; λ.sub.d, λ.sub.q and λ.sub.ε are the weight coefficients of the corresponding errors in the value function, respectively. In order to facilitate the setting of the weight coefficients, λ.sub.d=λ.sub.q=1, and λ.sub.ε is generally obtained by the empirical setting method based on the branch and bound principle;

[00023]$i_{\text{d}}^{\text{ref}}$

and

[00024]$i_{\text{q}}^{\text{ref}}$

are the reference values of d-axis current and q-axis current of the motor, respectively.

[0046] Aiming at the problem of setting a plurality of weight coefficients in the weighted sum value function by the empirical setting method, the present disclosure adopts a value function based on the free component of the error item, and proposes an adaptive online setting strategy of weight coefficients.

[0047] The specific embodiment of the present disclosure comprises the following steps:

[0048] 1) The torque synchronization error ε of two motors is introduced into the prediction process as a state variable, the current controllers of the two motors are integrated into one MPCC controller, the current inner loop control structure is simplified, and the closed loop control of torque synchronization error of the two motors is realized through state prediction and rolling optimization, thus improving the torque synchronization performance of the two-motor system.

[0049] By taking the d axis current and the q axis current and the torque synchronization error of two motors as state variables, and considering the time delay compensation, a unified prediction model of two motors is established:

[00025]$X\left(k+2\right)=G\left(k+1\right)\cdot X\left(k+1\right)+F\cdot U\left(k+1\right)+K\cdot D\left(k+1\right)$

[0050] The state vector X(k+1)=[i.sub.d1(k+1) i.sub.q1(k+1) i.sub.d2(k+1) i.sub.q2(k+1) ε(k+1)].sup.T; the input vector U(k+1)=[u.sub.d1(k+1) u.sub.q1(k+1) u.sub.d2(k+1) .sub.Uq2(k+1)].sup.T; the transfer vector D(k+1)=[D.sub.1(k+1) D.sub.2(k+1)].sup.T .

[0051] State matrix;

[00026]$G\left(k+1\right)=\left[\begin{array}{ccccc}{A}_1& B_1\left(k+1\right)& 0& 0& 0\\ -B_1\left(k+1\right)& A_1& 0& 0& 0\\ 0& 0& A_2& B_2\left(k+1\right)& 0\\ 0& 0& -B_2\left(k+1\right)& A_2& 0\\ -B_1\left(k+1\right)H_1& A_1{H}_1& B_2\left(k+1\right)H_2& -A_2{H}_2& 0\end{array}\right]$

[0052] Input matrix

[00027]$F=\left[\begin{array}{cccc}{C}_1& 0& 0& 0\\ 0& C_1& 0& 0\\ 0& 0& C_2& 0\\ 0& 0& 0& C_2\\ 0& H_1{C}_1& 0& -H_2{C}_2\end{array}\right];$

transfer matrix

[00028]$K=\left[\begin{array}{cc}0& 0\\ -1& 0\\ 0& 0\\ 0& -1\\ -H_1& H_2\end{array}\right];$

where

[00029]$B_i\left(k+1\right)=T_s{\omega }_{\text{r}i}\left(k+1\right);D_i\left(k+1\right)=T_s{\omega }_{\text{r}i}\left(k+1\right){\psi }_{\text{f}i}/L_i;H_i=1.5p_i{\psi }_{\text{f}i}.$

[0053] 2) Based on the two-motor unified prediction model, the composition of each error item in the weighted sum value function is analyzed, and it is concluded that each error item can be divided into fixed component ρ and free component .sub.τ. ρ is the fixed component of each error in the value function, which acts independently of the system controller and remains constant in any switch combination state; .sub.τ is the free component of each error in the value function, which depends on the action of the controller and has different values in different switch combinations.

[0054] Accordingly, the present disclosure designs a value function based on the free component of the error item as follows:

[00030]$C{F}_{\text{new}}={\lambda }_{\text{d}}^{\%}\cdot g_{\text{d}}^{\%}+{\lambda }_{\text{q}}^{\%}\cdot g_{\text{q}}^{\%}+{\lambda }_{\text{ε}}^{\%}\cdot g_{\text{ε}}^{\%}$

[00031]$\left\{\begin{array}{l}{g}_{\text{d}}^{\%}=g_{\text{d1}}^{\%}+g_{\text{d2}}^{\%}={\displaystyle \underset{i=1}{\overset{2}{.Math.}}\left|\frac{{\rho }_{\text{d}}^{\%}+{\tau }_{\text{d}i}}{2{\tau }_{\mathrm{d}i\text{max}}}\right|}\hfill \\ g_{\text{q}}^{\%}=g_{\text{q1}}^{\%}+g_{\text{q2}}^{\%}={\displaystyle \underset{i=1}{\overset{2}{.Math.}}\left|\frac{{\rho }_{\text{q}i}^{\%}+{\tau }_{\text{q}i}}{2{\tau }_{\text{q}i\max }}\right|}\hfill \\ g_{\epsilon }^{\%}=\left|\frac{{\rho }_{\epsilon }^{\%}+{\tau }_{\epsilon }}{2{\tau }_{\epsilon \text{max}}}\right|\hfill \end{array}\right)$

where

[00032]${\lambda }_{\epsilon }^{\%},$

[00033]${\lambda }_{\text{d}}^{\%}$

and

[00034]${\lambda }_{\text{q}}^{\%}$

are adaptive weight coefficients of the torque synchronization error, d-axis and q-axis current tracking errors, respectively; p̃.sub.ε, p̃.sub.di and p̃.sub.qi represent the simplified forms of the fixed components of the corresponding errors, and their definitions have the same form. By taking p̃.sub.ε as an example, there is

[00035]${\rho }_{\epsilon }^{\%}=\left\{\begin{array}{ll}{\rho }_{\epsilon },\hfill & \left|{\rho }_{\epsilon }\right|\le {\tau }_{\epsilon \max }\hfill \\ \text{sign}\left({\rho }_{\epsilon }\right).{\tau }_{\epsilon \max },\hfill & \left|{\rho }_{\epsilon }\right|>{\tau }_{\epsilon \max }\hfill \end{array}\right)$

where τ.sub.εmax is the maximum value of the free components of the torque synchronization errors corresponding to different switch combination states.

[0055] 3) In order to take both the current tracking performance and torque synchronization performance of the two-motor system into account and match the working conditions of the system in real time, the present disclosure designs an adaptive weight coefficient setting strategy. Taking the weight of torque synchronization error as an example, the adaptive weight coefficient is:

[00036]${\lambda }_{\text{ε}}^{\%}=G_{\text{ε}}\cdot \lambda$

where G.sub.ε and λ are the adaptive factor and initial weight coefficient of the torque synchronization error, respectively.

[0056] The adaptive factor is

[00037]$G_{\epsilon }=\left\{\begin{array}{ll}1,\hfill & {\rho }_{\epsilon \_\text{pu}}\le {\rho }_{\lim }\hfill \\ 1+\frac{h}{{\rho }_{\lim }}\cdot \left({\rho }_{\epsilon \_\text{pu}}-{\rho }_{\lim }\right),\hfill & {\rho }_{\epsilon \_\text{pu}}>{\rho }_{\lim }\hfill \end{array}\right)$

[00038]${\rho }_{\epsilon \_\text{pu}}=\left|\frac{{\rho }_{\epsilon }}{T_{\text{N}}}\right|$

where p.sub.lim and h are the fixed component limit value and linear variation coefficient of the adaptive weight factor, respectively; p.sub.ε_pu and T.sub.N are the per-unit value of the fixed component of the torque synchronization error and the rated torque of the motor, respectively.

[0057] The definition and parameter selection of the adaptive weight coefficients λ̃.sub.d and λ̃.sub.q corresponding to d-axis and q-axis current tracking errors are similar, in which the initial weight coefficient of the d-axis current tracking error is 1-λ, and the initial weight coefficient of the q-axis current tracking error is λ.

[0058] In a unit switching cycle, the controller adjusts the weight coefficient online and in real time through adaptive factors according to the system running state, which provides a practical method for the design of the weight coefficient. The adaptive weight coefficient can improve the adaptability of the system while maintaining the stable operation of the system. The adaptive weight coefficient of each error item obtained by online calculation is applied to the model prediction current control online rolling optimization process of the two-motor torque synchronization system, as shown in FIG. 3, and the process can be summarized as follows: [0059] 1) The current values of the two motors were obtained at kT.sub.s by sampling, all switch state combinations were substituted by considering the delay compensation into the two-motor unified prediction model, and the fixed components p.sub.di, p.sub.qi, p.sub.ε, free components τ.sub.di, τ.sub.qi, τ.sub.ε and the simplified form p̃.sub.di , p̃.sub.qi , p̃.sub.ε (i=1,2) of the fixed components of the d-axis and q-axis current tracking error and torque synchronization error of the two motors at (k+2)T.sub.s were calculated. [0060] 2) The adaptive weight coefficient of each error item and the error components of the two motors at (k+2)T.sub.s were substituted into the value function based on the free component of the error item for online evaluation. [0061] 3) A group of switch state feedbacks that can minimize the value of the value function is selected based on the free component of the error item as the output of the inverter stages of the two motors at (k+1)T.sub.s.. [0062] 4) The sampling time was moved back, k=k+1, and the above processes were repeated.

[0063] To sum up, in the method for model predictive current control of the two-motor torque synchronization system driven by an indirect matrix converter, the rectifier stage adopts a simple modulation solution with unit power factor controllability. The two motors and inverter stage adopt MPCC strategy, which can realize the independent control of the power grid side and motor side of the system. The value function based on the free components of error items and the adaptive weight coefficients provided by the present disclosure quantifies the offset degree of the free components of each error item to the fixed components, and adjusts the weight coefficients online through the adaptive factors, thereby improving the selection mechanism of the optimal voltage vector combination of the system, and simultaneously reducing the complexity and calculation amount of the system design. The MPCC strategy provided by the present disclosure can restrain the torque synchronization error and improve the torque synchronization performance of the system while ensuring the current tracking performance of the system, thereby realizing the dynamic balance of the performance of a plurality of control variables, and providing the possibility for expansion to a multi-motor system.

[0064] The present disclosure is not limited to the embodiments described above. The above description of specific embodiments is intended to describe and illustrate the technical solution of the present disclosure, and the above specific embodiments are illustrative but not restrictive. Without departing from the spirit and scope of the present disclosure, those skilled in the art can make other specific changes in various forms under the inspiration of the present disclosure, which are all within the scope of the present disclosure.