SPMSM sensorless composite control method with dual sliding-mode observers

Abstract

A PMSM sensorless composite control method with dual sliding-mode observers is provided. In particular, two sliding-mode observers are designed, one provides an exponential piecewise sliding-mode function for observation of back electromotive force, and the other sliding-mode observer is for observation of load torque and fine-tuning parameters of a piecewise PI controller while introducing an estimated load torque onto a q-axis for feedforward compensation. A q-axis current inner loop is designed with a second-order sliding-mode controller, which can improve tracking performance of q-axis current and indirectly control an electromagnetic torque. The exponential piecewise sliding-mode function is more conductive to the observation of back electromotive force and can weaken the buffeting phenomenon. The sliding-mode observer for observing the load torque fine-tunes parameters of the piecewise PI controller while performing the feedforward compensation, the load capability of the system is improved. The second-order sliding-mode controller can reduce a torque ripple.

Claims

1. A composite control method with dual sliding-mode observers for sensorless control of a permanent magnet synchronous motor (PMSM) in medium and high speed domains, comprising: (1) sampling a three-phase current i.sub.abc and a three-phase voltage u.sub.abc, obtaining a current i.sub.αβ and a voltage u.sub.αβ in a stationary coordinate system after performing Clark coordinate transformation on the three-phase current i.sub.abc and the three-phase voltage u.sub.abc, obtaining an estimated current in the stationary coordinate system after an integral operation based on a reconstructed PMSM current state equation, performing a difference operation between the estimated current in the stationary coordinate system and the current i.sub.αβ in the stationary coordinate system to obtain a current error , setting the current error as a sliding-mode surface s.sub.αβ, and observing a back electromotive force (EMF) according to an exponential piecewise sliding-mode function z(s.sub.αβ), wherein an expression of the exponential piecewise sliding-mode function is that: $z\left(s_{\alpha \beta }\right)=\{\begin{array}{cc}1,& s_{\mathrm{\alpha \beta }}\ge \sigma \\ \frac{s_{\mathrm{\alpha \beta }}^2}{{\sigma }^2\left(1+e^{-\sigma }\right)},& 0\le s_{\mathrm{\alpha \beta }}<\sigma \\ \frac{s_{\mathrm{\alpha \beta }}^2}{{\sigma }^2\left(1+e^{-\sigma }\right)},& -\sigma \le s_{\mathrm{\alpha \beta }}<0\\ -1,& s_{\mathrm{\alpha \beta }}<-\sigma \end{array}$ where σ is a thickness of a boundary layer, and s.sub.αβ is the sliding-mode surface; (2) determining a load sliding-mode observer for observation of load torque, using a mechanical angular speed and a feedback quadrature-axis (q-axis) current as input, outputting an estimated load torque , using a magnitude of the estimated load torque as a judgement condition to switch parameters of a rotational speed outer loop piecewise proportional-integral (PI) controller, and adding the estimated load torque on a q-axis estimated current for feedforward compensation; and (3) using a q-axis current error as a sliding-mode surface, and determining a second-order sliding-mode controller to indirectly control an electromagnetic torque.

2. The composite control method with dual sliding-mode observers for sensorless control of a permanent magnet synchronous motor in medium and high speed domains according to claim 1, wherein the load sliding-mode observer is to observe a load torque to thereby fine-tune parameters of the piecewise PI controller while add the estimated load torque on a q-axis for feedforward compensation.

3. The composite control method with dual sliding-mode observers for sensorless control of a permanent magnet synchronous motor in medium and high speed domains according to claim 1, wherein a q-axis current inner loop uses the second-order sliding-mode controller based on a super-twisting algorithm, and the sliding-mode surface using the q-axis current error is expressed as that:
s.sub.q=−i.sub.q; and the controller for q-axis current is expressed as that: $\{\begin{array}{c}{u}_q=-K_p{.Math.s_q.Math.}^{0.5}\mathrm{sign}\left(s_q\right)+u_{\mathrm{sq}}\\ \frac{{\mathrm{du}}_{\mathrm{sq}}}{\mathrm{dt}}=K_i\mathrm{sign}\left(s_q\right)\end{array},$ where u.sub.q is a q-axis output voltage, sign( ) is sign function, K.sub.p and K.sub.i adjustable parameters.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) The invention is further described below in combination with the accompanying drawings and embodiments.

(2) FIG. 1 illustrates a schematic principle block diagram of a SPMSM composite control method with dual sliding-mode observers according to the invention.

(3) FIG. 2 illustrates an exponential piecewise sliding-mode function according to the invention.

(4) FIG. 3 illustrates a schematic principle block diagram of an exponential piecewise sliding-mode observer according to the invention.

(5) FIG. 4 illustrates a schematic flowchart of a piecewise PI controller according to the invention.

(6) FIG. 5a illustrates a schematic diagram of rotational speed of a SPMSM sensorless composite control method with dual sliding-mode observers according to the invention.

(7) FIG. 5b illustrates a schematic diagram of rotational speed of a SPMSM sensorless control method with a traditional sliding-mode observer.

(8) FIG. 6a illustrates a schematic diagram of rotational speed error of the SPMSM sensorless composite control method with the dual sliding-mode observers according to the invention.

(9) FIG. 6b illustrates a schematic diagram of rotational speed error of the SPMSM sensorless control method with the traditional sliding-mode observer.

(10) FIG. 7a illustrates a schematic diagram of electromagnetic torque of the SPMSM sensorless composite control method with the dual sliding-mode observers according to the invention.

(11) FIG. 7b illustrates a schematic diagram of electromagnetic torque of the SPMSM sensorless control method with the traditional sliding-mode observer.

(12) FIG. 8 illustrates a schematic diagram of rotor position of the SPMSM sensorless composite control method with the dual sliding-mode observers according to the invention.

(13) FIG. 9 illustrates a schematic diagram of load torque estimated by a load sliding-mode observer according to the invention.

(14) FIG. 10 illustrates a schematic diagram of a load torque error between the load torque estimated by the load sliding-mode observer and an actual load torque according to the invention.

DETAILED DESCRIPTION OF EMBODIMENTS

(15) A hardware environment of the invention may use DSP28335 launched by TI (Texas Instruments) company as a main control chip of an experimental platform, and choose IKCM30F60GA model of Infineon company as a driver module. The experimental platform mainly carries out some basic protections for abnormal states such as overcurrent, overvoltage and overtemperature, and samples real-time current and voltage on PMSM three-phase windings. A control algorithm of the invention may be mainly realized by writing a C language program through CCS6.2 (code composer studio 6.2) software. FIG. 1 illustrates a schematic overall principle block diagram of an embodiment of the invention, and programmed logics are as follows.

(16) A three-phase current i.sub.abc and a three-phase voltage u.sub.abc on the PMSM windings are sampled through three sampling resistors of a phase current sampling circuit on the driver module, and then are converted into digital signals, and after equal amplitude Clark transformation, real-time sampled current i.sub.αβ and voltage u.sub.αβ in a stationary coordinate system are obtained.

(17) A current state equation of the permanent magnet synchronous motor in the stationary coordinate system is that:

(18) $\{\begin{array}{c}\frac{{\mathrm{di}}_{\alpha }}{\mathrm{dt}}=\frac{R_s}{L_s}{i}_{\alpha }+\frac{u_{\alpha }}{L_s}-\frac{e_{\alpha }}{L_s}\\ \frac{{\mathrm{di}}_{\beta }}{\mathrm{dt}}=\frac{R_s}{L_s}{i}_{\beta }+\frac{u_{\beta }}{L_s}-\frac{e_{\beta }}{L_s}\end{array}.$

(19) According to the exponential sliding-mode observer in FIG. 3, the current state equation of the permanent magnet synchronous motor in the stationary coordinate system is reconstructed as that:

(20) $\{\begin{array}{c}\frac{d\widehat{i_{\alpha }}}{\mathrm{dt}}=\frac{R_s}{L_s}\widehat{i_{\alpha }}+\frac{u_{\alpha }}{L_s}-\frac{\mathrm{Kz}\left(s_{\alpha }\right)}{L_s}\\ \frac{d\widehat{i_{\beta }}}{\mathrm{dt}}=\frac{R_s}{L_s}\widehat{i_{\beta }}+\frac{u_{\beta }}{L_s}-\frac{\mathrm{Kz}\left(s_{\beta }\right)}{L_s}\end{array}$

(21) where, K is a sliding-mode gain, R.sub.s and L.sub.s respectively are stator resistance and inductance, i.sub.α, i.sub.β, u.sub.α, u.sub.β respectively are stator currents and voltages in the stationary coordinate system; e.sub.α, e.sub.β respectively are components on α and β axes of a back EMF, w.sub.e is an electrical angular speed, ψ.sub.f is a permanent magnet flux linkage, θ.sub.e is an electrical angle, Z(s.sub.αβ) is an exponential piecewise sliding-mode function according to the invention and a function characteristic is shown in FIG. 2; “{circumflex over ( )}” represents an estimated value, and “˜” represent an error value.

(22) The real-time sampled current i.sub.αβ and voltage u.sub.αβ sampled by the phase current sampling circuit on the driver module are used as input, the estimated current is obtained after an integral operation, and then subtracted by the real-time sampled current i.sub.αβ to obtain the real-time current error . The real-time error is used as input of the exponential piecewise sliding-mode function Z(s.sub.αβ), then is multiplied by the sliding-mode gain K, and a low-pass filter is used to filter out redundant high-order harmonic interference in an equivalent back EMF to obtain the estimated back EMF and , at this time, =−ψ.sub.f sin , =ψ.sub.f cos . and are input to a divider for division operation to obtain a tangent value of an estimated electrical angle , and then the estimated electrical angle is obtained through an arctangent function operation, and are first performed with calculation of the sum of squares and then performed with calculation of square root to obtain Ψ.sub.f, and the obtained Ψ.sub.f then is divided by the permanent magnet flux linkage Ψ.sub.f through a divider to obtain an estimated electrical angular speed , and the estimated electrical angle and the estimated electrical angular speed are used to realize speed loop closed-loop and Park transformation of vector control for the permanent magnet synchronous motor.

(23) An embodiment of the invention transforms the estimated electrical angular speed calculated by the exponential sliding-mode observer in FIG. 3 into an estimated mechanical angular speed as follows:
=/p

(24) where p is a pole pair number.

(25) The transformed estimated mechanical angular speed and a feedback q-axis current i.sub.q (obtained by Clark transformation and park transformation after sampling the three-phase current on the PMSM windings) are input a load sliding-mode observer designed by the invention, and an estimated load torque is output. The load sliding-mode observer as designed is as follows:

(26) $\left[\begin{array}{c}\stackrel{\stackrel{.}{^}}{w_m}\\ \stackrel{\stackrel{.}{^}}{T_L}\end{array}\right]=\left[\begin{array}{cc}0& -\frac{1}{J}\\ 0& 0\end{array}\right]\left[\begin{array}{c}\widehat{w_m}\\ \widehat{T_L}\end{array}\right]+\left[\begin{array}{c}\frac{1}{J}\\ 0\end{array}\right]T_e+\left[\begin{array}{c}1\\ l\end{array}\right]U$

(27) where s.sub.w is a difference of a mechanical angular speed observed by the load sliding-mode observer subtracting the mechanical angular speed observed by the exponential sliding-mode observer, and a sliding-mode control law is U=−a.sub.1 sign(s.sub.w)−a.sub.2s.sub.w; a.sub.1 and a.sub.2 are control parameters.

(28) According to an electromagnetic torque formula of a surface-mounted permanent magnet synchronous motor that T.sub.e=T.sub.L=1.5ψ.sub.fi.sub.q, the load torque estimated by the load sliding-mode observer is transformed into a q-axis current compensation value, and added to the output of rotational speed loop piecewise PI controller for feedforward compensation, so that when the system is suddenly added with a load, a sudden drop of speed can be smaller and the response can be faster, thereby improving the load capability of the system.

(29) Because the temperature of a motor will rise and the inductance parameter of the motor will change greatly during an on-load operation of the motor, it is difficult for a single PI controller to adapt to the two working conditions of no-load and on-load, the illustrated embodiment of the invention uses the load torque estimated by the designed load sliding-mode observer as a judgment condition of the rotational speed loop piecewise PI controller, and fine-tunes parameters of the rotational speed loop piecewise PI controller. FIG. 4 illustrates a schematic flowchart of the piecewise PI controller according to the invention, and adjustment criteria of parameters of the piecewise PI controller as follows.

(30) (1) when the estimated load torque is less than a preset error tolerance ε, PI parameters of rotational speed outer loop with no-load operation are used.

(31) (2) when the estimated load torque is greater than the preset error tolerance ε, PI parameters of rotational speed outer loop with on-load operation are used.

(32) The output of the rotational speed outer loop piecewise PI controller after feedforward compensation is subtracted with the feedback q-axis actually sampled current i.sub.q (obtained by Clark transformation and park transformation after sampling the three-phase current on the PMSM windings) in a synchronous rotation coordinate system to obtain the current error , the current error then is input to a second-order sliding-mode controller based on a super-twisting algorithm according to the invention to output an estimated q-axis voltage . The second-order sliding-mode controller based on the super-twisting algorithm is as follows:

(33) $\{\begin{array}{c}{u}_q=-K_p{.Math.s_q.Math.}^{0.5}\mathrm{sign}\left(s_q\right)+u_{\mathrm{sq}}\\ \frac{{\mathrm{du}}_{\mathrm{sq}}}{\mathrm{dt}}=K_i\mathrm{sign}\left(s_q\right)\end{array},$

(34) Where, s.sub.q is a difference of an input value of the piecewise PI controller subtracting the feedback q-axis current value.

(35) The outputs of a d-axis current loop PI controller and the q-axis super-twisting based second-order sliding-mode controller, after Park inverse transformation, are input to the control chip DSP28335, and by means of a modulation of space vector pulse width modulation (SVPWM) algorithm, three pairs of complementary driving signals are obtained to drive on-off of IGBT transistors on three legs in a IPM driver module, and thereby output a three-phase sinusoidal current to the permanent magnet synchronous motor for power supply.

(36) In summary, the composite control method with the dual sliding-mode observers for realizing sensorless control of a permanent magnet synchronous motor in medium and high domains, designs an exponential piecewise sliding-mode function, which has a saturation characteristic of switching function outside a boundary layer, has a small part of step characteristics at the boundary layer, and has characteristics of continuity and exponential approach law inside the boundary layer, and therefore it can avoid multiple jump fluctuations at the sliding surface, and the back EMF observed by the exponential piecewise sliding-mode observer as shown in FIG. 3 is more accurately. The estimated back EMF components and are used to estimate a rotor position by means of an inverse tangent function to obtain an estimated rotor position angle and an estimated electrical angular speed , which can weaken the buffeting phenomenon and improve the accuracy. The estimated electrical angular speed then is transformed into an estimated mechanical angular speed as an input of the load sliding-mode observer, and an estimated load torque is output, and afterwards the estimated load torque is transformed into the q-axis current compensation value and added to the output of the rotational speed loop piecewise PI controller for feedforward compensation, and meanwhile the estimated load torque is used as an judgement condition to fine-tune the parameters of the piecewise PI controller, so that the system can adapt to the two working conditions of no-load and sudden load, thereby improving the load capability of the system. The q-axis current inner loop is designed with super-twisting algorithm based second-order sliding-mode controller to improve q-axis current tracking performance and thereby indirectly control electromagnetic torque and reduce torque ripple.

(37) A simulation model of an embodiment of the invention is built with MATLAB/Simulink, and an application effect of the embodiment of the invention will be described in detail below in combination with simulation waveforms.

(38) As seen from the comparison of FIG. 5a with FIG. 5b, a rotational speed graph of the embodiment of the invention is smoother than that of the traditional sliding-mode observer, the invention can weaken the buffeting phenomenon well, and when a sudden load of 5 N.Math.M is applied at the time of 0.2 s, compared with the traditional sliding-mode observer, the embodiment of the invention has a smaller sudden drop in rotational speed, faster rotational speed recovery and better load capacity. As seen from the comparison of FIG. 6a with FIG. 6b, a rotational speed estimation error of the embodiment of the invention is smaller than a rotational speed estimation error of the traditional sliding-mode observer, and the rotational speed estimation error of the embodiment of the invention is nearly close to 0. As seen from the comparison of FIG. 7a and FIG. 7b, an electromagnetic torque ripple of the embodiment of the invention is smaller than that of the traditional sliding-mode observer. It can be found from FIG. 9 that the load sliding-mode observer designed by the embodiment of the invention can be used to observe the actual load torque in real-time, and the observation effect is accurate and the response is fast. It can be found from FIG. 10 that an error between the estimated load torque of the embodiment of the invention and the actual load torque is close to 0. It can be seen from this set of simulation diagrams that the SPMSM sensorless composite control method with dual sliding-mode observers according to the invention can weaken the buffeting phenomenon and has better dynamic and steady state performances and load capability, which proves the correctness and effectiveness of the invention.