CN103560722B - A kind of permanent magnet linear synchronous motor controls device and method - Google Patents

Abstract

A kind of permanent magnet linear synchronous motor controls device and method, belongs to fields of numeric control technique.Given permanent magnet linear synchronous motor position signalling, this position signalling is converted to the voltage and current signal controlling motor rotation, makes motor movement.Gather the position of permanent magnet linear synchronous motor mover, speed and current signal；Adopt complementary Sliding mode variable structure control algorithm, it is determined that the control electric current of motor.Dsp processor utilizes the current controling signal adjusted, and produces six road pwm pulse signals, drives permanent magnet linear synchronous motor to run.The present invention adopts complementary Sliding Mode Controller that position error signal is processed and calculates, sliding-mode surface have employed the design that broad sense sliding-mode surface combines with complementary sliding-mode surface, this design can make system mode move to the point of intersection of two sliding-mode surfaces, system is made to have relatively Traditional control response speed faster, and site error precision is improved significantly, permanent magnet linear synchronous motor is made to have the servosystem performance of high speed, high accuracy and strong robustness.

Description

A kind of permanent magnet linear synchronous motor controls device and method

Technical field

The invention belongs to fields of numeric control technique, control device and method particularly to a kind of permanent magnet linear synchronous motor.

Background technology

In recent years, along with the performance of power electronic devices improves constantly, directly driving reaching its maturity of control technology, the permanent magnetic linear synchronous motor for Digit Control Machine Tool is subject to the people's attention, in body and control strategy, expand substantial amounts of research, and achieve considerable achievement.High-grade, digitally controlled machine tools employing linear electric motors driving is following development trend, high thrust linear electric motors are becoming the key foundation parts of high-grade, digitally controlled machine tools, country also will vigorously support and advance linear electric motors to control the research with actuation techniques, so the control technology that research linear electric motors are new, improve China's theoretical research in linear electric motors field and commercial Application level is significant.

Since nearly half a century, although the technology of feeding drive of Digit Control Machine Tool is being updated, but most of servosystem feeding modes are still " electric rotating machine+leading screw ", system stiffness is substantially reduced, intermediate link reduces its rapidity when acceleration and deceleration, and this leverages the servo performance of servosystem.And permanent magnet linear synchronous motor utilizes high-energy permanent magnet, save intermediate conversion mechanism, have that thrust strength is big, loss is low, operational reliability is high, time constant is little, device is simple, respond the features such as fast, drastically increase quick-reaction capability and the kinematic accuracy of feed system.Owing to permanent magnet linear synchronous motor is unshakable in one's determination dramatically different with the Distribution of Magnetic Field of intermediate position with two end regions of winding, adds the uncertain factors such as Parameter Perturbation, be difficult to set up accurately the mathematical model of permanent magnet linear synchronous motor.Simultaneously as linear electric motors adopt direct drive mode, the uncertain factor such as the load disturbance of system, Parameter Perturbation will bear directly against motor, without the buffering course of any centre, this considerably increases the control difficulty of linear electric motors.

At present, both at home and abroad after deliberation and delivered a lot of control theory and control algolithm to improve the precision of alignment system.But, under meeting the premise of reliability and stability of alignment system, site error being decreased to minimum is all the same target of these control theories.So, high-accuracy Based Intelligent Control has become as the trend of numerical control machine tool technique development.In these control strategies, Sliding mode variable structure control has better robustness compared with other control methods, and dynamic property is also better.But the tracking error of tradition Sliding mode variable structure control is relatively big, system response time is also relatively slow, and this is difficult to meet high precision performance requirement.

In sum, in order to meet the servosystem performance requirement of the high accuracy of Numeric Control Technology, high speed, need the servo-control system designed suitable in the high speed of permanent magnetic linear synchronous motor, high accuracy and strong robustness, so the present invention proposes a kind of permanent magnet linear synchronous motor and controls device and method.

Summary of the invention

For the defect of prior art existence, it is an object of the invention to provide a kind of permanent magnet linear synchronous motor and control device and method, make the performance of Numeric Control Technology meet the requirement of high accuracy, high speed and strong robustness.

The technical scheme is that and be achieved in that: a kind of permanent magnet linear synchronous motor controls device, including: commutation inversion output circuit, control circuit and permanent magnet linear synchronous motor, wherein,

Commutation inversion output circuit: the alternating current of the fixed amplitude phase value for being provided by power supply carries out ac-dc-ac transform, obtains amplitude, the adjustable alternating current of phase value, supplies permanent magnet linear synchronous motor；Commutation inversion output circuit farther includes: current rectifying and wave filtering circuit and IPM inverter circuit:

Current rectifying and wave filtering circuit: by being connected with three-phase alternating-current supply, is galvanic current by the AC conversion of change；

IPM inverter circuit: for the DC inverter of current rectifying and wave filtering circuit output is become alternating current, supply permanent magnet linear synchronous motor；

Control circuit: for controlling the switching tube break-make in IPM inversion unit, it is achieved the control to permanent magnet linear synchronous motor；Control circuit farther includes: dsp processor, IPM isolation drive protection circuit, current detection circuit and position and speed testing circuit:

Dsp processor: for according to the position, speed and the current signal that receive, performing complementary Sliding mode variable structure control algorithm, produce to control the driving signal of the switching tube break-make in IPM inversion unit；

IPM protective separation drive circuit: be used for isolating IPM inverter circuit and control circuit, and for driving six IGBT work in IPM inverter circuit；

Current detection circuit: for the current-mode analog quantity of collection is changed into the digital quantity that dsp processor may identify which；

Position and speed testing circuit: can by the digital quantity of dsp processor identification for the position and speed signal of grating scale collection is converted into；

Described current rectifying and wave filtering circuit connects permanent magnet linear synchronous motor through the outfan of IPM inverter circuit; IPM inverter circuit connects a road input of dsp processor through current detection circuit; the outfan of permanent magnet linear synchronous motor is connected to another road input of dsp processor through grating scale, position and speed testing circuit, and a road outfan of dsp processor is connected to another road input of IPM inverter circuit through IPM protective separation drive circuit.

The described signal processing in DSP is: after given permanent magnet linear synchronous motor position signalling, difference is done with the actual position signal detected through grating scale, produce position error signal, using the position error signal input quantity as complementary Sliding Mode Controller, current controling signal is calculated through complementary Sliding Mode Controller, current controling signal produces pwm pulse sequence through DSP, pwm pulse sequence controls conducting and the shutoff of six IGBT of IPM inverter circuit, it is met the three-phase alternating current of needs, deliver to the mover of permanent magnet linear synchronous motor, control the mover motion of permanent magnet linear synchronous motor.

A kind of permanent magnet linear synchronous motor control method, comprises the following steps:

Step 1: given permanent magnet linear synchronous motor position signalling, this position signalling is converted to the voltage and current signal controlling motor rotation, makes motor setting in motion；

Step 2: gather the absolute fix signal of permanent magnet linear synchronous motor mover, rate signal and current signal；

After motor movement, grating scale exports biphase quadrature square wave pulse signal and zero pulse signal through position and speed testing circuit, totally three road pulse signal, pulse signal send dsp processor, carry out quadruple process, determine the position skew of mover from the pulse number of biphase quadrature square wave pulse signal, the lead relationship of two-phase pulse obtain turning to of mover, it is thus achieved that the position signalling of mover；Pulse is counted by dsp processor trapped inside unit, obtains the speed of permanent magnet linear synchronous motor divided by the sampling period further according to umber of pulse；Current sensor is utilized to gather mover electric current；

Step 3: utilize the data that step 2 calculates, adopts complementary Sliding mode variable structure control algorithm, draws control rate, i.e. the control electric current of permanent magnet linear synchronous motor, and whole calculating process all realizes in dsp.Specifically comprise the following steps that

Step 3.1: by poor for the absolute fix signal of given permanent magnet linear synchronous motor position signalling Yu permanent magnet linear synchronous motor mover, obtaining system tracking error e is:

E=d_m(t)-d(t)(1)

Wherein, d is permanent magnetic linear synchronous motor rotor position, d_mFor given position；

Step 3.2: set up mechanical motion equation and the dynamical equation of permanent magnet linear synchronous motor, for the system tracking error that step 3.1 obtains, the complementary Sliding Mode Controller of design, obtain control rate, specific as follows:

Step 3.2.1: set up mechanical motion equation and the system dynamics equation of permanent magnet linear synchronous motor, it is determined that permanent magnet linear synchronous motor rotor position and control current relation formula；

Setting up d-q axis coordinate system: for permanent magnet linear synchronous motor, taking permanent magnet first-harmonic excitation field axis (permanent magnet pole axis) is d axle, and advanced 90 degree of electric degree angles of d axle are q axle；

Make current inner loop d shaft current component i_d=0, make stator current vector and magnetic field of permanent magnet spatially orthogonal, then the electromagnetic push equation of permanent magnet linear synchronous motor and mechanical motion equation expression formula are:

F_e=K_fi_q(2)

$F_e=M\stackrel{\·}{v}+Bv+F---\left(3\right)$

In formula, K_fFor electromagnetic push constant, i_qFor q shaft current, mover that M is permanent magnet linear synchronous motor and the load-carrying gross mass of mover, B is viscous friction coefficient, and v is mover speed,Representing the first derivative of mover speed, i.e. mover acceleration, F is disturbance, including parameter of electric machine change, system external disturbance and nonlinear normal modes；

Ignore the impact of disturbance F, utilize mechanical motion equation (3) to obtain dynamical equation ideally to be

$\stackrel{\·\·}{d}\left(t\right)=-\frac{B}{M}\stackrel{\·}{d}\left(t\right)+\frac{K_f}{M}{i}_q=A_n\stackrel{\·}{d}\left(t\right)+B_{n}u---\left(4\right)$

In formula,For the second dervative of rotor position, represent mover acceleration,For the first derivative of rotor position, expression mover speed, u is controller output, u=i_q, i.e. q shaft current, A_n=-B/M, B_n=K_f/M；

When having disturbance F, dynamical equation is:

$\begin{array}{c}\stackrel{\·\·}{d}\left(t\right)=(A_n+\mathrm{\Δ}A)\stackrel{\·}{d}\left(t\right)+(B_n+\mathrm{\Δ}B)u+(C_n+\mathrm{\Δ}C)F\\ =A_n\stackrel{\·}{d}\left(t\right)+B_{n}u+H\end{array}---\left(5\right)$

In formula, C_n=-1/M, Δ A, Δ B and Δ C are the Uncertainty caused by systematic parameter M and B, and H is lump indeterminate, is expressed as:

$H=\mathrm{\Δ}A\stackrel{\·}{d}\left(t\right)+\mathrm{\Δ}Bu+(C_n+\mathrm{\Δ}C)F---\left(6\right)$

Here, suppose that lump indeterminate H bounded, i.e. | H |≤ρ, wherein ρ is a given normal number；

Step 3.2.2: the complementary Sliding Mode Controller of design, sets up broad sense sliding-mode surface s_gWith complementary sliding-mode surface s_c, it is determined that two sliding-mode surface relations；

Broad sense sliding-mode surface s_gIt is defined as:

$\begin{array}{c}{s}_g={(\frac{d}{dt}+\mathrm{\λ})}^2{\∫}_0^{t}e\left(\mathrm{\τ}\right)d\mathrm{\τ}\\ =\stackrel{\·}{e}+2\mathrm{\λ}e+{\mathrm{\λ}}^2{\∫}_0^{t}e\left(\mathrm{\τ}\right)d\mathrm{\τ}\end{array}---\left(7\right)$

In formula, λ is a normal number,For the first derivative of tracking error, and then obtain equation below:

$\begin{array}{c}{\stackrel{\·}{s}}_g=\stackrel{\·\·}{e}+2\mathrm{\λ}\stackrel{\·}{e}+{\mathrm{\λ}}^{2}e\\ =\[{\stackrel{\·\·}{d}}_m\left(t\right)-\stackrel{\·\·}{d}\left(t\right)\]+2\mathrm{\λ}\stackrel{\·}{e}+{\mathrm{\λ}}^{2}e\\ =\[{\stackrel{\·\·}{d}}_m\left(t\right)-A_n\stackrel{\·}{d}\left(t\right)-B_{n}u-H\]+2\mathrm{\λ}\stackrel{\·}{e}+{\mathrm{\λ}}^{2}e\end{array}---\left(8\right)$

In formula,For broad sense sliding-mode surface s_gFirst derivative,For the second dervative of tracking error,Second dervative for given position signal；

Complementary sliding-mode surface s_cIt is defined as:

$\begin{array}{c}{s}_c=(\frac{d}{dt}+\mathrm{\λ})(\frac{d}{dt}-\mathrm{\λ}){\∫}_0^{t}e\left(\mathrm{\τ}\right)d\mathrm{\τ}\\ =\stackrel{\·}{e}-{\mathrm{\λ}}^2{\∫}_0^{t}e\left(\mathrm{\τ}\right)d\mathrm{\τ}\end{array}---\left(9\right)$

According to broad sense sliding-mode surface s_gWith complementary sliding-mode surface s_cObtaining sliding-mode surface summation σ, formula is as follows:

$\mathrm{\σ}\left(t\right)=s_g+s_c=2(\stackrel{\·}{e}+\mathrm{\λ}e)---\left(10\right)$

Determine broad sense sliding-mode surface s_gWith complementary sliding-mode surface s_cRelation be

${\stackrel{\·}{s}}_c+\mathrm{\λ}\mathrm{\σ}\left(t\right)={\stackrel{\·}{s}}_g---\left(11\right)$

Step 3.2.3: according to sliding formwork equivalent control part u_eqWith sliding formwork switching control part u_v, it is determined that Sliding mode variable structure control rate u, formula is:

U=u_eq+u_v(12)

$\begin{array}{cc}{u}_{eq}=\frac{1}{B_n}\[{\stackrel{\·\·}{d}}_m\left(t\right)-A_n\stackrel{\·}{d}\left(t\right)+\mathrm{\λ}(2\stackrel{\·}{e}+\mathrm{\λ}e+s_g)\]& \left(13\right)\\ u_v=\frac{1}{B_n}\[\mathrm{\ρ}sat\left(\frac{s_g+s_c}{\mathrm{\Φ}}\right)\]& \left(14\right)\end{array}$

In formula, Φ is boundary layer thickness, and sat () represents saturation function, and formula is as follows:

$sat\left(\frac{s_g+s_c}{\mathrm{\&Phi;}}\right)=\left\{\begin{array}{cc}1& s_g+s_c\&GreaterEqual;\mathrm{\&Phi;}\\ \frac{s_g+s_c}{\mathrm{\&Phi;}}& -\mathrm{\&Phi;}<s_g+s_c<\mathrm{\&Phi;}\\ 1& s_g+s_c\&le;-\mathrm{\&Phi;}\end{array}\right.---\left(15\right)$

The Sliding mode variable structure control rate u of step 3.2.4: step 3.2.3 output is current controling signal, and this current signal, through IPM inverter circuit, drives permanent magnet linear synchronous motor motion；

The current controling signal that step 4:DSP processor is adjusted according to step 3, DSP produces corresponding six road pwm pulse signals, drives permanent magnet linear synchronous motor to run.

The pwm signal that DSP exports is converted to driving signal by photoelectric isolating driving circuit, after the fixing rectified filter circuit of 220V three-phase alternating current, become galvanic current and deliver to IPM, IPM controls conducting and the shutoff of six IGBT in IPM inverter circuit according to the DSP six road pwm pulse signals produced, it is met the three-phase alternating current of needs, drives permanent magnet linear synchronous motor mover to run.

Beneficial effects of the present invention: the present invention adopts complementary Sliding Mode Controller that position error signal is processed and calculates, sliding-mode surface have employed the design that broad sense sliding-mode surface combines with complementary sliding-mode surface, this design can make system mode move to the point of intersection of two sliding-mode surfaces, and then make system have relatively Traditional control response speed faster, and site error precision is improved significantly, and complementary Sliding mode variable structure control still has the strong robustness feature of traditional sliding formwork.Adopt said method, also make permanent magnet linear synchronous motor have the servosystem performance of high speed, high accuracy and strong robustness.

Accompanying drawing explanation

Fig. 1 is that one embodiment of the present invention one permanent magnet linear synchronous motor controls device general construction block diagram；

Fig. 2 is the structural representation that a kind of permanent magnet linear synchronous motor of one embodiment of the present invention controls device；

Fig. 3 is the circuit theory diagrams of one embodiment of the present invention commutation inversion output circuit；

Fig. 4 is one embodiment of the present invention dsp processor circuit theory diagrams；

Fig. 5 is the circuit theory diagrams of the level-conversion circuit of one embodiment of the present invention DSP power supply；

Fig. 6 is the circuit theory diagrams of one embodiment of the present invention Fault signal acquisition circuit；

Fig. 7 is the circuit theory diagrams of one embodiment of the present invention DSP crystal oscillating circuit；

Fig. 8 is the circuit theory diagrams of one embodiment of the present invention jtag circuit；

Fig. 9 is the circuit theory diagrams of one embodiment of the present invention DSP reset circuit；

Figure 10 is one embodiment of the present invention complementation Sliding Mode Controller structural representation；

Figure 11 is the circuit theory diagrams of one embodiment of the present invention IPM protective separation drive circuit；

Figure 12 is the circuit theory diagrams of one embodiment of the present invention current detection circuit；

Figure 13 is the circuit theory diagrams of one embodiment of the present invention position and speed testing circuit；

Figure 14 is the one embodiment of the present invention permanent magnet linear synchronous motor control method flow chart based on complementary sliding moding structure；

Based on the system tracking error curve chart of tradition Sliding Mode Controller when Figure 15 is embodiment of the present invention permanent magnet linear synchronous motor zero load；

Based on the system tracking error curve chart of complementary Sliding Mode Controller when Figure 16 is embodiment of the present invention permanent magnet linear synchronous motor zero load；

Figure 17 is the embodiment of the present invention permanent magnet linear synchronous motor load when being 40N based on the system tracking error curve chart of tradition Sliding Mode Controller；

Figure 18 is the embodiment of the present invention permanent magnet linear synchronous motor load when being 40N based on the system tracking error curve chart of complementary Sliding Mode Controller.

Detailed description of the invention

Below in conjunction with accompanying drawing, embodiments of the present invention are described in further detail.

A kind of permanent magnet linear synchronous motor controls device, and its population structure is as it is shown in figure 1, include: commutation inversion output circuit 1, control circuit 2 and permanent magnet linear synchronous motor 3.Wherein, commutation inversion output circuit 1 farther includes current rectifying and wave filtering circuit 4 and IPM inverter circuit 5；Control circuit 2 farther includes IPM protective separation drive circuit 6, current detection circuit 7, position and speed testing circuit 8 and dsp processor 9.Additionally, be also associated with grating scale 11 between permanent magnet linear synchronous motor 3 and position and speed testing circuit 8, it is used for gathering actual position signal and the rate signal of permanent magnet linear synchronous motor 3.At the input of the outfan of IPM inverter circuit 5 and current detection circuit 7, being also associated with Hall element 10, be used for gathering current signal actual value, its overall structure schematic diagram is as shown in Figure 2.

In Fig. 2, commutation inversion output circuit 1, as the input of whole control device, is used for receiving the signal of the final movement position of the permanent magnet linear synchronous motor given by user.The alternating current of the fixed amplitude phase value that power supply is provided by commutation inversion output circuit passes through rectification circuit, obtain galvanic current, then unidirectional current passes through IPM inverter circuit, and inversion is the three-phase alternating current that can drive permanent magnet linear synchronous motor, drives permanent magnet linear synchronous motor motion.

In commutation inversion output circuit 1, being connected with IPM inverter circuit 5 of current rectifying and wave filtering circuit 4.Commutation inversion output circuit schematic diagram is as shown in Figure 3.Current rectifying and wave filtering circuit 4 is used for obtaining galvanic current, and the stable DC electricity inversion that IPM inverter circuit 5 is used for being obtained by current rectifying and wave filtering circuit 4 is the three-phase alternating current meeting needs.

Rectifier bridge anode in current rectifying and wave filtering circuit 4 is connected to the N end of IPM main power source, and its negative electrode is connected to the P end of IPM main power source, and the three-phase current of IPM output is connected to permanent magnetic linear synchronous motor PMLSM by lead-out terminal U, V, W.P, N are the IPM main power source input terminal after the rectifying conversion smothing filtering of converter, and P is anode, and N is negative terminal.Rectification filtering unit adopts the uncontrollable rectifier system of bridge-type, and bulky capacitor filters, and so can obtain the constant voltage being suitable for IPM work.

In present embodiment, if after normally opened contact switch A Guan Bi, relay k obtains electric, and then electric shock K and electric shock k all closes, and now whole commutation inversion output circuit and permanent magnet linear synchronous motor are started working.After motor work, if disconnecting normally-closed contact switch B, relay electric-loss, electric shock K and electric shock k all disconnects, and now whole system quits work.During circuit work, three-phase alternating current is through transformator, 220V voltage is changed into virtual value size and is about the three-phase alternating current of IPM input terminal voltage size, then rectified bridge transistor circuit, obtain the DC voltage of pulsation, after bulky capacitor C filters, it is possible to make the DC voltage of pulsation become stable or smooth, then stable voltage is added in the PN two ends of IPM.Now the transformed unidirectional current completed passes through IPM inverter circuit, and inversion is the variable-frequency frequency conversion three-phase alternating current of pressure-variable, drives permanent magnet linear synchronous motor.Wherein the IGBT in IPM inverter circuit is that the pwm pulse sequence exported by control circuit controls its break-make, it is therefore an objective in order to be met the three-phase alternating current of the amplitude phase place of requirement.

In control circuit 2; dsp processor 9 receives the defeated place signal of the output signal from current detection circuit 7 and position and speed testing circuit 8; through the dsp processor 9 process to this two paths of signals, consequential signal is exported to IPM inverter circuit 5 through IPM protective separation drive circuit 6.In present embodiment, the model of dsp processor is TMS320F2812, and its peripheral circuit attachment structure schematic diagram is as shown in Figure 4.Dsp processor peripheral circuit includes level shifting circuit 12, Fault signal acquisition circuit 13, DSP crystal oscillating circuit 14, jtag circuit 15, DSP reset circuit 16, as shown in Fig. 5～9.

12V supply voltage is converted to the DSP 3.3V running voltage powered by level shifting circuit.Fault signal acquisition circuit is connected with dsp processor external interrupt pin, dsp processor interrupt routine carry out handling failure,.Crystal oscillating circuit provides the operating frequency of 30MHz for dsp processor, and the pin 1 of crystal oscillating circuit and pin 4 connect the X1 (77 pin) of DSP, X2 (76 pin) interface respectively.Jtag circuit is for testing the electrical characteristic of chip, and whether detection chip is problematic, and the pin 1,2,3,5,7,11,13,14 of jtag interface circuit connects the pin 126,135,131,69,127,136,137,146 of DSP respectively.Reset circuit is for recovering whole circuit to initial state, and in reset circuit, 1 foot of DS1818 connects 160 feet of DSP.

IPM protective separation drive circuit, as shown in figure 11.IPM protective separation drive circuit has the feature of high integration and small size, its enclosed inside gate-drive control circuit, failure detector circuit and various protection circuit, replaces power device as power device with IPM protective separation drive circuit.After electric current is processed by IPM, passing in permanent magnet linear synchronous motor, motor realizes motion.In the process of motor movement, grating scale detects position and the speed of motor, and current detecting is realized by Hall element.Position, speed and three detection limits of electric current send into dsp processor by testing circuit, and operation result is sent in IPM module by the computing of the control algolithm in DSP, by the control of power device break-make in IPM module, realizing the control to motor.

Biphase current after the output of IPM inverter circuit is connected with two-way current detection circuit through Hall current sensor, and PMLSM is connected with position and speed testing circuit through grating scale.The control terminal of IPM protects circuit to be connected with IPM isolation drive.The input of IPM isolation drive is connected with the PWM port of DSP, and the outfan of current detection circuit is connected with the ADC port of DSP, and the outfan of position and speed testing circuit is connected with the QEP port of DSP.

Current detection circuit, as shown in figure 12.Current detection circuit is three phase promoter electric currents of permagnetic synchronous motor to be entered DSP after sensor convert to and be digital form and carry out a series of conversion.Owing to native system is three-phase balanced system, namely three-phase current vector is zero, therefore has only to detect wherein biphase current, it is possible to obtain three-phase current.Native system adopts LTS25-NP type sensor to detect electric current.

Position and speed testing circuit, as shown in figure 13.Grating scale signal cannot connect directly to DSP pin, so by biphase orthogonal square-wave pulse signal A and B, by high speed photo coupling HCPL4504, delivering to two capturing unit QEP1 of DSP (106 pin) and QEP2 (107 pin).DSP trapped inside unit can use software definition to be quadrature coding pulse input block, pulse can be counted afterwards, may determine that the direction of motion of permanent magnet linear synchronous motor, position and speed according to pulse train.

Complementary Sliding Mode Controller realizes in dsp processor 9, and complementary Sliding mode variable structure control result isoboles in dsp processor 9 is as shown in Figure 10.The input of complementary Sliding Mode Controller is position error signal, i.e. the difference of given position signal and actual position signal.

The described signal processing in DSP is: after given permanent magnet linear synchronous motor position signalling, difference is done with the actual position signal detected through grating scale, produce position error signal, using the position error signal input quantity as complementary Sliding Mode Controller, current controling signal is calculated through complementary Sliding Mode Controller, current controling signal produces pwm pulse sequence through DSP, pwm pulse sequence controls conducting and the shutoff of six IGBT of IPM inverter circuit, it is met the three-phase alternating current of needs, deliver to the mover of permanent magnet linear synchronous motor, control the mover motion of permanent magnet linear synchronous motor.

The permanent magnet linear synchronous motor based on complementary sliding moding structure that present embodiment adopts controls the method that permagnetic synchronous motor is controlled by device, as shown in figure 14, comprises the following steps:

Step 1: given permanent magnet linear synchronous motor position signalling, this position signalling is converted to the voltage and current signal controlling motor rotation, makes motor setting in motion；

Step 2: gather the absolute fix signal of permanent magnet linear synchronous motor mover, rate signal and mover electric current；

After motor movement, grating scale exports biphase quadrature square wave pulse signal and zero pulse signal through position and speed testing circuit, totally three road pulse signal, pulse signal send dsp processor, carry out quadruple process, determine the position skew of mover from the pulse number of biphase quadrature square wave pulse signal, the lead relationship of two-phase pulse obtain turning to of mover, it is thus achieved that the position signalling of mover；Pulse is counted by dsp processor trapped inside unit, obtains the speed of permanent magnet linear synchronous motor divided by the sampling period further according to umber of pulse；Hall element is utilized to gather mover electric current.

Step 3: utilize the data that step 2 calculates, adopts complementary Sliding mode variable structure control algorithm to adjust the position signalling of permanent magnet linear synchronous motor mover, specifically comprises the following steps that

Step 3.1: by poor for the absolute fix signal of given permanent magnet linear synchronous motor position signalling Yu permanent magnet linear synchronous motor mover, obtaining system tracking error e is:

E=d_m(t)-d(t)(1)

Wherein, d is permanent magnetic linear synchronous motor rotor position, d_mFor given position.

Step 3.2: set up permanent magnet linear synchronous motor system equation, for the system tracking error that step 3.1 obtains, the complementary Sliding Mode Controller of design, obtain control rate, specific as follows:

Step 3.2.1: set up mechanical motion equation and the system dynamics equation of permanent magnet linear synchronous motor, it is determined that permanent magnet linear synchronous motor rotor position and control current relation formula；

Setting up d-q axis coordinate system: for permanent magnet linear synchronous motor, taking permanent magnet first-harmonic excitation field axis (permanent magnet pole axis) is d axle, and advanced 90 degree of electric degree angles of d axle are q axle；

Make current inner loop d shaft current component i_d=0, make stator current vector and magnetic field of permanent magnet spatially orthogonal, then the electromagnetic push equation of permanent magnet linear synchronous motor and mechanical motion equation expression formula are:

F_e=K_fi_q(2)

$F_e=M\stackrel{\&CenterDot;}{v}+Bv+F---\left(3\right)$

In formula, K_fFor electromagnetic push constant, i_qFor q shaft current, mover that M is permanent magnet linear synchronous motor and the load-carrying gross mass of mover, B is viscous friction coefficient, and v is mover speed,Representing the first derivative of mover speed, i.e. mover acceleration, F is disturbance, including parameter of electric machine change, system external disturbance and nonlinear normal modes；

Ignoring the impact of disturbance F, utilize mechanical motion equation (3) to obtain dynamical equation ideally, formula is as follows:

$\stackrel{\&CenterDot;\&CenterDot;}{d}\left(t\right)=-\frac{B}{M}\stackrel{\&CenterDot;}{d}\left(t\right)+\frac{K_f}{M}{i}_q=A_n\stackrel{\&CenterDot;}{d}\left(t\right)+B_{n}u---\left(4\right)$

In formula,For the second dervative of rotor position, represent mover acceleration,For the first derivative of rotor position, expression mover speed, u is controller output, A_n=-B/M, B_n=K_f/M；

When having disturbance F, dynamical equation is:

$\begin{array}{c}\stackrel{\&CenterDot;\&CenterDot;}{d}\left(t\right)=(A_n+\mathrm{\&Delta;}A)\stackrel{\&CenterDot;}{d}\left(t\right)+(B_n+\mathrm{\&Delta;}B)u+(C_n+\mathrm{\&Delta;}C)F\\ =A_n\stackrel{\&CenterDot;}{d}\left(t\right)+B_{n}u+H\end{array}---\left(5\right)$

In formula, C_n=-1/M, Δ A, Δ B and Δ C are the Uncertainty caused by systematic parameter M and B, and H is lump indeterminate, is expressed as:

$H=\mathrm{\&Delta;}A\stackrel{\&CenterDot;}{d}\left(t\right)+\mathrm{\&Delta;}Bu+(C_n+\mathrm{\&Delta;}C)F---\left(6\right)$

Here, suppose that lump indeterminate H bounded, i.e. | H |≤ρ, wherein ρ is a given normal number.Controlling purpose is one control system of design, in order to rotor position d (t) can any given instruction d of asymptotic tracking_m(t), it is assumed that d_m(t) and its first derivativeSecond dervativeIt it is all the bounded function about the time.

Step 3.2.2: the complementary Sliding Mode Controller of design, sets up broad sense sliding-mode surface s_gWith complementary sliding-mode surface s_c, it is determined that two sliding-mode surface relations；

In order to realize depositing in case in uncertain factor, permanent magnet linear synchronous motor mover physical location d (t) can accurate tracking given position d_mT (), devises complementary Sliding Mode Controller, in order to solve control problem, it is necessary to find a control rate, reach to control target, the tracking error according to step 3.1 definition, broad sense sliding-mode surface s_gIt is defined as:

$\begin{array}{c}{s}_g={(\frac{d}{dt}+\mathrm{\&lambda;})}^2{\&Integral;}_0^{t}e\left(\mathrm{\&tau;}\right)d\mathrm{\&tau;}\\ =\stackrel{\&CenterDot;}{e}+2\mathrm{\&lambda;}e+{\mathrm{\&lambda;}}^2{\&Integral;}_0^{t}e\left(\mathrm{\&tau;}\right)d\mathrm{\&tau;}\end{array}---\left(7\right)$

In formula, λ is a normal number,For the first derivative of tracking error, formula (6) is differentiated, convolution (5), obtain equation below:

$\begin{array}{c}{\stackrel{\&CenterDot;}{s}}_g=\stackrel{\&CenterDot;\&CenterDot;}{e}+2\mathrm{\&lambda;}\stackrel{\&CenterDot;}{e}+{\mathrm{\&lambda;}}^{2}e\\ =\&lsqb;{\stackrel{\&CenterDot;\&CenterDot;}{d}}_m\left(t\right)-\stackrel{\&CenterDot;\&CenterDot;}{d}\left(t\right)\&rsqb;+\mathrm{\&lambda;}\stackrel{\&CenterDot;}{e}+{\mathrm{\&lambda;}}^{2}e\\ =\&lsqb;{\stackrel{\&CenterDot;\&CenterDot;}{d}}_m\left(t\right)-A_n\stackrel{\&CenterDot;}{d}\left(t\right)-B_{n}u-H\&rsqb;+2\mathrm{\&lambda;}\stackrel{\&CenterDot;}{e}+{\mathrm{\&lambda;}}^{2}e\end{array}---\left(8\right)$

In formula,For broad sense sliding-mode surface s_gFirst derivative,For the second dervative of tracking error,Second dervative for given position signal.

Then, the complementary sliding-mode surface s of design_cFor:

$\begin{array}{c}{s}_c=(\frac{d}{dt}+\mathrm{\&lambda;})(\frac{d}{dt}-\mathrm{\&lambda;}){\&Integral;}_0^{t}e\left(\mathrm{\&tau;}\right)d\mathrm{\&tau;}\\ =\stackrel{\&CenterDot;}{e}-{\mathrm{\&lambda;}}^2{\&Integral;}_0^{t}e\left(\mathrm{\&tau;}\right)d\mathrm{\&tau;}\end{array}---\left(9\right)$

Corresponding to same normal number λ, according to broad sense sliding-mode surface s_gWith complementary sliding-mode surface s_cObtaining sliding-mode surface summation σ, formula is as follows:

$\mathrm{\&sigma;}\left(t\right)=s_g+s_c=2(\stackrel{\&CenterDot;}{e}+\mathrm{\&lambda;}e)---\left(10\right)$

Determine broad sense sliding-mode surface s_gWith complementary sliding-mode surface s_cRelation be

${\stackrel{\&CenterDot;}{s}}_c+\mathrm{\&lambda;}\mathrm{\&sigma;}\left(t\right)={\stackrel{\&CenterDot;}{s}}_g---\left(11\right)$

The liapunov function that complementary Sliding Mode Variable Structure System is selected is:

$V=\frac{1}{2}(s_g^2+s_c^2)---\left(12\right)$

To liapunov function derivation, convolution (8) and formula (11), it is possible to obtain

$\begin{array}{c}\stackrel{\&CenterDot;}{V}=s_g{\stackrel{\&CenterDot;}{s}}_g+s_c{\stackrel{\&CenterDot;}{s}}_c\\ =(s_g+s_c)\&lsqb;{\stackrel{\&CenterDot;\&CenterDot;}{d}}_m\left(t\right)-A_n\stackrel{\&CenterDot;}{d}\left(t\right)-B_{n}u-H+2\mathrm{\&lambda;}\stackrel{\&CenterDot;}{e}+{\mathrm{\&lambda;}}^{2}e-{\mathrm{\&lambda;s}}_c\&rsqb;\end{array}---\left(13\right)$

Step 3.2.3: according to the formula (13) in step 3.2.2, obtains complementary Sliding mode variable structure control rate u；

U=u_eq+u_v(14)

$u_{eq}=\frac{1}{B_n}\&lsqb;{\stackrel{\&CenterDot;\&CenterDot;}{d}}_m\left(t\right)-A_n\stackrel{\&CenterDot;}{d}\left(t\right)+\mathrm{\&lambda;}(2\stackrel{\&CenterDot;}{e}+\mathrm{\&lambda;}e+s_g)\&rsqb;---\left(15\right)$

$u_v=\frac{1}{B_n}\&lsqb;\mathrm{\&rho;}sat\left(\frac{s_g+s_c}{\mathrm{\&Phi;}}\right)\&rsqb;---\left(16\right)$

In formula, u_eqRepresent sliding formwork equivalent control part, u_vRepresenting sliding formwork switching control part, Φ is boundary layer thickness, and sat () represents saturation function, and formula is as follows:

$sat\left(\frac{s_g+s_c}{\mathrm{\&Phi;}}\right)=\left\{\begin{array}{cc}1& s_g+s_c\&GreaterEqual;\mathrm{\&Phi;}\\ \frac{s_g+s_c}{\mathrm{\&Phi;}}& -\mathrm{\&Phi;}<s_g+s_c<\mathrm{\&Phi;}\\ -1& s_g+s_c\&le;-\mathrm{\&Phi;}\end{array}\right.---\left(17\right)$

By formula (8), formula (11) and formula (14) (16), it is substituting in formula (13), can obtain:

$\begin{array}{c}\stackrel{\&CenterDot;}{V}=-\mathrm{\&lambda;}{(s_g+s_c)}^2+(s_g+s_c)(-B_n{u}_v)+(s_g+s_c)(-H)\\ \&le;-\mathrm{\&lambda;}{(s_g+s_c)}^2+(s_g+s_c)(-B_n{u}_v)+|s_g+s_c|\left|H\right|\\ \&le;-\mathrm{\&lambda;}{(s_g+s_c)}^2+|s_g+s_c|\left(\right|H|-\mathrm{\&rho;})\\ =-\mathrm{\&lambda;}{(s_g+s_c)}^2-\mathrm{\&mu;}|s_g+s_c|\&le;0\end{array}---\left(18\right)$

Wherein, | s_g+s_c| >=Φ represents outside boundary region；μ be one on the occasion of.Which ensure that arbitrary site error can arrive boundary region in finite time, namely | s_g+s_c|≤Φ.Additionally, the ultimate bound of position tracking error can be defined as formula:

$\left|e\right|\&le;\frac{\mathrm{\&Phi;}}{2\mathrm{\&lambda;}},\left|\stackrel{\&CenterDot;}{e}\right|\&le;\mathrm{\&Phi;}---\left(19\right)$

Wherein, random time has in boundary region | s_g+s_c|≤Φ。

Owing to two sliding-mode surfaces meet the reaching condition of formula (18) simultaneously, then start from the tracking error outside boundary region and can arrive boundary region in finite time, and along two sliding-mode surface (s_g=s_c=0) common factor slides to zero neighborhood of a point, namelyWithIt may therefore be assured that the convergence of the stability of complementary Sliding mode variable structure system and the tracking error in finite time inner sealing region.

The Sliding mode variable structure control rate u of step 3.2.4: step 3.2.3 output is current controling signal, and this current signal, through IPM inverter circuit, drives permanent magnet linear synchronous motor motion；

The current controling signal that step 4:DSP processor is adjusted according to step 3, DSP produces corresponding six road pwm pulse signals, drives permanent magnet linear synchronous motor to run.

The pwm signal that DSP exports is converted to driving signal by photoelectric isolating driving circuit, after the fixing rectified filter circuit of 220V three-phase alternating current, become galvanic current and deliver to IPM, IPM controls conducting and the shutoff of six IGBT in IPM inverter circuit according to the DSP six road pwm pulse signals produced, it is met the three-phase alternating current of needs, drives permanent magnet linear synchronous motor mover to run.

In order to verify the effectiveness of this algorithm, select permanent magnet linear synchronous motor parameter as follows: electromagnetic push constant K_f=50.7N/A, the mover mass M=16.4kg of permanent magnet linear synchronous motor, viscous friction coefficient B=8.0N s/m.MATLAB is adopted to emulate.

According to the parameter of electric machine provided, and the complementary Sliding Mode Controller of design in the present invention, repeatedly to debug through MATLAB so that effect is optimum, parameter selects as follows: ρ=1.5, λ=8.5, Φ=0.0015.Follow the tracks of signal d_mSetting signal is as follows: 0～10 second is 1mm for amplitude, and frequency is the sine wave of 0.2Hz；10～20 seconds is 1mm for amplitude, and frequency is the sine wave of 0.3Hz.

It is two kinds of situations of 40N with load that load is chosen as unloaded.During permanent magnet linear synchronous motor zero load, based on tradition Sliding Mode Controller system tracking error curve as shown in figure 15, based on complementary Sliding Mode Controller system tracking error curve as shown in figure 16；When permanent magnet linear synchronous motor load is 40N, based on tradition Sliding Mode Controller system tracking error curve as shown in figure 17, based on complementary Sliding Mode Controller system tracking error curve as shown in figure 18.

According to analogous diagram it can be seen that when zero load and load 40N, the tracking error of complementary Sliding Mode Variable Structure System is about the half of the tracking error of tradition Sliding Mode Variable Structure System.And two kinds of Sliding Mode Variable Structure System compare, the tracking error of complementary Sliding Mode Variable Structure System can comparatively fast level off to zero.From analogous diagram it can be seen that complementary Sliding mode variable structure control improves the tracking accuracy of system, the dynamic response of system faster, has stronger robust performance simultaneously, demonstrates the effectiveness of this algorithm.

Although the foregoing describing the specific embodiment of the present invention, but the those skilled in the art in this area should be appreciated that these are merely illustrative of, it is possible to these embodiments are made various changes or modifications, without departing from principles of the invention and essence.The scope of the present invention is only limited by the claims that follow.

Claims (1)

1. a permanent magnet linear synchronous motor control method, adopts permanent magnet linear synchronous motor to control device and is controlled, this device, including: commutation inversion output circuit, control circuit and permanent magnet linear synchronous motor, wherein,

Commutation inversion output circuit: the alternating current of the fixed amplitude phase value for being provided by power supply carries out ac-dc-ac transform, obtains amplitude, the adjustable alternating current of phase value, supplies permanent magnet linear synchronous motor；Commutation inversion output circuit farther includes: current rectifying and wave filtering circuit and IPM inverter circuit:

Current rectifying and wave filtering circuit: by being connected with three-phase alternating-current supply, is galvanic current by the AC conversion of change；

IPM inverter circuit: for the DC inverter of current rectifying and wave filtering circuit output is become alternating current, supply permanent magnet linear synchronous motor；

Control circuit: for controlling the switching tube break-make in IPM inverter circuit, it is achieved the control to permanent magnet linear synchronous motor；Control circuit farther includes: dsp processor, IPM isolation drive protection circuit, current detection circuit and position and speed testing circuit:

Dsp processor: for according to the position, speed and the current signal that receive, performing complementary Sliding mode variable structure control algorithm, produce to control the driving signal of the switching tube break-make in IPM inverter circuit；

IPM protective separation drive circuit: be used for isolating IPM inverter circuit and control circuit, and for driving six IGBT work in IPM inverter circuit；

Current detection circuit: for the current-mode analog quantity of collection is changed into the digital quantity that dsp processor may identify which；

Position and speed testing circuit: can by the digital quantity of dsp processor identification for the position and speed signal of grating scale collection is converted into；

Described current rectifying and wave filtering circuit connects permanent magnet linear synchronous motor through the outfan of IPM inverter circuit; IPM inverter circuit connects a road input of dsp processor through current detection circuit; the outfan of permanent magnet linear synchronous motor is connected to another road input of dsp processor through grating scale, position and speed testing circuit, and a road outfan of dsp processor is connected to another road input of IPM inverter circuit through IPM protective separation drive circuit；

The process processing signal in described dsp processor is: after given permanent magnet linear synchronous motor position signalling, difference is done with the actual position signal detected through grating scale, produce position error signal, using the position error signal input quantity as complementary Sliding Mode Controller, current controling signal is calculated through complementary Sliding Mode Controller, current controling signal produces pwm pulse sequence through DSP, pwm pulse sequence controls conducting and the shutoff of six IGBT of IPM inverter circuit, it is met the three-phase alternating current of needs, deliver to the mover of permanent magnet linear synchronous motor, control the mover motion of permanent magnet linear synchronous motor；

It is characterized in that: comprise the following steps:

Step 1: given permanent magnet linear synchronous motor position signalling, this position signalling is converted to the voltage and current signal controlling motor rotation, makes motor setting in motion；

Step 2: gather the absolute fix signal of permanent magnet linear synchronous motor mover, rate signal and current signal；

After motor movement, grating scale exports biphase quadrature square wave pulse signal and zero pulse signal through position and speed testing circuit, totally three road pulse signal, pulse signal send dsp processor, carry out quadruple process, determine the position skew of mover from the pulse number of biphase quadrature square wave pulse signal, the lead relationship of two-phase pulse obtain turning to of mover, it is thus achieved that the position signalling of mover；Pulse is counted by dsp processor trapped inside unit, obtains the speed of permanent magnet linear synchronous motor divided by the sampling period further according to umber of pulse；Current sensor is utilized to gather mover electric current；

Step 3: utilize the data that step 2 calculates, adopts complementary Sliding mode variable structure control algorithm, draws control rate, i.e. the control electric current of permanent magnet linear synchronous motor, and whole calculating process all realizes in dsp；Specifically comprise the following steps that

Step 3.1: by poor for the absolute fix signal of given permanent magnet linear synchronous motor position signalling Yu permanent magnet linear synchronous motor mover, obtaining system tracking error e is:

E=d_m(t)-d(t)(1)

Wherein, d is permanent magnetic linear synchronous motor rotor position, d_mFor given position；

Step 3.2: set up mechanical motion equation and the dynamical equation of permanent magnet linear synchronous motor, for the system tracking error that step 3.1 obtains, the complementary Sliding Mode Controller of design, obtain control rate, specific as follows:

Step 3.2.1: set up mechanical motion equation and the system dynamics equation of permanent magnet linear synchronous motor, it is determined that permanent magnet linear synchronous motor rotor position and control current relation formula；

Set up d-q axis coordinate system: for permanent magnet linear synchronous motor, take permanent magnet first-harmonic excitation field axis and permanent magnet pole axis is d axle, and advanced 90 degree of electric degree angles of d axle are q axle；

Make current inner loop d shaft current component i_d=0, make stator current vector and magnetic field of permanent magnet spatially orthogonal, then the electromagnetic push equation of permanent magnet linear synchronous motor and mechanical motion equation expression formula are:

F_e=K_fi_q(2)

$F_e=M\stackrel{\&CenterDot;}{v}+Bv+F---\left(3\right)$

In formula, K_fFor electromagnetic push constant, i_qFor q shaft current, mover that M is permanent magnet linear synchronous motor and the load-carrying gross mass of mover, B is viscous friction coefficient, and v is mover speed,Representing the first derivative of mover speed, i.e. mover acceleration, F is disturbance, including parameter of electric machine change, system external disturbance and nonlinear normal modes；

Ignore the impact of disturbance F, utilize mechanical motion equation (3) to obtain dynamical equation ideally to be:

$\stackrel{\&CenterDot;\&CenterDot;}{d}\left(t\right)=-\frac{B}{M}\stackrel{\&CenterDot;}{d}\left(t\right)+\frac{K_f}{M}{i}_q=A_n\stackrel{\&CenterDot;}{d}\left(t\right)+B_{n}u---\left(4\right)$

In formula,For the second dervative of rotor position, represent mover acceleration,For the first derivative of rotor position, expression mover speed, u is controller output, u=i_q, i.e. q shaft current, A_n=-B/M, B_n=K_f/M；

When having disturbance F, dynamical equation is:

$\begin{array}{c}\stackrel{\&CenterDot;\&CenterDot;}{d}\left(t\right)=(A_n+\mathrm{\&Delta;}A)\stackrel{\&CenterDot;}{d}\left(t\right)+(B_n+\mathrm{\&Delta;}B)u+(C_n+\mathrm{\&Delta;}C)F\\ =A_n\stackrel{\&CenterDot;}{d}\left(t\right)+B_{n}u+H\end{array}---\left(5\right)$

In formula, C_n=-1/M, Δ A, Δ B and Δ C are the Uncertainty caused by systematic parameter M and B, and H is lump indeterminate, is expressed as:

$H=\mathrm{\&Delta;}A\stackrel{\&CenterDot;}{d}\left(t\right)+\mathrm{\&Delta;}Bu+(C_n+\mathrm{\&Delta;}C)F---\left(6\right)$

Here, suppose that lump indeterminate H bounded, i.e. | H |≤ρ, wherein ρ is a given normal number；

Step 3.2.2: the complementary Sliding Mode Controller of design, sets up broad sense sliding-mode surface s_gWith complementary sliding-mode surface s_c, it is determined that two sliding-mode surface relations；

Broad sense sliding-mode surface s_gIt is defined as:

$\begin{array}{c}{s}_g={(\frac{d}{dt}+\mathrm{\&lambda;})}^2{\&Integral;}_0^{t}e\left(\mathrm{\&tau;}\right)d\mathrm{\&tau;}\\ =\stackrel{\&CenterDot;}{e}+2\mathrm{\&lambda;}e+{\mathrm{\&lambda;}}^2{\&Integral;}_0^{t}e\left(\mathrm{\&tau;}\right)d\mathrm{\&tau;}\end{array}---\left(7\right)$

In formula, λ is a normal number,For the first derivative of tracking error, and then obtain equation below:

$\begin{array}{c}{\stackrel{\&CenterDot;}{s}}_g=\stackrel{\&CenterDot;\&CenterDot;}{e}+2\mathrm{\&lambda;}\stackrel{\&CenterDot;}{e}+{\mathrm{\&lambda;}}^{2}e\\ =\&lsqb;{\stackrel{\&CenterDot;\&CenterDot;}{d}}_m\left(t\right)-\stackrel{\&CenterDot;\&CenterDot;}{d}\left(t\right)\&rsqb;+2\mathrm{\&lambda;}\stackrel{\&CenterDot;}{e}+{\mathrm{\&lambda;}}^{2}e\\ =\&lsqb;{\stackrel{\&CenterDot;\&CenterDot;}{d}}_m\left(t\right)-A_n\stackrel{\&CenterDot;}{d}\left(t\right)-B_{n}u-H\&rsqb;+2\mathrm{\&lambda;}\stackrel{\&CenterDot;}{e}+{\mathrm{\&lambda;}}^{2}e\end{array}---\left(8\right)$

In formula,For broad sense sliding-mode surface s_gFirst derivative,For the second dervative of tracking error,Second dervative for given position signal；

Complementary sliding-mode surface s_cIt is defined as:

$\begin{array}{c}{s}_c=(\frac{d}{dt}+\mathrm{\&lambda;})(\frac{d}{dt}-\mathrm{\&lambda;}){\&Integral;}_0^{t}e\left(\mathrm{\&tau;}\right)d\mathrm{\&tau;}\\ =\stackrel{\&CenterDot;}{e}-{\mathrm{\&lambda;}}^2{\&Integral;}_0^{t}e\left(\mathrm{\&tau;}\right)d\mathrm{\&tau;}\end{array}---\left(9\right)$

According to broad sense sliding-mode surface s_gWith complementary sliding-mode surface s_cObtaining sliding-mode surface summation σ, formula is as follows:

$\mathrm{\&sigma;}\left(t\right)=s_g+s_c=2(\stackrel{\&CenterDot;}{e}+\mathrm{\&lambda;}e)---\left(10\right)$

Determine broad sense sliding-mode surface s_gWith complementary sliding-mode surface s_cRelation be

${\stackrel{\&CenterDot;}{s}}_c+\mathrm{\&lambda;}\mathrm{\&sigma;}\left(t\right)={\stackrel{\&CenterDot;}{s}}_g---\left(11\right)$

Step 3.2.3: according to sliding formwork equivalent control part u_eqWith sliding formwork switching control part u_v, it is determined that Sliding mode variable structure control rate u, formula is:

U=u_eq+u_v(12)

$u_{eq}=\frac{1}{B_n}\&lsqb;{\stackrel{\&CenterDot;\&CenterDot;}{d}}_m\left(t\right)-A_n\stackrel{\&CenterDot;}{d}\left(t\right)+\mathrm{\&lambda;}(2\stackrel{\&CenterDot;}{e}+\mathrm{\&lambda;}e+s_g)\&rsqb;---\left(13\right)$

$u_v=\frac{1}{B_n}\&lsqb;\mathrm{\&rho;}sat\left(\frac{s_g+s_c}{\mathrm{\&Phi;}}\right)\&rsqb;---\left(14\right)$

In formula, Φ is boundary layer thickness, and sat () represents saturation function, and formula is as follows:

$sat\left(\frac{s_g+s_c}{\mathrm{\&Phi;}}\right)=\left\{\begin{array}{cc}1& s_g+s_c\&GreaterEqual;\mathrm{\&Phi;}\\ \frac{s_g+s_c}{\mathrm{\&Phi;}}& -\mathrm{\&Phi;}<s_g+s_c<\mathrm{\&Phi;}\\ -1& s_g+s_c\&le;-\mathrm{\&Phi;}\end{array}\right.---\left(15\right)$

The liapunov function that complementary Sliding Mode Variable Structure System is selected is:

$V=\frac{1}{2}(s_g^2+s_c^2)---\left(16\right)$

To liapunov function derivation, convolution (8) and formula (11), it is possible to obtain

$\begin{array}{c}\stackrel{\&CenterDot;}{V}=s_g{\stackrel{\&CenterDot;}{s}}_g+s_c{\stackrel{\&CenterDot;}{s}}_c\\ =(s_g+s_c)\&lsqb;{\stackrel{\&CenterDot;\&CenterDot;}{d}}_m\left(t\right)-A_n\stackrel{\&CenterDot;}{d}\left(t\right)-B_{n}u-H+2\mathrm{\&lambda;}\stackrel{\&CenterDot;}{e}+{\mathrm{\&lambda;}}^{2}e-{\mathrm{\&lambda;s}}_c\&rsqb;\end{array}---\left(17\right)$

By formula (8), formula (11) and formula (12)-(14), it is substituting in formula (17), can obtain:

$\begin{array}{c}\stackrel{\&CenterDot;}{V}=-\mathrm{\&lambda;}{(s_g+s_c)}^2+(s_g+s_c)(-B_n{u}_v)+(s_g+s_c)(-H)\\ \&le;-\mathrm{\&lambda;}{(s_g+s_c)}^2+(s_g+s_c)(-B_n{u}_v)+|s_g+s_c|\left|H\right|\\ \&le;-\mathrm{\&lambda;}{(s_g+s_c)}^2+|s_g+s_c|\left(\right|H|-\mathrm{\&rho;})\\ =-\mathrm{\&lambda;}{(s_g+s_c)}^2-\mathrm{\&mu;}|s_g+s_c|\&le;0\end{array}---\left(18\right)$

Wherein, | s_g+s_c| >=Φ represents outside boundary region；μ be one on the occasion of；Which ensure that arbitrary site error can arrive boundary region in finite time, namely | s_g+s_c|≤Φ；Additionally, the ultimate bound of position tracking error can be defined as formula:

$\left|e\right|\&le;\frac{\mathrm{\&Phi;}}{2\mathrm{\&lambda;}},\left|\stackrel{\&CenterDot;}{e}\right|\&le;\mathrm{\&Phi;}---\left(19\right)$

Wherein, random time has in boundary region | s_g+s_c|≤Φ；

Owing to two sliding-mode surfaces meet the reaching condition of formula (18) simultaneously, then start from the tracking error outside boundary region and can arrive boundary region in finite time, and along two sliding-mode surface s_g=s_cThe common factor of=0 slides to zero neighborhood of a point, namelyWithIt may therefore be assured that the convergence of the stability of complementary Sliding mode variable structure system and the tracking error in finite time inner sealing region；

The Sliding mode variable structure control rate u of step 3.2.4: step 3.2.3 output is current controling signal, and this current signal, through IPM inverter circuit, drives permanent magnet linear synchronous motor motion；

The current controling signal that step 4:DSP processor is adjusted according to step 3, DSP produces corresponding six road pwm pulse signals, drives permanent magnet linear synchronous motor to run；

The pwm signal that DSP exports is converted to driving signal by photoelectric isolating driving circuit, after the fixing rectified filter circuit of 220V three-phase alternating current, become galvanic current and deliver to IPM, IPM controls conducting and the shutoff of six IGBT in IPM inverter circuit according to the DSP six road pwm pulse signals produced, it is met the three-phase alternating current of needs, drives permanent magnet linear synchronous motor mover to run.