CN101691020A - Sliding formwork control method used in motion control of virtual axis machine tool cutter - Google Patents

Abstract

The invention discloses a sliding formwork control method used in motion control of a virtual axis machine tool cutter, comprising the following steps: planning the space motion trail of the cutter in the processing procedure of a virtual axis machine tool; determining the expected motion trail of each active pair of the virtual axis machine tool in the processing procedure; then establishing the mathematical models of the controlled objects of each control branch circuit of the virtual axis machine tool; detecting and determining the actual motion state of each active pair of the virtual axis machine tool; calculating the function of the switching surface according to the sliding formwork control theory; determining the motor drive controlled variable of each control branch circuit of the virtual axis machine tool and sending to each motor driver; and finally driving each active pair by the motor drive controlled variable of each control branch circuit so as to drive the virtual axis machine tool cutter to realize the expected motion. In the invention, the precise models of the controlled objects of each branch circuit are not needed to be established, and the high-precision control towards the motion of the cutter can be realized by utilizing the excellent characteristics of the sliding formwork control technology; and the controlled variable of the sliding formwork is constituted by continuous functions with no trembling problems.

Description

A kind of sliding-mode control that is used for the virtual axis machine tool cutter motion control

Technical field

The present invention relates to a kind of virtual-shaft machine tool, relate in particular to its motion control method by motor-driven cutter.

Background technology

The key technology of the digital control system of virtual-shaft machine tool (also claiming parallel machine) is by the control to the virtual-shaft machine tool real axis, realizes the interlock control of imaginary axis, thereby obtains desired cutting tool path.Yet because virtual-shaft machine tool is made of many bars parallel moving mechanism, its kinetic model is the complication system of a multiple degrees of freedom, multivariable, highly non-linear, multi-parameter coupling.In mechanism kinematic and machine tooling process, the parameter and the external interference of mechanism model alter a great deal, and have uncertainty.Compare with the machine tool of cascaded structure, the accumulation of its driving error reduces greatly, but still have other factor that influences machining accuracy, as: the manufacturing of lathe and alignment error, drive rod up and down the long deviation of gap, drive rod bar of ball pivot to the kinematic error of influence, executing agency and the kinematic pair of moving platform positional precision, elastic deformation that gravity causes, the deformation that causes of being heated, sensor accuracy or the like.Therefore at present virtual-shaft machine tool is realized that accurate control remains the difficult problem that the control circle generally acknowledges, and become virtual-shaft machine tool and realize one of biggest obstacle of industrialization, practicability at the high accuracy manufacture field, seriously restrict its advantage performance, become the key issue that needs to be resolved hurrily at present.

Improve one of key technology of virtual-shaft machine tool location and machining accuracy, it is the degree of accuracy that improves virtual-shaft machine tool parallel institution Tool Control that moving platform connects firmly, for this reason, people have proposed different control methods, mainly contain error compensation control method, intelligence control method at present and based on self-adaptation control method of model etc.Wherein, the error compensation control method spininess is to specific virtual-shaft machine tool, and produces factor such as rubbing action, vibration effect, gravity effect etc. at specific error and carry out, and therefore, dissimilar virtual-shaft machine tools do not had versatility; Intelligence control method normally carries out the compensation or the inhibition of virtual-shaft machine tool coupling or load disturbance based on artificial neural network, this class control method is comparatively complicated, present many The Realization of Simulation, rare practical application; Carry out the Self Adaptive Control or the robust control method of virtual-shaft machine tool based on model, not only be difficult to realize, and, therefore need set up the mathematical models of virtual-shaft machine tool in advance because its control accuracy depends on model accuracy.Because the complexity of virtual-shaft machine tool parallel institution and add the uncertainty of external interference in man-hour, accurately set up not only unusual difficulty of its Mathematical Modeling, and institute's established model usually very complexity be difficult to be actually used in control.Domestic existing experimental prototype is ignored the coupling between each branch road of virtual-shaft machine tool more, and each branch road is used as fully independently system, implements traditional PID control, must take the error compensation measure could satisfy the virtual-shaft machine tool required precision usually simultaneously.In addition, consult domestic and international patent situation aspect virtual-shaft machine tool as seen, the virtual-shaft machine tool patent is various virtual-shaft machine tool novel mechanisms designs, so far, does not see that pertinent literature proposes more satisfactory control method to virtual-shaft machine tool.

Becoming structure control has developed at present and has a kind ofly controlled the important method of research to having uncertain dynamic system.Variable structure system is a kind of discontinuous feedback control system, and its main feature is that it sets up gliding model on a kind of switching surface, is called " sliding formwork ", and the general type of conventional sliding formwork control law is

u＝u _eq+ηsgn(s)(1)

In the formula (1), η is positive constant; S is the switching surface function; u _EqFor keeping the equivalent control amount of sliding formwork motion; η sgn (s) is intended to the control system uncertainty and interference waits unknown portions.

When digital control systems such as conventional sliding-mode control employing computer realized, its sampling interval can make control output produce small trembling, and influences the accuracy of sliding-mode control.

Summary of the invention

The objective of the invention is to overcome above-mentioned the deficiencies in the prior art, provide a kind of by the sliding-mode control that is used for the virtual axis machine tool cutter motion control motor-driven virtual-shaft machine tool, that have the optimal dynamic quality.

The technical solution used in the present invention is to adopt following steps:

1) cooks up the space motion path of virtual-shaft machine tool process cutter according to processing request, determine the desired motion track of each driving pair of virtual-shaft machine tool in the process;

2) set up the Mathematical Modeling that virtual-shaft machine tool is respectively controlled the branch road controlled device;

3) the actual motion state of detection and definite each driving pair of virtual-shaft machine tool;

4) according to sliding mode control theory compute switch toroidal function;

5) determine that virtual-shaft machine tool respectively controls branch road motor-driven controlled quentity controlled variable and send to each motor driver;

6) drive each driving pair with each control branch road motor-driven controlled quentity controlled variable, realize desired motion thereby drive virtual axis machine tool cutter.

The present invention is applied to sliding-mode control the motion control of the cutter of virtual-shaft machine tool first, and its characteristics and beneficial effect are:

1, with prior art in based on the contrast of the self-adaptation control method of model, sliding-mode control of the present invention is insensitive to system parameter variations and external interference, thereby adopt the control system of sliding-mode control to need not to set up accurate controlled device Mathematical Modeling, its control accuracy need not to depend on model accuracy, need not to consider the coupled problem between a plurality of branch road multivariables of controlled device, only need utilize the good characteristic of sliding formwork control technology, realization can have good control quality to the high accuracy control of virtual axis machine tool cutter motion.

2, sliding formwork gauge tap curved surface parameter not only makes the virtual-shaft machine tool system have the optimal dynamic quality after forming the sliding formwork motion according to the design of second order optimal dynamic QC Quality System, and can reduce control parameter testing workload greatly.

3, definite tool optimal dynamic quality sliding-mode control law is made of continuous function, has continuity, has solved the problem of trembling that conventional sliding formwork control technology exists, and has strengthened the practicality of sliding formwork control technology greatly.

Description of drawings

Below in conjunction with the drawings and specific embodiments the present invention is described in further detail.

Fig. 1 is the System with Sliding Mode Controller schematic diagram of virtual-shaft machine tool.

Fig. 2 is each branch road driving pair desired motion of virtual-shaft machine tool and an actual motion trajectory diagram among Fig. 1, wherein: Fig. 2 a is branch road 1 a driving pair motion tracking curve map, Fig. 2 b is branch road 2 driving pair motion tracking curve maps, Fig. 2 c is branch road 3 driving pair motion tracking curve maps, Fig. 2 d is branch road 4 driving pair motion tracking curve maps, Fig. 2 e is branch road 5 driving pair motion tracking curve maps, and Fig. 2 f is branch road 6 driving pair motion tracking curve maps.

Fig. 3 is each branch road driving pair kinematic error figure of virtual-shaft machine tool, wherein: Fig. 3 a is branch road 1 driving pair kinematic error figure, Fig. 3 b is branch road 2 driving pair kinematic error figure, Fig. 3 c is branch road 3 driving pair kinematic error figure, Fig. 3 d is branch road 4 driving pair kinematic error figure, Fig. 3 e is branch road 5 driving pair kinematic error figure, Fig. 3 f branch road 6 driving pair kinematic error figure.

Fig. 4 is the driving controlled quentity controlled variable of each branch road motor of virtual-shaft machine tool, wherein: Fig. 4 a is the driving control spirogram of branch road 1 motor, Fig. 4 b is the driving control spirogram of branch road 2 motors, Fig. 4 c is the driving control spirogram of branch road 3 motors, Fig. 4 d is the driving control spirogram of branch road 4 motors, Fig. 4 e is the driving control spirogram of branch road 5 motors, and Fig. 4 f is the driving control spirogram of branch road 6 motors.

The specific embodiment

As Fig. 1, cook up the space motion path of process cutter according to processing request after, at first pre-determine the desired motion track of each driving pair of virtual-shaft machine tool in the process and set up the controlled device Mathematical Modeling that virtual-shaft machine tool is respectively controlled branch road; Secondly, obtain each driving pair actual motion state according to each the motor movement state that is detected by each branch road encoder; Then, adopt the tool optimal dynamic quality sliding formwork control law of design in advance to calculate each motor-driven instruction, send to each motor driver (motor servo amplifier), the ball-screw that finally drives virtual-shaft machine tool makes cutter realize desired motion.Concrete grammar is as follows:

1, determines each driving pair desired motion according to the virtual-shaft machine tool processing request in advance

Finish the planning of cutter machining locus according to the virtual-shaft machine tool processing request after,, determine each driving pair of virtual-shaft machine tool (establishing each driving pair is translational motion) expectation displacement x according to the inverse kinematic of virtual-shaft machine tool parallel institution _d(unit is mm), desired motion speed

(unit is mm/s) and desired motion acceleration (unit is mm ²/ s).

2, set up virtual-shaft machine tool in advance and respectively control branch road controlled device Mathematical Modeling

Because the present invention adopts sliding formwork control, its design process nature decoupling zero, therefore can adopt each branch road tool motion control scheme of independent control respectively, compare with the control scheme of having to consider coupling between each branch road (as the Based Intelligent Control scheme of carrying out the coupling compensation), this control scheme need not to analyze coupling and the complicated coupling model of foundation, and therefore design is convenient with realization; Compare with the PID control scheme that each branch road of same employing is independently controlled, when machine tooling, system parameter variations and load are disturbed and are often made PID control can not obtain gratifying control effect, but the performance of System with Sliding Mode Controller is not influenced by system parameter variations and load interference etc.

When adopting each branch road respectively during the sliding mode control schemes of independent control, institute builds the control mathematical model of controlled plant and can independently carry out at each Electric Machine Control branch road, and need not to consider system parameter variations on each branch road and load variations interference etc.Because identical motor and the driver part thereof of the general employing of each branch road of virtual-shaft machine tool parallel institution, therefore to virtual-shaft machine tool, change and during external interference in taking into account system parameter not, at each motor-driven branch road, the Mathematical Modeling of its controlled device has identical form, is made as third-order model here:

$\stackrel{\·\·\·}{x}=a_2\stackrel{\·\·}{x}+a_1\stackrel{\·}{x}+\mathrm{bu}---\left(2\right)$

In the formula (2), u is the controlled quentity controlled variable input, through the digital control system conversion, becomes the instruction that sends to motor servo amplifier (driver), is generally the input pulse number or is aanalogvoltage input quantity (unit is V), and the present invention adopts the latter; B is the controlled quentity controlled variable coefficient; (unit is mm/s) is the actual motion speed of each driving pair of virtual-shaft machine tool;

(unit is mm ²/ s) be the actual motion acceleration of each driving pair of virtual-shaft machine tool;

Be three order derivatives of each driving pair actual displacement of virtual-shaft machine tool; a ₂, a ₁With b be respectively constant coefficient, determine by be provided with parameter and the parameter of electric machine of motor servo amplifier.

If the taking into account system parameter changes and external interference, then virtual-shaft machine tool should be at the controlled device Mathematical Modeling of each motor-driven branch road

$\stackrel{\·\·\·}{x}=a_2\left(t\right)\stackrel{\·\·}{x}+a_1\left(t\right)\stackrel{\·}{x}+\mathrm{bu}+d\left(t\right)---\left(3\right)$

In the formula (3), d (t) is for disturbing.Since in the virtual-shaft machine tool process, systematic parameter a ₂(t), a ₁(t) variation and interference d (t) have uncertainty, so the model of formula (3) in fact is difficult for accurately setting up.

If not adopt each branch road control scheme of independent control respectively, then the dynamics mathematical model of setting up will be one group extremely long and nonlinear time-varying differential equation group that highly be coupled, generally can not provide analytic solutions, can't be used for real-time control.

The above analysis, because the present invention has adopted the sliding formwork control technology, therefore when setting up the controlled device Mathematical Modeling, the linear model of setting up suc as formula (2) gets final product.

Why the performance of System with Sliding Mode Controller does not rely on the degree of accuracy of the controlled device Mathematical Modeling of building, and is that its performance is irrelevant with the original system characteristic, and is determined by the characteristic of switching surface equation because System with Sliding Mode Controller is owing to form sliding formwork.This is the essential attribute of System with Sliding Mode Controller.

3, the actual motion state of detection and definite each driving pair of virtual-shaft machine tool

Detect the motor movement state with encoder that virtual-shaft machine tool is equipped with,, determine the actual motion state of each driving pair of virtual-shaft machine tool according to reducing gear speed reducing ratio or leading screw pitch.

4, compute switch toroidal function

According to sliding mode control theory compute switch toroidal function, corresponding to virtual-shaft machine tool third-order system formula (2), its computing formula is

$s=\stackrel{\&CenterDot;\&CenterDot;}{e}+k_1\stackrel{\&CenterDot;}{e}+{\mathrm{<figure-callout\; id="2e"\; label="k"\; filenames="H2009100360684E0000021.png"\; state="\{\{state\}\}">k</figure-callout>}}_{2}e---\left(4\right)$

In the formula (4), e=x _d-x is the site error (unit is mm) of each driving pair motion of virtual-shaft machine tool; X (unit is mm) is each driving pair actual displacement of virtual-shaft machine tool,

Velocity error (unit is mm/s) for each driving pair motion of virtual-shaft machine tool;

(unit is mm to the acceleration error of moving for each driving pair of virtual-shaft machine tool ²/ s).

In this switching surface function, two adjustable parameter k ₁And k ₂General determine that method is: at first stable for guaranteeing control system, these two parameters must be respectively greater than 0, and then determines finally that by the test adjustment before Computer Simulation or the actual processing obvious, this requires a great deal of time and energy.

For addressing the above problem, the present invention proposes a kind of method of carrying out the switching surface parameter designing by second order optimal dynamic QC Quality System.

According to becoming the structure sliding mode control theory, in a single day System with Sliding Mode Controller forms the sliding formwork motion, and its system performance is determined by the switching surface equation s=0 that the switching surface function is constituted.Because damped coefficient ξ=0.707 an o'clock second-order system has the optimal dynamic quality, according to switch hyperplane equation s=0, has So

By this relation design switch hyperplane parameter, then parameter testing workload will reduce greatly, and can make the virtual-shaft machine tool system have the optimal dynamic quality after producing the sliding formwork motion.According to the switching surface Parameters design that the present invention proposes, switching surface function calculation formula proposed by the invention and that adopt is

$s=\stackrel{\&CenterDot;\&CenterDot;}{e}+1.414\sqrt{{\mathrm{<figure-callout\; id="2e"\; label="k"\; filenames="H2009100360684E0000021.png"\; state="\{\{state\}\}">k</figure-callout>}}_2}\stackrel{\&CenterDot;}{e}{+\mathrm{<figure-callout\; id="2e"\; label="k"\; filenames="H2009100360684E0000021.png"\; state="\{\{state\}\}">k</figure-callout>}}_{2}e---\left(5\right)$

5, determine that virtual-shaft machine tool respectively controls branch road motor-driven controlled quentity controlled variable

Respectively control branch road for virtual-shaft machine tool, motor-driven controlled quentity controlled variable computing formula is:

$u=\frac{1}{b}[{\stackrel{\&CenterDot;\&CenterDot;\&CenterDot;}{x}}_d-a_2{\stackrel{\&CenterDot;\&CenterDot;}{x}}_d-a_1{\stackrel{\&CenterDot;}{x}}_d+(1.414\sqrt{{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="H2009100360684E0000021.png,H2009100360684E0000022.png"\; state="\{\{state\}\}">k</figure-callout>}}_2}+a_2)\stackrel{\&CenterDot;\&CenterDot;}{e}+({\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="H2009100360684E0000021.png,H2009100360684E0000022.png"\; state="\{\{state\}\}">k</figure-callout>}}_2+a_1)\stackrel{\&CenterDot;}{e}]+\mathrm{\&eta;s}---\left(6\right)$

Formula (6) is the designed tool optimal dynamic quality sliding formwork control law of the present invention, wherein

For keeping the equivalent control amount of sliding formwork motion, η s is intended to the control system uncertainty and interference waits unknown portions, and η is positive constant, and its size depends on systematic uncertainty and interference.

Can theoretical proof and simulating, verifying, as long as adjustable parameter η is not too small, when system takes place to disturb or during system parameter variations, because this moment

Bigger, so the virtual-shaft machine tool control system forms the condition of sliding formwork

Certain satisfy, according to sliding mode control theory, this moment virtual-shaft machine tool motion and the processing influence that not changed by parameters such as interference such as load variations or system inertia, have high control precision; When undisturbed or systematic parameter is stablized when system,

Less, system may not meet the sliding formwork condition, but this moment, the motion of virtual-shaft machine tool was near the expectation state place, by control law computing formula (6) and set switching surface function s as seen, non-equivalent control amount part η s in the sliding formwork control law of this moment is equivalent to a PID increment type controller, concerning the virtual-shaft machine tool system running state of this moment, the PID controller can produce fully controls effect preferably.

The present invention is according to the computational methods of sliding formwork control each branch road motor-driven controlled quentity controlled variable that basic theories proposed, the characteristics that are different from conventional computational methods are: replace conventional compute sign function sgn (s) (referring to formula (1)) with slide switch toroidal function s, the change of its symbol is actual identical with former sign function, but its control law is made of continuous function, thereby this sliding mode controller the problem of trembling can not occur when being realized by digital control system, and this has improved the practicality of sliding-mode control greatly.This atremia sliding-mode control is by the motion control of first Application of the present invention in the cutter of virtual-shaft machine tool.

6, drive each driving pair with each control branch road motor-driven controlled quentity controlled variable

By determined each the branch road motor-driven controlled quentity controlled variable of step 5, see computing formula (6),, become (10V, voltage analog 10V) through the digital control system D/A switch.This analog quantity sends to each motor servo amplifier as driving instruction, controls each each driving pair of branch road motor-driven virtual-shaft machine tool, finishes desired motion thereby drive virtual axis machine tool cutter.

One embodiment of the present of invention below are provided:

Embodiment

If virtual-shaft machine tool is made of 6 branch road parallel institutions, drive by AC servomotor, and adopt rolling screw transmission (ball-screw), its control system block diagram is as shown in Figure 1.The specific embodiment of this control method is as follows:

1, determines each driving pair desired motion of virtual-shaft machine tool according to processing request in advance

If according to processing request needs cutter from (20mm) spatial point is linearly moved to (30mm, 30mm, 30mm) spatial point for 20mm, 20mm.According to the virtual-shaft machine tool inverse kinematic, the desired motion track that obtains each branch road driving pair of virtual-shaft machine tool is respectively shown in each subgraph ringlet track among Fig. 2.

2, set up the transfer function of each branch road control object in advance

Each branch road is a controlled device with motor driver and motor, is load with virtual-shaft machine tool parallel institution and cutter, establishes the AC servomotor driver and is set to speed control mode, and its current feedback gain is K _i, the power amplification gain is K _a, the speed ring gain is K _Pre, the speed feedback coefficient is K _vIf the AC servomotor winding resistance is R _p(unit is Ω), winding inductance is L _p(unit is H), torque constant is K _Tp(unit is Nm/A), total rotary inertia is that (unit is kgm to J on the AC servomotor axle ²); If ball-screw pitch is h (unit is mm), then the transfer function of each branch road control object of virtual-shaft machine tool is

$\frac{{1.5K}_{\mathrm{tp}}{K}_a{K}_{\mathrm{pre}}h}{{\mathrm{<figure-callout\; id="3"\; label="L\; p\; JS"\; filenames="H2009100360684E0000032.png,H2009100360684E0000041.png"\; state="\{\{state\}\}">L</figure-callout>}}_p{\mathrm{JS}}^{}{}^3+(R_p+K_a{K}_i){\mathrm{<figure-callout\; id="2"\; label="JS"\; filenames="H2009100360684E0000021.png,H2009100360684E0000022.png"\; state="\{\{state\}\}">JS</figure-callout>}}^2+{1.5K}_{\mathrm{tp}}(K_{\mathrm{tp}}+K_a{K}_v{K}_{\mathrm{pre}})S}=\frac{X\left(S\right)}{U\left(S\right)}---\left(7\right)$

In the formula (7), S is a differential operator, and (corresponding analog quantity is the Laplace transformation amount of (10V, 10V)) to U (S), and X (S) is the Laplace transformation amount of each driving pair displacement x of virtual-shaft machine tool parallel institution (unit is mm) for controller output u.

According to driver setting and motor model, establish that each parameter is in the formula (7): J=0.39kgm ², L _p=0.03837H, R _p=5.09 Ω, K _Pre=88, K _v=0.54, K _i=2.2, K _a=6, K _Tp=3.41Nm/A, leading screw pitch is 5mm.With each parameter substitution formula (7), and formula (7) is turned to the differential equation have

$\stackrel{\&CenterDot;\&CenterDot;\&CenterDot;}{x}=-475.533\stackrel{\&CenterDot;\&CenterDot;}{x}-98388.733\stackrel{\&CenterDot;}{x}+143.692u---\left(8\right)$

3, detect each branch road driving pair actual motion of virtual-shaft machine tool

Directly record the motion state of corresponding each branch road motor by each branch road encoder reading, for leading screw pitch is the virtual-shaft machine tool of 5mm, motor whenever rotates a circle, and the driving pair on the respective branch produces the displacement of 5mm, can obtain each driving pair actual motion state of virtual-shaft machine tool thus.

4, compute switch toroidal function s

By switching surface function s computing formula of carrying out parameter designing proposed by the invention be by second order optimal dynamic QC Quality System

$s=\stackrel{\&CenterDot;\&CenterDot;}{e}+1.414\sqrt{{\mathrm{<figure-callout\; id="2e"\; label="k"\; filenames="H2009100360684E0000021.png"\; state="\{\{state\}\}">k</figure-callout>}}_2}\stackrel{\&CenterDot;}{e}{+\mathrm{<figure-callout\; id="2e"\; label="k"\; filenames="H2009100360684E0000021.png"\; state="\{\{state\}\}">k</figure-callout>}}_{2}e$

5, determine respectively to control branch road motor-driven controlled quentity controlled variable

According to each the branch road motor-driven controlled quentity controlled variable computing formula (6) that is proposed by the present invention, the computing formula of determining respectively to control branch road motor-driven controlled quentity controlled variable is as follows:

$u=0.007{\stackrel{\&CenterDot;\&CenterDot;\&CenterDot;}{x}}_d+3.309{\stackrel{\&CenterDot;\&CenterDot;}{x}}_d+684.720{\stackrel{\&CenterDot;}{x}}_d+(0.010\sqrt{k_2}-3.309)\stackrel{\&CenterDot;\&CenterDot;}{e}+(0.007k_2-684.720)\stackrel{\&CenterDot;}{e}+\mathrm{\&eta;s}---\left(9\right)$

In the formula (9), k ₂With η be adjustable parameter.k ₂Bigger to the systematic function influence, can determine by the test before Computer Simulation or the actual processing.And as long as η can overcome systematic uncertainty and interference to make system obtain better controlling performance not too small, but its value wider range need not accurately.

6, drive each driving pair with each control branch road motor-driven controlled quentity controlled variable

The controlled quentity controlled variable of determining by step 5 is behind the digital control system D/A switch, become the aanalogvoltage instruction and send to motor servo amplifier (driver), each branch road motor movement drives the virtual-shaft machine tool parallel institution and cutter is finished the processing desired motion thereby drive.Each branch road driving pair actual motion track of virtual-shaft machine tool is respectively shown in solid line in each subgraph of Fig. 2.Each branch road driving pair kinematic error of virtual-shaft machine tool is respectively shown in each subgraph of Fig. 3.The driving controlled quentity controlled variable of each branch road motor is respectively shown in each subgraph among Fig. 4.

Fig. 4 shows, designed tool optimal dynamic quality sliding-mode control, and its controlled quentity controlled variable is continuous, does not have the problem of trembling of conventional sliding-mode control, has very strong practicality.Fig. 2 and Fig. 3 show that each branch road control of virtual-shaft machine tool precisely has good dynamic and stable state quality.

Claims (2)

1. sliding-mode control that is used for the virtual axis machine tool cutter motion control is characterized in that adopting following steps:

1) cooks up the space motion path of virtual-shaft machine tool process cutter according to processing request, determine the desired motion track of each driving pair of virtual-shaft machine tool in the process;

2) set up the Mathematical Modeling that virtual-shaft machine tool is respectively controlled the branch road controlled device;

3) the actual motion state of detection and definite each driving pair of virtual-shaft machine tool;

4) according to sliding mode control theory compute switch toroidal function;

5) determine that virtual-shaft machine tool respectively controls branch road motor-driven controlled quentity controlled variable and send to each motor driver;

6) drive each driving pair with each control branch road motor-driven controlled quentity controlled variable, realize desired motion thereby drive virtual axis machine tool cutter.

2. a kind of sliding-mode control that is used for the virtual axis machine tool cutter motion control according to claim 1 is characterized in that:

In the step 1), determine the expectation displacement x of each driving pair of virtual-shaft machine tool _d, desired motion speed

The desired motion acceleration

Step 2) in, each Mathematical Modeling of controlling the branch road controlled device is; $\stackrel{\&CenterDot;\&CenterDot;\&CenterDot;}{x}=a_2\stackrel{\&CenterDot;\&CenterDot;}{x}+a_1\stackrel{\&CenterDot;}{x}+\mathrm{bu},$ In the formula: u is the input pulse number or is the aanalogvoltage input quantity; B is the controlled quentity controlled variable coefficient;

Be the actual motion speed of each driving pair of virtual-shaft machine tool;

It is the actual motion acceleration of each driving pair of virtual-shaft machine tool;

Be three order derivatives of each driving pair actual displacement of virtual-shaft machine tool; a ₂, a ₁, b is respectively constant coefficient, by motor driver parameter is set and the parameter of electric machine is determined;

In the step 4), pass through formula $s=\stackrel{\&CenterDot;\&CenterDot;}{e}+1.414\sqrt{k_2}\stackrel{\&CenterDot;}{e}+k_{2}e$ Calculate switching surface function s; In the formula: e=x _d-x is the site error of each driving pair motion of virtual-shaft machine tool; X is each driving pair actual displacement of virtual-shaft machine tool;

Velocity error for each driving pair motion of virtual-shaft machine tool;

Acceleration error for each driving pair motion of virtual-shaft machine tool;

In the step 5), pass through formula $u=\frac{1}{b}[{\stackrel{\&CenterDot;\&CenterDot;\&CenterDot;}{x}}_d-a_2{\stackrel{\&CenterDot;\&CenterDot;}{x}}_d-a_1{\stackrel{\&CenterDot;}{x}}_d+(1.414\sqrt{k_2}+a_2)\stackrel{\&CenterDot;\&CenterDot;}{e}+(k_2+a_1)\stackrel{\&CenterDot;}{e}]+\mathrm{\&eta;s}$ Determine that virtual-shaft machine tool respectively controls branch road motor-driven controlled quentity controlled variable; In the formula, adjustable parameter k ₂Should be greater than 0, η is positive constant, size depends on systematic uncertainty and interference; For keeping the equivalent control amount of sliding formwork motion.

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