CN104898413A - Large-stroke high-resolution driver system - Google Patents

Abstract

The invention discloses a large-stroke high-resolution driver system, which is composed of three parts: a mechanical drive part, a data acquisition part and a computer control part. The mechanical drive part includes components such as a servo motor. The servo motor is fixed to the motor support. The output shaft of the output shaft is connected with the ball screw through the coupling, the ball screw passes through the bearing seat, the screw nut is fixed with one end of the nut sleeve, the other end of the nut sleeve is fixed with the angle plate, and the angle plate is fixed on the On the sliding table assembly, a push rod is installed on one side of the corner plate, and the rotary motion of the servo motor can be converted into the linear motion of the push rod; the data acquisition part includes a dual-frequency laser interferometer connected to each other, an AD port of a data acquisition card, and a computer. The control part includes the interconnected industrial computer and the DA port of the data acquisition card. The invention has a relatively large moving range, and the resolution of 100nm can already be realized through a preliminarily built experimental platform.

Description

Large stroke high resolution drive system

technical field

The invention relates to a driver system, in particular to a driver system with a large stroke and high resolution.

Background technique

Large-aperture gratings are in increasing demand in research fields such as astrophysics and high-energy laser pulses. However, it is difficult to obtain a large-aperture diffraction grating by using a grating scriber or a holographic method. At present, two or more small gratings are used to form a large grating by splicing, and the phase difference between them is reduced by mechanical adjustment, which has become an important method for obtaining large-aperture gratings at home and abroad. In this process, how to improve the positioning accuracy of the drive adjustment, so that the resolution of the drive during fine-tuning can reach 20nm-100nm, and the adjustment range can reach the millimeter level, has become one of the important research contents.

There are many designs for large-scale high-resolution drivers at home and abroad, among which the most widely used is the form of piezoelectric ceramics plus ball screws, but due to the small travel of piezoelectric ceramics and the existence of nonlinearity, hysteresis and creep, macro The micro-two-stage driving method greatly increases the cost and control difficulty; the high-precision linear motor is expensive and the control system is complicated; the new hysteresis telescopic drive has electromagnetic leakage and heat generation and other factors that affect positioning. However, in the design of the control system, due to the existence of friction, there are obvious differences in the field of macro motion and micro motion of the driver. New control theories such as neural network and fuzzy control do not show a particularly obvious effect in solving practical problems. Advantage.

Contents of the invention

In view of the above-mentioned problems, the present invention proposes a large-stroke high-resolution driver system, which is based on a ball screw plus a servo motor and based on a dual-frequency laser interferometer for precise positioning control, and is used to achieve a wide range of high-resolution Precision drive control.

The technical solution adopted by the present invention to solve the above technical problems is as follows: a large-stroke high-resolution drive system, characterized in that it consists of three parts: a mechanical drive part, a data acquisition part and a computer control part, and the mechanical drive part includes a servo motor , motor support, coupling, bearing seat, ball screw, screw nut, nut sleeve, corner plate, slide table assembly, the servo motor and the motor support are fixed, and the output shaft of the servo motor passes through the coupling and the ball wire The rods are connected, the ball screw passes through the bearing seat, the screw nut is fixed with one end of the nut sleeve, the other end of the nut sleeve is fixed with the angle plate, the angle plate is fixed on the sliding table assembly, and one side of the angle plate The ejector rod is installed, and the rotary motion of the servo motor can be finally converted into the linear motion of the ejector rod; the data acquisition part includes an interconnected dual-frequency laser interferometer and the AD port of the data acquisition card, and the computer control part includes an interconnected industrial computer and data Acquisition card DA port.

Further, the analog signal collected by the data acquisition part is converted into a digital quantity through the AD port of the data acquisition card and input into the industrial computer, and the industrial computer calculates the control amount of the servo motor according to the detected displacement, And complete the output control of the servo motor through the DA port of the data acquisition card.

Further, the mathematical model of the large-stroke high-resolution drive system is obtained through system identification experiments and the identified transfer function is as follows:

$\mathrm{<span\; class="notranslate">\; G</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 247.6</span>}}{\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 120.5</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; .</span>$

Compared with the prior art, the present invention has the following beneficial effects: First, the moving range of the driver proposed by the present invention can reach 10 mm, and combined with high-precision sensors, it can realize precise positioning in a large stroke. Second, it is cost-effective and has better motion stiffness. Third, through the optimization of the control algorithm, the resolution of the driver can be improved conveniently without changing the hardware structure of the driver.

Description of drawings

Fig. 1 is a structural schematic diagram of the mechanical driving part of the large-stroke high-resolution driver system of the present invention.

Figure 2 is a schematic diagram of a theoretical mathematical model of the drive.

Figure 3 is a schematic diagram of the overall control of the system.

Figure 4 is a schematic diagram of the basic structure of the designed controller.

Fig. 5 is a schematic diagram of the experimental results of the driver's 1mm step response.

Figure 6 is a schematic diagram of the driver's 20 μm step response results.

Figure 7 is a schematic diagram of the driver's 100nm step response results.

Detailed ways

The specific implementation of the present invention is described as follows in conjunction with the accompanying drawings:

Refer to Figure 1 for the structure of the large stroke and high resolution drive system in this implementation example. The mechanical driving part of the large-stroke high-resolution driver system of the present invention includes a servo motor 1, a motor support 2, a shaft coupling 3, a bearing seat 4, a ball screw 5, a screw nut 6, a nut sleeve 7, an angle plate 8, The sliding table assembly 10, the servo motor 1 is fixed with the motor support 2, the output shaft of the servo motor 1 is connected with the ball screw 5 through the coupling 3, the ball screw 5 passes through the bearing seat 4, the screw nut 6 and the nut One end of the sleeve 7 is fixed together, the other end of the nut sleeve 7 is fixed with the angle plate 8, and the angle plate 8 is fixed on the sliding table assembly 10, and the ejector rod 9 is installed on one side of the angle plate 8, and the rotation of the servo motor The motion can eventually be converted to linear motion of the ejector pin. The screw assembly of the ball screw is installed on the sliding table assembly through the angle plate, which is used to ensure the linear guidance of the output, and the final driving motion is realized through the ejector rod.

The theoretical mathematical model of the driver in this implementation example is shown in Figure 2, where the output control voltage V is converted into the output torque T _app of the servo motor and drives the servo motor to rotate. The screw nut pair can be equivalent to a spring damping system, Finally, the rotation of the servo motor is transformed into the linear displacement X of the ejector rod through the screw nut pair. The meanings represented by each parameter are shown in Table 1:

Table 1

symbol meaning m slide quality J Moment of inertia of the rotating part R _m motor resistance _Ki Moment constant _k back emf constant C _sd Rotational damping k _n Elastic coefficient between screw and nut C _n Damping coefficient between screw and nut h transfer ratio G _m Servo magnification

The overall control schematic diagram in this example is shown in Figure 3. The large-stroke high-resolution driver system of the present invention is composed of three parts: a mechanical drive part, a data acquisition part and a computer control part. The data acquisition part includes an interconnected dual-frequency laser interference instrument and data acquisition card AD port, the computer control part includes the interconnected industrial computer and data acquisition card DA port, the dual-frequency laser interferometer is fixed in the linear driving direction of the mechanical drive part, and the laser beam emitted by it passes through the angle plate The reflective prism 11 above returns, and produces interference fringes with the incident beam on the beam splitter, and outputs through the analog output port of the dual-frequency laser interferometer. In order to realize the position detection of the end of the driver, a dual-frequency laser interferometer with nanoscale resolution is used as the position feedback link. The laser emitted by the dual-frequency laser interferometer is reflected by the reflective prism installed on the mechanical structure of the driver and forms interference fringes. Then it is converted into an analog output under the action of the internal processor. The analog signal collected by the data acquisition part is converted into a digital quantity through the AD channel of the data acquisition card (that is, the AD port of the data acquisition card) and input to the industrial computer. The industrial computer calculates the displacement of the servo motor according to the detected displacement. Control the size of the amount, and complete the output control of the servo motor through the DA channel of the data acquisition card (that is, the DA port of the data acquisition card).

In order to obtain the mathematical model of the large-stroke high-resolution drive system of the present invention, the transfer function between the control voltage U and the displacement X of the drive is obtained, that is, the present invention can obtain the identification transfer function through system identification experiments as formula (1) :

$\mathrm{<span\; class="notranslate">\; G</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 247.6</span>}}{\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 120.5</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

Among them, G(s) is the expression form of the Laplace transform of the transfer function, X(s) represents the Laplace transform of the drive system displacement, and U(s) represents the Laplace transform of the control voltage.

In order to test the performance of the driver, the present invention designs a PID controller to realize the control experiment of the step output signal. The controller structure is shown in Figure 4, which includes a proportional link K _p and an integral link and differential link Three parts, at the same time, in order to suppress the interference of high-frequency signals, a first-order inertial link is added to the differential link to form a low-pass filter.

The selection of the three parameters of the PID controller is obtained by the zero-pole configuration method, and the specific calculation process is as follows:

Let the transfer function of the servo driver be as formula (2):

${\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; d</span>}}{\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

Referring to formula (1), it can be seen that d=247.6 and c=120.5.

The closed-loop transfer function T(s) of the ball screw positioning system is written as formula (3):

$\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; [</span><span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}}{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; the\; s</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}}<span\; class="notranslate">\; ]</span>}{{\mathrm{<span\; class="notranslate">\; the\; s</span>}}^{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; the\; s</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}}{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}}\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; ]</span>{\mathrm{<span\; class="notranslate">\; the\; s</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; [</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}}<span\; class="notranslate">\; ]</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}\mathrm{<span\; class="notranslate">\; d</span>}\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}}}<span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

Among them, Kp is the proportional coefficient, Ti is the integral time constant, Td is the differential time constant, and Tf is the coefficient of the filter.

If it is configured as multiple poles (-p, 0), the expression (3) of the closed-loop system transfer function can be rewritten as formula (4):

$\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span>}{{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 4</span>}}}<span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

Among them, p represents the value of multiple poles, and Gk(s) represents the molecular term of the expression after the simplified Laplace transform.

Corresponding the denominator in formula (4) and the denominator of formula (3) one by one, the four parameters in formula (3) can be known by solving the equation, such as formula (5):

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 15</span>}{\mathrm{<span\; class="notranslate">\; p</span>}}^{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 4</span>}{\mathrm{<span\; class="notranslate">\; cp</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}}{\mathrm{<span\; class="notranslate">\; d</span>}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}\\ {\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 15</span>}\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; c</span>}}{\mathrm{<span\; class="notranslate">\; 4</span>}{\mathrm{<span\; class="notranslate">\; p</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; cp</span>}}\\ {\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 81</span>}{\mathrm{<span\; class="notranslate">\; p</span>}}^{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 108</span>}{\mathrm{<span\; class="notranslate">\; cp</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 54</span>}{\mathrm{<span\; class="notranslate">\; c</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; p</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 12</span>}{\mathrm{<span\; class="notranslate">\; c</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; c</span>}}^{\mathrm{<span\; class="notranslate">\; 4</span>}}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 15</span>}{\mathrm{<span\; class="notranslate">\; p</span>}}^{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 4</span>}{\mathrm{<span\; class="notranslate">\; cp</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; )</span>}\\ {\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; c</span>}}\end{array}\right.<span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

Therefore, the four parameters of the controller can be determined through calculation, and finally determined after analysis and comparison combined with actual experiments.

Further, the present invention selects the positions of different poles P to obtain a series of parameters of different PID controllers, as shown in Table 2 below:

Table 2

p K _p T _i T _{d f} 20π 26.94 0.0560 0.0014 0.0077 40π 76.92 0.0292 0.0041 0.0026

60π 157.94 0.0197 0.0039 0.0016 80π 269.02 0.0148 0.0035 0.0011 100π 410.01 0.0119 0.0031 0.0008

The present invention conducts preliminary experimental verification through the experimental hardware platform built, wherein the sampling frequency of the data acquisition card is 1000 Hz, the saturation voltage of the servo motor is 2 V, and the maximum speed is 130 r/min. Corrected according to the actual experiment, the values of the closed-loop experiment PID controller are K _p =26.94, T _i =0.056, T _d =0.0014, T _f =0.0077.

In order to test the control performance of the designed PID controller, it is necessary to sample the data of each sensor and calculate it through the closed-loop control system shown in Figure 4. The real-time calculation of the driving voltage is based on formula (6):

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; error</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; k</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\frac{\mathrm{<span\; class="notranslate">\; error</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; error</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ {\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}}{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}\frac{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}}{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; error</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; error</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>\end{array}\right.<span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span>$

The output control voltage of the controller is as formula (7):

u(k)=u _p (k)+u _i (k)+u _d (k)......(7)

Figure 5, Figure 6, and Figure 7 are the experimental results of step responses of 1mm, 20um, and 100nm respectively. After calculation, the steady-state error values corresponding to the steps of 100nm to 1mm are all less than ±50nm, and the step responses of 1mm and 20μm, Experiments and simulations are in good agreement, and the step response of 100nm is slightly slower due to the greater influence of friction. When the system response enters a steady state, the steady-state error is almost the same as the noise distribution of the measurement system, and there is no obvious overshoot, and the adjustment time is within 1s, which can meet the requirements of most high-precision positioning control systems, so it is suitable for high-resolution Among the high-speed servo positioning control systems.

The invention has a relatively large moving range, a resolution of 100nm can already be achieved through a preliminarily built experimental platform, and the structure has high rigidity and fast response speed, and is suitable for working environments requiring large strokes and high resolution. The present invention conducts step response experiments from the nanometer level to the millimeter level, compares and analyzes the response of drivers with different moving ranges, and calculates the steady-state error of the end position of the driver. The precise positioning, and the response speed is fast, the overshoot is very small.

Claims (3)

1. a Long Distances high resolving power drive system, it is characterized in that, it is by Mechanical Driven part, part of data acquisition and computing machine control section three part composition, Mechanical Driven part comprises servomotor, motor support base, shaft coupling, bearing seat, ball screw, feed screw nut, nut sleeve, gusset, slide unit assembly, servomotor and motor support base are fixed, the output shaft of servomotor is connected with ball screw by shaft coupling, ball screw is through bearing seat, one end of feed screw nut and nut sleeve is fixed together, the other end and the gusset of nut sleeve are fixed together, gusset is fixed on above slide unit assembly, the side of gusset is provided with push rod, the rotary motion of servomotor finally can be converted to the rectilinear motion of push rod, part of data acquisition comprises interconnective two-frequency laser interferometer and data collecting card AD mouth, and computing machine control section comprises interconnective industrial computer and data collecting card DA mouth.

2. Long Distances high resolving power drive system according to claim 1, it is characterized in that, the analog signals that described part of data acquisition collects, being converted to digital quantity by data collecting card AD mouth is input in industrial computer, at industrial computer according to the displacement detected, calculate the controlled quentity controlled variable size of servomotor again, and complete the output control of servomotor by data collecting card DA mouth.

3. Long Distances high resolving power drive system according to claim 1, is characterized in that, the mathematical model of described Long Distances high resolving power drive system tested by System Discrimination the transport function that obtains identification for as shown in the formula:

。