CN110442015B - Macro-micro composite platform coupling error elimination method - Google Patents
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Abstract
The invention discloses a macro and micro composite platform coupling error elimination method, which is used for detecting a macro motion displacement error of a macro motion platform; judging whether the macro-motion displacement error is within the macro-motion error threshold range, if so, determining the micro-motion compensation displacement of the micro-motion platform according to the macro-motion displacement error, namely the distance that the micro-motion platform should move, so as to make up for the error of the macro-motion platform; determining the micro-motion reaction force of the micro-motion stage on the macro-motion stage according to the micro-motion compensation displacement; according to the micro reaction force, the macro driver applies a macro compensation action force in an opposite direction to the macro platform at the same time. When applying displacement effort to the micro-motion platform, exert opposite direction's counter force to the macro-motion platform to offset the effort of micro-motion platform to the macro-motion platform, the macro-motion platform can not produce the displacement because of the effort of fine motion basically, makes displacement control more accurate.
Description
Technical Field
The invention relates to the technical field of precision control of motion platforms, in particular to a macro-micro composite platform coupling error elimination method.
Background
The high-precision control motion platforms at home and abroad are mostly realized by adopting macro and micro two-stage driving, the macro motion platform realizes large-stroke high-speed positioning, and the micro motion platform realizes high-precision positioning by compensating the error of the macro motion platform. The macro-motion stage is usually driven by a linear motor, and the micro-motion stage is usually driven by a voice coil motor or piezoelectric ceramics.
As shown in fig. 1, it is a schematic diagram of the motion of the macro stage 01 and the micro stage 02; the micro-motion platform is arranged on the macro-motion platform, the micro-motion platform is driven to synchronously move when the macro-motion platform moves, the macro-motion platform stops after moving for a distance L1 from an initial position, and the positioning error between the micro-motion platform and a target position is L2; to compensate for this error, a micropositioner movement l2 is initiated to bring the micropositioner to the target position.
However, the micro-motion platform is arranged on the macro-motion platform, the macro-motion platform and the micro-motion platform form a whole, the macro-motion platform provides support for the micro-motion platform, when the micro-motion platform moves forwards, the macro-motion platform provides forward acting force for the micro-motion platform, and the micro-motion platform generates backward reacting force for the macro-motion platform, so that the macro-motion platform moves backwards by a small distance.
The situation can cause the whole positioning error to be enlarged, the stretching amount of the piezoelectric ceramic or the voice coil motor is saturated, even exceeds the stroke range of the piezoelectric ceramic or the voice coil motor, and the purpose of compensating the error cannot be achieved.
For those skilled in the art, it is a technical problem to be solved at present to reduce the error caused by the micro-motion stage to the reaction force of the macro-motion stage.
Disclosure of Invention
The invention provides a macro-micro composite platform coupling error elimination method, which counteracts the coupling influence of a micro-motion platform by applying acting force to the macro-motion platform, and reduces the error caused by the reaction force of the micro-motion platform to the macro-motion platform, and the specific scheme is as follows:
a macro-micro composite platform coupling error elimination method comprises the following steps:
detecting a macro motion displacement error of a macro motion platform;
judging whether the macro-motion displacement error is within a macro-motion error threshold range;
if so, determining the micro-motion compensation displacement of the micro-motion platform according to the macro-motion displacement error;
determining the micro-motion reaction force of the micro-motion stage on the macro-motion stage according to the micro-motion compensation displacement;
and according to the micro reaction force, the macro motion compensation acting force in the opposite direction is simultaneously applied to the macro motion platform by the macro motion driver.
Optionally, the macro-motion compensation acting force in the opposite direction is simultaneously applied to the macro-motion stage by the macro-motion driver, and is calculated according to the following formula:
wherein: n is a radical of hydrogen 12 (s) is a macro motion compensation function; g p11 (s) is the macro-actuator current to displacement transfer function; g p12 (s) is a coupling transfer function of the reaction force of the macro-motion stage on the micro-motion stage; s represents a complex field, and a transfer function is obtained from a differential equation by laplace transform. Optionally, the macro-actuator current to displacement transfer function G p11 (s) fitting according to the test result to obtain;
the macro-motion stage is reacted by the micro-motion stageCoupling transfer function G of force p12 (s) is obtained by a step response method.
Optionally, for the macro compensation function N 12 (s) low pass filtering to obtain:
wherein: τ is constant.
Optionally, the method further comprises:
and monitoring the action interference of the micro-motion platform through a interference observer, converting the action interference into feedback control output, and applying a feedback signal to the macro-motion driver.
The invention provides a macro and micro composite platform coupling error elimination method, which is used for detecting a macro movement displacement error of a macro movement platform; judging whether the macro-motion displacement error is within the macro-motion error threshold range, if so, determining the micro-motion compensation displacement of the micro-motion platform according to the macro-motion displacement error, namely the distance that the micro-motion platform should move, so as to make up for the error of the macro-motion platform; determining the micro reaction force of the micro-motion stage on the macro-motion stage according to the micro compensation displacement; according to the micro reaction force, the macro driver applies a macro compensation action force in an opposite direction to the macro platform at the same time. When applying displacement effort to the micro-motion platform, exert opposite direction's counter force to the macro-motion platform to offset the effort of micro-motion platform to the macro-motion platform, the macro-motion platform can not produce the displacement because of the effort of fine motion basically, makes displacement control more accurate.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to these drawings without creative efforts.
FIG. 1 is a schematic diagram of the motion of a macro stage and a micro stage;
FIG. 2 is a flow chart of a macro-micro composite platform coupling error cancellation method according to the present invention;
FIG. 3 is a schematic diagram of the macro-micro composite platform coupling error cancellation method according to the present invention;
FIG. 4 is a diagram of four step responses of the displacement of the macro stage;
FIG. 5 is a block diagram of a compound control with dual effects of feedforward compensation and feedback compensation.
Detailed Description
The invention provides a macro-micro composite platform coupling error elimination method, which is used for counteracting the coupling influence of a micro-motion platform by applying acting force to the macro-motion platform and reducing the error caused by the micro-motion platform on the counterforce of the macro-motion platform.
In order to make those skilled in the art better understand the technical solution of the present invention, the macro-micro composite platform coupling error elimination method of the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.
As shown in fig. 2, a flowchart of a macro-micro composite platform coupling error elimination method provided by the present invention specifically includes the following steps:
s1, detecting a macro motion displacement error of the macro motion platform; the macro-motion platform moves to drive the micro-motion platform arranged on the macro-motion platform to synchronously move, and after the macro-motion platform stops, whether the movement distance of the macro-motion platform meets the requirement or not is detected, namely the distance between the macro-motion platform and the micro-motion platform is equal to the distance between the macro-motion platform and the micro-motion platform and the target position.
S2, judging whether the macro motion displacement error is within the range of the macro motion error threshold value; if the macro-motion displacement error is too large, the macro-motion platform can be driven to move again until the macro-motion displacement error reaches the macro-motion error threshold range.
If the judgment result is yes, namely when the macro-motion displacement error reaches the macro-motion error threshold range, executing step S3, and determining the micro-motion compensation displacement of the micro-motion stage according to the macro-motion displacement error; the macro-motion displacement error is equal to the micro-motion compensation displacement, and the micro-motion platform compensates the motion error of the macro-motion platform so as to enable the micro-motion platform to reach the target position.
S4, determining the micro-motion reaction force of the micro-motion platform on the macro-motion platform according to the micro-motion compensation displacement; the micro-motion platform is driven by the micro-motion driver, the micro-motion driver adopts piezoceramics usually, piezoceramics assembles between macro-motion platform and micro-motion platform, exert the effort of motion to the micro-motion platform, make the micro-motion platform produce the displacement, confirm the effort size that piezoceramics produced the micro-motion platform according to the fine motion compensation displacement, because the macro-motion platform supports the micro-motion platform, consequently the micro-motion platform produces the fine motion reaction force to the macro-motion platform, can cause the macro-motion platform to the opposite direction displacement, the motion intercoupling of macro-motion platform and micro-motion platform is superimposed after, the deviation appears in the position that the micro-motion platform finally reaches, can't reach the precision that should.
In order to prevent the macro stage from being displaced by the reaction force of the micro stage, step S5 is executed, and according to the micro reaction force, the macro driver simultaneously applies a macro compensation force in an opposite direction to the macro stage. The acting force direction that the macro-motion driver applyed the macro-motion platform is opposite with fine motion reaction force direction to the size is unanimous, is used for offsetting the acting force that the micro-motion platform applyed the macro-motion platform, and when the micro-motion platform moved, the macro-motion platform kept the force balance, and the macro-motion platform was located and remains motionless in situ, and only the micro-motion platform was made the compensation motion, and the macro-motion platform does not receive the influence of fine motion reaction force, can realize more accurate error compensation, and displacement control is more accurate.
On the basis of the scheme, the macro-motion compensation acting force with opposite directions is simultaneously applied to the macro-motion platform by the macro-motion driver, and the calculation is carried out according to the following formula:
wherein: n is a radical of hydrogen 12 (s) is a macro motion compensation function and is a decoupling controller; g p11 (s) is the macro-actuator current to displacement transfer function; g p12 (s) is a coupling transfer function of the reaction force of the macro-motion stage on the micro-motion stage; s represents a complex domain and a transfer function is obtained from a differential equation through laplace transform.
S is explained below: 1. the output y is the derivative of the input x, then the differential equation in the time domain can be written as:
the corresponding transfer function between the representation output and input is (L represents laplace transform):
can be pushed out: y(s) x(s) s, s is a differential operator.
2. The output y is the integral of the input x, then the differential equation in the time domain can be written as:
then:
FIG. 3 is a schematic diagram of the macro/micro composite platform coupling error cancellation method according to the present invention; x is the number of 1 Representing the displacement output, x, of the macro-stage 2 Representing the displacement output of the micropositioner; g p11 (s) is a transfer function from the current of the macro-motion driver to the displacement, namely the displacement output by the macro-motion driver after receiving the current signal, and the displacement output by the current with different magnitudes is also different; g p12 (s) is a coupling transfer function of the reaction force of the micro-motion platform on the macro-motion platform, namely, when the micro-motion platform receives the reaction force of the micro-motion platform, the macro-motion platform generates displacement, and the larger the reaction force of the micro-motion platform is, the larger the displacement of the macro-motion platform is; n is a radical of 12 (s) represents the macro compensation function, i.e., the force provided to the macro stage based on the micro-motion reaction force.
Implementing x in FIG. 3 1 And x 2 The decoupling control between the two main loops needs to satisfy the following conditions:
U 2 G p12 (s)+U c2 N 12 (s)G p11 (s)＝0
U 2 and U c2 Is the voltage of the microactuator, here U 2 ＝U c2 Then, one can obtain:
specifically, the two transfer functions, the transfer function G from the current to the displacement of the macro-motion driver p11 (s) fitting according to the test result; respectively inputting different current signals for multiple times, measuring output displacement corresponding to each current signal, obtaining the frequency and the phase of a sinusoidal displacement curve correspondingly output when sinusoidal signals with different frequencies are input, comparing the frequency and the phase with the frequency and the phase of the current, and fitting by using a self-contained tool box in MATLAB software and the like. I.e. the transfer function G from the current to the displacement of the macro actuator p11 (s)。
Coupling transfer function G of reaction force of macro-motion stage and micro-motion stage p12 (s) obtaining U by using a step response method 2 Measuring the displacement x of the macro-motion stage for a voltage step command with the amplitude value of +5V 1 The four step response is shown in figure 4. The step method is used for fitting a first-order transfer function, the first-order transfer function only has two simple parameters, and the first-order transfer function can be directly obtained by a macro-motion stage response displacement diagram through a drawing method.
G in FIG. 3 c1 (s) is the transfer function of the macro station master controller, G c2 (s) is the transfer function of the micropositioner master controller, where PID controllers are used:
G c2 (s) and G c1 (s) is the same, wherein k is p ，k i ，k d Is an adjustable parameter. The PID controller is a widely used controller based on control quantity error; the PID controller does not need to know how much current or voltage the PID controller outputs to achieve the specified displacement, and only needs to know whether the error from the target position is positive or negative or zero, and the error is output in a regular modeThe positive voltage moves the motor forward until the error is zero. Given that the transfer function between the input signal and the output displacement is known, the input signal can be given directly to obtain the desired displacement, in which case no error feedback is required, which is not an error-based controller, but a model-based controller, the decoupled controller in this context being a model-based controller.
To further improve the accuracy, the macro compensation function N is applied 12 (s) low pass filtering to obtain:
wherein: τ is constant.
Decoupling controller N 12 (s) for non-causal systems, adding a low-pass filter
The high frequency signal is filtered.
The process is feedforward compensation, namely, the acting force is synchronously applied to the macro-motion platform when the acting force is applied to the micro-motion platform, in order to further improve the precision, the motion is monitored in real time and needs to be subjected to feedback compensation, the action interference of the micro-motion platform is monitored by an interference observer, the action interference is converted into feedback control output, a feedback signal is applied to a macro-motion driver, and the precision of the overall motion of the macro-motion platform and the micro-motion platform is ensured by utilizing the dual functions of the feedforward compensation and the feedback compensation. FIG. 5 shows a composite control block diagram for feedforward compensation and feedback compensation, in which N is within a small dashed box 12 Q N Representing a decoupled controller, N 12 As a transfer function, Q N For the low pass filter function:
the large dashed box represents a disturbance observer, PID represents a controller, PZT represents a micro-actuator piezoelectric ceramic, and PMLSM represents a macro-actuator linear motor.
The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
Claims (4)
1. A macro-micro composite platform coupling error elimination method is characterized by comprising the following steps:
detecting a macro motion displacement error of a macro motion platform;
judging whether the macro-motion displacement error is within a macro-motion error threshold range;
if so, determining the micro-motion compensation displacement of the micro-motion platform according to the macro-motion displacement error;
determining the micro-motion reaction force of the micro-motion stage on the macro-motion stage according to the micro-motion compensation displacement;
according to the micro reaction force, the macro driver simultaneously applies macro compensation acting force in opposite directions to the macro platform;
the macro motion compensation acting force with opposite directions is simultaneously applied to the macro motion platform by the macro motion driver, and the calculation is carried out according to the following formula:
wherein: n is a radical of 12 (s) is a macro compensation function; g p11 (s) is the macro-actuator current to displacement transfer function; g p12 (s) is a coupling transfer function of the reaction force of the macro-motion stage on the micro-motion stage; s represents a complex domain and a transfer function is obtained from a differential equation through laplace transform.
2. According to the claimsThe macro-micro composite platform coupling error elimination method of 1 is characterized in that the transfer function G from the current to the displacement of the macro-motion driver p11 (s) fitting according to the test result to obtain;
the coupling transfer function G of the reaction force of the macro-motion stage on the micro-motion stage p12 (s) is obtained by a step response method.
3. The method as claimed in claim 2, wherein the macro compensation function N is applied to the macro motion compensation function 12 (s) low pass filtering to obtain:
wherein: τ is constant.
4. The macro-micro composite platform coupling error cancellation method of claim 3, further comprising:
and monitoring the motion interference of the micro-motion platform through a disturbance observer, converting the motion interference into feedback control output, and applying a feedback signal to the macro-motion driver.
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