JPS6132120A - Positioning control system - Google Patents

Abstract

PURPOSE:To attain positioning without vibration by deciding the feedback gain so that the transfer function of the control system is expressed with a product of 1st-order delay elements while taking notice that the characteristic such as overshoot and response time are clarified from the transfer function of the control system in the positioning characteristic of the control system. CONSTITUTION:A motor 1 is driven, a drive shaft is turned to position an XY state 3, and the stage position theta and state speed omegas of the XY stage 3 are detected by a stage detector 4. Further, a motor position thetaM and motor speed omegaM are detected by a motor detector 5 and the four detected state variables X are fed back to a position control circuit 6. The position control circuit 6 uses a position command thetas0 given from a position command circuit 7 and the fedback state X to apply positioning control operation so as to decide a motor current ia inputted to the motor 1. Further, the transfer function of the XY stage 3 is selected as the 2nd order delay system including the vibrating system.

Description

DETAILED DESCRIPTION OF THE INVENTION [Field of Application of the Invention] The present invention relates to a positioning control method for positioning a moving body including a vibration system at high speed and with high precision.

[Background of the invention]

In a moving body that needs to be positioned at high speed, such as an XY stage in a projection exposure apparatus, vibration components included in the control system have a large influence on control characteristics. Therefore, as a positioning control method for suppressing this vibration, for example, as shown in Japanese Patent Application Laid-Open No. 57-71281,
speed of the moving object.

A method is known in which a plurality of state quantities such as position are detected and these state quantities are fed back to perform optimal control. According to this method, control is performed so as to minimize the evaluation function determined using a plurality of states, so that optimal control can be performed under the evaluation function. However, because it is difficult to understand the relationship between the evaluation function and characteristics such as response speed and overshoot that are problematic during positioning, it has been necessary to determine the evaluation function by trial and error.

[Purpose of the invention]

An object of the present invention is to provide a positioning control system that can perform high-speed positioning without vibration of a moving body by optimally selecting feedback gains of a plurality of state quantities.

[Summary of the invention]

The present invention focuses on the fact that in the positioning characteristics of a control system, characteristics such as the amount of overshoot and response time are revealed from the transfer function of the control system. In addition, by determining the feedback gain, positioning is performed without vibration.

According to the most preferred embodiment of the present invention, the motor speed, motor position, speed of the moving body, and position of the moving body are fed back as state quantities, and the transfer function of the control system is transformed into a quadruple root using these feedback gains. The structure is configured such that vibrations in the vibration system existing between the motor and the moving object are suppressed by controlling the motor so that the vibrations occur.

[Embodiments of the invention] Hereinafter, one embodiment of the present invention will be described with reference to the drawings.

FIG. 1 shows an embodiment of a positioning device using an XY stage as a moving body, and the XY stage 3 is positioned by driving a motor 1 and rotating a drive shaft 2. The stage position θB and stage speed ωB of the XY stage 3 are detected by the stage detector 4. Further, the motor position θM and the motor speed ω are detected by the motor detector 5. These four detected state quantities X are fed back to the positioning control circuit 6. This positioning control circuit 6 performs positioning control calculations using the position command θsO given from the position command circuit 7 and the fed back state X, and determines the motor current in input to the motor 1.

Motor 1. An equivalent block diagram of the drive shaft 2 and the XY stage 3 is shown in FIG.

In Fig. 2, the motor 1 is described as being driven by current, but
Even voltage drive can be regarded as almost current drive by increasing the current control speed. Further, the transfer function of the XY stage 3 is a second-order lag system including a vibration system. moreover,
A specific embodiment of the positioning control circuit 6 is shown in FIG. This positioning control circuit 6 is
As shown in Japanese Patent No. 81, the structure is similar to the conventional control system using a state foot check. However, the method of determining the feedback gain is different.

Conventionally, the feedback gain was determined so as to minimize a determined evaluation function J. For example, JP-A-57-
In the example of Publication No. 71281, the deviation r (
K) -y (K) and the amount of change in input u (K) - u
(K-1) was used to determine the evaluation function (1). In this next equation (1), the input change amount u (K)-u (K-
1) while reducing the deviation r (K) between the command and the output.
The purpose is to reduce -y(K) in a short time.

Therefore, optimal control for this purpose can be achieved by determining the feedback gain so as to minimize the result of equation (1). As described above, in conventional control using state feedback, it has been common practice in modern control theory to determine the feedback gain from the evaluation function. However, it is difficult to grasp the relationship between the evaluation function of the amount of overshoot, which is most important in high-precision positioning control.

Therefore, in the present invention, firstly, by introducing the concept of state variables in modern control theory, motor speed ωM is shown in FIG.
, motor position θM, stage speed ω8, and stage position θB can be used as state variables. At this time, motor current 1. When the stage position θB is the output y for the input U, the state equation in FIG. 2 is expressed by the following equation.

where input u=i, output y-θ day θS to stage position θ8 transfer function HPG(S')
In order to obtain , the feedback gain matrix F and the feedforward gain g may be selected as shown in the following equation, as is known from the pole placement problem.

g−βo[cA”B]' ・・・・・・
・・・・・・・・・(4) F=g(CA'+αICA3
+α2C,4-2+α3CA+α4C)・・・・・・
・・・・・・・・・(5) However, F-CKIKx K
3 to 4] Therefore, in equation (3), the transfer function Hro
As shown in (8) by the product of first-order lags, α1. α2. α3Iα4Iβ0 is determined, and feedforward gain g and feedback gain matrix F are given by equations (4) and (5), respectively. This is a feature of the present invention. Thereby, the XY table including the vibration system can be positioned without vibration. Therefore, the present invention differs from the conventional one in that vibration-free control is performed using the transfer function HFG(S), which has not attracted attention in conventional state feedback control.

Specifically, in order to obtain Equation (6), for example, the feedforward gain g and feedback gain matrix F are calculated from Equations (4) and (5).・(9) (However, FT indicates the transposed matrix of F).

You can give it as

In this way, according to the embodiment, X can be stably carried out without vibration.
Since the Y stage 3 can be controlled, the static friction plate -' is applied to an XY stage having one vibration system in this example, but it can also be used to a control system having a plurality of vibration systems.

〔Effect of the invention〕

According to the present invention, since the controlled object including the vibration system can be controlled without vibration, there is an effect that positioning can be performed at high speed and with high precision.

[Brief explanation of the drawing]

FIG. 1 is a block diagram showing an example of a positioning device according to the present invention, FIG. 2 is a block diagram showing an example of a motor and a controlled object, and FIG. 3 is a block diagram showing an example of a positioning control circuit. be.

Claims (1)

[Claims] 1. A movable body positioned at a target position given by a position command circuit, a motor that drives this movable body, a detection circuit that detects the speed and position status of the movable body and the motor, and information obtained from this detection circuit. a positioning control circuit that determines an input to the motor based on a feedback amount of the state and a feedforward amount of the target position, and a vibration system is included between the motor and the moving body, A positioning control method characterized in that the gain of the feedback amount and the gain of the feedforward amount are selected such that a transfer function from a target position to a position of the moving body is represented by a product of first-order lags.