JP3909528B2 - Integral proportional system controller and integral proportional system control method - Google Patents

Description

  The present invention relates to an integral proportional system control device and an integral proportional system control method, and in particular, has an integral element and an element including a proportional term, and inputs a deviation amount between a target value and an output of a controlled object to the integral element, and controls the integral element. The present invention relates to an integral proportional system control device and a control method in which a control signal is supplied to a controlled object by subtracting the output of the object from an output of an integral element by a subtractor through an element including a proportional term.

  In recent years, as represented by nanotechnology, high precision, high speed, and high response conditions are simultaneously required in the field of precision positioning control. Under such circumstances, it is inevitable to increase the control width.

  However, when the bandwidth of the control system is widened, the response performance with respect to the target value is improved, but the control input is limited, and the control input is likely to be saturated. In particular, in a servo system in which the controller has an integral characteristic, a windup phenomenon occurs. FIG. 7 shows the windup phenomenon in precision positioning.

In general, the wind-up phenomenon due to the integration operation is that even if the deviation e changes from e ₁ to -e _{1 as} shown in FIG. 8, it is still held at the saturation value until the integration value becomes zero. . That not the state of a output at the time of t ₁ from the controller 8, is still kept in b, and decreasing the control input u is when the output of the integrator is equal to or less than u _max start.

  In the conventional proportional integration control shown in FIG. 9, the deviation value e, which is the output of the comparator 5, is input to the proportional element 6 and the integral element 7, respectively, and the outputs of the proportional element 6 and the integral element 7 are added. The value is added by the device 8 and input to the control object 10 through the saturator 9.

  Here, especially during the saturation operation by the saturator 9, the wind-up phenomenon can be prevented by stopping the integration operation of the integrator 7. That is, one of the antiwindup techniques is to stop the integration operation when the saturator 9 is saturated. When the integrator 7 stops the integration operation, the wind-up phenomenon does not occur because the control operation using only the proportional element 6 is performed.

  On the other hand, in the integral proportional control, as shown in FIG. 10, the deviation value which is the output of the comparator 5 is added to the integral element 7, and the output to be controlled is input to the subtractor 12 through the proportional element 6. Thus, the output of the proportional element 6 is subtracted from the output of the integral element 7, and this is supplied to the controlled object 10 through the saturation element 9.

  In the case of such integral proportional control, if the integration operation by the integrator 7 is stopped when the saturator 9 is saturated due to anti-windup, the output of the comparator 5 is cut off and the control target becomes the control system. The control system loses its target, becomes uncontrollable, and in some cases diverges.

  In this way, the conventional windup prevention technique for stopping the integration when the saturator 9 is saturated is windup with respect to the integral proportional control in which the output feedback is subtracted in parallel with the integral operation for the control deviation input. There is a problem that it is impossible to prevent the phenomenon and the conventional anti-windup method for stopping the integration operation cannot be applied to the integral proportional control system.

  Japanese Patent Laid-Open No. 2001-195102 proposes a method for performing anti-windup control by estimating a saturation value using an estimator. Here, when the saturation value changes, the saturation value is estimated, and anti-windup is performed based on the estimated value, and methods such as integration reset and input correction are adopted. This control does not actively change the saturation value, and the control system is not intended for the integral proportional control system.

JP-A-6-202706 discloses that proportional control is used for speed control, integral proportional control is used for position control, switching control between speed control and position control is performed by bumpless, and the control system is balanced. The target value information is changed and the contents are reflected on the integral controller. This control is not anti-windup, and the target value information changes because the integral controller does not have a proportional term.
JP 2001-195102 A JP-A-6-202706 JP 2002-229604 A

  An object of the present invention is to provide a control device and a control method capable of improving an overshoot amount with respect to a target value, preventing deterioration of control performance due to a change in the target value and the magnitude of disturbance, and achieving desired control performance Is to provide.

  Another object of the present invention is to provide a technique for preventing a wind-up phenomenon in an integral proportional system control apparatus and method.

  Another object of the present invention is to provide a control device and a control method capable of improving the bandwidth and target value tracking characteristics of a system.

  Another object of the present invention is to provide an integral proportional system control device and a control method suitable for use in controlling a precision stage capable of high-precision positioning.

  Another subject of the present invention is clarified by the technical idea and embodiments of the present invention described below.

The main invention of the present application has an integral element and an element including a proportional term, and inputs a deviation amount between a target value and an output of the controlled object to the integral element, and an element including the proportional term of the controlled object output In the integral proportional system control device that supplies a control signal to the control object by subtracting from the output of the integral element by a subtractor through
An equivalent saturation element is provided on the output side of the integration element and before the subtractor, and a correction element for correcting a deviation amount input to the integration element is provided, and the correction element is provided according to the saturation amount of the equivalent saturation element. The correction element corrects the deviation amount input to the integration element ,
A forward element that adds a value obtained by multiplying the deviation input of the integrator by a constant to the output of the integrator, and the correction element that corrects the deviation amount input to the integral element is a constant of the forward element; The present invention relates to an integral proportional system control device characterized by being a proportional component of a fraction .

  Here, the input value and the output value of the equivalent saturation element are compared by the comparison means, the saturation amount is obtained from the difference, and the correction element corrects the deviation amount input to the integration element by the saturation amount. You may do it. And a forward element that adds a value obtained by multiplying the deviation input of the integrator by a constant to the output of the integrator, and the correction element that corrects the deviation amount input to the integral element is the forward element of the forward element. It may be a proportional factor of a constant.

The main invention related to the control method has an integral element for discretizing the amount of information and an element including a proportional term, and inputs a deviation amount between the target value and the output of the controlled object to the integral element, In the integral proportional system control method, the control signal is supplied to the control object by subtracting the output of the integral element from the output of the integral element by the subtractor through the element including the proportional term,
An equivalent saturation means is set on the output side of the integral element and before the subtractor, and the deviation amount input to the integral element is corrected using information on the saturation amount by the equivalent saturation means , and
The integrator further includes a forward element, and the correction element for correcting a deviation amount input to the integral element is a proportional element that is a constant part of the forward element, and the integration is performed by the forward element. The present invention relates to an integral proportional system control method, characterized in that a value obtained by multiplying a deviation input of a generator by a constant is added to an output of the integrator.

  Here, the integral element, the element including the proportional term, and the equivalent saturation means may be set on a computer for control. Further, bilinear transformation may be used for discretizing the output of the integrator so that the input value of the equivalent saturation means has a steady term.

  In the present application, the integral proportional control means not only integral proportional control but also control including integral proportional derivative control and integral proportional state feedback control.

  In a preferred aspect of the present invention, for the purpose of preventing deterioration of control performance due to windup of integral proportional control, an equivalent saturation amount is set to the output of the integral controller, and the control deviation information is corrected using the information. . Here, in the discretization of the integral controller, the control deviation amount can be corrected by using bilinear transformation so that a stationary term exists. By such a method, an effect equivalent to the stop of the integral operation can be obtained, and the integral proportional control system can be anti-winded up.

  Such an aspect is applied to industrial control fields that require a high-response and high-precision control while having a simple control configuration, such as precision stage control and motion control in the semiconductor industry, Without significantly changing the current system, it is possible to further increase the bandwidth and improve the target value follow-up, thereby improving productivity and quality. In particular, the driving method of the semiconductor manufacturing apparatus will be changed from the step-and-repeat method to the continuous-pass method in the future, and as a result, it will be an extremely effective method for preventing high-frequency vibration and overshoot. Therefore, application to a semiconductor manufacturing apparatus is particularly optimal.

The main invention of the present application has an integral element and an element including a proportional term, and inputs a deviation amount between the target value and the output of the controlled object to the integral element, and subtracts the output of the controlled object through the element including the proportional term. In the integral proportional system control device that supplies the control signal to the controlled object by subtracting from the output of the integral element by the multiplier, an equivalent saturation element is provided at the output side of the integral element and before the subtractor, a correction element for correcting the deviation amount input to the integral element provided, correction factors are to make modifications to the deviation amount input to the integrating element in accordance with the saturation of the equivalent saturation element, the deviation input of the integrator It has a forward element that adds a value multiplied by a constant to the output of the integrator, and the correction element that corrects the deviation amount input to the integration element is a proportional element that is a constant part of the forward element. .

  Therefore, according to such an integral proportional system control device, the deviation input to the integral element is corrected so that the saturation amount of the equivalent saturation element becomes an optimum value according to the output of the controlled object. Therefore, saturation of the integral element is suppressed, and an anti-windup operation is possible.

  FIG. 1 shows a system configuration of an integral proportional control device according to the present embodiment, and this control device includes a comparator 16. Another comparator 17 is connected to the lower side of the comparator 16, and the output terminal of the comparator 17 is connected to the integration element 18. The integral element 18 is further connected to an equivalent saturation element 19, and this equivalent saturation element 19 is further connected to a subtracter 20.

  The other input terminal of the subtracter 20 is connected to the proportional element 21, and the output side of the subtractor 20 is connected to the saturation element 22. The output end of the saturation element 22 is connected to the control object 23. A comparator 26 for comparing the input side and output side values of the equivalent saturation element 19 is provided, and the output of the comparator 26 is connected to the correction feedback element 27. The output terminal of the correction feedback element 27 is connected to the comparator 17. Here, in FIG. 1, the portion indicated by a chain line 30 is constituted by a computer, and an arithmetic operation is performed by a computer algorithm to achieve a function as each element.

  Next, the operation of the integral proportional control device configured as described above will be described. When the difference between the position information output from the controlled object 23 and the target value given to the comparator 16 is small, the normal control operation is performed, and the correction information is input from the correction feedback element 27 to the comparator 17. Therefore, the comparator 17 does not perform a subtraction operation. Therefore, the integration element 18 integrates and inputs the value to the subtracter 20 through the saturation element 19, where the output from the proportional element 21 is subtracted and applied as a control signal to the controlled object 23 through the saturation element 22. .

  On the other hand, when the integration element 18 is saturated, the input and output values of the equivalent saturation element 19 are compared and subtracted by the comparator 26, and the difference is input to the comparator 17 through the correction feedback element 27. Accordingly, the deviation information is further subtracted by the comparator 17 and input to the integration element 18, and then passes through the equivalent saturation element 19 and is added to the subtractor 20. The subtracter 20 subtracts the value input from the proportional element 21 and then supplies a control signal to the controlled object 23 through the saturation element 22.

  Next, an equivalent system configuration of the integrating element 18 will be described with reference to FIG. The integrating element 18 includes a proportional element 33, a shift operator 34, a proportional element 35, a feedback element 36, an adder 37, a feedforward element 38, and an adder 39.

  Next, the operation of the control device comprising the system shown in FIGS. 1 and 2 will be described. First, paying attention to the adder 37 in FIG. 2, the adder 37 adds the outputs of the proportional element 33 and the feedback element 36 at the sampling time k to obtain the calculation amount x at the next sampling time k + 1. To do.

x (k + 1) = Ax (k) + be (k) (1)
Next, paying attention to the adder 39, the adder 39 adds the output of the proportional element 35 and the output of the feedforward element 38 and calculates the output u at that time k, so that the following equation is established.

u _I (k) = cx (k) + de (k) (2)
In the above formula (2) u _I represents the output of the integral element 18, e indicates the position tracking error. When an equivalent saturated amount _{u Imax} of the integral element 18 is the actual amount of saturation and _{u max, u Imax = | sgn} {u I (k)} u max + u p (k) | to become. Here, u _P is the output of the proportional element 21.

Next, the control input is increased, so that the state space model when the saturated state is developed is corrected using _uImax . The addition operation by the adder 37 is corrected as follows.

Next, in the adder 39,

また比較器２６による比較動作は次式で表される。 The following equation is derived from the subtraction operation in the comparator 17.

The comparison operation by the comparator 26 is expressed by the following equation.

Δu _I (k) = u _I (k) −sgn {u _I (k)} u _Imax (6)
As apparent from the above equation (5), the difference value Δu _I (k) of the saturator 19 is multiplied by 1 / d so as to prevent the integral element 18 from reaching saturation, and is fed back to the position error information. By executing this correction within the same sample time point k at which saturation occurs, an excessive wind-up phenomenon of the integration element 18 is prevented, and position overshoot and vibration characteristics can be improved.

  By such a control operation, it becomes possible to avoid the deterioration of the control performance due to the saturation of the control input of the integral proportional control system, particularly the windup phenomenon. In this embodiment, the overshoot amount with respect to the target value can be improved, and at the same time, it is possible to prevent the control performance from being deteriorated due to the target value and the magnitude of the disturbance and achieve the desired control performance.

  The portion indicated by the chain line 30 in FIG. 1 including the integration element 18 shown in FIG. 2 is constituted by a computer, and the above-described wind-up can be prevented by the calculation operation of this computer. This calculation operation will be described based on the flowchart shown in FIG.

を得る。この値が

となる。これに対して上記の飽和の判別において飽和が存在しない場合には、制御入力ｕ（ｋ）は、ｕ（ｋ）＝ｕ_Ｉ （ｋ）−ｕ_Ｐ （ｋ）とする。このように修正された値あるいは修正されない値が制御対象２３に制御入力として供給される。 The control input u (k) is compared with u _max to determine saturation. If saturation is confirmed, the equivalent saturation amount is calculated, and then the saturation is calculated. Then, the operation value is multiplied by 1 / d, and then the subtraction operation is performed. Then, after correcting the deviation value e (k), the integral operation is performed by bilinear transformation, and the integral output

Get. This value is

It becomes. On the other hand, if saturation does not exist in the above saturation determination, the control input u (k) is set to u (k) = u _I (k) −u _P (k). The value corrected in this way or the value not corrected is supplied to the controlled object 23 as a control input.

  Thus, the control device of the present embodiment is an integral proportional control device, and relates to an anti-windup technique in such a device. Here, the equivalent saturation element 19 is set as the output of the integration element 18 and the tracking error information for the target value is corrected based on the saturation amount.

Here, for the discretization of the integration element 18, the above correction can be made possible by performing a bilinear transformation so that a stationary term exists between the input and output without using a general backward difference transformation. Yes. That is, when the backward difference is used, in order to derive the output of the integration element 18 only from the input information of the integration element 18 up to one sample before, the second term on the right side of the equation (2) becomes 0 and the steady term. No longer exists. On the other hand, by using bilinear transformation, the second term on the right-hand side in equation (2) is used to perform the calculation using the two information amounts of the k + 1 sampling value and the previous k sampling value. Does not become 0, and there is always a stationary term.
In this way, the tracking error information can be corrected by using bilinear transformation so that a steady term exists between the input and output. By such a technique, the overshoot amount with respect to the target command can be reduced, and good control performance can be achieved without depending on the target value of the control input or the magnitude of the load disturbance.

  Next, an embodiment in which the above integral proportional control is used to control a precision stage for semiconductor manufacturing will be described. As shown in FIG. 4, the control device includes a stage 42 and is supported by a pair of linear guides 43 so as to be movable in the length direction thereof. The stage 42 is moved along the linear guide 43 by a non-resonant ultrasonic motor 44. The non-resonant type ultrasonic motor 44 is controlled by a controller 45 including a computer 30 that performs the integral proportional control described above.

  The controller 45 receives the output of the linear encoder 47 that reads position information from the output of the linear scale 46 and the output of the limit sensor 48. Further, the controller 45 is connected to the operation personal computer 49.

  The non-resonant type ultrasonic motor 44 includes driving legs 51 and 52. These drive legs 51 and 52 are each provided with an expansion / contraction deformation part 53 and a shear deformation part 54 as shown in FIG. The expansion / contraction deformation part 53 is polarized in the expansion / contraction direction, that is, the length direction, while the shear deformation part 54 is polarized in the lateral direction.

  Here, when a voltage is applied to the expansion / contraction deforming portion 53 of the driving leg 51, the driving leg 51 expands, and the tip side portion of the driving leg 51 comes into contact with the stage 42. In this state, the shear deformation portion 54 is subjected to shear deformation, so that the distal end portion of the drive leg 51 applies a driving force to the stage 42 in the feed direction. At this time, since the expansion / contraction deformation portion 53 of the driving leg 52 on the opposite side is contracted, the tip end portion of the driving leg 52 is separated from the stage 42. The shear deformation portion 54 of the drive leg 52 having the tip portion separated from the stage 42 in this way is shearing in the opposite direction in preparation for the next drive.

  Such an operation is alternately and sequentially repeated by the two drive legs 51 and 52, whereby the stage 42 is moved in the length direction of the linear guide 43 indicated by an arrow. The position is read by a linear encoder 47 that contacts the linear scale 46 and input to the controller 45.

  Actually, a control operation was performed with the parameters shown in Table 1 on a precision stage having a stroke of 100 mm. That is, the bandwidth is 50 Hz and the sampling time is 0.1 msec. Then, when a time response related to the position of the stage 42 to be controlled was measured when a step position signal of 3 mm was applied as a target value, a time response waveform shown in FIG. 6 was obtained. In FIG. 6, the dotted line indicates the case where anti-windup is not performed, and the thick line indicates the case where anti-windup is performed. For comparison, the result of applying the conventional anti-windup method to the proportional-integral control system is shown by a thin line. As is clear from this result, it was confirmed that the amount of overshoot with respect to the target value can be improved to about 0% compared to the conventional method to almost 0% and the settling time can be improved.

  In the control system composed of the integral proportional control device, even if the target value follow-up characteristic is improved as the bandwidth becomes wider, the overshoot amount with respect to the target value increases with the control input. In this embodiment and this example, the amount of overshoot with respect to the target value can be improved by a simple control structure called integral proportional control, and the deterioration of control performance depending on the target value and the magnitude of the load disturbance due to the antiwindup. It was confirmed that the desired control performance can be achieved.

  Although the present invention has been described with reference to the embodiments and examples, the present invention is not limited to the above embodiments and examples, and various modifications can be made within the scope of the technical idea of the invention included in the present application. It is. For example, in the above embodiment, an example in which a proportional element is used as an element including a proportional term has been shown. However, the present invention can also be applied to a control system including a proportional differential element and a proportional state feedback element as an element including a proportional term. is there. Moreover, although the said Example is related with the precision stage for manufacture of a semiconductor, the control apparatus and control method of this application are widely applicable to various positioning and other control.

  The present invention is widely applicable to various controls such as precision positioning.

It is a block diagram which shows the system configuration | structure of an integral proportional control apparatus. It is a block diagram which shows the equivalent system structure of the integral element of an integral proportional control apparatus. It is a flowchart which shows control operation. It is a block diagram of the positioning device of a stage. It is a principal part front view which shows operation | movement of a non-resonance type | mold ultrasonic motor. It is a graph of the time response waveform of the same stage. It is a time response waveform which shows the conventional windup operation | movement. It is a graph which shows the integration operation at the time of saturation. It is a block diagram of a proportional integral control device. It is a block diagram of an integral proportional control device.

Explanation of symbols

5 Comparator 6 Proportional Element 7 Integral Element 8 Adder 9 Saturation Element 10 Control Target 12 Subtractor 16, 17 Comparator 18 Integration Element 19 Equivalent Saturation Element 20 Subtractor 21 Proportional Element 22 Saturation Element 23 Control Target 26 Comparator 27 Modification Feedback element 30 Computer 33 Proportional element 34 Shift operator 35 Proportional element 36 Feedback element 37 Adder 38 Feed forward element 39 Adder 42 Stage 43 Linear guide 44 Non-resonant ultrasonic motor 45 Controller 46 Linear scale 47 Linear encoder 48 Limit sensor 49 PC for operation 51, 52 Driving leg 53 Stretching deformation part 54 Shearing deformation part

Claims (5)

An integral element and an element including a proportional term, and a deviation between the target value and the output of the controlled object is input to the integral element, and the output of the controlled object is input to the integral element by a subtractor through the element including the proportional term. In the integral proportional system control device that supplies a control signal to the controlled object by subtracting from the output of
An equivalent saturation element is provided on the output side of the integration element and before the subtractor, and a correction element for correcting a deviation amount input to the integration element is provided, and the correction element is provided according to the saturation amount of the equivalent saturation element. The correction element corrects the deviation amount input to the integration element ,
A forward element that adds a value obtained by multiplying a deviation input of the integrator by a constant to the output of the integrator, and the correction element that corrects a deviation amount input to the integration element is a constant of the forward element; An integral proportional system control device characterized by being a proportional component of a fraction .   The input value and the output value of the equivalent saturation element are compared by the comparison means, the saturation amount is obtained by the difference, and the correction element corrects the deviation amount input to the integration element by the saturation amount. The integral proportional system control device according to claim 1, wherein: An integral element for discretizing the amount of information and an element including a proportional term are included, and a deviation amount between a target value and an output of the controlled object is input to the integral element, and an output of the controlled object includes the proportional term In the integral proportional system control method in which a control signal is supplied to the control object by subtracting from the output of the integral element by a subtractor through an element,
An equivalent saturation means is set on the output side of the integral element and before the subtractor, and the deviation amount input to the integral element is corrected using information on the saturation amount by the equivalent saturation means , and
The integrator further includes a forward element, and the correction element for correcting a deviation amount input to the integral element is a proportional element that is a constant part of the forward element, and the integration is performed by the forward element. A method of controlling an integral proportional system , comprising: adding a value obtained by multiplying a deviation input to a constant by a constant to an output of the integrator. 4. The integral proportional system control method according to claim 3 , wherein the integral element, an element including a proportional term, and an equivalent saturation means are set on a computer for control. 4. The integral proportional system control method according to claim 3 , wherein control is performed so that an input value of the equivalent saturation means has a stationary term by using bilinear transformation for discretization of the output of the integrator.

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