JP2007272279A - Control device - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a control device capable of attaining a quick startup even in a control object having disturbance and characteristic fluctuation. <P>SOLUTION: The control device comprises a sensor 21 for detecting an output quantity outputted from a mechanism part 10 according to control to the mechanism part 10 that is the control object; and a sliding mode controller 22 calculating, based on a target value of output quantity in the mechanism part 10 and the output quantity detected by the sensor, a control quantity to the mechanism part 10 by sliding mode control, and outputting a control signal based on the control quantity to the mechanism part 10. The sliding mode controller 22 is configured to attenuate a predetermined frequency component in the output quantity detected by the sensor 21 and calculate the control quantity based on the output quantity in which the predetermined frequency component is attenuated. <P>COPYRIGHT: (C)2008,JPO&INPIT

Description

  The present invention relates to a control device using sliding mode control.

  In order to realize highly accurate positioning and target value tracking of a controlled object in motion control, it is necessary to suppress disturbances and fluctuations in characteristics of the controlled object. Although linear feedback control represented by PID control is easy to design, sufficient performance for the above-mentioned purpose cannot always be obtained. On the other hand, the sliding mode control includes the property of the variable structure control system, that is, the nonlinear characteristic in the controller itself, and it is possible to effectively suppress the disturbance and the characteristic variation of the controlled object.

  In the sliding mode control, a predetermined slip plane is set in the state space, and the controlled system is constrained to the slip plane. This restriction makes the system insensitive (to be unaffected) by disturbances and characteristic fluctuations, and enables highly accurate positioning and target value tracking. Here, the control force for constraining the slip plane can be obtained as follows.

  A general equation of motion of a one-degree-of-freedom control object in motion control is represented by equation (1). Here, m is mass, x is displacement, F is control force, and d is disturbance force.

Assuming x ₁ = x and the time derivative of x ₁ is x ₂ , equation (1) can be expressed in matrix form as equation (2).

In order to the control system positioning control system or target value follow-up system, to define a new state variable x _i obtained by integrating the difference between the target value r and the displacement x.

  The characteristic of the slip plane σ is expressed using a linear combination of state quantities as shown in equation (4). In the equation (4), S is a linear combination gain set by the user. A number of methods for determining the linear combination gain S have been proposed. For example, there is a method of utilizing a feedback gain in optimal control (for example, see Non-Patent Document 1).

In order to give the system the characteristic of the slip plane σ expressed by the equation (4), σ = 0 is solved for F, and F at this time is applied as the first control force f ₁ (ie, control force F). . When there is no disturbance or model fluctuation, the system is constrained to the slip plane by the above operation, and highly accurate positioning and target value tracking are possible.

  On the other hand, when there is a disturbance or model variation, the following operation is added to constrain the system to the slip plane (that is, to establish σ = 0). First, a quadratic function V of σ representing the characteristics of the slip plane is defined as in equation (5).

If the time derivative of V is smaller than 0, it converges to σ = 0. Therefore, the second control force f ₂ is added to the first control force f ₁ obtained previously, and f ₁ + f ₂ is set as a new control force F. To do. Here, f ₂ is given in a form including a sign function of σ as shown in equation (6). In Equation (6), K is a control gain set by the user.

When the control input F is f ₁ + f ₂ and the time derivative of V is obtained, equation (7) is obtained. If the magnitude of the control gain K is set appropriately, convergence to σ = 0 is guaranteed.

  At this time, the system is constrained to the slip plane, and is insensitive to disturbances and characteristic variations of the controlled object.

  In addition, when not only positioning and target value tracking but also a fast rise is required, it is common to use feedforward control in addition to feedback control. For example, as shown in FIG. 8, a feedforward controller 102 is provided in parallel with the feedback controller 101, and the control target 103 is obtained by adding the output from the feedback controller 101 and the output from the feedforward controller 102. Is input. Feedforward control is a technology that compensates for response delays mainly due to inertia and realizes quick rise. Here, the equation of motion of the one-degree-of-freedom control object that is not affected by disturbance is represented by equation (8).

  If the target trajectory is r and the control force F is obtained as shown in equation (9), the controlled object can be driven without delay.

  From this, the feedforward compensation calculation in FIG. Here, FF is a gain by the feedforward controller 102, and u is an operand.

By adding such an operation, a quick rise can be realized.
Mita Tsutomu, Chen Geifeng, “Sliding Mode Control and Robot Arm Trajectory Control”, “System / Control / Information”, System Control Information Society, 1990, Vol. 34, No. 1, p. 50-55

  When the sliding mode control is used, it is necessary to estimate in advance the magnitude of the disturbance and the characteristic variation of the controlled object. By setting the control gain K of the equation (6) according to the magnitude, the disturbance and the control are controlled. The characteristic variation of the target can be suppressed. However, when the controlled object includes a resonance characteristic, a large gain setting excites resonance and destabilizes the controlled object. For this reason, when the control target includes resonance characteristics, the gain K of the sliding mode control cannot be set large, and disturbance and fluctuations in the characteristics of the control target cannot be sufficiently suppressed.

  Also, when driving the controlled object at a low speed, the effects of friction and resistance components included in the controlled object become relatively stronger than the delay due to inertia, and feedforward control that compensates for the delay due to inertia, Even if the calculation of equation (10) is performed, a quick rise cannot be expected. For this reason, it is necessary to suppress disturbances and fluctuations in the characteristics of the controlled object in order to realize high-speed rising during low-speed driving.

  The present invention has been made in view of such a problem, and an object of the present invention is to provide a control device capable of realizing a quick rise even in a controlled object having disturbance and characteristic fluctuation.

  In order to achieve such an object, a control device according to the present invention includes a detector that detects an output amount that is output from a control target in response to control on the control target, and a target value and a detector for the output amount in the control target. The sliding mode controller includes a sliding mode controller that calculates a control amount for the control target by sliding mode control based on the detected output amount, and outputs a control signal based on the control amount to the control target. A predetermined frequency component in the output amount detected by the unit is attenuated, and the control amount is calculated based on the output amount in which the predetermined frequency component is attenuated.

  In the above-described invention, the control target includes a base, a stage that is slidable on the base, and a drive source that slides the stage, and the detector is the stage on the base. The relative speed is detected as the output amount, and the sliding mode controller attenuates the high-frequency component in the relative speed of the stage detected by the detection unit, and the stage which is the relative speed of the stage attenuated the high-frequency component and the target value The driving force of the driving source may be calculated as a control amount by sliding mode control based on the target speed, and a control signal based on the driving force may be output to the driving source.

  According to the present invention, it is possible to realize a quick rise even in a controlled object having disturbance and characteristic fluctuation.

  Hereinafter, preferred embodiments of the present invention will be described with reference to the drawings. An outline of a stage apparatus provided with a control device (control unit 20) according to the present invention is shown in FIG. This stage apparatus 1 is mainly composed of a mechanism unit 10 and a control unit 20 that controls the operation of the mechanism unit 10 to be controlled. The mechanism unit 10 includes a base 11, two guides 12 fixed on the base 11, a stage 13 slidably mounted on the guide 12, and a motor 14 for sliding the stage 13. The screw 15 is connected to the output shaft of the motor 14, and the nut 16 is coupled to the stage 13 while being screwed with the screw 15.

  The base 11 is formed in a rectangular plate shape using a metal material, and each component of the mechanism unit 10 is attached on the base 11. The two guides 12 are formed in a linearly extending rail shape, and are attached to the base 11 so as to be arranged in parallel to each other. The stage 13 is formed in a rectangular plate shape using a metal material and is slidably mounted on the guide 12. As a result, the stage 13 can slide on the base 11 in one direction (in the left-right direction in FIG. 1).

  The motor 14 is a so-called servo motor, and the output shaft of the motor 14 is connected to the screw 15 via a coupling 17. The screw 15 is rotatably attached to the base 11, and is configured such that its rotation axis is parallel to the direction in which the guide 12 extends, that is, the direction in which the stage 13 slides on the base 11. As described above, the nut 16 is coupled to the side portion of the stage 13 while being screwed with the screw 15.

  When the screw 15 is rotated by the driving torque (rotational driving force) of the motor 14, the rotational force is converted into a translational force by the nut 16. The stage 13 is driven by a linear constraint by the guide 12 and a force converted in the translation direction by the nut 16.

  Further, the drive control of the motor 14 (that is, the operation control of the mechanism unit 10) is performed by the control unit 20 calculating the speed of the stage 13 from the value of the position sensor 21, and the torque to the motor 14 obtained by calculation on the CPU. This is performed by giving a command to a motor driver (not shown). As shown in FIG. 3, the control unit 20 is mainly configured by a position sensor 21 that detects the relative position of the stage 13 on the base 11 and a sliding mode controller 22. The position sensor 21 is attached in the vicinity of the stage 13 in the base 11.

  Machine elements such as the motor 14, screw 15, nut 16, guide 12, and the like include frictional resistance, and can be regarded as characteristic variation of the control target. The screw 15 and the nut 16 are important parts for transmitting the torque of the motor 14 to the stage 13, but it is difficult to ensure sufficient rigidity to realize high-speed driving. These correspond to the incorporation of a spring component inside the controlled object, and adversely affect the control characteristics in the form of resonance. Therefore, in the present embodiment, both characteristic fluctuations such as friction and resonance are suppressed by applying frequency shaping sliding mode control.

  That is, in the sliding mode control performed by the sliding mode controller 22, it is possible to appropriately attenuate the high frequency component included in the control force and perform stable control by appropriately shaping the characteristics of the slip plane on the frequency axis. Become. By this stabilization, the control gain K in the equation (6) can be set to a large value, and a quick rise can be realized even in a controlled object having disturbance and characteristic fluctuation. The frequency shaping of the slip plane is realized by applying a filter (low-pass filter) designed to suppress the resonance characteristics of the system to the state quantities constituting the slip plane. A filter that shapes the slip plane can be expressed in matrix form as shown in equation (11).

  Then, in the design of the slip plane of the formula (4), the frequency of the slip plane is applied by applying the filter of the formula (11), and then the procedure of the formulas (5) to (7) is applied to resonate. Stable control can be performed even in a system including In the case where the filter is expressed by a scalar, equation (12) is obtained. In the equation (12), s is a Laplace operator, and m and n are orders of the denominator numerator.

  By the way, a simple model of a controlled object including resonance can be considered as shown in FIG. This simple model includes a first object 31 having one degree of freedom, a second object 32 having one degree of freedom, and a spring 33 and a damper 34 that connect the first object 31 and the second object 32. Is done. The first object 31 in FIG. 2 represents the inertia of the rotating system such as the motor 14 and the screw 15 in FIG. 1, and the second object 32 represents the inertia of the stage 13. Note that there is no significant difference between the rotation and translation here, so both can be considered as translational components.

When the simple model of FIG. 2 is described by an equation of motion, equation (13) is obtained. Here, F is a control force, m ₁ and m ₂ are masses of the first and second objects 31 and 32, x ₁ and x ₂ are displacements of the first and second objects 31 and 32, and k is a spring 33. Is a damping coefficient in the damper 34.

The specific values of the parameters in the equation (13) are m ₁ = 45 kg, m ₂ = 5 kg, k = 100000 N / m, c = 100 Ns / m, and the friction assumed as the variation of the controlled object is 50 N. Here, when the frequency response of the control target (the speeds of the first and second objects 31 and 32) with respect to the input of the control force F is obtained, FIG. 4 is obtained. From this, it can be seen that the controlled object has a resonance of 23.7 Hz.

  In general, a model used for control design is a simplified model of the characteristics of the controlled object. In the present embodiment, it is assumed that the spring component in FIG. 2 is sufficiently rigid and the equation (14) is ignored, ignoring the spring component and the damper component.

Here, M = m ₁ + m ₂ , v is a time derivative of x ₁ (= x ₂ ). The state space model expression of equation (14) corresponding to equation (2) becomes equation (15) when v is selected as the state quantity.

  One method for obtaining a frequency-shaped slip plane using equation (11) is to include a filter directly in the controlled object. Therefore, when the filter to be applied is designed in consideration of the characteristics of the control target in FIG. 4, the first order and the cut-off frequency ω = 5 Hz can be set as one candidate. FIG. 5 shows the frequency response of the designed filter.

From equation (11), the state equation of the designed filter is expressed as equation (16), where state quantity z is _xfil . Therefore, when the filter of the equation (16) is applied to the control design model of the equation (15), the enlarged model (17) is obtained. In this embodiment, in = v.

In order to the control system positioning control system or target value follow-up system is defined as a new state variable x _i obtained by integrating the difference between the target velocity r and filtered velocity x _fil (18) equation.

  The final equation (19) for control design is obtained by combining the equations (17) and (18). The expression (19) can be expressed as the expression (20) except for the term of the target speed r.

  The characteristic of the slip plane σ in the control design model (19) is expressed as in (21) in the same manner as in (4). In Equation (21), S is a linear combination gain set by the user.

  Here, it is considered to determine the linear combination gain S of the equation (21). Many methods for determining the gain S have been proposed. In the present embodiment, a method of utilizing a feedback gain in optimal control is used. In the method of utilizing the feedback gain in the optimal control, S is determined using the Riccati-type algebraic equation expressed by the equation (22).

Here, P is a solution of the algebraic equation, and Q and R are parameters given by the designer. A ₁ and B ₁ are parameters of the controlled object model shown in the equation (23).

In the equation (23), x and u indicate general state quantities and control inputs. In the present embodiment, A ₁ corresponds to A in the equation (20), and B ₁ represents B in the equation (20). It corresponds to.

By using this method, the linear combination gain S obtained by substituting specific values for the parameters (M = m ₁ + m ₂ , ω, etc.) of each equation is S = (2.0663e + 003, 2.5263e + 000, -2.0027e + 004). Further, the control gain K in the equation (6) is set to K = 100000 as a value sufficient to suppress the set frictional force 50N.

  Here, a control method of the mechanism unit 10 by the control unit 20 in which the linear combination gain S and the control gain K are determined as described above will be described with reference to FIG. First, in step S101, the position sensor 21 detects the displacement amount y of the stage 13 on the base 11 (that is, the relative position of the stage 13 on the base 11). At this time, the speed v of the stage 13 is calculated (detected) from the change of the displacement amount y over time.

Next, in step S102, the sliding mode controller 22 calculates the state quantity x _fil using the equation (16) from the velocity v calculated in step S101, and uses the equation (18) to calculate the state quantity x _i. Is calculated. The target speed r is set to 100 μm / s (a constant value), for example.

Next, in step S103, the sliding mode controller 22 calculates the slip plane σ using the equation (21) from the respective state quantities x _fil , x _i , v calculated in step S102.

Next, in step S104, the sliding mode controller 22 solves σ = 0 in equation (21) for F, and calculates F at this time as the first control force f ₁ (ie, control force F). In order to solve σ = 0 for F, first, since σ = 0, equation (24) is obtained.

  By substituting equation (20) into equation (24), equation (25) is obtained.

Then, when equation (25) is solved for F, equation (26) is obtained. By substituting the state quantities x _fil , x _i , and v calculated in step S102 into this equation (26), the control force F Is calculated.

Next, in step S105, the sliding mode controller 22 calculates the second control force f ₂ using the equation (6) from the slip plane σ calculated in step S103.

Next, in step S106, the sliding mode controller 22, the second control force f ₂ in addition to the first control force f ₁ calculated in step S104, calculates the f ₁ + f ₂ as a new control force F .

  Next, in step S107, the sliding mode controller 22 outputs a control signal based on the control force F calculated in step S106 (in this embodiment, the rotational driving force of the motor 14) to the motor 14 of the mechanism unit 10. To do. When step S107 ends, the process returns to step S101.

  FIG. 7 shows the simulation results from 0 second to 1 second when the target speed of the stage 13 is 100 μm / s (constant value). It can be seen that when the conventional sliding mode control is used, the response is oscillating, whereas a smooth response can be obtained by using the frequency-shaped sliding mode control.

  As a result, according to this embodiment, it is possible to perform stable control by appropriately attenuating the high-frequency component included in the control force. By this stabilization, the control gain K in the equation (6) can be set to a large value, and a quick rise can be realized even in a controlled object having disturbance and characteristic fluctuation. Note that the frequency shaping of the slip plane is realized by applying a filter designed to suppress the resonance characteristics of the system with respect to the state quantities constituting the slip plane.

In this embodiment, a low-pass filter is applied to the speed v (output of the control target) of the stage 13, and the slip plane σ and the control are controlled based on the speed v (x _fil ) of the stage 13 in which the high-frequency component is appropriately attenuated. The force F is calculated. In this way, the slip plane σ and the control force F can be calculated by a relatively simple calculation.

  In the above-described embodiment, the speed of the control target is set as the target value. However, the present invention is not limited to this, and the displacement of the control target may be set as the target value.

Further, in the above-described embodiment, a slip plane is applied based on the speed v (x _fil ) of the stage 13 in which a low-pass filter is applied to the speed v (output of the control target) of the stage 13 and the high-frequency component is appropriately attenuated. Although σ and control force F are calculated, the present invention is not limited to this, and a high-pass filter, a band rejection filter, or the like may be used depending on the resonance characteristics of the system.

  Furthermore, in the above-described embodiment, the control target is the mechanism unit 10 of the stage apparatus 1 that includes the base 11, the stage 13 that is slidably provided on the base 11, and the motor 14 that slides the stage 13. However, the present invention is not limited to this, and the present invention can be applied to any control target model in which sliding mode control is performed.

It is the schematic of the stage apparatus provided with the positioning control apparatus which concerns on this invention. It is explanatory drawing which shows the simple model of a stage apparatus. It is a control block diagram of a stage apparatus. It is a graph which shows the frequency response of the controlled object (simple model) with respect to control input. It is a graph which shows the frequency response of a filter. It is a flowchart which shows the sliding mode control in this embodiment. It is a graph which shows the simulation result of this embodiment. It is a control block diagram which shows an example of feedforward control.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Stage apparatus 10 Mechanism part (control object) 11 Base 13 Stage 14 Motor (drive source)
20 control unit (control device) 21 position sensor (detector)
22 Sliding mode controller F Control force (control amount) v Speed (output amount)

Claims (2)

A detector for detecting an output amount output from the control object in response to control on the control object;
Based on a target value of the output amount in the control target and the output amount detected by the detector, a control amount for the control target is calculated by sliding mode control, and a control signal based on the control amount is controlled by the control A sliding mode controller that outputs to the target,
The sliding mode controller is configured to attenuate a predetermined frequency component in the output amount detected by the detection unit and calculate the control amount based on the output amount attenuated the predetermined frequency component. A control device. The control object includes a base, a stage slidably provided on the base, and a drive source that slides the stage.
The detector detects the relative speed of the stage on the base as the output amount,
The sliding mode controller attenuates the high-frequency component in the relative speed of the stage detected by the detection unit, and sets the relative speed of the stage and the target speed of the stage, which are the target values, after the high-frequency component is attenuated. The driving force of the driving source is calculated as the control amount based on sliding mode control, and a control signal based on the driving force is output to the driving source. The control device described.

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