KR20030020781A - Unified PID Position Controller for Linear Motor and Gain Design Method Using The Same - Google Patents

Abstract

PURPOSE: A unified PID(proportional integral differential) position controller for a linear motor and a gain setting method using the same are provided to allow for an ease of gain setting, while effectively increasing the stiffness of the linear motor. CONSTITUTION: A unified PID position controller comprises a first mixer for extracting an error between the actual position and the reference position of a mover; a PID gain control unit including a first proportional control section for outputting a proportional gain with respect to the output value of the first mixer, a first differential control section for outputting a differential gain with respect to the output value of the first mixer, and a first integral control section for outputting an integral gain with respect to the output value of the first mixer; a second mixer for summing output values of the PID gain control unit; a position gain control unit including a second differential control section for obtaining a differential gain with respect to the actual position of the mover, a second proportional control section for taking, as an input, the output value of the second differential control section, and a third proportional control section for taking, as an input, the actual position of the mover, wherein the position gain control unit sums the output value of the second proportional control section and the output value of the third proportional control section and outputs the result; and a third mixer for summing output values of the PID gain control unit and the position gain control unit.

Description

Unified PID Position Controller for Linear Motor and Gain Design Method Using The Same}

The present invention relates to a position controller of a linear motor, and more particularly, to an integrated PID position controller of a linear motor with a simplified gain design and a gain setting method using the same.

Recently, the demand for a linear motor that realizes direct linear reciprocating movement is increasing as the need for high precision and fast response performance is emerging in the field of industrial devices requiring linear reciprocating movement such as semiconductor equipment or tool transfer equipment such as CNC. It is increasing. Since linear motors can be linearly moved without mechanical shifting devices such as chains and gears, they are noisy, unlike ball-screw or rack-pinion linear kinematics, which basically use rotors. There is no problem due to backlash or backlash, and it has the advantage of long life and easy maintenance. In particular, linear motors generate thrust directly from the electric force, which makes it possible to easily obtain much higher acceleration performance than other linear motion devices, and has a unique advantage of precise position control of several μm.

In general, the linear motor is mainly used in the field that requires the movement of the mover by linear motion. Accordingly, the general rotary motor has the priority of the torque control operation and the speed control performance of the motor. Excellent dynamic characteristics for the position control operation are absolutely required.

The industry uses a position control loop of cascade control structure in which a position compensator composed of P (Proportional) or Proportional-Integral (PI), a PI speed compensator, and a lowest current controller are connected in series. This control structure is relatively simple in setting gains because each compensator can be operated independently, and when connecting each compensator, limiting the maximum value for reference values such as speed and current in consideration of the maximum speed and torque of the motor. There is an advantage of being easy. However, this method has a problem in that the operation time is long and the dynamic characteristics of the entire position control loop are greatly reduced because the control dynamics of the lower compensator affect the upper control loop. Therefore, the position control algorithm of the serial control structure has a problem that is difficult to apply to a high speed high performance linear motor used at a speed of 2 to 5 m / s.

In recent years, as the trend of linear motors becomes more common, interest in high-speed, high-precision position control algorithms has increased, and the dynamic compensator of the control system has been improved by eliminating the series compensator structure and omitting the speed controller or current controller corresponding to the inner loop. Some research has been done on position controllers. However, most of the preceding algorithms are too academically oriented and do not meet the actual industry requirements that they should be easy to implement. They tend to go beyond theory, and the position control algorithms that some controller manufacturers actually apply. Even without establishing a solid theoretical basis, it relies on the classical method of 'Try-and-Error' in selecting the controller's gain.

One remarkable achievement of the previously studied position controller is the Proportional Integral Differential (PID) position controller based on the two degree of freedom (TDOF). In this method, the dynamics of the system are improved by inputting the output of the position compensator composed of PID directly to the current (or torque) control loop without the intermediate internal speed control loop. In addition, this method solves the inevitable vibration problem of the system by changing the pole and zero positions of the system by dividing the gain of the controller into two, like the method used in the TDOF speed control algorithm. Is proposing.

The position control method based on the TDOF shows a very good performance in the sense of improving the stability, and has the possibility of securing excellent popularity by using the PID used in the existing industry as a basic compensator. However, this method has its own problem that it is difficult to use the degrees of freedom given the fixed system-wide responsiveness due to the application of the existing TDOF algorithm. There is a problem in that it is sensitive to noise due to the gain of each branch to be set.

1 is a functional block diagram of a general PID position controller.

In Fig. 1, the PID position controller takes as input the feedback values of the reference position (x ^* ) of the mover and the actual position (x) of the mover. PID position control section 18 is larger, G _C (s) state error compensating unit 10, which take sloth as, G _F (s) represented by the state Feedforward unit represented by (12) and G _B (s) The state feedback compensator 14 is provided. The linear motor, a model of the control target system, is represented by G _S (s). In FIG. 1, the current controller and the power converter assume that the cut-off frequency of the current control system is 5 to 10 times greater than the frequency of the position control system.

FIG. 2 is a detailed circuit diagram of the PID position controller shown in FIG. 1 and shows an example in which each device is configured with an operator.

As shown, when the reference position (x ^* ) and the actual position (x) of the linear motor mover are input, the first mixer 20 is the error (x ^* -) of the actual position (x) at the reference position (x ^* ). Perform an operation that prints x). The error is first input to the main error compensator 10. The main error compensator 10 outputs the first proportional control part 22 that outputs the proportional gain K _p (x ^* -x) of the difference value, and the difference. First derivative controller 24 which outputs the differential gain K _D S (x ^* -x) of the value and the integral gain of the differential value It includes a first integration control unit 26 for outputting the.

On the other hand, the reference position (x ^* ) of the mover is input to the state forward compensation unit 12. The state redirecting compensator 12 performs a second derivative of the reference position x ^* of the mover by the second and third differential control units 28 and 30 and delays the first delay unit 32 to the acceleration term of the linear motor. Outputs the ^second derivative gain K _Af S ² x ^* , while the reference position x ^{* of the} mover is differentiated in the fourth derivative controller 34 and the proportional gain is added in the second proportional controller 36 to speed Output the differential gain (K _Df Sx ^* ) for the term. In addition, the state redirecting compensator 12 outputs a proportional gain K _Pf x ^* with respect to the reference position x ^* of the mover by the third proportional controller 38.

The output values of the main error compensator 10 and the state redirecting compensator 12 are input to the second mixer 40 and summed.

On the other hand, the actual position x of the mover is input to the state feedback compensator 14. The state feedback compensator 14 is a fourth proportional controller 42 which outputs a proportional gain K _P Bx of the actual position x by inputting the actual position x of the mover, and the derivative gain K of the actual position. And a third mixer 46 for summing output values of the fourth differential control unit 44 and the fourth proportional control unit 43 and the fifth differential control unit 44 for outputting _DB Sx).

Now, the output values of the second mixer 40 and the third mixer 46 are input to the fourth mixer 48 and summed, resulting in the output of the resulting gain A *.

The mechanical system of the motor to which the PID position controller shown in FIGS. 1 and 2 is applied may be modeled as shown in [Equation 1].

In Equation 1 Represents the control force (Force [N]) Indicates a disturbance. In addition, M denotes the mass (Mass [Kg]) of the linear motor mover, and B denotes viscous friction. In general, it is assumed that there is no B because frictional force hardly occurs in a bearing used in a linear motor.

When the speed control system directly controls the power (torque) of the motor as shown in FIG. 1, the entire control system may diverge. Due to this problem, an additional safety device is used in the main compensator and the position command input terminal in the industry. Doing. Another example is a lead-lag compensator, in which only a PD (Proportional Differential) controller is used as the main compensator. In addition, a textbook example uses PID as the main compensator. The PID compensator may have better responsiveness than PI or PD, but it is very difficult to set a control gain capable of suppressing a vibration phenomenon affecting the precision of a workpiece, which is a load of a control system.

On the other hand, when the gain of the current controller can be replaced by 1 in the frequency band where the position control is made because the dynamic characteristics of the current control unit in the overall position control system of the linear motor are very large, the control constant that affects the position control loop is the power of the motor. It can be summarized as the force constant and the mass of the mover. In synchronous linear motors using permanent magnets, the force constant is generally assumed to be constant and accurate. However, depending on the material of the magnet, if the temperature fluctuates, the force constant may fluctuate relatively largely due to the weakening of the magnetic flux.

In addition, it can be assumed that the weight of the transfer part of the motor can be known relatively accurately, but the mass of the entire transfer part can be increased or decreased in a very large amount when the movement of raising or lowering the object to be transferred to the mover is repeated during the transfer operation. This variation in the control constant acts as an uncertainty factor for the pole and zero placement of the controller in the entire control loop, reducing the stability of the controller and causing undesirable consequences such as over-shoot. There is this.

Most of the applications where linear motors are actually applied are related to feeding, and machine tools such as NC (Numeric Control) are also important applications for linear motors. High performance linear motors with accelerations of 2 to 5G and speeds of 1 to 3 m / s are also used for high acceleration and high precision in machine tools. In addition, unlike other applications, in the machine tool field, since a direct contact occurs between the workpiece and the processing tool, an external force acts on the entire control loop, and the degree of resistance to the force is defined as stiffness. .

If there is a force applied to the system from the outside, this force acts as a disturbance in the control loop, and in order to increase the performance of the position control loop, the stiffness corresponding to the rigidity against the disturbance must be greater than a certain degree. do. In order to increase the degree of machining of the workpiece, it is necessary to have a controller with a large stiffness, so that despite the many opportunities in the industrial field for the large stiffness, there is little practical approach to this.

This stiffness is different depending on the mass and material of the workpiece, but generally shows a big difference according to the algorithm of the position controller. The problem is that it is difficult to set the gain to increase the stiffness because it is difficult to predict how much the stiffness appears when the gain is set in the conventional controller structure. In general, as the gain of the whole controller is larger, the stiffness tends to be higher. However, if the gain is set too high, oscillation may occur in the position control loop due to noise and detection delay time displayed in the position detector. Gain setting guide is necessary.

In particular, machine tools such as CNC machines that directly apply force to the work to perform cutting operations, etc., often require high stiffness of at least 10 ⁷ to 10 ⁸ [N / m]. Measures must be taken.

The present invention has been made to solve the above problems, by designing a PID compensator as the main controller and directly connected to the current controller, an integrated PID position controller of the linear motor that can increase the dynamic characteristics of the system and minimize the computational burden; There is a technical problem in providing a gain setting method using the same.

Another technical problem of the present invention is to apply all available state forward compensation techniques and state feedback compensation techniques to a controller, and design the entire position control system to be configured in the form of a first order low pass filter, thereby responsiveness and stability of the system. And to ensure complete freedom in setting the control gain.

Another technical problem of the present invention is to configure the integrated PID position controller in the form of a first-order low pass filter to accurately predict the dynamic characteristics of the system and to suppress the over-shoot phenomenon, thereby reducing the work load corresponding to the load of the control system. To improve the precision.

In addition, the present invention, while maintaining the dynamic characteristics of the system according to the degree of freedom of gain setting derived from the design of the integrated PID position controller, the system performance does not change even when there are fluctuations and uncertainties of the system constant, and the stiffness of the control system ( It is a technical task to make it possible to increase stiffness.

In addition, the present invention has a technical problem to prevent the non-linearity of the system by the current limiting element by passing the current limiter before the output of the integrated PID position controller to the linear motor.

1 is a functional block diagram of a general PID position controller.

FIG. 2 is a detailed circuit diagram of the PID position controller shown in FIG. 1.

3 is a functional block diagram of a PID position controller applied to the present invention.

4 is a functional block diagram of an integrated PID position controller according to the present invention.

FIG. 5 is a detailed circuit diagram of the integrated PID position controller shown in FIG. 4.

6 is a graph showing a frictional force model of the linear motor.

7A to 7C, 8A and 8B are graphs showing simulation results of low pass filter characteristics of the integrated PID position controller according to the present invention.

9A to 9C and 10A to 10C are graphs showing simulation results of step response characteristics of the integrated PID position controller of the present invention.

11A and 11B are graphs showing experimental results of frequency response characteristics of the integrated PID position controller according to the present invention.

12A and 12B are graphs showing experimental results of step response characteristics of the integrated PID position controller according to the present invention.

13A and 13B are open loop board diagrams of an integrated PID position controller according to the present invention.

14A and 14B are graphs showing the step response characteristics according to the system constant change in the integrated PID position controller according to the present invention.

15 is a functional block diagram of an integrated PID position controller according to another embodiment of the present invention.

16A and 16B are graphs showing experimental results of step response characteristics when the cutoff frequency is 200 rad / s in the integrated PID position controller of the present invention.

17A and 17B are graphs showing experimental results of step response characteristics when the cutoff frequency is 50 rad / s in the integrated PID position controller of the present invention.

18A and 18B are graphs for explaining position control capability according to stiffness in the integrated PID position controller of the present invention.

<Description of the symbols for the main parts of the drawings>

10: main error compensation unit 12: state forward compensation unit

14: state feedback compensation unit 16: linear motor

18 PID position controller 20 first mixer

22: first proportional control unit 24: first differential control unit

26: first integral control unit 28: second differential control unit

30: third differential control unit 32: first delay unit

34: fourth derivative controller 36: second proportional controller

38: third proportional control unit 40: second mixer

42: fourth proportional control unit 44: fifth differential control unit

46: third mixer 100: PID controller

200: integrated PID position controller 102: state forward compensation unit

104: state feedback compensation unit 106: main error compensation unit

108: PID gain control unit 110: position gain control unit

112: fourth mixer 114: fifth mixer

116: fifth proportional control unit 118: sixth differential control unit

120: second integration controller 122: sixth mixer

124: seventh differential control unit 126: sixth proportional control unit

128: seventh proportional controller 130: seventh mixer

132: current limiter

According to an aspect of the present invention, there is provided a PID position controller of a linear motor, comprising: a first mixer for extracting an error value of an actual position with respect to a reference position of a mover; A first proportional control unit for outputting a proportional gain with respect to the output value of the first mixer, a first differential control unit for outputting a differential gain with respect to the output value of the first mixer, and an integral gain for the output value of the first mixer A PID gain control unit including a first integration control unit for performing the control; A second mixer for summing respective output values of the PID gain control unit; A second proportional control unit that obtains a differential gain with respect to the actual position of the mover, a second proportional control unit that takes an output value of the second differential control unit as an input value, a third proportional control unit that uses the actual position of the mover as an input value, and the second A position gain control unit for summing and outputting the output value of the second proportional control unit and the output value of the third proportional control unit; And a third mixer for summing output values of the PID gain controller and the position gain controller. It is provided.

Hereinafter, exemplary embodiments of the present invention will be described in detail with reference to the accompanying drawings. In the following description, the implementation of the integrated PID position controller of the present invention will be described according to the process of simplifying the gain items to be controlled by the PID position controller.

3 is a functional block diagram of a PID position controller according to the present invention, in which a state forward compensation unit 102 and a state feedback compensation 104 are used to apply a PID as a main controller and improve the stability of the system. Indicates.

In FIG. 3, the main error compensator 106 is a PID controller, where K _P ′ is proportional gain, K _I ′ is integral gain, and K _D ′ is differential gain. The input of the PID is the error between the reference position (x ^* ) and the actual position (x) and the output is the reference acceleration ( Were considered to have the same units. The target motor, linear motor, was modeled as a secondary mechanical system with two poles. The dynamic characteristics of the electric system, which consisted of armature resistance and inductance, were excluded from the modeling. However, since the current acts as a link between the actual motor and the control system, it corresponds to the coefficient of force against the current. Is considered in the target system.

In Figure 3 M is the mass of the motor has a unit system of Kg. Is the information about the mass of the motor feeder known from the control system. Corresponds to information about the force constant. These information are generally assumed to be relatively accurate, but considering the characteristics such as the specificity and temperature change of the use of the linear motor, the possibility of not knowing the exact value or changing during operation is very high.

The output of the main error compensating portion (106) (A _err ^*) are state feedforward term output with respect to a reference position ^{_{(x *) (A xff *}} , A vff *, A aff *) and state feedback of the actual position (x) term output ^{_{(a xfb *, a vfb *}} ) and combined to serve as an acceleration reference value (a ^*) for the motor. In addition, the acceleration reference value is And It is assumed that the reference value of the current controller omitted from the loop is changed by using information about the current controller, and the current controller assumes that the current is applied to the motor as it is. In the drawings, K _PF ′, K _DF ′, and K _AF ′ correspond to proportional gains, differential gains, and second derivative gains for the position term, velocity term, and acceleration term of the state forward compensation portion 102, respectively, and K _PB. ', K _DB ' means proportional gain and differential gain of the state feedback compensation unit 104.

In the state feedback compensator 104, the first derivative is required for the position differential calculation, and the result corresponds to the speed of the motor. The speed of the motor can be used to avoid errors due to noise that can occur in direct derivative operations, and the speed of the motor can be determined very accurately in the hundreds [rad / s] by configuring a simple observer. Although the acceleration term may be used in the state feedback compensator 104, it is not used because there is almost no way to find the acceleration relatively accurately in the practical implementation problem. The transfer function of the PID position controller shown in FIG. 3 is shown in [Equation 2].

In Equation 2, k is It is represented by, which is the rate of change of the system constant. As can be seen from the above equation, each term of the state forward compensation unit 102 affects the zero of the closed loop transfer function and the feedback compensation terms affect the poles. In particular, by adding the gain K _AF 'of the loop corresponding to the acceleration reference value in the state forward compensator 102, it can be seen that the transfer function order of the system zero increases by one, and in this case, the pole arrangement by the analysis of the system Difficulties arise. However, in the present invention, since the output of the position compensator omits the internal speed control loop and is directly connected to the torque controller, K _AF 'can be set to zero. In this case, the whole control system is simpler because it is given by a closed loop transfer function having the zero point of the secondary system and the pole point of the tertiary system, but still has the problem of determining the seventh constant corresponding to the gain of each loop.

In practical terms, however, the seven gains are not all independent variables in the system configuration, making it possible to simplify the control system. In Equation 2, the gain may be redefined as in Equation 3 below.

By [Equation 3], the transfer function of [Equation 2] can be changed as shown in [Equation 4].

Therefore, only five loop gains need to be determined, and it is possible to remove all the forward compensation terms from the transfer function and leave only the feedback compensation terms. On the contrary, it is possible to remove all the compensation terms, but in this case, it is difficult to obtain the dynamic characteristics for the step response in the configuration of the input actual system, and the S curve pattern must be used as the position reference value corresponding to the input. There is a burden.

4 is a functional block diagram of the integrated PID position controller according to the present invention, and shows an example configured based on [Equation 4]. The controller structure shown in FIG. 4 is referred to as a unified PID position controller 200 in the present invention in the sense that the state forward compensator and the state feedback compensator are integrated.

FIG. 5 is a detailed circuit diagram of the integrated PID position controller shown in FIG. 4.

As shown, if the reference position (x ^* ) and the actual position (x) of the linear motor mover are input, the fourth mixer 112 is the error (x ^* ) of the actual position (x) with respect to the reference position (x ^* ). -x) outputs the operation. This error is first input to the PID gain control unit 108. The PID gain control unit 108 outputs the proportional gain K _p (x ^* -x) of the difference value, and the fifth proportional control unit 116 outputs the difference value. Integral gain of the sixth differential control unit 118 and the differential value, which outputs the differential gain K _D S (x ^* -x) It includes a second integral control unit 120 for outputting.

The output values of the fifth proportional control unit 116, the sixth differential control unit 118, and the second integration control unit 120 are input to the sixth mixer 122 and summed.

On the other hand, the actual position (x) of the mover is input to the position gain control unit 110. The position gain controller 110 differentiates the actual position x of the mover from the seventh derivative controller 124 and adds the proportional gain from the sixth proportional controller 126 to output the derivative gain K _v Sx for the speed term. do. In addition, the position gain control unit 110 outputs a proportional gain K _x x for the actual position x of the mover by the seventh proportional control unit 128. The output values of the sixth proportional controller 126 and the seventh proportional controller 128 are summed in the seventh mixer 130. Thereafter, the output values of the sixth mixer 122 and the seventh mixer 130 are input to the fifth mixer 114 and summed, whereby the resultant gain value A ^* is output.

The integrated PID position controller can be modified in many ways by modifying the transfer function structure of Equation 4.

For example, it is also possible to convert the PD controller structure by setting the loop gains K _I and K _X of the controller to zero. Five independent loop gains to be changed depending on the operation purpose of the system can be solved by configuring the integrated PID position controller according to the present invention in the form of a first order low pass filter.

Application Example 1: Gain Design of Integrated PID Position Controller for Machine Tools

As an embodiment, when the linear motor is applied to a machine tool, a gain design algorithm of the integrated PID position controller of the present invention will be described.

Most linear motors are mainly used for the transfer operation of moving the equipment to a specific position by connecting the equipment due to the characteristics of the linear reciprocating motor. A representative example is the XY stage for testers or machine tools used in the semiconductor process. can do. In either case, it is common to control the operation of the conveying device according to the position pattern in the form of an S-curve in order to prevent the impact of the apparatus. However, many restrictions occur on the S-curve pattern according to the dynamic characteristics of the entire control system, and of course, the higher the dynamic characteristics of the position control system is advantageous in order to enable the operation having a high acceleration / deceleration rate.

In the present invention, the gain setting guideline that can be used in the case of using the integrated PID position controller as an X-Y stage for machine tools is determined as follows. First, the dynamics of the system should be clearly presented, and second, there should be no over-shoot. The second overshoot phenomenon is a factor that hinders the machining precision of the workpiece when the motor is operated with a very high acceleration / deceleration rate. Therefore, it is necessary to eliminate this phenomenon especially in applications such as machine tools.

In addition, although not modeled because it is outside the scope of the present invention, many types of mechanical systems are composed of two or more different mass units, for example, two mass systems. exist. If overshoot occurs in a high performance machine tool operating at a high speed of 1 to 3 [m / s], this phenomenon may cause secondary vibration in response to the stiffness of the system. good.

There may be various forms suitable for the above two guidelines, but the most easily implemented form is a first order low pass filter as shown in Equation 5 below.

The first order low pass filter has a clear dynamical characteristic expressed in cut-off frequency and is well suited to the above guideline because there is no over-shoot when the system is designed correctly. In order to facilitate the interpretation of the system, assuming that the system constant is relatively accurate, assuming that the ratio k of the system constant is 1, the open loop transfer function of the integrated PID controller is Equation 6] can be obtained. Correction of the system constant variation ratio k will be described in detail in the gain setting method described later.

Therefore, in order to have the same shape as the open loop transfer function of the first order low pass filter of Equation 5, the gain K _D is set to ω _C in Equation 6, and the parentheses of the denominator and the parentheses of the numerator are [ The same shape may be maintained as in Equation 7].

In Equation 7, ζ is the damping ratio of the zero point of the system, ω _n is the natural undamped frequency ratio of the zero point of the system. However, the present invention is used to obtain a degree of freedom of gain.

When [Equation 7] is established, the closed loop transfer function of [Equation 4] has a first-order low pass filter type as shown in [Equation 5]. In [Equation 7], the loop gain as shown in [Equation 8] can be obtained by comparing the left term and the right term.

As shown in [Equation 8], only three values of ω _C , ω _n and ζ need to be determined to determine the loop gain of the controller. ω _C is the cut-off frequency of the entire control system, indicating the dynamics of the system and is usually determined by the requirements of the system. For example, if a reciprocating operation is required 10 times per second, such as in a vibrating mechanism, the ratio of the force (maximum acceleration) of the force of the linear motor to the mass of the conveying part should be large enough. It is necessary to set ω _C to a more sufficient value in consideration of this, because the desired result can be obtained at about 63 rad / s) or more.

ω _n and ζ only appear in the gain term during system design and are theoretically perfect degrees of freedom since they do not affect the closed loop of the actual control system. In other words, even if these constants are set to any value, the dynamic characteristics of the system represented by ω _C are kept constant. However, since ω _n and ζ are related to the individual loop gains, they affect factors such as the stiffness of the system for the disturbance. Therefore, it can be used for the purpose of increasing the rigidity of the system while maintaining the dynamic characteristics of the system, or designing the system to be insensitive to fluctuations in the constant of the system. The use of such degrees of freedom will be described in detail in the gain setting method described below.

Experimental Results on the Performance of Integrated PID Position Controller

The integrated PID controller of the present invention has a merit of being able to be modified in various forms according to the value of each loop gain, but first, the system is configured as a first order low pass filter by selecting the loop gain according to [Equation 8]. We will evaluate the performance against. For the performance evaluation, the control target system was configured based on JUST10-420 model, which is a permanent magnet linear motor of Justech Co., Ltd. [Table 1] shows the control parameter list of the linear motor used as the control target.

essence value Remarks M 3.0 [kg] Mover mass M _load 4 [㎏] Load mass K 37 [N / A] DC model I _max 8 [A] DC model V _max 3 [m / s]

In order to investigate the theoretical performance of the proposed controller, we performed a digital simulation using a computer. The simulation package uses Mitchell & Gauthier's ACSL series and omits the current controller's ideal operation of gain 1 with a sampling time of 0.5 msec.

6 is a graph showing a frictional force model of a general linear motor.

The motor to be controlled is implemented by using the integers in Table 1 and the frictional force of the form shown in FIG. 6 is reflected in the simulation in order to consider the influence of the friction coefficient slightly present in the actual motor. The frictional force of the motor is represented by the ball bearings in the linear guide of the linear motor, and in general, the friction coefficient is expressed as Equation 9 as a function of speed as shown in FIG.

The coefficient of friction function is very difficult to know the exact value, but it is approximated through repeated experiments. Silver 5.Ns / m, Selected a value of 10.N.

7A to 7C are graphs showing a simulation result of the low pass filter characteristic of the integrated PID position controller according to the present invention. FIG. 7A is an actual position of a starter according to a position command, and 7b is a speed of a motor. , 7c represents the amount of current applied to the motor.

In FIGS. 7A to 7C, a position command (Position ^* ) is input in the form of a sinusoidal wave of 11. Hz and the gain of the controller is selected as ω _C = 70 rad / s to determine the characteristics of the controller. This is the simulation result for the case having the frequency.

Ω _n and ζ corresponding to the remaining degrees of freedom of control gain were selected as 30 rad / s and 1, respectively. As shown in the figure, the proposed controller has a 45 ° phase difference between the position command (Position ^* ) corresponding to the input / output relationship and the position of the motor. It can be seen that it shows a very ideal low pass filter characteristic that decreases to. In this case, the proposed controller exhibits the same characteristics regardless of the theoretical values of ω _n and ζ corresponding to gain degrees of freedom, and a simulation result to confirm this is shown in FIG. 8.

8A and 8B are graphs for explaining the low pass filter characteristic of the integrated PID position controller according to the present invention, and show the actual position of the mover according to the position command Position ^* .

For this simulation, ω _n was set to 70 rad / s and ζ was set to 1 in FIG. 8A, ω _n was set to 30 rad / s and ζ was set to 10 in FIG. 8B. As shown, it can be seen that the characteristics of the controller appear the same no matter what value ω _n , ζ is selected for a particular controller.

9A and 9C are graphs showing a simulation result of the step response characteristic of the integrated PID position controller of the present invention, where 9a represents the actual position of the mover according to the position command (Position ^* ), and 9b represents the speed of the motor. 9c represents the amount of current applied to the motor.

Controller gain terms = 70 rad / s, ω _n = 30 rad / s, ζ = 1 and it is assumed that the current of the motor can be used infinitely to observe the ideal dynamic characteristics. As shown, even when the position command (Position ^* ) is given in the form of a step, it can be seen that the motor position converges to the reference position without the over-shooting phenomenon according to the response characteristic of the low pass filter.

However, in order to realize the characteristics of the perfect low pass filter, the current flowing into the motor reaches several hundreds [A] as the derivative term in the controller initially generates a very large output, which far exceeds the current level typical of the actual motor. Corresponds to the value. To reduce this large initial input current, it is necessary to reduce the size of the step input or limit the gain to very small. On the other hand, in general, as shown in Figure 4, the current term connecting the actual motor and the controller is provided with a limiter (limiter) for limiting the maximum value according to the capacity of the inverter and the allowable current of the motor is installed as shown in Can not flow.

The operation of these current limiters presents a problem of generating non-linear disturbances in the system, and is also associated with the anti-windup countermeasures of the integral controller, which creates complex problems. This will be described later, and only the simulation results when the limiter operates are shown first.

10A to 10C are graphs showing the step response characteristics of the integrated PID position controller of the present invention, in particular, the control gain is set to ω _C = 70, ω _n = 30, ζ = 4 and the current is limited to about 8 [A]. The simulation result of one case is shown.

Here, Figure 10a shows the actual position of the mover according to the position command (Position ^* ), 10b represents the speed of the motor, 10c represents the amount of current applied to the motor. The motor position is not perfect, but it is a low pass filter that converges to the position command (Position ^* ) without overshooting.

Next, based on the above simulation results, the actual experimental results for verifying the practicality and feasibility of the integrated PID position controller of the present invention are presented. The motor driver used in the experiment uses TI's 32-bit floating-point DSP (Digital Signal Processor) as the main computing device.It performs current control every 50μs sampling time and an integrated PID position controller every 0.5msec. The control program was configured as possible.

11A and 11B are graphs showing the results of experiments on the frequency response characteristics of the integrated PID position controller according to the present invention.

As in the simulation environment described with reference to FIG. 7, a sinusoidal position input (Position ^* ) of 11 Hz was used, and control gains of ω _C = 70 rad / s and ω _n = 30 rad / s, ζ = 1. On the experimental waveforms, we can observe almost the same results as the simulation, but with some distortion in the current shape. This occurs because the counter electromotive force of the motor is not a perfect sinusoidal wave and there is no significant effect on the overall control.

12A and 12B are graphs showing the results of experiments on the step response characteristics of the integrated PID position controller according to the present invention.

In this experiment, the control gain is used as ω _C = 70rad / s, ω _n = 30rad / s, ζ = 4, and if possible, position command (Position ^* ) is set from 0 to 9mm and 9mm to suppress the motor current saturation. The command was returned to position 0 after applying in step form with 18mm at. The maximum current of the motor was limited to about 7.5 [A] in consideration of the capacity of the motor and the power supply capacity of the driver. When the moving distance is 9mm, some saturation occurs in the current, but when the command is input in the step form of 18mm, the saturation of the current lasts for a long time. However, while maintaining a certain shape of the low-pass filter, and even if the actual position (Position) can be seen that convergence to the position instruction (Position ^*) values, simulation results can be seen that the agreement. When the gain is high, it can be observed that the saturation phenomenon of the motor current lasts longer even when the same distance is moved, which will be described in detail later.

In the above, the integrated PID position controller for linear motor driving capable of high speed operation has been proposed. The integrated PID position controller of the linear motor proposed in the present invention can be applied to CNC and semiconductor process equipment by using the existing PID controller with excellent stability as it is, and giving the controller freedom in the arrangement of poles and zeros using state feedback technique. It is an excellent feature that can modify the operating characteristics of the system in a suitable form. In particular, we proposed a method to easily predict the operation of the controller and obtain high stability by maintaining the dynamic characteristics of the entire system in the form of a first-delay filter.In this process, it is possible to flexibly cope with various disturbances while maintaining the dynamic characteristics. It has been shown that full freedom can be achieved.

Next, by using the above-mentioned degrees of freedom, a gain setting method for securing the stability of the controller to variations in the system control parameters such as variation in the weight of the conveying unit and gain setting for considering the robustness against the disturbance defined by the stiffness The method will be described.

If there is a force applied to the system from outside, this force acts as a disturbance in the control loop, and in order to increase the performance of the position control loop, the stiffness corresponding to the robustness against the disturbance must be greater than a certain degree. do. In particular, machine tools such as CNC machines that directly apply force to the work to perform cutting operations, etc., often require high stiffness of at least 10 ⁷ to 10 ⁸ [N / m]. Measures must be taken.

How to set gain using degrees of freedom

Based on the integrated PID position controller of the present invention shown in FIG. 4, it is possible to derive [Equation 8] from [Equation 4], so that the transition function of the entire control loop can be simplified to a first order low pass filter. . Therefore, when selecting the gain of the controller, the cut-off frequency ω _C is determined in the same way as the cutoff frequency of the low pass filter is set according to the control performance required in the system, and ζ and ω _n remain in the degrees of freedom. If you select as appropriate value, gain setting of position control loop is completed.

In general, if ω _C and ω _n are increased, the gain of each loop constituting the position controller is increased, so that it is strong in the disturbance, but if it is too high, there is a problem in that it is sensitive to high-frequency noise flowing into the feedback circuit. . If the constant of the motor is correct, even if the gain is set based on this general method, the whole controller always operates in the form of a first-order low pass filter, so there is no big problem in setting the control gain. If the constant of the motor fluctuates, the problem may be different.

In particular, in systems that operate mainly on motion movements, such as linear motors, the weight of the feeder may fluctuate as frequently as in the workpiece transfer operation. Integer fluctuations can easily occur. In this case, the closed loop transfer function of Equation 4 can no longer maintain the first-order low pass filter shape, and unpredictable behavior such as an over-shoot phenomenon can be derived.

In this case, if ζ and ω _n remaining in the degree of freedom of gain setting are used efficiently, stable operation characteristics without over-shooting, such as a first-order low pass filter, can be easily implemented regardless of a constant variation within a certain range.

First, it is assumed that the gain ω _C of the controller is given arbitrarily according to the requirements of the system in which the position controller operates. Experimental results show that 50-100 rad / sec is appropriate for applications requiring low-speed motion that operates at speeds of less than 1 m / s, and high-speed operation above 2 m / s. The value of 150-250 rad / sec is appropriate for this. In addition, one of the ω _n of the gain freedom is assumed that any change in accordance with the requirements of the rigidity (stiffness) to be described next, and here the place of the ratio of ω _C and ω _n by η = ω _C / ω _n. The method of setting the gain now results in the problem of setting the value of ζ according to η.

In order to set the gain, it is necessary to first consider the effect of the entire position control loop when the system constant variation ratio k is not 1 in [Equation 4]. Since k exists only in the higher order term of the denominator, it always operates in the form of convergence to the position reference value, so the variation of k does not matter much in terms of stability of the DC level. However, considering the basic direction of gain setting that suppresses over-shooting, the value of k can greatly change the system characteristics. In order to consider this problem, the open loop transfer function of Equation (1) can be obtained as shown in Equation 10 below.

If the loop gain ratio of [Equation 9] is applied to [Equation 10], [Equation 11] can be obtained.

Considering Equation 11, it is easy to see that the variation of k causes a very unusual behavior. In other words, if k is equal to or greater than 1, no matter where ω _n and ζ have any value, the pole position always maintains a value larger than zero so that the phase delay does not exceed 90 °. To simplify this, a board diagram for Equation 11 is shown in FIG. 13. 13A and 13B are open loop board diagrams of an integrated PID position controller according to the present invention. Changing ω _n and ζ to different values can always yield similar results.

This result means that in closed loop system, if k≥1, it is always over-damped, so that over-shooting does not occur, but it can be a problem when k <1. In the present invention, the following method is used to select a controller gain that provides stable operation without over-shoot even when k varies from 2 to 0.5.

Equation 11 is composed of three-order equations, and when all of them are considered, the problem becomes very complicated. If only k is intended to perform over-shoot-free operation when k has a value near 0.5, the system can be simplified by limiting ζ to significantly greater than 1 to simplify [Equation 11]. . The zero point is obtained from the molecular term in [Equation 11].

If ζ》 1 Therefore, a zero point is obtained as shown in [Equation 13].

According to Equation 13, the molecular term of Equation 11 can be approximated as follows.

Likewise, if the same assumption is applied to the denominator of Equation 11, Equation 11 can be approximated as follows.

Therefore, the second-order approximated closed-loop equation is given by Equation 16 below.

The zero point of Equation 16 is always fixed at -2 ζ ω _n on the real axis. In order to have a complete damping effect without over-shooting in the step response characteristic, the pole of the common sense should always be on the negative real axis. First, the root of the denominator term in [Equation 16] is shown in [Equation 17].

In Equation 17, when the root axis has a negative value and the value in the root is greater than 0, the pole of Equation 16 always exists on the negative real axis. On the other hand, if k is greater than 1, the value in the radical in Equation 17 is always greater than 0, so it can be confirmed that it has a complete damping effect as mentioned above. Equation 17 summarizes the condition that always has a real value as follows.

only,

Therefore, by selecting the combination of ζ and η, which is satisfied by Equation (18), for the value of k , which is defined in advance, it is possible to obtain stable operation without over-shooting in the step response characteristic of Equation (15). As an example, the following conditions can be easily obtained by applying [Equation 18] for the case of k = 0.5.

Using the above equation, we can determine the minimum value of ζ according to the ratio η of ω _C and ω _n . If η is determined to be 2, the minimum value of ζ is about 5.8. If ζ is set to a value of 5,8, only about 1.5% error occurs in Equation 12, so there is no problem in the approximation method.

In order to show the validity of the gain determination method, a result of computer simulation of the step response characteristic for the entire position control loop shown in the original [Equation 4], which is not approximated, is shown in FIG. 14.

14A and 14B are graphs showing the step response characteristics according to the system constant change in the integrated PID position controller according to the present invention, and show the step response when ω _n and ζ are differently selected when ω _C is 200 rad / s. to give and was assumed that k is variable from 0.2 to 2, to see the effect of the variation of k.

14b corresponds to the case where η = 2 and ζ were selected as 5.8 when ω _{n was set} to 100 rad / s based on [Equation 19], and in all cases where k is 0.5 or more, a very stable response characteristic can be seen. . Equation 19 is derived using an approximation equation, but it can be seen from the response characteristic of FIG. 14B that the approximation error is not largely problem since the ζ value corresponds to a value larger than 1.

On the other hand, in the case of Fig. 14a in which ω _n and ζ are selected so as to violate [Equation 19], it can be seen that an over-shooting phenomenon occurs in most regions where k <1, and excessive damping occurs in a region where k> 1. It can be seen that the characteristics of the first order low pass filter are distorted.

Gain setting method considering stiffness

From the controller's point of view, the stiffness is the positional deviation with respect to the distorted force F _d It is related to the ratio of. From the control point of view, when the position command (x ^* ) is set to 0, the ratio between the disturbance and the actual position (F _d / x) is expressed as the disturbance rejection ratio, which is used as a measure of the performance of the control. Doing. Stiffness corresponds to the size of the disturbance removal rate, and high-performance machine tools typically require values of about 10 ⁷ to 10 ⁸ N / m.

In the proposed integrated PID position controller, assuming that the motor constants are known correctly, the disturbance removal rate is expressed as follows.

In Equation 20, M denotes the total weight of the mover. The stiffness is expressed using Equation 8 as follows.

In the equation, ω _d corresponds to the frequency of the external force input into the disturbance. Of course, it is very difficult to know exactly all the frequencies of the distortion. Practically, it is desirable to select the main frequency of the disturbance that appears when operating a machine tool such as a milling-machine, to determine the required stiffness in advance, and to set an appropriate gain. As can be seen from the above equation, assuming that the cut-off frequency ω _C of the position controller in the overall control process is given in advance, there may be a large number of combinations of ω _n and ζ that satisfy a specific stiffness. Therefore, since a lot of effort is required to select a gain and a complicated calculation may be required many times, the present invention proposes the following example in consideration of simpler operation.

To simplify [Equation 21], by fixing ζ to a value of 1 arbitrarily and expanding the equation, the following equation can be obtained without difficulty.

By substituting ω _C and ω _d previously selected in Equation 22, the value of ω _n according to the required stiffness can be easily obtained. If stiffness equal to 10 ⁸ N / m is required for a disturbance with a frequency of 31 rad / s (5 Hz) in a system with 100 Kg of mover mass and ω _C of 300 rad / s, then ω _n when ζ = 1 The calculation says that it should be set to about 320rad / s. This can be fully achieved by using a linear motor that can generate a force of about 3000N (3G at 100Kg mass) with a cycle of position control loop of 0.5ms. For reference, the stiffness of 10 ⁸ N / m means that the position error is only 10 μm at the maximum when the 1000N size of the disturbance is applied in the form of a sine wave.

Another embodiment of an integrated PID position controller for preventing saturation of the controller

The problem that is inevitably encountered in applying the position control algorithm to the practical model is a limiter according to the rating of the controller or the power component. The limiting elements present in the position control loop are largely divided into the speed limit according to the maximum speed of the motor and the current limit according to the maximum current of the motor. Among these, the speed limiting factor may cause a problem such as a system stop due to the over speed of the motor, but it is not considered to be a relatively large problem because it does not directly affect the state of the PID controller.

However, in the control structure in which the output of the position controller directly acts as a reference value of current (or force, acceleration), such as the integrated PID position controller according to the present invention, the non-linearity of the system due to the current limiting factor is controlled entirely. Appropriate measures must be taken because it directly affects the state of the loop. The present invention considers this problem as part of the anti-windup of the integrator and proposes a 'variable controller' structure in which the PID controller is changed to a PD (Proportional Differential) control structure in the situation where the current limiting element is acting. By solving the problem of the current limiting element, the minimum requirement as a practical position controller was met.

In the case of a limiter that limits the size of the control variable in the control loop, integrator operation can be saturated, a problem that has long been addressed in the field of control as a classic and very difficult challenge to solve. Since the integrated PID position controller according to the present invention also includes an integrator, when the current limit occurs in the element limiting the current of the motor in FIG. 4, the saturation problem of the integrator inevitably occurs. This saturation may occur mainly in a transient state when a step-type position command having a large position variable is input and easily occurs even when the gain is too large.

Once the saturation of the integrator occurs, the balance of all the control loop states involved in the control is broken, making it difficult for control to recover to its original state even when the current limit is released. All position control loops will stop due to system fault due to malfunction of the system. Therefore, if a current limit occurs, an integrated anti-windup compensator is necessary. The simplest typical of these compensators is to limit the integrator output itself, but this method does not provide satisfactory performance in both transient and steady state.

15 is a functional block diagram of an integrated PID position controller according to another embodiment of the present invention. In the following description, the same reference numerals are used for the same or similar parts as the integrated PID position controller shown in FIG.

The integrated PID position controller shown in FIG. 15 configures a current limiter 132 at the connection end of the integrated PID position controller and the linear motor.

In the present embodiment, when the current limiter 132 operates, the output term I _out of the second integration controller 120 of the PID gain controller 108 and the sixth proportional controller of the position gain controller 110 ( By removing a part of the position feedback term (X _out ) output from the control unit 126 from the control, the entire position controller operates in the structure of the PD (Proportional Differential) controller instead of the PID, and when the current limit is released, control is performed again by the PID.

When using the loop gain when the position controller of FIG. 15 operates as a PD controller in the form of Equation 8 used in the present invention, the response characteristics of the entire position controller are in the form of a first order low pass filter as follows. Same as the original PID position controller.

The advantage of the PD controller is that there is no integral term, so there is no saturation even when there is a limiting factor in the transient state, and it is very stable because it maintains the same first-order lowpass filter type as in [Equation 23].

In order to verify the characteristics of the integrated PID position controller gain setting method according to the present invention, the experiment using the linear motor used in the previous experiment was performed.

First, in order to show the step operation characteristic when the constant variation ratio k is not 1, 3Kg load is applied to the motor and the controller is set to have no load, and the force constant K is assumed to be known correctly. In this case, since the mass of the mover itself of the electric motor is 3 Kg, the constant variation ratio k becomes 0.5. As mentioned above, when k is larger than 1, since the control is made stable within a certain range (about 1 to 3), no big problem occurs. However, if the constant is set so that k is too large, care should be taken because the gain of the entire controller is actually increased by k times and there is a possibility that an abnormal phenomenon such as vibration may occur in the control loop.

16A and 16B show an experimental result of a step response characteristic when the cutoff frequency is 200 rad / s in the integrated PID position controller of the present invention. FIG. 16A and 16B illustrate a position controller for a displacement of 10 mm when the integer variation ratio k is 0.5. Step response characteristics are shown.

16a corresponds to a case where ω _n = 100rad / s and ζ = 1 when ω _C is 200 rad / s and violates Equation 19, and some over-shooting occurs. On the other hand, referring to FIG. 16B, it can be seen that stable operation with almost no over-shooting is performed when ω _n = 50 and ζ = 5.

On the other hand, in this experiment, since the displacement is relatively large (10 mm) compared to the given gain, the current limiting element with the maximum current set to 7.5 A operates. In this case, since PD control is performed by the variable structure position controller described with reference to FIG. 15, it may be unclear whether overshooting is caused by gain or current limiting element. In any case, if the gain setting is correct as in FIG. 16B, there is no big problem, but if possible, the same experiment was performed by reducing the overall gain to exclude the influence of the current limiting factor. The results are shown in FIG.

17A and 17B are graphs showing the results of step response characteristics when the cutoff frequency is 50 rad / s in the integrated PID position controller of the present invention.

FIG. 17A shows a waveform in which the step response is tested with a gain of ω _n = 30 rad / s and ζ = 1 when ω _C is 50 rad / s. The current limiting element operates briefly at the beginning of the step response, but overall the effect of this limiting element is almost negligible. In FIG. 17A, a very large over-shoot phenomenon occurs. However, when gain is selected as ω _n = 30rad / s and ζ = 4 as in FIG. 17B, very stable position control is performed.

On the other hand, in order to verify the validity of the gain setting method considering the stiffness, an experiment using a specially designed linear motor was performed. In the experiment, a linear motor of two movers was mounted on a single linear guide, and a fixing device was attached so that the distance between the two movers was constant. The controller is configured to perform position control on the zero position of one mover, and the controller is configured to generate sinusoidal force to generate a disturbance known to the other mover. At this time, the mass of the whole mover that the controller bears corresponds to the sum of the masses of the two movers. This device was used to verify the position control capability of the controller against predefined disturbances and the results are shown in FIG. 18.

18A and 18B are graphs for explaining position control capability according to stiffness in the integrated PID position controller of the present invention.

FIG. 18A shows a predefined distance force and the actual position of the mover operated by the position controller. The experimental conditions were ω _n = 217rad / s and ζ = 1 when ω _C was 300 rad / s, and the disturbance was set to have a frequency of 10 Hz with a size of 75N. If there is no disturbance, the position of the mover operated by the position controller should be constant in the state of 0mm, but the position error is caused by the disturbance injected in the form of sinusoidal wave. Stiffness at frequency can be measured.

18B shows the stiffness according to the frequency of the disturbance to be injected. In FIG. 18B, the value indicated by the solid line indicates the theoretical stiffness according to Equation 22 using a computer, and the dotted line indicates the data obtained in the experiment. In the experimental results, NS indicates normalized stiffness (NS) and corresponds to the stiffness divided by the mass of the whole mover. The reason for introducing such NS is to make an absolute comparison because the actual stiffness is directly proportional to the mass of the conveying part. If the NS is 10 ⁶ in a linear motor with a mass of 100 kg, the actual stiffness is 10 ⁸ . As can be seen from the experimental results, the proposed gain setting method can utilize the degree of freedom of the integrated PID position controller to achieve the desired stiffness relatively simply.

As such, those skilled in the art will appreciate that the present invention can be implemented in other specific forms without changing the technical spirit or essential features thereof. Therefore, the above-described embodiments are to be understood as illustrative in all respects and not as restrictive. The scope of the present invention is shown by the following claims rather than the above description, and all changes or modifications derived from the meaning and scope of the claims and their equivalents should be construed as being included in the scope of the present invention. do.

As described above, the integrated PID position controller of the present invention is very simple in structure and maintains the dynamics of the entire position control loop in the form of a first-order low pass filter, making it easier to set control gains and over-shoot than any other type of position controller. It can perform very stable operation without any phenomenon.

In addition, due to the dynamic characteristics of the first-order low pass filter, it is possible to obtain the degree of freedom of the complete gain setting while maintaining the constant cut-off frequency of the whole system, and by setting the degree of freedom, the stiffness of the linear motor can be effectively increased.

In addition, the current limiter is configured at the output of the integrated PID position controller, and when the current controller operates, the output terms of the integral control unit in the PID gain control unit and the proportional control unit in the position gain control unit are removed to operate the PID position controller as a PD controller. Thus, not only the integrator saturation in the transient state can be efficiently limited, but also the influence of the saturation can be greatly reduced even in the steady state.

Claims (2)

In the PID position controller of the linear motor, A first mixer for extracting an error value of an actual position with respect to the reference position of the mover; A first proportional control unit for outputting a proportional gain with respect to the output value of the first mixer, a first differential control unit for outputting a differential gain with respect to the output value of the first mixer, and an integral gain for the output value of the first mixer A PID gain control unit including a first integration control unit for performing the control; A second mixer for summing respective output values of the PID gain control unit; A second proportional control unit that obtains a differential gain with respect to the actual position of the mover, a second proportional control unit that takes an output value of the second differential control unit as an input value, a third proportional control unit that uses the actual position of the mover as an input value, and the second A position gain control unit for summing and outputting the output value of the second proportional control unit and the output value of the third proportional control unit; And A third mixer for summing output values of the PID gain controller and the position gain controller; Integrated PID position controller of the linear motor having a. According to claim 1, And a current limiter provided at an output end of the third mixer, the current limiter for driving the integral first integration controller and the third proportional controller according to the flow of current.