JP5457894B2 - Full closed position controller - Google Patents

Description

  The present invention relates to a full-closed position control device, and more particularly to a full-closed position control device for directly detecting the position of a load end and controlling it according to a position command value in axis control of a numerically controlled machine. Is.

ここで、駆動側慣性モーメントＩ_ｍ，負荷側慣性モーメントI_Ｌ，剛性K，負荷外乱ｄ，モータ速度ｖ_ｍ，負荷速度ｖ_Ｌ，負荷伝達トルクτ_ｒである。また、プラントモデルＰの構成から、この場合の伝達零点ω_ｚは、ω_ｚ ^２＝K/I_Ｌとなり、伝達極ω_ｐは、ω_ｐ ^２＝K｛（１/Ｉ_m）＋（１/I_Ｌ）｝になる。 In general, a full-closed position control device applied to axis control of a numerically controlled machine appropriately controls a control input u of a drive motor, thereby controlling a control target according to a position command value _Xc commanded from a host device. and it controls the load position x _L of the target plant is. Fully closed position control devices are required to have system stability (including vibration suppression), high command tracking performance, and load disturbance suppression performance. On the other hand, since the target plant has the transmission pole ω _p and the transmission zero ω _z as the transfer characteristics, the plant model represented by the state equation of the equation (1), in which the basic characteristic is usually a two-inertia model. Represented by P. Note that • (dot) means time differentiation, and for convenience of explanation, a rotary system conversion expression is used.

Here, the drive-side inertia moment I _m , the load-side inertia moment I _L , the rigidity K, the load disturbance d, the motor speed v _m , the load speed v _L , and the load transmission torque τ _r . Further, from the configuration of the plant model P, the transmission zero point ω _{z in} this case is ω _z ² = K / _IL , and the transmission pole ω _p is ω _p ² = K {(1 / I _m ) + (1 / I _L )}.

FIG. 7 is a block diagram of the state equation expression of Equation (1). Further, an integrator (1 / s: s is an operator of Laplace transform) is added to the motor position x _m (= v _m / s) and load position x _L (= v _L / s) are appended. This figure can be regarded as a block diagram showing the basic characteristics of the plant model P. Although not shown, a position detector is installed in the drive motor, and a linear scale is installed on the load side. The motor speed v _m , motor position x _m , load speed v _L , and load position x _L are detected directly. It shall be possible. The lead lines w ₁₁ , p ₁ , w ₁₂ , and p ₂ in the figure are for expressing plant fluctuations in the present invention to be described later, and are not described here.

Figure 6 is described in Patent Document 1 "Japanese Patent No. 3351990", is a block diagram showing an example of a servo system configuration in a conventional full-closed position controller. In this conventional system, the feedback configuration of the position control device 100 is as follows. That is, the adder / subtracter 50 adds the position command value _Xc commanded from the host device (not shown) and the deflection compensation value _Xdf input from the feedforward block 300 ( _BFF ), and from the addition result subtracting the position feedback _{x f.} Position deviation which is the output of which is amplified in the position loop gain Kp fold at the position deviation amplifier 51 adds the velocity compensation value V _cmp, becomes the input of the adder-subtracter 52 which subtracts the motor speed v _m. The output speed deviation is normally proportional-integral amplified by the speed deviation amplifier 53. Equation (2) shows this speed loop gain Gv. (The proportional gain Gp and the integral gain Gi.)
Gv = Gp + (Gi / s) (2)
The output of the speed deviation amplifier 53 and the control input compensation value _uf are added by the adder 54 and become the control input u to the target plant 200 (P).

Position feedback _{x f} and _{x m,} x _L, the relationship of _{X df} is the subtractor 58, and adder 60, 64 shown in FIG. 6,
_{x f = x m + H (} x L -x m + X df) ····· (3)
It is represented by Here, the transfer function H of the compensator 59 is 0 ≦ | H | ≦ 1, and is a low-pass type characteristic that is large (→ 1) with respect to the low frequency input and small (→ 0) with respect to the high frequency input. have. Therefore, in a steady state, x _f = x _L + X _df and X _c = x _L can be achieved by feedback control. That is, it controls the load position _{x L} in street position command value _{X c.}

Next, the feedforward configuration of the position control device 100 will be described. The feedforward configuration is introduced to increase the response speed, and FIG. 8 is a block diagram illustrating the configuration of the feedforward block 300 (B _FF ). The deflection calculation unit 61 calculates the deflection of the transmission system that occurs with respect to the position command value _Xc , and calculates the deflection compensation value X _df using equation (4).
X _df = Cd · X _c = (K / I _L ) s ² · X _c (4)
The speed compensation value V _cmp is obtained by adding a speed command value V _{c obtained} by time differentiation of the position command value X _c by the differentiator 55 and a deflection speed compensation value V _df obtained by time differentiation of the deflection compensation value X _df by the differentiator 62 by the adder 63. in addition to being computed, which is the speed feedforward amount corresponding to the ideal response of the motor speed v _m. The speed command value V _c is time-differentiated by the differentiator 56 and converted by the control input conversion unit 57 into the control input compensation value _uf by the equation (5).
u _f = Ct · s · V _c = (I _m + I _L ) s · V _c (5)
_uf is a feedforward amount with respect to the control input.

Here, the control performance of the conventional full-closed position control device shown in FIG. 6 will be examined. Prior to this, since the speed loop gain Gv of the equation (2) does not directly mean the control performance, the speed control system in which the plant model P is rigidly approximated with the rigidity K → ∞ has an inherent second-order lag characteristic. the vibration frequency as a speed control band omega _v, integral gain Gi and proportional gain Gp from omega _v, shall be determined by the expression (6).
Gp = 2 (I _m + I _L ) ω _v , Gi = (I _m + I _L ) ω _v ² (6)

これは、伝達零点ω_ｚで、制御性能が単純に制約される事を示しており、伝達零点ω_ｚが低い対象プラントでは、振動が発生して速度制御帯域ω_ｖや位置制御帯域である位置ループゲインＫｐを高くとれないことになる。 First, in FIG. 6, when the transfer function H of the compensator 59 is fixed to H = 1 and the stability limit of the complete fully closed position control system is obtained, the stability condition of Expression (7) is obtained. Here, R is the load inertia moment ratio R (= I _L / I _m ). In the following conventional examples, when considering the stability limit, since the integral gain Gi is not directly involved, the study is made with Gv = Gp (Gi = 0).

This is a transmission zeros omega _z, shows that the control performance is simply constraints, the transmission zeros omega _z is lower object plant, the speed control bandwidth omega _v and position control band vibration is generated position The loop gain Kp cannot be increased.

Next, an example of the position control characteristic when the transfer function H of the compensator 59 is selected as the first-order lag characteristic (H = H _b / (s + H _b )) in order to suppress vibration generation will be shown. Here, I _m = 0.7 [kg · m ² ], I _L = 0.3 [kg · m ² ], K = 5000 [Nm / rad] as plant conditions, and Kp = 20 as control parameters. , Ω _v = 60, and H _b = 40. FIG. 9 shows the frequency characteristics of the fully closed position control system (command response: X _c → x _L , disturbance suppression response: d → x _L ). It can be seen that the control band is restricted by the transmission zero point ω _z (in this plant condition, ω _z = 129 [rad / sec]).

The left side of FIG. 10 shows real-time responses of x _L and x _m when a stepwise load disturbance d = 1 [Nm] is given. Although the load-side vibration can be suppressed by selecting the transfer function H as the first-order lag characteristic, the response has a large position fluctuation due to disturbance. Further, the right side of FIG. 10 shows a position error x _e (= X _c −x _L ) when a speed command value V _c is given by quadratic function type acceleration. Because it compensates the deflection occurring in the transmission system in a feed-forward, the amount of deflection is constant, but the position error x _e in equal acceleration are suppressed, suppressing effect on acceleration change portion is smaller I understand that.

FIG. 11 is a block diagram showing another example of a conventional full-closed position control device. Hereinafter, a different part from the conventional apparatus demonstrated by the prior example is demonstrated. In this conventional example, the subtractor 70 calculates the bending speed (v _m −v _L ), multiplies this by α · Gp times with α as the control parameter, and feeds it back to the control input by the subtractor 71. This technology aims at characteristic operation of the target plant. This technique is described in Patent Document 2 "JP Rights 3-110607 JP".

ここで、制御パラメータαは、α＜Ｒ/（１＋Ｒ）が前提である。
Ｒ≫１なる条件だと、α→１に選定でき、式（８）の安定限界は、近似的に式（９）となって、制御性能が向上できることがわかる。

一方で、Ｒ≒１だと制御効果は殆ど発生せず、前述のプラント条件でも、制御効果は小さい。 Similarly to the above, when the stability limit of the full-closed position control system in this conventional example is obtained, Expression (8) is obtained with an expression corresponding to Expression (7).

Here, the control parameter α is premised on α <R / (1 + R).
Under the condition of R >> 1, it is possible to select α → 1, and the stability limit of the equation (8) is approximately the equation (9), which shows that the control performance can be improved.

On the other hand, when R≈1, almost no control effect occurs, and the control effect is small even under the above-mentioned plant conditions.

以下、式（１０）中のω_ｓを状態フィードバック帯域ω_ｓと呼ぶ。 Figure 12 is described in Patent Document 3 "Japanese Patent No. 3870028", a further block diagram showing another example of a conventional full-closed position controller. This conventional example is intended to improve the performance of the fully closed position control, and constitutes a speed control system in which the load speed v _L is a speed feedback. In order to avoid the stability problem, the characteristics of the target plant are stabilized by an observer (not shown) for estimating the load transmission torque τ _r and state feedback. Specifically, the state feedback gain vector F = [f ₁ , f ₂ , f ₃ ] applied to the state vector [v _m , v _L , τ _r ] ^T which is the input of the amplifier 80 is set by the equation (10). To do.

Hereinafter, ω _s in the equation (10) is referred to as a state feedback band ω _s .

The output of the amplifier 80 is fed back to the control input by the subtractor 81. Thereby, the characteristic polynomial of the target plant is converted from the original s (s ² + ω _p ² ) to the stable s (s + ω _s ) ² . The band compensator 82 is introduced so that the transfer gain of u → v _L in the low band is apparently not changed by the state feedback, and the band compensation gain Q = (ω _s / ω is added to the output of the speed deviation amplifier 53. _p ) Multiply by ² and add to subtractor 81.

つまり、本従来例においては、状態フィードバック帯域ω_ｓを高くとることで、速度制御帯域ω_ｖと位置制御帯域Ｋｐの設定限界を高くすることができる。特に、本従来例では、負荷速度ｖ_Ｌを速度帰還とした速度制御系を構成しているため、高い負荷外乱抑制性能が期待できる技術である。 Next, the stability limit in this conventional example is obtained. First, ω _s > ω _v in the speed control system, and can be expressed by Expression (11) in the fully closed position control system.

That is, the present in the prior art, by taking a high state feedback band omega _s, it is possible to increase the set limit position control bandwidth Kp and the speed control bandwidth omega _v. In particular, in the conventional example, a speed control system using the load speed v _L as speed feedback is configured, and therefore, this is a technology that can be expected to have high load disturbance suppression performance.

The control effect of this conventional example is not affected by the plant conditions as in the conventional example of FIG. 11 described above, but because the characteristic operation of the target plant is realized by the observer + state feedback, the actual plant When the characteristic difference between the characteristic and the modeled plant characteristic P increases, vibration is generated and stability is lost. Therefore, there is a problem that the state feedback band ω _s cannot be increased.

Japanese Patent No. 3351990 Japanese Patent Laid-Open No. 3-110607 Japanese Patent No. 3870028

  As described above, in the conventional full-closed position control device, if importance is attached to the stability and vibration suppression of the system, the command tracking performance and the load disturbance suppression performance are limited. Further, in the conventional technology aimed at high performance, the control effect is limited by the conditions of the target plant and the plant error between the plant model and the target plant. The problem to be solved by the present invention is that the system stability (including vibration suppression) and high command follow-up performance according to changes in plant characteristics including plant modeling errors regardless of the conditions of the target plant It is another object of the present invention to provide a fully closed position control device that achieves both load disturbance suppression performance.

The present invention has characteristics that achieve both system stability, high command tracking performance, and load disturbance suppression performance in consideration of plant characteristic fluctuations, a speed deviation calculated using the load speed v _L , a motor and an input speed v _m, by constituting the speed control system in two inputs and one output of the speed controller, is intended to solve the above problems.

The fully closed position control device according to the present invention uses the load speed v _L for speed feedback, thereby configuring a speed control system having high command following performance and load disturbance suppressing performance on the load side. Furthermore, the speed controller, in addition to the speed deviation by taking the two-input structure motor speed v _m also as input, after including the presence of a plant variation, the characteristics ensuring robust stability and robust performance Have. For this reason, the performance improvement according to the magnitude | size of a plant fluctuation can be anticipated irrespective of the conditions of an object plant. Specifically, by not restricted in transmission zeros omega _z, and enlargement control band of command follow-up performance, load disturbance suppression performance at a low-frequency can also be considerably improved in.

It is a block diagram which shows the structural example of the full closed position control apparatus by an Example. It is a block diagram explaining the design method of the speed controller by an Example. It is a figure which shows an example of the frequency characteristic of each block of FIG. It is a figure of an example of the frequency characteristic of the full closed position control apparatus by an Example. It is a figure which shows an example of the step load disturbance response of the full closed position control apparatus by an Example, and a quadratic function type acceleration response. 10 is a block diagram of a configuration example of a full-closed position control device described in Patent Literature 1. FIG. It is a block diagram representation of the target plant model. It is the block diagram which showed the structure of the feedforward block with respect to an object plant model. It is a figure of an example of the frequency characteristic of the full closed position control apparatus of patent document 1. It is a figure which shows an example of the step load disturbance response of the full closed position control apparatus of patent document 1, and a quadratic function type acceleration response. 10 is a block diagram illustrating a configuration example of a fully closed position control device described in Patent Literature 2. FIG. It is a block diagram which shows the structural example of the full closed position control apparatus of patent document 3. FIG.

The present invention will be described below with reference to examples of modes for carrying out the present invention (hereinafter referred to as examples). First, the robust stability problem is quantified so that the stability of the system is not compromised in the presence of plant fluctuations. Therefore, as a typical example of characteristic variation, a plant error between actual plant characteristics and plant model characteristics is determined. In the present embodiment, the plant error with respect to the aforementioned plant conditions: I _m = 0.7 [kg · m ² ], I _L = 0.3 [kg · m ² ], K = 5000 [Nm / rad]. : Δ _L = 0.045 [kg · m ² ] (± 15%), δ _K = 500 [Nm / rad] (± 15%). (Note, [delta] _L is a _{I L} variation, [delta] _K represents the K variations.)

  Next, a robust performance requirement based on the existence of plant fluctuations is formulated. In this embodiment, the performance requirement is “1. The command follow-up band of the load is wide. 2. The load disturbance suppression performance in the middle and low range is high. 3. The high range that is not included in the plant error described above. "Inhibit the high-frequency gain of the controller, including the response to plant fluctuations in the plant."

FIG. 2 is a block diagram in which the aforementioned robust stability problem and robust performance problem are formulated and incorporated in the generalized plant G. P in the figure is the plant model used in the above description of the prior art. For the robust stability problem, the input w ₁ = [w ₁₁ , w ₁₂ ] ^T and the evaluation output z ₁ = [z ₁₁ , z ₁₂ ] ^T, and for the robust performance problem, the input w ₂ = [w ₂₁ , w ₂₂ ] ^T , Evaluation output z ₂ = [z ₂₁ , z ₂₂ ] ^T. Kr is an input for suppressing a speed deviation e (= V _c −v _L ) between the speed command value V _c and the load speed v _L, and a motor speed v _m for easily stabilizing the speed control system. 1 is a one-output speed controller that outputs a control input u of the target plant P, and W _u , W _d , W _r , and W _s are stable minimum phase systems. Is a performance weighting function.

In FIG. 2, in order to combine the robust stability problem and the robust performance problem into one robust control problem, the relationship between the evaluation output and the input is expressed by Expression (12) using the partial block expression of the transfer matrix M. Then, the robust stability problem of M _11, because the robust performance problem in question inhibit H _∞ norm of M _22, if suppressed H _∞ norm of the transfer matrix M, of solving the robust stability problems and robust performance problems at the same time Can do.

Here, in solving the robust control problem, the non-diagonal element of the equation (12) is not a formulation of the requirement, and the design of the speed controller 1 (Kr) is restricted by this block element. It is not preferable. Therefore, in this embodiment, the robust control problem is solved by μ design, thereby scaling the non-diagonal elements and reducing the restrictions imposed. Δ _L and δ _{K in} FIG. 2 are weight functions for formulating the robust stability problem with the aforementioned plant error. W _s , W _u , W _d , and W _r are performance weight functions when formulating the robust performance problem.

The performance weight function W _s is multiplied by the speed deviation e between the speed command value V _c and the load speed v _L to become an evaluation output z ₂₁ . W _s is the primary / secondary mixture to create a broader range of command follow-up characteristics of the load (robust performance requirement 1) and load disturbance suppression performance (robust performance requirement 2) in the mid-low range. Select a low-pass weight function. Equation (13) is an example of a _{W s} used in this embodiment.

The performance weight function W _u is multiplied by the control input u to become an evaluation output z ₂₂ . W _u selects a second-order high-pass weighting function to create controller gain suppression (robust performance requirement 3) in the high band. Equation (14) is an example of W _u used in this example.

Performance weighting function W _d and W _r, with respect to the speed deviation e and a control input u is an evaluation output, a constant for adjusting the mutual influence of the load disturbance d and the speed command value V _c is input, this embodiment In the example, formula (15) is selected.
W _d = 0.01, W _r = 1 · 10 ⁻⁶ (15)
FIG. 3 shows the transfer characteristics (u → v _m , u → v _L ) of the plant model P and the frequency characteristics of the performance weight functions W _s , W _u , W _d , and W _r described above.

FIG. 1 is a block diagram showing an example of a full-closed position control apparatus according to the present embodiment, which is configured using a speed controller Kr designed under the above-described conditions. In FIG. 1, the same components as those of the conventional apparatus shown in FIG. The internal configuration of the feedforward block 300 (B _FF ) shown in FIG. 1 is the same as that illustrated in FIG. Hereinafter, a different part from the conventional example demonstrated so far is demonstrated.

In this embodiment the speed feedback, which is subtracted in subtracter 3 becomes the load velocity v _L. Therefore, the speed command value V _c in FIG. 8 is used as the output of the feedforward block 300 (B _FF ) added to the adder / subtracter 3. The speed deviation which is the output of the adder / subtracter 3 is amplified by the speed controller Kr of this embodiment. The input of Kr is, e input side in FIG. 1 to the output side of the adder-subtractor 3, v _m input side is the output side of the subtracter 2. The output of the speed controller Kr is added to the control input compensation value _uf by the adder 54 and becomes the control input u of the target plant (for example, a ball screw drive system).

On the other hand, the subtractor 2 subtracts the speed compensation value V _cmp from the motor speed v _m, taking a configuration in which the result is input to the speed controller Kr. Since the motor speed v _m is feedback for obtaining system stability, when an ideal response corresponding to the speed compensation value V _cmp is shown, the feedback amount is not generated and controllable. This is to prevent drifting of the equilibrium point. That is, the speed controller Kr takes the structure of two inputs and one output (Kr (s) = [Kr1 (s), Kr2 (s)]) as described above, and u = [Kr1 (s), Kr2 (s). ]] [E, v _m ] ^T = Kr1 · e + Kr2 · v _m becomes an amplifier for calculating the output u. Here, Kr1 (s) becomes an amplifier for reducing the speed deviation e (= V _c −v _L ), and Kr2 (s) receives v _m to generate a component that guarantees the stability of the speed control system. It becomes an amplifier. If the load speed v _L is speed-feedback as it is, as described above with respect to Patent Document 3, the system becomes unstable. On the other hand, in this example, by inputting the speed deviation e (= V _c −v _L ) to the speed controller Kr, the command follow-up performance and the disturbance suppression performance on the load side are improved, and the motor speed v _m the result of subtracting the speed Doho償値V _cmp from can easily ensures stable system by inputting to the Kr. As described above, the speed compensation value V _cmp used here is a speed command value V _{c obtained} by time-differentiating the position command value X _c with the differentiator 55 and a time difference obtained by the differentiator 62 with respect to the deflection compensation value X _df . It is intended to be added to the deflection speed compensation value V _df in the adder 63 with calculation (see FIG. 8), representing the speed feedforward amount corresponding to the ideal response of the motor speed v _m.

FIG. 4 shows frequency characteristics (command response: X _c → x _L , disturbance suppression response: d → x _L ) according to the present embodiment. By internal speed control system becomes configurable speed feedback according to the load rate v _L, controllability is not restricted in transmission zeros omega _z, and can set the position loop gain Kp = 80. For this reason, the position control band is expanded 3 to 4 times compared to the conventional example. Furthermore, since the speed control system directly has the load disturbance suppression capability, the load disturbance suppression performance in the middle and low range is greatly improved (10 times or more).

The two graphs on the left side of FIG. 5 show real-time responses of x _L and x _m when a stepwise load disturbance d = 1 [Nm] is given. Positional variation and convergence time of x _L due to a disturbance is possible to control to 1/10 or less with respect to the prior art. Also, the two graphs on the right side of FIG. 5 show the position error x _e (= X _c −x _L ) when the speed command value V _c is given by quadratic function type acceleration. By command follow-up performance is improved relative to the prior art, and can sufficiently suppress the occurrence of the position error x _e also in the acceleration change section.

As described above, in the full-closed position control apparatus according to the embodiment, the speed command value V _c is the time derivative of the commanded position command value from the host device, originally, since the speed command value for the load speed v _L In consideration of the characteristic variation of the target plant, a robust stable speed control system for making V _c and v _L coincide with each other is configured in the position control device. For this reason, the command follow-up performance and load disturbance suppression performance related to the load position can be greatly improved.

  1 speed controller, 2 subtractor, 3 adder / subtractor, 10 position controller, 50 adder / subtractor, 51 position deviation amplifier, 52 adder / subtractor, 53 speed deviation amplifier, 54 adder, 55 differentiator, 56 differentiator, 57 control Input conversion unit, 58 subtractor, 59 compensator, 60 adder, 61 deflection compensation unit, 62 differentiator, 63 adder, 64 adder, 70 subtractor, 71 subtractor, 80 amplifier, 81 subtractor, 82 bands Compensator, 100 Position control device (Patent Document 1), 101 Position control device (Patent Document 2), 102 Position control device (Patent Document 3), 200 Target plant, 300 Feed forward block.

Claims (1)

The object plant driven by motors, the full-closed position control device of the numerical control machine for controlling the load position of the object plant according commanded position command value from the host device,
From the result of adding the speed command value, which is the time derivative of the position command value, and the output of the position deviation amplifier that amplifies the position deviation between the position command value and the load position of the target plant, An adder / subtractor that subtracts the load speed to calculate the speed deviation;
A subtractor for subtracting a speed compensation value, which is an addition value of the speed command value and the deflection speed compensation value, from the motor speed;
A speed controller that receives the speed deviation and the output of the subtractor as inputs, and obtains an output from the inputs, wherein the output of the speed controller is a feedforward amount of a control input to the target plant A speed controller that is added to the control input compensation value to become the control input to the target plant ;
A fully-closed position control device for a numerically controlled machine, characterized in that it has a speed control system comprising:

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