Fully-closed loop position controller

Abstract

A fully-closed loop position controller with a velocity control system based on a velocity feedback of mixed velocities of a motor velocity and a load velocity. The fully-closed loop position controller identifies a ratio of load moment of inertia in real time to select an optimum mix gain in accordance with a changing ratio of load moment of inertia such that a position loop gain and a speed loop gain can be varied accordingly. The fully-closed loop position controller controls the load position based on the mix gain, the position loop gain, and the velocity loop gain.

Claims

1. A fully-closed loop position controller of a numerically-controlled machine configured to control a load position of a target plant by driving the target plant in accordance with a position command value supplied from a higher-level device, wherein a velocity feedback control system is formed with mixed velocities of a motor velocity and a load velocity, the fully-closed loop position controller comprising: an identification calculator configured to identify a ratio of load moment of inertia based on a control input, the motor velocity, and the load velocity; an integrating amplifier configured to calculate a ratio of load moment of inertia to be applied to a servo gain variable rate calculator based on the identified ratio of load moment of inertia; a mix gain calculator configured to calculate a mix gain representing a mix ratio between mixed velocities based on the ratio of load moment of inertia; and a servo gain identifier configured to calculate a position loop gain and a velocity loop gain based on the ratio of load moment of inertia and the mix gain, wherein fully-closed loop position controller is configured to control the load position based on the mix gain, the position loop gain, and the velocity loop gain.

2. The fully-closed loop position controller according to claim 1, further comprising: the servo gain variable rate calculator configured to calculate a servo gain variable rate based on the ratio of load moment of inertia and the mix gain; wherein the servo gain identifier is configured to calculate the position loop gain and the velocity loop gain based on the ratio of load moment of inertia and the servo gain variable rate.

Description

BRIEF DESCRIPTION OF DRAWINGS

(1) Embodiment(s) of the present disclosure will be described based on the following figures, wherein:

(2) FIG. 1 is a block diagram showing an example of a fully-closed loop position controller according to the present disclosure;

(3) FIG. 2 is a graph showing a relationship between an amplifier input e and an integral gain Ge at an integrating amplifier 3 according to the present disclosure;

(4) FIG. 3 is a graph showing an example of position control frequency characteristics by a fully-closed loop position controller according to the present disclosure;

(5) FIG. 4 is a graph showing another example of position control frequency characteristics by a fully-closed loop position controller according to the present disclosure;

(6) FIG. 5 is a block diagram showing an example configuration of a conventional fully-closed loop position controller;

(7) FIG. 6 is a graph showing a stability limit increased rate h(fb) against the mix gain fb with the ratio of load moment of inertia R used as a parameter;

(8) FIG. 7 is a graph showing an example of frequency characteristics of a position control system of a conventional fully-closed loop position controller; and

(9) FIG. 8 is a graph showing another example of frequency characteristics of a position control system of a conventional fully-closed loop position controller.

DESCRIPTION OF EMBODIMENTS

(10) Embodiments according to the present disclosure are described below. It should be noted that the following embodiments are provided merely as examples. The present disclosure is not limited to the following embodiments. FIG. 1 is a block diagram showing an example of a fully-closed loop position controller according to the present disclosure, in which a position command X.sub.c is supplied from a higher-level device 100. The following descriptions indicate only differences from those described above in the conventional arts.

(11) The equation of motion of a target plant 200 shown in Equation (1) can be represented by the following equation by using the ratio of load moment of inertia R.

(12) $\begin{array}{cc}{}_m=I_m\frac{d{}_m}{\mathrm{dt}}+R.Math.I_m\frac{d{}_L}{\mathrm{dt}}+{}_d& \mathrm{Equation}\left(8\right)\end{array}$

(13) This equation can be transformed to the following Equation (9) as a parametric representation:

(14) $\begin{array}{cc}\frac{{}_m-I_m\frac{d{}_m}{\mathrm{dt}}}{{}_L\left(11\right)}=\frac{\left[I_m\frac{d{}_L}{\mathrm{dt}}1\right]}{\left(12\right)}\frac{\left[\begin{array}{c}R\\ {}_d\end{array}\right]}{\left(21\right)}& \mathrm{Equation}\left(9\right)\end{array}$

(15) A motor acceleration velocity dm/dt and a load acceleration velocity dL/dt can be calculated by sensing motor velocities m and load velocities L at sampling times. Further, because the control input m is a calculated value by the position controller and the motor moment of inertia Im is a known parameter, the load torque L on the left side of the Equation (9) and the signal row vector on the right side can be obtained. Thus, the unknown parameter, column vector , on the right side of Equation (9) can be identified because by collecting n number of the load torques L and the signal row vectors in time series while acceleration velocity changes and arranging them in the row direction, the signal row vectors form a signal matrix (n2) in which each column vector is linearly independent.

(16) An identification calculator 1 performs identification calculation of the above described unknown parameter, column vector , by using a well-known identification algorithm with signals m, L, m as inputs when a change in acceleration velocity is sensed. In FIG. 1, the identified ratio of load moment of inertia R is represented by RID. The identified ratio of load moment of inertia RID which is an output from the identification calculator 1 is updated at each identification calculation.

(17) A subtractor 2 subtracts the ratio of load moment of inertia R to be used in the control (hereinafter referred to as the ratio of load moment of inertia R to be applied in the control) from the identified ratio of load moment of inertia RID. The output e from the subtractor (input to an amplifier) is amplified by the integral gain Ge by an integrating amplifier 3 to be used as the ratio of load moment of inertia R to be applied in the control. This series of calculations can be represented by the following Equation (10).

(18) $\begin{array}{cc}R=\left(R_{\mathrm{ID}}-R\right)\frac{\mathrm{Ge}}{s}& \mathrm{Equation}\left(10\right)\end{array}$

(19) The integral gain Ge is transformed by the amplifier input e as shown in FIG. 2.

(20) The values represented by 1, 2 (2<1<0) and Ge1, Ge2 (Ge1<Ge2) are predetermined constants which are preset in consideration of a possible variable range and the rate of change over time of the actual ratio of load moment of inertia R, and the filtering effect of the integrating amplifier 3. In this way, a position control operation within the stability limit range shown in FIG. 6 can be ensured by controlling the increase in the ratio of load moment of inertia R to be applied in the control such that, in the case of e>0 (RID>R), the increase in the ratio of load moment of inertia R is controlled to be moderate, whereas in the case of e<0 (RID<R), the integral gain Ge is increased more rapidly to enhance the following performance to RID and to decrease the R more rapidly with smaller RID (RID<<R).

(21) A mix gain calculator 4 calculates the mix gain fb from the following Equation (11) based on the ratio of load moment of inertia R to be applied in the control:

(22) $\begin{array}{cc}\{\begin{array}{cc}{f}_b=\frac{R-1}{1+R}& \left(R>1\right)\\ f_b=0& \left(R1\right)\end{array}& \mathrm{Equation}\left(11\right)\end{array}$

(23) where is a derating factor to apply a stability margin to the mix gain fb which achieves the maximum stability limit increase rate h(fb) shown in FIG. 6. The derating factor is typically set within a range from 0.8 to 1. The calculated mix gain fb is set as an amplification factor of an amplifier 55.

(24) In the present disclosure, the initial value R0 of the ratio of load moment of inertia is predetermined and fb0 corresponding to the initial value R0 is set in advance in a servo gain variable rate calculator 5. Further, when the target plant 200 to be controlled is determined, rigidity K can be obtained. Then, a velocity control band V0 and position loop gain KP0 are obtained for R0 and fb0 from Equation (7), and set in a servo gain identifier 6. Based on Equation (3), the proportional gain GP0 and the integral gain Gi0 forming the velocity loop gain GV0 are determined for the velocity control band V0 from the following Equation (12):

(25) $\begin{array}{cc}\{\begin{array}{c}{G}_{p0}=2\left(1+R_0\right)I_m{}_{v0}\\ G_{i0}=\left(1+R_0\right)I_m{}_{v0}^2\end{array}& \mathrm{Equation}\left(12\right)\end{array}$

(26) The servo gain variable rate calculator 5 calculates a servo gain variable rate A from Equation (13) below by using the initial values R0, fb0 and the ratio of load moment of inertia R to be applied in the control and the mix gain fb. The ratio of load moment of inertia R to be applied in the control and the mix gain fb are calculated in real time. The calculated value is output to the servo gain identifier 6.

(27) 0$\begin{array}{cc}A=\frac{K_p{}_v}{K_{p0}{}_{v0}}=\frac{\frac{1}{R}\left\{\frac{R-\left(1+R\right)f_b}{\left(1+R\right){\left(1-f_b\right)}^2}\right\}}{\frac{1}{R_0}\left\{\frac{R_0-\left(1+R_0\right)f_{b0}}{\left(1+R_0\right){\left(1-f_{b0}\right)}^2}\right\}}& \mathrm{Equation}\left(13\right)\end{array}$

(28) The servo gain identifier 6 calculates the velocity control band v and the position loop gain Kp in real time from Equation (14) based on the predetermined initial values R0, V0, KP0, and the servo gain variable rate A (it should be noted that the velocity control band v is not essential in this example):

(29) $\begin{array}{cc}\{\begin{array}{c}{}_v=\sqrt{A}{}_{v0}\\ K_p=\sqrt{A}{K}_{p0}\end{array}& \mathrm{Equation}\left(14\right)\end{array}$

(30) The proportional gain GP and the integral gain Gi forming the velocity loop gain GV are calculated from the following Equation (15) for the initial values GP0 and Gi0 based on the servo gain variable rate A and the ratio of load moment of inertia R to be applied in the control:

(31) $\begin{array}{cc}\{\begin{array}{c}{G}_p=\frac{\left(1+R\right){}_v}{\left(1+R_0\right){}_{v0}}{G}_{p0}=\frac{1+R}{1+R_0}\sqrt{A}{G}_{p0}\\ G_i=\frac{\left(1+R\right){}_v^2}{\left(1+R_0\right){}_{v0}^2}{G}_{i0}=\frac{1+R}{1+R_0}\sqrt{A}{G}_{i0}\end{array}& \mathrm{Equation}\left(15\right)\end{array}$

(32) The calculated position loop gain Kp is set as an amplification factor of a positional deviation amplifier 51. The proportional gain GP and the integral gain Gi are set as amplification factors of a velocity deviation amplifier 53.

(33) FIG. 3 shows frequency characteristics of the command response L/XC and the disturbance response L/d when the position control system is configured by a servo gain (the position loop gain Kp and the velocity control band v) which is set from Equation (7) in a fully-closed loop position controller according to the present disclosure shown in FIG. 1, with the derating factor =1 and the mix gain fb=0.5 in the case of the ratio of load moment of inertia R=3.

(34) The position control characteristics of a fully-closed loop position controller according to the present disclosure are described in the case where the ratio of load moment of inertia R changes from R=3 to R=10. For the sake of convenience, conditions used in FIG. 3 are assumed to be the initial values (R0=3, fb0=0.5). The identification calculator 1 outputs an identified ratio of load moment of inertia RID=10. Then, the ratio of load moment of inertia R to be applied in the control converges from 3 to 10.

(35) The mix gain calculator 4 calculates and outputs the mix gain fb0.81 from Equation (11) (by assuming =1). The servo gain variable rate calculator 5 calculates and outputs the servo gain variable rate A=0.82 from Equation (13). The servo gain identifier 6 determines the position loop gain Kp from Equation (14) and the proportional gain GP and the integral gain Gi from Equation (15). Because A0.9, the position loop gain Kp and the velocity control band v are 0.9 times the initial values KP0 and V0. The proportional gain GP is about 2.5 times the initial value GP0 (11/40.92.5). The integral gain Gi is about 2.3 times the initial value Gi0 (11/40.822.3). FIG. 4 shows the frequency characteristics of the command response L/XC and the disturbance response L/d under these conditions.

(36) In this way, the cutoff frequency of the command response L/XC is broadened from 15 Hz to 24 Hz and the load disturbance suppression performance in the middle and low frequency band is improved about 10 dB in the case of the ratio of load moment of inertia R=10 in comparison to the control characteristics for conventional arts shown in FIG. 8.

(37) As described above, a fully-closed loop position controller according to the present disclosure identifies the ratio of load moment of inertia R and selects an optimum mix gain fb in accordance with the changing R such that the proportional gain GP and the integral gain Gi of the velocity loop gain, and the position loop gain Kp can be appropriately varied. Therefore, a fully-closed loop position controller system constantly having a high level of command following performance and load disturbance suppression performance can be achieved even for a control shaft having a significantly variable ratio of load moment of inertia R.