Abstract:
A position control system for a closed loop type numerical-controlled machine tool in which detected position information is fed back to the input side from a movable machine part or a motor driving it. In the closed loop there are provided an integrating element and a device for compensating for unstableness of the closed loop caused by the integrating element. The integrating element and the compensating device serve to improve the position deviation characteristic of the closed loop, thereby permitting accurate position control.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to a position control system which permits accurate position control of a numerical-controlled machine tool. 
     2. Description of the Prior Art 
     A position control system that has heretofore been proposed for numerical-controlled machine tools, as shown in FIG. 1, employs a semi-closed loop type servomechanism. With this conventional system, for example, the rotational angle of a motor shaft is detected by a position detector DET1, such as a resolver or the like, and the detected position information x is negatively fed back to a position control section NC of a numerical control unit, wherein it is provided via an A-D converter AD to an adder A. In the adder A, a difference is detected between position information x and commanded position information r to obtain a position deviation e. The position deviation e is applied via a gain setting circuit GC and a D-A converter DA to a velocity amplifier AMP, by which a motor M is driven in such a manner as to reduce the position deviation e to zero, and the motor rotating a reduction gear GEAR and a ball screw V controlling the position of a moving table MC. FIG. 2 shows an example of a block diagram corresponding to FIG. 1. In FIG. 2, reference character K indicates the gain of the gain setting circuit GC; G 1  (s) designates the transfer function of a velocity control section composed of the velocity amplifier AMP; G 2  (s) identifies the transfer function of the motor shaft M; and ω v  denotes the break point angular frequency of the transfer function of the velocity control section. As is evident from FIG. 2, since the mechanical system is placed outside the closed loop system, the semi-closed loop type servomechanism allows easy maintenance of the closed loop system stability, and accordingly it is adopted in various machine tools. A discussion follows of the movement x of the motor shaft in the case where the ramp input specified in equation (1) is applied as the commanded position information r to a numerical-controlled machine tool. 
     
         r=F×t                                                (1) 
    
     where F is a feed rate and t is time. The transfer function G(s) of the abovesaid closed loop is given as follows: ##EQU1## Letting the Laplace transformation of the input r be represented by R(s), a deviation E(s) on its desired value R(s) becomes as follows: ##EQU2## Accordingly, the steady-state deviation e (t→∞) becomes as follows: ##EQU3## The movement of the motor shaft, and accordingly the movement of the moving table MC, in its steady-state, has a certain amount of time lag which is proportional to the feed rate and inversely proportional to the gain K. This delay has a direct influence on the actual cutting accuracy. For example, when cutting a workpiece by straight cutting into the configuration indicated by reference numeral 1 of FIG. 3, the actual locus of movement of a tool causes a cut as indicated by reference numeral 2; namely, the corner of the work is rounded in proportion to the delay. When making a circular cut, the locus of movement 2 of the tool deviates from a true circle 3, as illustrated in FIG. 4. When the tool is suddenly stopped while running at a constant speed, the actual tool movement overruns by the delay. Consequently, the overrun poses a problem when stopping the cutting operation by stepping on a stroke switch of the machine tool. As is apparent from equation (4), an increase in the gain K decreases the delay, however, there is an upper limit to the magnitude of the gain K which can be used and still remain in a stable region and it is difficult to correct the delay in that upper range. 
     Various problem resulting from such steady-state deviation are encountered not only in the aforesaid semi-closed loop type numerical-controlled machine tool but also in a closed loop type numerical-controlled machine tool such, for example, as shown in FIG. 5. In the closed loop type a position detector DET2, such as an inductive detector or the like, is mounted on a moving part of the machine tool to be ultimately controlled, for example, the moving table. The detected position information is negatively fed back so that it may coincide with the commanded position information r. Accordingly, it has been desired to solve the above outlined problems. 
     SUMMARY OF THE INVENTION 
     It is an object of the present invention to provide a position control system for numerical-controlled machine tools which permits highly accurate position control. 
     Another object of the present invention is to provide a position control system for closed-loop type numerical-controlled machine tools in which the closed loop is stabilized by a compensator using the operating function of a processor to facilitate the adjustment. 
     Yet another object of the present invention is to provide a simple method for stabilizing the closed loop without using the operating function of a processor. 
     Briefly stated, according to the present invention, in a closed loop type numerical-controlled machine tool the detected position information from a movable machine part or a motor driving it is fed back to the input. Provided in the closed loop is an integrating element and a device means for compensating for the instability of the closed loop caused by the integrating element, by which the closed loop is stabilized and the position deviation characteristic of the closed loop is improved allowing highly accurate position control. The abovesaid compensating device is a compensator using the operating function of a processor which contains characteristics of the closed loop including the integrating element, or a proportional element connected in parallel with the integrating element, the constant of the proportional element is adjusted together with the constant of the integrating element so that the closed loop is stable. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a block diagram of a conventional semi-closed loop type numerical-controlled machine tool; 
     FIG. 2 is a block diagram of the machine tool shown in FIG. 1; 
     FIGS. 3 and 4 are graphs illustrating the influence of a steady-state deviation on cutting accuracy; 
     FIG. 5 is a system diagram of a conventional closed loop type numerical-controlled machine tool; 
     FIG. 6 is a block diagram illustrating an example of a numerical-controlled machine tool embodying the position control system of the present invention; 
     FIG. 7 is a block diagram of the machine tool shown in FIG. 6; 
     FIG. 8 is a block diagram showing the effect produced by the present invention; and 
     FIG. 9 is a block diagram of another example of the numerical-controlled machine tool embodying the present invention. 
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     FIG. 6 illustrates the construction of an example of a numerical-controlled machine tool embodying the position control system of the present invention. In FIG. 6, parts corresponding to those in FIG. 1 are identified by the same reference characters. Reference character CPS indicates a compensator; and GC1 designates a gain setting circuit. FIG. 7 shows in block form the position control system utilized in FIG. 6. In FIG. 7, reference characters G 1  (s) and G 2  (s) identify the transfer functions of the velocity control section and the motor; and K/s denotes the transfer function of the gain setting circuit GC1. 
     According to this embodiment, in the semi-closed type numerical-controlled machine tool, the gain setting circuit is a proportional element and an integrating element while in the prior art the gain setting circuit an integrating element alone. In this embodiment the compensator CPS is inserted in the closed loop to stabilize it. Setting the following equation: 
     
         Gp(s)=(K/s)×G.sub.1 (s)×G.sub.2 (s)            (5) 
    
     and considering such a closed loop as shown in FIG. 8 in which the compensator CPS is not included, the steady-state deviation e (t→∞) relative to the ramp input r becomes ##EQU4## from ##EQU5## That is, when the gain setting circuit GC1 is equipped with an integrating characteristic, the steady-state deviation e is zero. With such an arrangement, however, the closed loop is unstable since the characteristic equation of the closed loop is as follows: 
     
         (s.sup.3 /ω.sub.V)+s.sup.2 +K=0                      (8) 
    
     In the present embodiment, the compensator CPS inserted in the stage preceding the gain setting circuit GC1 is to stabilize the closed loop which is made unstable by the gain setting circuit GC1 having the integrating characteristic. A description will be given of the construction of the compensator CPS. 
     Generally, it is known, as in the J. B. Pearson&#39;s dynamic compensator, that when a compensator having a transfer function of second degree Gc(s) is provided at a stage preceding a transfer function of third degree Gp(s), the characteristic root of the closed loop transfer function Gc(s) Gp(s) of a compensated system can be designated arbitrarily. Then, introducing the transfer function of second degree Gc(s) as follows: ##EQU6## the compensated system has a transfer function of fifth degree. If the characteristic root is determined in such a manner as to stabilize the closed loop and in consideration of its rapid response, then the characteristic equation of the closed loop is given by the following equation, using the determined characteristic root -r 0  to -r 4  : 
     
         1+Gc(s)×Gp(s)=(s+r.sub.0)(s+r.sub.1)(s+r.sub.2)(s+r.sub.3)(s+r.sub.4) (10) 
    
     Since coefficients a 0 , a 1 , b 0 , b 1  and b 2  of the transfer function Gc(s) in the equation (8) are determined by a simple algebraic equation from the above equation, the transfer function Gc(s) of the compensator CPS is determined completely. 
     Once the coefficients of the compensator CPS have thus been determined, the compensator CPS can be realized, using the operating function of a processor in the manner described below. Transforming the equation (9), it becomes as follows: ##EQU7## In general, the status equation of minimal degree of a system having such a transfer function Gc(s) is expressed by a differential equation such, for example, as follows: ##EQU8## where x=(d/dt)x, u is an input, y is an output and x is expressed by ##EQU9## where x 1  and x 2  are status variables. Since the equation (12) is a continuous system, it is transformed into the following difference equation in the actual processing by the processor: ##EQU10## where φ(T) and h(T) are functions including a 0 , a 1 , b 0 , b 1  and b 2 . The compensator CPS is realized by performing this operation on an online basis by the processor simultaneously with the cutting control. 
     As described above, according to the present embodiment, in the semi-closed loop type numerical controlled machine tool, the gain setting circuit GC1 is equipped with the integrating characteristic alone and the compensator CPS, which is constructed by using the operating function of a processor, is provided at the stage proceeding the gain setting circuit GC1 for stabilizing the closed loop. Since the steady-state deviation e can be removed without making the closed loop unstable, highly accurate position control can be achieved. Further, since the adjustment for stabilizing the closed loop is carried out by the processor, this embodiment has an advantage that no cumbersome adjustment is involved unlike an embodiment described later. 
     The position where the integrating element is inserted may be a position where the integrating element will appear in the total transfer function. For example, it may also be inserted in the velocity control section, but since the velocity control section is usually produced as one unit and sold together with a machine tool, it is difficult in practice to insert the integrating element in the velocity control section and, further, since the arrangement of the velocity control section differs from machine to machine, this poses a problem in that the method of realizing the integrating element differs with individual arrangements of the velocity control section. That is the reason the integrating element is provided in the gain setting circuit in the present embodiment. By providing the integrating element on the input side of the position control section NC which precedes the stage of the velocity control section, one numerical control unit can easily be used with various machine tools and, in additon, the compensator CPS, including the integrating element, can be realized by the operating function of a processor. The foregoing description has been given of the case where the compensator CPS is designed on the basis of the idea of the J. B. Pearson&#39;s dynamic compensator, but a similar compensator can be designed, using known output regulator theories. 
     The foregoing embodiment shows an example of the arrangement of the control system based on current control theory introducing status variables, but the object of the present invention can also be attained by a system based on classical control theory. FIG. 9 illustrates in block form a semi-closed loop type numerical controlled machine tool embodying that system. In FIG. 9, reference character GC2 indicates a gain setting circuit; and G 1  (s) and G 2  (s) designate the transfer functions of the velocity control section and the motor. 
     In this embodiment, an integrating element is provided in the gain setting circuit GC2 for the position deviation, and a proportional element is connected in parallel with the integrating element. The stabilization of the closed loop is achieved by adjusting constants K and T of the proportional element and the integrating element. 
     In the case of applying the ramp input r to the control system in FIG. 9, the steady-state deviation e (t→∞) becomes as follows: ##EQU11## from ##EQU12## where G 3  (s) is the total transfer function of the gain setting circuit GC2, the velocity control section and the motor. Accordingly, no delay is caused by the steady-state deviation. Since the characteristic equation of the closed loop in this case becomes as follows: 
     
         (s.sup.3 /ω.sub.V)+s.sup.2 +Ks+(1/T)=0               (16) 
    
     it is possible to stabilize the closed loop and obtain a desired response characteristic by adjusting the constants K and T within the range of K&gt;1/Tω V  so that the response characterisic of the closed loop may become a desirable one. The present embodiment does not necessitate the use of a processor unlike the foregoing embodiment, and hence is advantageous in that the system is simple in arrangement and easy to realize. It is also possible to adopt such an arrangement in which the aforesaid dynamic compensator is provided in the stage preceding the stage of the gain setting circuit GC2 in the present embodiment, and in such a case, the adjustment of the constants K and T can be omitted. 
     In the foregoing embodiments, the present invention is applied to the semi-closed loop type numerical-controlled machine tool in which the position information is fed back from the motor shaft, but it is a obvious of course that the invention is also applicable to the closed loop type numerical-controlled machine tool in which the position information is fed back directly from a movable machine part. 
     As has been described in the foregoing, according to the present invention, in the closed loop type numerical-controlled machine tool, an integrating element is inserted in the closed loop at a proper place and a device is provided for compensating for unstableness of the closed loop which is caused by inserting the integrating element. Since the steady-state deviation can be eliminated without making the closed loop unstable, highly accurate position control can be achieved. 
     It will be apparent that many modifications and variations may be effected without departing from the scope of the novel concepts of this invention.