GB2270998A

GB2270998A - Positioning system

Info

Publication number: GB2270998A
Application number: GB9317794A
Authority: GB
Inventors: Takashi Aihara
Original assignee: Fuji Electric Co Ltd
Current assignee: Fuji Electric Co Ltd
Priority date: 1992-09-02
Filing date: 1993-08-26
Publication date: 1994-03-30
Anticipated expiration: 2013-08-26
Also published as: GB9317794D0; DE4329484A1; GB2270998B

Description

2270998 POSITIONING SYSTEM The present invention relates to a positioning

system that moves an object from an initial location to a destination location by using servo control in a driving apparatus like mobile robots, and various types of transporting systems.

In a positioning system which comprises a position command portion and a position control portion, it is generally required that the force or torque command to be provided to the position control portion be within its maximum output capacity. If a position command, which demands acceleration greater than the position control portion can provide, is applied to the position control portion. the actual position will not be able to follow the command. This results in large positional error, and may cause unstable operation such as overshoot or hunting.

Therefore-, in the conventional positioning system. unstable operations as mentioned above may occur depending on the setting of parameters of the position command portion or the position control portion. When the unstable operations have actually occurred, the parameters must be readjusted to remove these unstable operations.

Fig. 1 is a block diagram showing a conventional positioning system.

In this figure, the acceleration set value X" is successively integrated by integrators 12a and 12b in a position command portion 1, and a first position command value X, is generated therefrom. The first position command value X, is supplied to a position control portion 2 which drives a controlled object 3. During this process, the first position command value X, is converted to a second position command value X2 by a filter 5a in the position control portion 2. In addition, a position detector 3A detects the position of the controlled object 3. and outputs the actual position value X.

An adder 21 outputs the difference between the second position command value X2 and the actual position value X of the controlled object 3. A position adjuster 22 multiplies the difference by a gain Kp, and the product is outputted as a velocity command value n. The velocity command value n is inputted to a velocity control portion 23 which controls the controlled objects by the force F.

When the first position command value X1 is provided which demands acceleration greater than the position control portion 2 can output, the actual position value X cannot follow the command value, and hence unstable operations may result.

Methods for limiting acceleration in order to prevent the unstable operations may be as follows: Limiting the acceleration set value X" in the position command portion 1; increasing the time constant of the filter 5a; and reducing the gain Kp of the position adjuster 22.

The best method of these is to reduce the acceleration set value X" in the position command portion 1. A comparatively low cost system, however, may not have a position command portion that can freely limit the acceleration. In such a case, the time constant of the filter 5a must be increased as the second best method.

In a system which has no such f ilter, the gain Kp of the position adjuster 22 must be reduced.

Thus, in conventional positioning systems. unstable operations may occur as soon as the set value of a parameter of the position command portion or the position control portion exceeds a certain limit which changes depending on the state of the controlled object. To prevent such unstable operations. the parameters must be readjusted. Such a readjustment usually takes a long time. and further readjustments are often required depending on operation conditions.

It is therefore an object of the present invention to provide a positioning system which can eliminate unstable operations caused by the setting condition of parameters, and thus obviates tedious readjusting.

According to a first aspect of the present invention, there is provided a positioning system comprising:

position command means for outputting a position command value for a controlled object; position detecting means for detecting the actual position of the.controlled object, and for outputting an actual position value of the controlled object; position control means for controlling force exerted on the controlled object so that the actual position value of the controlled object agrees with the position command value; mass estimation means for estimating the mass of the controlled object; 20 maximum acceleration computing means for computing maximum acceleration of the controlled object on the basis of the mass which is estimated by the mass estimation means, and maximum force which can be provided by the position control means; and acceleration limiting means for limiting the second-order time derivative of the position command value within the maximum acceleration obtained by the maximum acceleration computing means.

According to a second aspect of the present invention, there is provided a positioning system comprising:

position command means for outputting a first position command value for a controlled object; position detecting means for detecting the actual position of the controlled object, and for outputting an actual position value of the controlled object; position control means for controlling force exerted on the controlled object so that the actual position value of the controlled object agrees with the position command value; mass estimation means for estimating the mass of the controlled object; maximum acceleration computing means for computing maximum acceleration of the controlled object on the basis of the mass which is estimated by the mass estimation means, and maximum force which can be provided by the position control means; 25 smoothing means for smoothing the first position command value with regard to time, and outputting a second position command value; and acceleration control means for limiting the second-order time derivative of the second position command value within the maximum acceleration obtained by the maximum acceleration computing means. 5 Here, the acceleration control means may control a constant of the smoothing means in such a manner that the degree of smoothing is only emphasized. The constant of the smoothing means may be reset to its initial value only when the input and output of the smoothing means agrees with each other.

The smoothing means may be a low-pass filter, and the constant of the smoothing means may be the time constant of the low-pass filter.

According to a third aspect of the present invention, there is provided a positioning system comprising:

position command means for outputting a position command value for a controlled object; position detecting means for detecting the actual position of the controlled object. and for outputting an actual position value of the controlled object; position control means for controlling force exerted on the controlled object so that the actual position value of the controlled object agrees with the position command value. the position control means including a position adjuster for obtaining a velocity command value by multiplying the difference between the position command value and the actual position value by a gain Kp, and a velocity control means for controlling the controlled object so that its actual velocity value agrees with the velocity command value; mass estimation means for estimating the mass of the controlled object; maximum acceleration computing means for computing maximum acceleration of the controlled object on the basis of the mass which is estimated by the mass estimation means, and maximum force which can be provided by the position control means; and acceleration control means for limiting the first-order time derivative of the velocity command value outputted from the position adjuster within the maximum acceleration obtained by the maximum acceleration computing means. The acceleration limiting means may control the gain Kp of the position adjuster in such a manner that the gain Kp is only reduced. 25 The gain Kp of the position adjuster may be reset to its initial value only when the position command value and the actual position value agrees with each other.

According to a fourth aspect of the present invention, there is provided a positioning system comprising: position command means for outputting a position command value for a controlled object; position detecting means for detecting the actual position of the controlled object. and for outputting an actual position value of the controlled object; position control means for controlling force exerted on the controlled object so that the actual position value of the controlled object - agrees with the position command value, the position control means including a position adjuster for obtaining a velocity command value by multiplying the difference between the position command value and the actual position value by a gain Kp, and a velocity control means for controlling the controlled object so that its actual velocity value agrees with the velocity command value; mass estimation means for estimating the mass of the controlled object; maximum acceleration computing means for computing maximum acceleration of the controlled object on the basis of the mass which is estimated by the mass estimation means, and maximum force which can be provided by the position control means; and display means for displaying the maximum acceleration, or an acceleration and deceleration time which is computed on the basis of the mass and the maximum force which the position control means can provide.

According to the first to third aspects of the present invention, the force outputted from the position control means is limited within its maximum output value. As a result. the difference between the.position command value and the actual position value of the controlled object does not exceeds a certain value. This prevents overshoot or hunting, thereby achieving stable operation. Furthermore. this makes it possible to eliminate an adjustment of parameters. or a readjustment of operation conditions when the operation conditions are changed.

According to the fourth aspect of the present invention. set values of parameters can be readily obtained from the maximum acceleration and the like which are displayed on the display means. Thus, the apparatus can be adjusted to an appropriate operation condition by only the first test operation, thereby simplifying the adjusting operation.

The above and other objects. effects, features and advantages of the present invention will become more apparent from the following description of the embodiments thereof taken in conjunction with the accompanying drawings. 5

Fig. 1 is a block diagram showing a conventional positioning system; -Fig. 2 is a block diagram showing a first embodiment of a positioning system in accordance with the present invention; Fig. 3 is a block diagram showing a second embodiment of the positioning system in accordance with the present invention; Fig. 4 is a graph illustrating waveforms of f irst-order derivatives X, and X2' and the maximum acceleration Qma. during high acceleration and deceleration in the second embodiment shown in Fig. 3; Fig. 5 is a graph illustrating waveforms of the f irst-order derivatives X, 1 and X2 1 and the maximum acceleration o, a. during low acceleration and deceleration in the second embodiment shown in Fig. 3; Fig. 6 is a block diagram showing a third embodiment of the positioning s ystem in accordance with the present invention; Figs. 7A and 7B are graphs illustrating waveforms of first-order derivatives X,' and X2' and the maximum acceleration Cnax during high acceleration and deceleration in the third embodiment shown in Fig. 6; Fig. 8 is a graph illustrating waveforms of the first-order derivatives X,' and X21 and the maximum acceleration Qax during low acceleration and deceleration in the third embodiment shown in Fig. 6; and Fig. 9 is a block diagram showing a fourth embodiment of the positioning system in accordance with the present invention.

The invention will now be described with reference to the accompanying drawings.

EMBODIMENT 1 Fig. 2 is a block diagram showing a first embodiment in accordance with the present invention. In Fig. 2, the reference numeral 1A designates a position command portion incorporating an acceleration limiter 11 which will be described later, in addition to the integrators 12a and 12b. The reference numerals 2 and 3 designate the position control portion and the controlled object, respectively, as in Fig. 1.

The reference numeral 4 designates a mass estimation portion newly added in this - 12 embodiment. This mass estimation portion 4 estimates the mass or the inertia value of the controlled object 3 from the operation characteristic of the controlled object 3, such as the force F and the actual position value X fed by the position detector 3A. the force F and the velocity command value, the force F and the actual velocity n, the force F and the acceleration X",, etc. The details of a method for estimating the mass or the inertia value is described in 3 "Instantaneous Speed Detection with Parameter Identification for ac Servo Systems". by K. Fujita, et al, IEEE Transactions on Industry Applications. Vol. 28. No. 4. July/August. 1992. The reference numeral 4A designates a maximum acceleration computing portion that computes the maximum acceleration ocmax (or the maximum angular acceleration) on the basis of the estimated mass (or inertial value) and the maximum force Fmx or torque which the position control portion 2 can providef and supplies the maximum acceleration Ctmax to the acceleration limiter 11 in the position command portion 1A.

The acceleration limiter 11 limits the acceleration command value Xtt inputted thereto so that the value X" does not exceed the maximum acceleration value Otmax fed from the mass estimation portion 4. The position command portion 1A carries out the position command calculation on the basis of the output of the acceleration limiter 11.

According to the first embodiment. the second-order time derivative X" of the position command value X is limited within the maximum acceleration Ctmax by the acceleration limiter 11.

Thus, the force F outputted from the position control portion 2 does not exceed the possible maximum output of the position control portion 2. This prevents an excessive position error, thereby achieving a stable operation.

Since the present embodiment limits only the acceleration command value X" that would exceed the maximum acceleration Ccmax, the acceleration command value X" smaller than the maximum acceleration U..ax may be treated as in the conventional system.

EMBODIMENT 2 Fig. 3 shows a second embodiment in accordance with the present invention. This embodiment is substantially different from the conventional system in Fig. 1 in that the position control portion 2 in Fig. 1 is divided into the filter 5a and a position control portion 2A. and that the mass estimation portion 4 and an acceleration controller 5b are added. Here, the filter 5a functions as a smoothing portion, and the acceleration controller 5b functions as an acceleration limiting portion. The position command portion 1 is the same as that of Fig. 1.

The acceleration controller 5b receives the maximum acceleration Qax from the maximum acceleration computing portion 4A and the second position command value X2 from the filter 5a.

and provides the filter 5a with a signal for adjusting the time constant of the filter 5a.

More specifically, the acceleration controller 5b controls the time constant of the filter 5a so that the second-order time derivative of the second position command value X2 does not exceed the maximum acceleration C6a. when the second-order time derivative is greater than 06ax.

The time constant is handled as follows when the filter 5a is a discrete time-domain primary filter.

First. the filtering characteristic is expressed by the following equation (1).

X2(i) = X2(i-1) + {Xl (i) - X2 (i-1)}Ts/Tf (1) where T. is a sampling interval. and Tf is the time constant of the filter 5a.

When the following expression (2) holds between the left-hand side associated with the second-order time derivative of the second position command value X2 and the right-hand side (i.e., the maximum acceleration (Xma.,), the time constant Tf of the filter 5a is calculated using equation (3b), into which X2M obtained by equation (3a) is substituted. when expression (2) holds.

{X2 (i) - X2 (i-1) {X2 (i-1) - X2 (i-2) > (Xmax (2) X2 (i) = 2X2 (i-1) X2 (i-2) + 06ax (3a) Tf XI (i) - X2 (i-1). Ts (3b) X2 (i) - X2 (i-1) Once the time constant Tf of the filter 5a has been increased in the process of adjusting by the acceleration controller 5b, it is preferable that the time constant be not decreased again. This is because it is very likely that the maximum value amax is exceeded during the deceleration when it has been exceeded during the acceleration. In addition, since the filter 5a is associated with position, it includes a delay proportional to its time constant when the 16 position is changing. Accordingly, decreasing the time constant Tf which has been once increased will decrease the delay in proportion thereto. In such a case, a deceleration operation, which coincides with the decrease in the time constant. will not be able to follow the position command value, and induces overshoot. Thus, it is preferable that the time constant Tf be only increased to maintain stable operation.

Figs. 4 and 5 illustrate relationships between the time. and the first-order time derivatives X,' and X2' of the first and second position command values X, and X2, and the maximum acceleration C6ax, respectively. As shown in these figures, the time constants T1 and T2 (T1 > T2)Of the filter required to obtain the same acceleration for different estimationvelocities are different.

More specifically, in order to limit the actual acceleration within the maximum acceleration U,,,:x, the time constant Tf of the filter must be set at a rather large value T1 in a high acceleration and deceleration range as shown in Fig. 4, but may be set at a rather small value T2 in a low acceleration and deceleration range as shown in Fig. 5.

If the time constant Tf is set at T1 in the case of Fig. 5, the operation will be unduly delayed. An optimum time constant can always be achieved by returning the time constant Tf of the filter 5a to its initial value every time one cycle of operation has been completed, because the input and output of the filter 5a become usually identical by the operation.

The filter 5a may be a second- or thirdordek filter having an S-curve characteristic that makes the acceleration waveform as smooth as a character S.

When the first-order time derivative of the first position command value X, changes stepwise, the filter computation defined by the following equation (4) makes it possible for the first-order time derivative of the second position command value X2 to change linearly, and the acceleration can be limited within the maximum acceleration c,,,, in this case.

dX2/dt = -42(Xl - X2)0Cma. (4) EMBODIMENT 3 Fig. 6 shows a third embodiment in accordance with the present invention. This embodiment comprises the mass estimation portion 4 and the maximum acceleration computing portion 4A as in Figs. 2 and 3. In addition, it comprises an acceleration controller 5 for limiting acceleration. The acceleration controller 5 controls the gain Kp of the position adjuster 22 in the position controlling portion 2A on the basis of the velocity command value n from the position adjuster 22 and the maximum acceleration amax from the maximum acceleration computing portion 4A.

The acceleration controller 5 controls the gain Kp of the position adjuster 22, when the first-order time derivative of the velocity command value n outputted from the position adjuster 22 exceeds the maximum acceleration C6ax, so that the first-order time derivative falls within the maximum acceleration omax.

The velocity command value n is obtained in accordance with the following equation (5) in the discrete time system.

n(i) = {X(i) - X(i)} Kp (5) Accordingly, the acceleration controller 5 computes n(i) and Kp using the following equations (6) and (7) when n(i) n(i-1) ' Cnax.

n (i) = n (i-1) + amax (6) Kp = n (i) / {X (i) - X (i) (7) Once the gain Kp has been reduced. it is usually preferable that the gain be not increased again for the same reason as described in the second embodiment of the present invention.

Since the gain Kp of the position adjuster 22 functions in a manner similar to the time constant of a filter, the actual position value X during movement somewhat delays with regard to the position command value X, and the delay is inversely proportional to the gain Kp. As a result. when the gain Kp which has once been decreased is increased again during the movement, the delay will reduce in inverse proportion. This makes it difficult for the deceleration to follow the position command value, and induces overshoot. Thus, the stable operation can be achieved only by decreasing the gain Kp rather than increasing it.

Figs. 7A and 7B illustrate relationships between the time, and the first-order time derivative X' of the position command value X, the velocity command value n, and the-maximum acceleration CC.. ax in the high acceleration and deceleration range. and Fig. 8 illustrates those in the low acceleration and deceleration range. As shown in these figures. the gain Kp required to obtain the same acceleration for different velocities is different.

More specifically, the maximum slope of the velocity command value n, when the first-order time derivative X takes a step change, is 1/Kp as shown in Fig. 7B. This maximum slope 1/Kp must not exceed the slope of the maximum acceleration Qax. In other words, in order to limit the actual acceleration within the maximum acceleration (Xmax, the gain Kp must be set at a rather small value 1/T1 in the high acceleration and deceleration range as shown in Figs. 7A and 7B, but may be set at a rather large value 1/T2 in the low acceleration and deceleration range as shown in Fig. 8, where T1 > T2.

When the gain Kp were set at 1/T1 in the case of Fig. 8, the operation would be unduly delayed. An optimum gain can always be achieved by returning the gain Kp to its initial value every time one cycle of operation has been completed, because the actual position X and the position command value X become usually identical by the operation.

EMBODIMENT 4 Fig. 9 shows a fourth embodiment in accordance with the present invention. This embodiment is applied to the arrangement in which no information other than the velocity command value n is available because the position control portion 2 is divided into two separate portions, that is, a position control portion 2B comprising the adder 21 and the position adjuster 22, and a velocity control portion 23. The apparatus is substantially the same as that of Fig. 1 plus the mass estimation portion 4, the maximum acceleration computing portion 4A and an acceleration display portion 6.

The acceleration display portion 6 displays the maximum acceleration C6ax (or maximum angular acceleration) computed by the maximum acceleration computing portion 4A.

In this embodiment, it is not required to limit the acceleration command X" by the acceleration limiting portion as in the first embodiment shown in Fig. 2, to adjust the time constant of the filter 5a as in the second embodiment shown in Fig 3, or to control the gain Kp as in the third embodiment shown in Fig. 6.

Accordingly, adjustment of parameters such as an acceleration parameter of the position command -portion 1 is essential.

For this reason, the maximum acceleration CCma. is displayed so that the set value of each parameter is specified.

More specifically, a test operation is carried out so that the maximum acceleration (Xmaxf which is calculated by the acceleration computing portion 4A. is displayed on the acceleration display portion 6. The maximum acceleration c,ax displayed is used to set the acceleration parameter of the position control portion 1.

Thus, a single test operation allows to determine the value of the parameter, and hence trial-anderror testing is unnecessary. As a result. the adjusting operation is simplified and carried out quickly.

The present invention has been described in detail with respect to.various embodiments,, and it will now be apparent from the foregoing to those skilled in the art that changes and modifications may be made without departing from the invention in its broader aspects, and it is the intention, therefore, in the appended claims to cover all such changes and modifications as fall within the true spirit of the invention.

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Claims

CLAIMS: 1. A positioning system characterized by comprising: 5 position

command means for outputting a position command value for a controlled object; position detecting means for detecting the actual position of the controlled object, and for outputting an actual position value of the controlled object; position control means for controlling force exerted on the controlled object so that the actual position value of the controlled object agrees with the position command value; mass estimation means for estimating the mass of the controlled object; maximum acceleration computing means for computing maximum acceleration of the controlled object on the basis of the mass which is estimated by said mass estimation means, and maximum force which can be provided by said position control means; and acceleration limiting means for limiting the second-order time derivative of the position command value within the maximum acceleration obtained by said maximum acceleration computing means.
2. A positioning system characterized by comprising: position command means for outputting a first position command value for a controlled object; position detecting means for detecting the actual position of the controlled object, and for outputting an actual position value of the controlled object; position control means for controlling force exerted on the controlled object so that the actual position value of the controlled object agrees with the position command value; mass estimation means for estimating the mass of the controlled object; maximum acceleration computing means for computing maximum acceleration of the controlled object on the basis of the mass which is estimated by said mass estimation means, and maximum force which can be provided by said position control means; smoothing means for smoothing the first position command value with regard to time, and outputting a second position command value; and 25 acceleration control means for limiting the second- order time derivative of the second position command value within the maximum acceleration obtained by said maximum - acceleration computing means.
3. The positioning system as claimed in claim 2, characterized in that said acceleration control means controls a constant of said smoothing means in such a manner that the degree of smoothing is only emphasized.
4. The positioning system as claimed in claim 3, characterized in that the constant of said smoothing means is reset to its initial value only when the input and output of said smoothing means agrees with each other.
5. The positioning system as claimed in claim 3.

characterized in that said smoothing means is a low-pass filter, and the constant of said smoothing means is the time constant of the lowpass filter. 20
6. A positioning system characterized by comprising: position command means for outputting a position command value for a controlled object; 25 position detecting means for detecting the actu-al position of the controlled object. and for outputting an actual position value of the controlled object; position control means for controlling force exerted on the controlled object so that the actual position value of the controlled object agrees with the position command value, said position control means including a position adjuster for obtaining a velocity command value by multiplying the difference between the position command value and the actual position value by a gain Kp, and a velocity control means for controlling the controlled object so that its actual velocity value agrees with the velocity command value; mass estimation means for estimating the mass of the controlled object; maximum acceleration computing means for computing maximum acceleration of the controlled object on the basis of the mass which is estimated by said mass estimation means, and maximum force which can be provided by said position control means; and acceleration control means for limiting the first-order time derivative of the velocity command value outputted from said position adjuster within the maximum acceleration obtained by said maximum acceleration computing means.
7. The positioning system as claimed in claim 6, characterized in that said acceleration limiting means controls the gain Kp of said position adjuster in such a manner that the gain Kp is only reduced.
8. The positioning system as claimed in claim 7. characterized in that the gain Kp of said position adjuster is reset to its initial value only when the position command value and the actual position value agrees with each other.
9. A positioning system characterized by comprising: position command means for outputting a position command value for a controlled object; position detecting means for detecting the actual position of the controlled object, and for outputting an actual position value of the controlled object; position control means for controlling force exerted on the controlled object so that the actual position value of the controlled object agrees with the position command value, said position control means including a position adjuster for obtaining a velocity command value by multiplying the difference between the position command value and the actual position value by a gain Kp, and a velocity control means for controlling the controlled object so that its actual velocity value agrees with the velocity command value; mass estimation means for estimating the mass of the controlled object; 5 maximum acceleration computing means for computing maximum acceleration of the controlled object on the basis of the mass which is estimated by said mass estimation means, and maximum force which can be provided by said position control means; and display means for displaying the maximum acceleration, or an acceleration and deceleration time which is computed on the basis of the mass and the maximum force which said position control means can provide.
10. A positioning system including: position detecting means for detecting the actual position of an object; positioning means for moving the object to a required position; means for providing an indication of the mass of the object; and acceleration limiting means whichuses said indication to control the maximum acceleration of the object produced by the positioning means.
11. A positioning system substantially as hereinbefore described with reference to Figures 2-9 of the accompanying figures.