JPH0721735B2 - Non-linear servo control method - Google Patents

Description

The present invention relates to a non-linear servo control method, and more particularly to a non-linear servo control method suitable for position control of industrial machines such as industrial robots and NC machine tools. .

[Prior Art] Conventionally, PID, that is, a method using a combination of proportional, integral, and derivative has been used for servo control. This is generally called a linear servo control method. This method has the following problems.

FIG. 3 shows a block diagram of a conventional servo system based on the linear servo control method. In the figure, s is a Laplace operator, Xi (i =
1 to 9) are control variables, especially X1 is a commanded position, X4 is a commanded speed, X7 is a commanded acceleration, X8 is a current speed, X9 is a current position, K
1 and K2 are proportional gains.

In this servo system, the transfer function G (s) from X1 to X9 is Is asked. If K1K2 >> 1, that is, focusing on the low frequency region, the time constant of this response may be considered to be substantially equal to 1 / K1. This is equivalent to considering the transfer function from X4 to X8 as 1, which is shown in FIG. If saturation is ignored, this transfer function G2 (s)
Is And the time constant is 1 / K1.

[Problems to be solved by the invention]

By the way, in the servo control system shown in FIG. 4, considering the gains from X2 to X4, it should be K1 if there is no saturation, but as shown in FIG. On the other hand, the output becomes X4 <K1X2, which is the same as the decrease in gain. That is, the time constant becomes large and the time required for positioning increases. This is K1
Even if you try to increase the value and decrease the time constant, there is no effect unless the saturation value changes. Also, K1 cannot be increased infinitely, and it cannot exceed the limit value that is uniquely determined by the inertia of the servo system and motor power.

FIG. 6 shows the response at the speed X4 when a step input of 1 / s is applied to the first-order delay system shown in FIG. It can be seen that the time constant apparently increases when there is saturation.

It is difficult to analyze and adjust because it becomes nonlinear in the saturated region.

Next, in the conventional servo system based on the above-mentioned servo control method, how to adjust each element of proportional, integral, and derivative to reduce the overshoot amount called overshoot or undershoot, or to shorten the positioning time is a general question. It's hard to decide, and you have to rely on a skilled engineer.
In other words, it is difficult to harmonize the gains of proportional, integral, and derivative, and sophisticated adjustment is required.

Furthermore, in the conventional servo system, it is difficult to make the acceleration during acceleration equal to that during deceleration, and even if either one can be adjusted to the maximum acceleration determined by the mechanical system strength, the other will be raised to the limit. Therefore, there is also a problem that the average moving speed is lowered.

Therefore, an object of the present invention is to provide a non-linear servo control method capable of shortening the time required for positioning, facilitating adjustment of a servo system, and making accelerations during acceleration and deceleration substantially the same. Is to provide.

An apparatus for generating a speed control pattern is, for example, Japanese Patent Application No.
The one described in JP-A-14788 (JP-A-63-182715) has been proposed. In this proposal, a standard pattern of acceleration / deceleration is stored in advance in the storage means, and the position command signal X ^* and the current position signal Xi are subtracted at the time of start-up to obtain the position deviation ΔX and the reciprocal of the position deviation. By the square root of
The speed at which the standard pattern of acceleration / deceleration is read is determined. Also, the peak value of the standard pattern of acceleration / deceleration is determined. However, this is performed after the acceleration / deceleration operation is determined in advance based on the stored standard pattern when the start signal is given, and the position command signal changes continuously from moment to moment. In the case of the trajectory operation, it was not possible to generate a correct speed pattern for acceleration / deceleration.

[Means for Solving the Problems]

According to the present invention, the above object is to preset the maximum speed,
The maximum acceleration is set to match the maximum acceleration peculiar to the servo system, and at the time of acceleration, the acceleration is limited to the peculiar maximum acceleration by the acceleration limit of the servo system, and the positioning time is set in advance. The distance required for positioning using the set maximum acceleration is given by the following formula: l = αmax T ^{2 where} l: Distance required for positioning αmax: Set maximum acceleration (maximum acceleration specific to servo system) T: Determined by the set positioning time, ε = Y2 −l where ε: Deviation Y2: Difference between command position and current position l: Find deviation ε from the distance required for positioning, and use the following formula when decelerating However, Y3: Command speed αmax: Set maximum acceleration (maximum acceleration peculiar to the servo system) ε: Deceleration is controlled by the deviation, and this is achieved by setting the position to start deceleration by a distance l before this point. It

[Action]

In the present invention configured as described above, the square root of the deviation ε related to the difference between the commanded position and the current position is calculated and used as the commanded speed. Since the restriction is substantially removed and the servo system is operated at its own maximum speed and maximum acceleration, which are the limits of operation, high-speed positioning without overshoot or undershoot is possible. Further, since at least two elements of the maximum speed and the maximum acceleration need only be set in advance, anyone can optimize the servo system. Furthermore, by matching the set maximum acceleration with the maximum acceleration specific to the servo system, both acceleration and deceleration
It is controlled to the same acceleration.

〔Example〕

An embodiment of the present invention will be described below with reference to FIGS. 1 and 2.

FIG. 1 is a block diagram of a servo system that implements the nonlinear servo control method of the present invention. In the figure, reference numeral 1 is an element that generates a command speed Y3 from a command position Y1 and a current position Y5. It is shown in a flow chart. This element can be configured by a microcomputer, and its algorithm is stored in the ROM in advance. Command speed Y
3 is input to a mechanical system 2 including an amplifier and a motor, and this mechanical system 2 is represented as a temporary delay system. The actual speed Y4 of the mechanical system 2 is integrated by the element 3 and fed back to the element 1 as the current position Y5.

The maximum velocity vmax, the maximum acceleration αmax, and the positioning time are preset in this element 1. At this time, the maximum speed
The vmax and the maximum acceleration αmax are set to match the maximum speed and the maximum acceleration specific to the mechanical system 2, respectively.
Whether the positioning time T matches the time constant of the mechanical system 2,
Or it is set to any value larger than that.

Generally speaking, the algorithm of element 1 calculates a non-linear command speed Y3 from the deviation between the command position and the current position and the set maximum speed, maximum acceleration and positioning time, and calculates this command speed as a machine speed. It is input to the system 2 to perform positioning. The details will be described below with reference to the flowchart in the element 1 shown in FIG.

First, in step a, a deviation Y2 between the command position Y1 and the current position Y5 is obtained. Then, in steps b and c, it is checked whether or not the distance 1 required for positioning in the positioning time T remains. That is, in step b, the distance l required for positioning from the set maximum acceleration αmax and the set positioning time T is calculated by the following formula l = αmaxT ² (1), and then Y2 <l is determined in step c to determine the deviation Y2. Check if that distance l remains.

If it is determined in step c that there is a remaining amount, the process proceeds to step d, a deviation ε obtained by subtracting the distance 1 required for the positioning from the deviation Y2 is calculated, and it is determined in steps e and f whether or not the deceleration range is constant acceleration. That is, the command speed Y3 previously obtained in step e and the set maximum acceleration αmax
From the above, the deceleration distance l ′ with a constant acceleration is calculated by the following formula l ′ = (Y3 ² / αmax) / 2 (2), and ε <l ′ is determined in step f. From the command speed Y3 to the command speed 0, the time t to decelerate at the maximum acceleration αmax is t = Y3 / αmax, and the advance distance l ′ is 1 ′ = Y3t / 2, and the deceleration distance with constant acceleration is Equation (2) is obtained.

In step f, the distance to the command position is sufficiently long,
If it is determined that the acceleration is not within the deceleration range 1 ', the process moves to step g, and the set maximum speed vmax is set to the command speed.
Output as Y3. As a result, during acceleration, the actual velocity Y4 increases at a constant acceleration while being limited to its own maximum acceleration due to the acceleration limitation of the mechanical system 2. After reaching the maximum speed specific to the mechanical system 2, the actual speed Y4 moves at the maximum speed.

If it is determined in step f that the vehicle is in the deceleration region 1'where the acceleration is constant, the process proceeds to step h, and the velocity Y3 where the deceleration is constant is calculated from the set maximum acceleration αmax and the deviation ε by the following equation. Is calculated and the speed is output as the command speed Y3.
As a result, the actual speed Y4 decreases at a constant acceleration of the set maximum acceleration αmax.

If it is determined in step c that the distance l required for positioning does not remain, the process proceeds to step i and the deviation Y3
Using the setting positioning time T and the final positioning speed, the speed at the final positioning is calculated by the following formula Y3 = Y2 / T (4) to perform normal linear control. As a result, when the deviation ε reaches the distance l obtained by the above equation (1), the normal linear control is smoothly performed.

In the above embodiment, however, in step h, the square root of the deviation ε related to the difference between the commanded position and the current position is calculated and used as the commanded speed. However, the restriction of saturation in the conventional servo system is substantially removed, and the mechanical system 2
High-speed positioning that is determined by the gain K1 of is possible, and the movement time can be shortened. Also the maximum speed vm
Since it is only necessary to preset the three elements of ax, maximum acceleration αmax, and positioning time T, it is possible to easily adjust the servo system. Furthermore, since the maximum acceleration αmax can be controlled to be the same during acceleration and deceleration, the moving time can be shortened compared to the conventional case also in this respect.

Further, according to this embodiment, the deceleration start position is determined by the determination in step c from the deceleration distance l'calculated in step e by a distance l = αmaxT ² further, so that the conventional linear control is performed. Overshooting, undershooting, etc. can be prevented, and since the time constant for the final positioning is given in a one-to-one correspondence with the actual movement in step i, the control becomes smooth. It is easy to adjust the servo system in terms of points as well.

FIG. 2 shows a computer simulation result of the nonlinear servo control method according to the above embodiment. From this figure, it can be seen that even if the positioning time T is changed, good speed characteristics without overshoot can be obtained.

In the above embodiment, the actual speed Y4 increases at a constant acceleration due to the acceleration limitation of the mechanical system 2 even if the maximum speed vmax is output in step g. However, in the case of a servo system where this assumption does not hold, After step g, α = Y3−v is further calculated, and then α> αmax is determined,
If α> αmax, the command speed is calculated by v = v + αmax,
If α> αmax is not satisfied, a first-order lag element may be added from the input Y3 to the output v, which consists of the step of setting v = Y3 and using Y3 as the command speed as it is.

Further, in the above embodiment, in steps b and c,
It was judged whether or not the distance l required for positioning was left with the positioning time T and the acceleration αmax. If this is not done, the deviation ε may be replaced by the deviation Y2 in steps f and h, and in this case as well, saturation in the servo system may occur. It is possible to obtain the effects of shortening the movement time by removing the restriction of 1), facilitating the adjustment of the servo system, and making the maximum accelerations during acceleration and deceleration the same.

〔The invention's effect〕

As is apparent from the above, according to the nonlinear servo control method of the present invention, the time required for positioning can be shortened, the servo system can be easily adjusted, and the accelerations during acceleration and deceleration are substantially the same. Therefore, effective servo control that compensates for the drawbacks of the linear servo control can be performed.

[Brief description of drawings]

FIG. 1 is a block diagram showing a non-linear servo control method according to a position embodiment of the present invention, and is a diagram showing a result of a computer-side simulation of the non-linear servo control method of FIG. 2, and FIG. FIG. 4 is a block diagram showing a conventional linear servo control method, FIG. 4 is a block diagram showing a conventional linear servo control method focusing on low frequencies, and FIG. 5 is a conventional linear servo control method shown in FIG. 6 is a diagram showing a decrease in gain due to saturation with respect to a speed signal in FIG. 6, and FIG. 6 is a diagram showing a difference in step response between when there is saturation and when there is no saturation in servo control. Explanation of symbols 1 …… Element, 2 …… Mechanical system (servo system) Y1 …… command position, Y2 …… deviation Y3 …… command speed, Y5 …… current position vmax …… set maximum speed, αmax …… set maximum acceleration

Claims (2)

[Claims] 1. A maximum speed is set in advance, the maximum acceleration is set to match the maximum acceleration peculiar to the servo system, and during acceleration, the acceleration is limited to the peculiar maximum acceleration by the acceleration limit of the servo system, and the positioning time is set. Set in advance,
The distance required for positioning using this set positioning time and the set maximum acceleration above is given by the following formula: l = αmax T ^{2 where} l: Distance required for positioning αmax: Set maximum acceleration (maximum acceleration specific to servo system) T: Set positioning time Ε = Y2−l where ε: Deviation Y2: Difference between command position and current position l: Deviation ε is calculated from the distance required for positioning. However, Y3: Command speed αmax: Set maximum acceleration (maximum acceleration unique to the servo system) ε: Deceleration is controlled by deviation, and the position to start deceleration is further moved by distance l from this side. Non-linear servo control method. 2. A command speed at the final positioning using the deviation Y2 between the command position and the current position and the set positioning time T.
Y3 is determined by the following equation Y3 = Y2 / T, and when the deceleration ε reaches the distance determined by the above equation l = αmaxT ² , the normal linear control is performed at the time of deceleration. The nonlinear servo control method according to claim 1.