JP2522658B2 - Automatic control method - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION [Industrial field of application] The present invention can be used in a wide range of fields of servo and process system closed loop automatic control devices that feed back a control amount detection value to control so as to match the target value. ,
In particular, it is useful for positioning servo devices such as machine tools and robots that place importance on the dynamic characteristics of target value tracking.

[Conventional technology]

A method is known in which a non-linear element is used in the feedback compensation loop of an automatic control system to obtain a finite settling response that matches the controlled variable with a target value within a predetermined time.
81-8 of the journal of the Society of Instrument and Control Engineers Vol.21.No.6 published in June 60
It is described in the document "Learning design method for positioning servo system" (Nakano, Imai) published on page 5.

FIG. 2 is a block diagram of an example of such a servo system, in which 1 is an input terminal of a target value γ, 2 and 3 are subtractors, 4 is a first-order lag element, 5 is an integral element, and 6 is non-linear compensation. Element 7 is an output terminal for the controlled variable X ₁ .

The first-order lag element 4 and the integral element 5 represent a system to be controlled. Here, an example of a second-order system is shown, but it is possible to deal with a higher-order system. is there.

Compensation element 6 is + when the input is positive, negative, and zero respectively.
Although a bang-bang element that produces an output of h, -h, or zero is shown, a saturation characteristic element or a comparator having hysteresis may be used in addition to this.

FIG. 3 is a response waveform diagram of the apparatus shown in FIG.
When a unit step such as is input as the target value γ at time 0, the control amount X ₁ is an overshoot of θ ₁ at time tm as shown in FIG.
After that, it is assumed that there is an overshoot of θ ₂ , θ ₃ ... θ _n (undershoot when the polarity is negative).

When the characteristic roots of the control target (γ _{0 +} j) ω ₀ is, tm and theta _1, is θ _{2 ......} θ _n is known to be expressed by the following equation.

When the compensating element 6 such that h = θ ₁ + θ ₂ + ………… + θ _n …… is added to the system having such characteristics, the control amount X ₁ becomes as shown in FIG.
As shown in, the finite settling response that matches the target value comes to appear at time tm.

This can be understood as follows.
If h = θ ₁ is selected for the purpose of preventing the _first overshoot θ ₁ when there is no compensation, the subtracter 3
By the action of, there is no compensation element 6 and the target value γ becomes the same response waveform as 1-θ ₁ , so the first overshoot is the original target value 1 from the overshoot by γ θ _1. The following formula is obtained by subtraction, which coincides with θ ₂ .

Similarly, the initial overshoot can be set to θ ₃ by setting h = θ ₁ + θ ₂ and a finite settling response with zero overshoot can be set by using h as an expression.

Even if the characteristic of the controlled object is unknown and h in the equation cannot be accurately determined in advance, it is possible to deal with the learning method of actually measuring the overshoot amount and sequentially correcting h.

The above contents are described in detail in the above-mentioned documents, so please refer to them.

[Problems to be solved by the invention]

In the device shown in FIG. 2, the height h of the compensating element is selected according to the formula so as to give a finite response when the target value γ is input in unit steps, but h is fixed. When the magnitude of the target value γ changes, the same response cannot be obtained and the vibration becomes again.

This is because the amounts of overshoot and undershoot θ ₁ , θ _2, ... θ _m shown in FIG. 3B depend on the magnitude of the target value γ, and FIG. 4 shows this state. Indicates. In the figure (a), the target value γ is changed from 1 to 1.5, and the figure (b)
Shows the response when the value becomes 0.5, and both show a vibration waveform and the settling time is significantly extended.

In view of such a point, the present invention aims to obtain a feedback-compensated closed-loop automatic control system by a non-linear element that can always obtain a finite settling response without depending on the value of the target value γ.

[Means for solving problems]

The main purpose of the present invention is that the non-linear compensation element 6 in the apparatus shown in FIG. 2 is a hysteresis element having the characteristics shown in FIG.

This hysteresis element operates as follows. First, when the input X ₂ increases from zero in the positive direction, the output X ₃ becomes kX ₂ with the proportionality coefficient k. When the input X ₂ reaches the maximum value X _A , outputs kX _A, and then decreases toward zero, the output X 2
₃ keeps a constant value kX _A, and when the input X ₂ becomes zero, the output X ₃
Also returns to zero.

If the maximum value of the input X ₂ is 0 <a X _B ≦ X _A becomes X _B is first
As indicated by the broken line in the figure, the output X ₃ holds kX _B in the interval where the input X ₂ returns to zero. Even if the input X ₂ is negative,
As shown in FIG. 1, the operation is symmetrical to the origin with respect to the case of positive polarity.

That is, when the absolute value of the input signal increases, an output proportional to the input signal is generated, and when the input signal absolute value decreases in the same polarity input area, the maximum output value in this area is held,
It is a hysteresis element whose output returns to zero when the input signal is zero.

The value of the proportionality coefficient k can be set to an appropriate value in advance by analysis or simulation.

[Action]

A comparison will be made between the case where the compensating element 6 of the device shown in FIG. 2 is a bang-bang element and the case where it is a hysteresis element having the characteristics shown in FIG. 1 according to the present invention.

FIG. 5 is a diagram showing the output of the compensating element, and FIG. 5 (a) shows the output of the bang-bang element when the unit step as shown in FIG. 3 (a) is input to the device as the target value γ,
When there is no compensation element 6, the control amount X ₁ initially causes an overshoot of θ _1, but by the action of the compensation element 6 and the subtractor 3, the target value γ input 1 is reduced by the amount shown in FIG. Overshoot is prevented and finite settling is performed.

FIG. 5B shows this output X ₃ when the compensating element 6 is a hysteresis element. The value in the initial response is lower than that of the bang-bang element, but by selecting the proportional coefficient k appropriately. The output in the latter period can be increased to compensate for this, and a finite settling response similar to the case of the bang-bang element can be obtained.

Next, considering the case where the target value γ is increased to 1.5 instead of 1, in the case of the conventional Bang-Bung element, the output X ₃ remains as shown in FIG. Despite the increase in the addition input in, the amount of compensation is insufficient because the subtraction input is constant, resulting in the overshoot shown in FIG.

However, if a hysteresis element having the characteristic shown in FIG. 1 is used for the compensation element 6, this output X ₃ also increases the input X _{2 in the} initial response due to the increase of the target value γ,
As shown in FIG. 5C, the target value γ can be increased more than when it is 1, and appropriate compensation can be performed so that the optimum response of the controlled variable X ₁ can be obtained.

When the target value γ decreases to 0.5, the hysteresis element output X ₃ decreases as shown in FIG.
After all, the optimum response of the controlled variable X ₁ can be obtained.

As described above, when the hysteresis element is used as the compensating element 6, the feedback compensation amount can be adjusted according to the change of the target value γ, and the finite settling response can be always obtained.

〔Example〕

FIG. 6 is a circuit diagram of an embodiment for realizing the hysteresis element having the characteristics shown in FIG. 1, 61 is an input terminal of X ₂ ,
62 and 63 are comparators, 64 and 65 are analog switches, 66 and 67 are diodes, 68 is a capacitor, 69 is an operational amplifier, 70 and 71 are resistors, and 72 is an output terminal of X ₃ .

Comparator 62 produces an output while input X ₂ is zero or positive, causing analog switch 64 to close. Comparator 63 produces an output while input X ₂ is zero or negative, closing analog switch 65.

The resistors 70 and 71 are for gain adjustment of the operational amplifier 69,
The input / output proportional coefficient k is defined. In the connection of FIG. 6, k>
Although only 1 can be obtained, if k ≦ 1, it can be easily dealt with by dividing the output of the operational amplifier 69 from the output terminal 72 and taking it out.

Next, the operation of this circuit will be described. Input terminal 61 input X ₂
As R increases from zero in the positive direction, comparator 62 closes analog switch 64 and capacitor 68 is charged to X ₂ through diode 66.

This voltage is amplified by the action of the operational amplifier 69 and the resistors 70, 71, causing kX ₂ at the output terminal 72. When the input X ₂ reaches the maximum value X _A and then decreases, the discharge is blocked by the capacitor 66, so the voltage X _A is held and the output X ₃
Also keeps kX _A.

When the input X ₂ decreases to zero, the comparator 63 also produces an output and closes the analog switch 65.
The voltage of is discharged to zero through the diode 67 and the output X ₃ becomes zero.

When the input X ₂ has a negative polarity, the same principle operation is performed, and the first
This is to realize the hysteresis characteristics shown in the figure.

〔The invention's effect〕

As described above in detail, in the automatic control method according to the present invention, the closed loop automatic control system is provided with the feedback compensation by the hysteresis element, so that the controlled variable can be always made a finite enactment response regardless of the target value. It is extremely useful for applications that emphasize dynamic characteristics.

Further, since the automatic control method according to the present invention is a kind of parallel compensation, the characteristic can be improved by adding a simple circuit as shown in FIG. 6 to the automatic control system.
It can be easily applied to existing equipment.

[Brief description of drawings]

FIG. 1 is a characteristic diagram of a hysteresis element used in the automatic control method according to the present invention, FIG. 2 is a block diagram of an example of a conventional automatic control device, and FIGS. 3 and 4 show the response of the device of FIG. FIG. 5 is a diagram showing the output of the compensation element, and FIG. 6 is a circuit diagram of an embodiment for realizing the hysteresis element having the characteristics shown in FIG. 1,61 …… Input terminal, 2,3 …… Subtractor, 4 …… First-order lag element, 5 …… Integration element, 6 …… Compensation element, 7,72 …… Output terminal, 62,63 …… Comparison Vessel, 64,65 ... Analog switch, 6
6,67 ... Diode, 68 ... Capacitor, 69 ... Operational amplifier, 70,71 ... Resistor.

Claims (1)

(57) [Claims] 1. In a closed-loop automatic control system that performs feedback compensation via a non-linear element, an output proportional to the input signal is generated when the absolute value of the input signal increases as the non-linear element, and the absolute value of the input signal in the same polarity input region is generated. An automatic control method characterized by using a hysteresis element that holds the maximum output value in this region when decreasing and the output returns to zero when the input signal is zero.