JPH1124706A - Feedback controller - Google Patents

Abstract

PROBLEM TO BE SOLVED: To eliminate stable stationary deviation with respect to disturbance and a command signal by providing a resonance controller with transmitting characteristic making a gain infinite or maximum and preventing a phase from delaying more than 0 deg. with respect to a frequency included in disturbance to input to a controlling object as a component. SOLUTION: A transmitting function device 22 is constituted by serially connecting a resonance controller 24 inputting the deviation between a command signal (r) and a controlled variable (y) and outputting the result of PI (proportional integration) arithmetic and PID(proportional integration/ differentiation) arithmetic in order to satisfactorily control transient disturbance and DC disturbance and a resonance controller 24 inputting the output of the controller 23 and outputting a manipulated valuable (u). The controller 24 is provided with transmitting characteristic preventing the phase from delaying more than 0 deg. and making the gain infinite or maximum in the frequency of the disturbance when sine or periodical disturbance exists. Consequently, it is difficult to generate the reduction of gain margin due to the reduction of a phase and the fluctuation of a stable limit frequency.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a system that requires suppression of disturbances including a specific frequency component, a system that requires tracking of a sine wave command, and a tracking capability of a repetitive waveform command. The present invention relates to a feedback control device used for a system.

[0002]

2. Description of the Related Art As a general feedback control device in system control, a PID (proportional-integral-derivative) control device is widely used. Control targets to which the feedback control device is applied include those that have a disturbance of a specific frequency, such as the mold level control of a steel continuous casting machine and compressor control, and those that are specified, such as the voltage control of an uninterruptible power supply. In some cases, a sine wave or a repetitive waveform having a frequency of? As an example of the control target by the feedback control device, for example, “Application of modern control theory to continuous casting mold level control: Instrumentation, Vol. 38, No. 11, 1995, P.
The molding liquid level control system of the steel continuous casting machine described in 1 to P4 "is shown below. FIG. 9 is a schematic diagram of the molding liquid level control system of the steel continuous casting machine. A slab (slab) 6 (not shown) is obtained by pouring the welding wire 3 from a welding wire tank called a tundish 2 into a mold (mold) 4 and pulling it out with a support roll 5 while continuously solidifying with the mold 4. To manufacture.

At this time, the liquid surface level 7 of the molten steel 3 in the mold 4 is detected by a level sensor 8 and controlled so that the amount of the molten steel 3 flowing into the mold 4 and the amount of the slab 6 pulled out of the mold 4 are balanced. The liquid level 7 is controlled by the device 9 so as to be kept constant. Specifically, the sliding nozzle 1 is moved by the actuator 10 in accordance with the liquid level 7 detected by the level sensor 8.
By operating the opening degree of 1, the amount of the molten steel 3 flowing into the mold 4 is adjusted. In this steel continuous casting machine 1, stabilization of the mold liquid level 7 is indispensable technology for safe operation and improvement of the quality of the slab to be manufactured. Conventionally, in general, a PI control device or a PID control device is generally used. Was controlled.

[0004] In the control system for the mold liquid level 7 of the continuous steel casting machine 1 described above, various disturbances occur depending on the operating conditions. For example, due to the bulging 12 (bulging of the slab 6 between the support rolls 5), the mold liquid level 7 is increased at a frequency proportional to the drawing speed of the slab 6.
Fluctuations occur. This drawing speed is usually constant, but if you set a high drawing speed for the purpose of improving productivity,
The frequency of the disturbance due to the bulging described above also increases.

In the conventional PI control and PID control, a steady-state deviation having a frequency component remains for a disturbance or a command signal including a specific frequency component, and when the frequency becomes higher than a control band, the disturbance is controlled. The effect on the target output cannot be reduced at all. In particular, for a disturbance having a frequency component near the limit of the control band, if the control gain is increased to suppress the disturbance, the stability of the control system becomes worse. There was a problem of getting up. For this reason, it is necessary to reduce the gain of the feedback control device,
As a result, the transient response also deteriorated. In order to reduce the influence of the disturbance, a method of estimating the disturbance using a disturbance observer and compensating the disturbance has been proposed. However, the method does not reduce the steady-state error but does not eliminate it, but has a similar problem.

[0006] In servo control and robot position control with repetitive operations, for example, “Measurement and control: Vol.
o.12, P.1111 to P1119 ", a repetitive control or the like has been proposed for the purpose of eliminating a steady-state deviation. However, in the repetitive control, a controlled object has an integral characteristic like a steel continuous casting machine. In such a case, it is necessary to ensure stability by using a filter that is effective only in the low frequency region, and since such a filter is also complicated in design, the frequency component near the limit of the control band is also required. It was difficult to suppress a disturbance having

In order to solve the above problems, a sine wave transfer function in which the gain is infinite or maximal with respect to a frequency component included in a command or disturbance to a controlled object is introduced into a control device. Is disclosed in JP-A-07-02
No. 0906 proposes a feedback control device capable of reducing the steady-state deviation to zero with respect to a command or disturbance to a control target. FIG. 10 is a configuration diagram of a feedback control device described in Japanese Patent Application Laid-Open No. 07-020906. As shown in FIG.
Reference numeral 3 denotes a series load of a resistance R and an inductance L, which controls a deviation between a sine wave current command value 14 and an output current 15 by the control device 1.
6 to control the output current 15. Here, the control device 16 includes a sine wave transfer function unit 17, an integral transfer function unit 18, and a proportional transfer function unit 19, and these are connected in parallel and used. In addition, a sine wave current command value 1
4 is detected by the frequency detection unit 20, and the sine wave transfer function 17a in the sine wave transfer function unit 17 is
By setting the gain to infinity or maximum at that frequency, the steady-state deviation of the component can be made zero.

[0008]

By the way, at a frequency when the phase delay of the closed loop transfer function is 180 degrees,
When the gain is smaller than 0 (dB), the closed loop transfer function becomes stable. In general, the open loop transfer function has a gain greater than 0 (dB) at low frequencies and 0 (d
B) Designed to be smaller. The frequency at which the gain of the open loop transfer function is 0 (dB) is called a crossover frequency, and the crossover frequency means a control band. The phase margin at this crossover frequency (when the gain is 0 (dB),
The closed loop transfer function is stable if the margin is 180 degrees, which is the stability limit, which indicates how much margin there is. However, the sine wave transfer function 17a in the sine wave transfer function unit 17 of the above-described conventional example has a phase displacement from 90 degrees when the gain becomes infinity or local maximum at the frequency included in the sine wave current command value 14. 90
It changes every time. That is, by connecting the sine wave transfer function 17a, the phase is further delayed.
Beyond 80 degrees, the phase margin becomes negative, and the closed-loop transfer function may become unstable. In addition, three transfer function units 17, 18, and 19 are connected in parallel, and it is difficult to set the gain of each transfer function unit 17, 18, and 19, and the closed-loop transfer function becomes similarly unstable depending on conditions. Met.

SUMMARY OF THE INVENTION The present invention has been made to solve the above-described problems, and it is intended to stably eliminate a steady-state error with respect to a disturbance or a command signal including a frequency component such as a sine wave. It is an object of the present invention to provide a highly-reliable feedback control device that can perform the feedback control.

[0010]

A feedback control device according to a first aspect of the present invention has means for generating a command signal for a controlled object, and transmits the command signal and the output of the controlled object to a transfer function unit. An input device for controlling the controlled object by an output signal from the transfer function device, wherein a gain becomes infinite or maximal with respect to a frequency included as a component by a disturbance input to the controlled object, and furthermore, the phase is changed. The above-mentioned transfer function unit includes a resonance control device having a transfer characteristic not delayed by more than 0 degrees.

According to a second aspect of the present invention, there is provided a feedback control device having means for generating a command signal for a controlled object, inputting the command signal and the output of the controlled object to a transfer function unit, A control device for controlling the controlled object by an output signal from a device, wherein the gain has an infinity or a maximum with respect to a frequency included as a component of the command signal, and further has a transfer characteristic in which a phase is not delayed from 0 degree. A control device is included in the transfer function unit.

A feedback control device according to a third aspect of the present invention includes the transfer characteristic of the resonance control device as a product element in a transfer function unit.

According to a fourth aspect of the present invention, in the feedback control device, the resonance control device has a transfer characteristic represented by the following equation.

(Equation 3)

In a feedback control device according to a fifth aspect of the present invention, the resonance control device has a transfer characteristic represented by the following equation.

(Equation 4)

[0015]

BEST MODE FOR CARRYING OUT THE INVENTION

Embodiment 1 FIG. FIG. 1 shows a configuration diagram of a feedback control device according to Embodiment 1 of the present invention. Reference numeral 21 denotes an object to be controlled when the mold liquid level of the steel continuous casting machine is controlled. Reference numeral 22 denotes a transfer function unit that constitutes a feedback control device. The transfer function device 22 performs calculations such as PI (proportional integral) and PID (proportional integral derivative), and a resonance control device 24.
It consists of. Reference numeral 25 denotes a frequency detection unit that detects a frequency included in the disturbance, and detects a frequency included in the disturbance based on, for example, a slab pull-out speed. 26 is a command signal generator.

Next, the operation will be described. Although the case of performing the mold liquid level control of the steel continuous casting machine will be described,
This control system is the same as that shown in FIG. 9 of the related art. First, the control target 21 inputs a command for the opening degree of the sliding nozzle 11 as an operation amount u, and detects the mold liquid level 7 as a control amount y. When the dynamic characteristic of the actuator 10 is approximated by a first-order lag, the transfer function P (s) of the control target 21 is expressed by the product of the dead time characteristic, the integral characteristic, and the first-order lag as shown in Expression 3 below.

[0017]

(Equation 5)

In Equation 3, T _d is a dead time, A is an integration time constant, and ω _a is a response frequency of the actuator. The transfer function unit 22 inputs the command signal r and the control amount y, and outputs an operation amount u, thereby controlling the control amount y to match the command signal r. Further, the transfer function unit 22 receives the deviation between the command signal r and the control amount y, and performs PI (proportional integral) calculation or PID to perform favorable control on transient disturbance and DC disturbance.
(Proportional-integral-differential) A control device 23 that outputs a result of calculation or the like and a resonance control device 24 that receives an output of the control device 23 and outputs an operation amount u are connected in series.
Here, the resonance control device 24 functions to reduce the deviation between the command signal r and the control amount y with respect to disturbance of a specific frequency, and has a resonance transfer function Cr (s) shown in the following Expression 4.

[0019]

(Equation 6)

In Equation 4, ω _r is the resonance frequency,
Match the detected disturbance frequency. At this frequency ω _r , the transfer characteristic of Expression 4 is controlled such that the gain becomes infinite and the steady-state deviation between the command signal r and the control amount y becomes zero.

Next, the control principle of the first embodiment will be described. First, the principle of the control device 23 will be described. That it will be described a case where the control unit 23 and the resonance control apparatus 24 has a zero gain K _r in the transfer characteristic of the resonance control apparatus 24 in the transfer function unit 22 connected in series Formula 4. The control device 23 may be the same as a conventional general control device, and performs a PI operation and a PID operation, and performs control so as to respond favorably to a transient disturbance or a DC disturbance. Transfer function P (s) of control target 21, control device 23
The open-loop transfer function Pm as the transfer function Cm (s)
FIG. 2 shows a Bode diagram of (s) · Cm (s). As shown in FIG. 2, the gain of the open-loop transfer function P (s) · Cm (s) is larger than 0 (dB) at a low frequency and 0 at a high frequency.
It is designed to be smaller than (dB). The frequency at which the gain of the open loop transfer function is 0 (dB) is referred to as the crossover frequency ω _c , and the frequency at which the phase is −180 degrees is referred to as the stable limit frequency ω ₁ . Here, the crossover frequency ω _c means a control band.

[0022] Since the phase margin at the crossover frequency omega _c is positive, it can be said that the closed loop transfer function is stable.
Further, it the gain margin is also positive in the stable limit frequency omega _1, the value is set to 20log ₁₀ (M). Here, the phase margin is close to unstable closed-loop transfer function when close to 0 degrees, the controlled variable y at the frequency component close to the crossover frequency omega _c
The fluctuation of is greatly excited, if the detected disturbance frequency omega _d is close to the crossover frequency omega _c is the phase margin, for example, 90
It is necessary to secure a large value close to the degree.

Next, the principle of the resonance control device 24 having the resonance transfer characteristic represented by the equation (4) will be described. FIG. 3 is a Bode diagram of the transfer characteristic of the resonance control device 24. The transfer characteristic gain becomes infinite at the frequency ω _r. Also, the phase is delayed by 180 degrees before and after the frequency ω _r , but the first term on the right side of Equation 4 is a constant, so the phase is 0 degree, and the phase of the second term on the right side of Equation 4 is from +180 degrees to 0 degrees. Varies with range. Therefore, the entire expression 4, that is, the phase of the resonance control device 24 changes in the range from +180 degrees to 0 degrees, and does not lag behind 0 degrees. Also, in FIG.
The value of the gain G, which has become stable over the frequency ω _r is 20l
og ₁₀ (1 + K _r ).

FIG. 4 shows the open loop transfer function P (s) .Cr (s) .Cm when the resonance controller 24 is properly adjusted.
FIG. 4B is a Bode diagram of FIG. 2, in which the gain and the phase of FIGS. 2 and 3 are respectively added on a graph. Here, the open-loop transfer function P (s) ·
Cm (s) is adjusted so that stability is maintained as shown in FIG. It is also assumed that the phase of the open loop transfer function at the disturbance frequency ω _d is adjusted so as to be larger than −180 degrees. Further resonant frequency omega _r of the resonance control apparatus 24 to match the disturbance frequency omega _d.

At this time, at the stability limit frequency ω ₁ ,
If the gain is smaller than 0 (dB), that is, if the gain margin in FIG. 4 is positive, the closed loop transfer characteristic is always stable. That is, from FIG. 2 and FIG. 3, M− (1 + K _r )>
0, adjusting the gain K _r of the resonance control apparatus 24 (M-
1) If smaller, it is stable. Here, M is an open-loop transfer function P (s) · Cm ignoring the resonance control device 24.
Is a value indicating the gain margin in the stable limit frequency omega ₁ of the (s). Therefore, the adjustment gain K of the resonance control device 24
By increasing _r little by little from 0 to less than (M-1), a stable and easily controllable system with zero steady-state deviation against disturbances including frequency can be easily obtained.

In general, in order to make the steady-state deviation zero with respect to a sine wave disturbance having a specific frequency ω _d , the closed loop transfer function composed of the transfer function unit 22 and the control target 21 is stable and the transfer function unit the gain of the transfer function of 22 and there is a need to be infinite by the disturbance frequency ω _d. Here, in the control device in which the transfer function unit 22 has the pole of ± j · ω _d , the gain becomes infinite at the frequency ω _d , but the gain becomes 180 around the frequency ω _d .
In order to delay the phase, the closed loop is likely to be unstable if configured simply. In this embodiment, the resonance control device 2
The transfer characteristic of No. 4 has a pole of ± j · ω _d and is configured so that the phase is not delayed from 0 ° regardless of the adjustment. As described above, since the transfer characteristic of the resonance control device 24 does not delay the phase, even if the resonance control device 24 is connected in the transfer function unit 22, the gain margin due to the decrease in the phase margin and the fluctuation of the stable limit frequency is reduced. It is hard to cause decrease. Therefore, it is difficult to cause instability of the closed-loop transfer function,
Be zero steady-state error becomes possible to stably against disturbance including a frequency omega _d by a simple adjustment.

Further, since the control device 23 and the resonance control device 24 are configured in series and the transfer characteristic of the resonance control device 24 is included in the transfer function device 22 as a product element, the phase characteristic of the transfer function device 22 is controlled by the control device. There is no phase delay from 23,
It is hard to cause instability, and adjustment is easy.

The effects of the first embodiment of the present invention will be described using simulation. FIG. 5 shows a document (“ROBU
ST MOLTEN STEEL LEVEL CON
TROL FOR CONTINUOUSCASTIN
G ", Kazuya Asano et al., Proceedings of the 35th Con
ference Decision and Control, p. 1245-P. 1
250) A command for a 2 rad / sec sine wave disturbance when the control target has a dead time of 0.3 sec when the control target and the constant of the control device in the mold liquid level control of the continuous steel casting machine described in 250) are used as they are. The response of the deviation between the signal and the mold liquid level is shown. FIG. 5A shows a case where the PI control is performed, and FIG. 5B shows a case where a disturbance observer is added to the PI control described in the literature.
(C) shows a resonance control device 2 according to the first embodiment of the present invention.
4 is used. In the conventional PI control, the influence of disturbance remains steadily, and in the system in which the disturbance observer is added to the conventional PI control, the stability is deteriorated. As a result, the amplitude of the deviation is excited to be larger. It can be seen that the steady-state error becomes zero stably in the method according to mode 1.

In Equation 4, the first example on the right side is a typical example.
Although the term is 1, other constants may be used and Equation 1 is generally used. When the resonance control device 24 is connected in series with another control device 23, K ₀ ≠ 0.

Embodiment 2 FIG. In the first embodiment, Equation 1 is used as the transfer characteristic of the resonance control device 24 so that the steady-state error becomes zero with respect to a disturbance of a constant frequency. However, the oscillation of the output of the transfer function the purpose of increasing the attenuation, and the transfer characteristic of the resonance control apparatus 24 in equation 2 below to have a damping zeta, they can be configured to have a maximum value not infinity at the resonant frequency omega _r, is the steady-state deviation It is not completely zero, but has the effect of minimizing it.

[0031]

(Equation 7)

In the first and second embodiments, the adjustment of the control device 23 has been described as fixed. However, in order to further ensure the stability of the closed loop transfer function, the adjustment gain K _r of the resonance control device 24 is adjusted. It is easily conceivable to make an adjustment such that the gain of the control device 23 is reduced as the value is increased.

Further, although the disturbance frequency omega _d has been described near the crossover frequency omega _c, because it can adjust in exactly the same manner even when disturbance frequency omega _d is considerably smaller than the crossover frequency omega _c, targeting a wide frequency range It is possible to reduce the deviation of a specific frequency component from disturbance.

Embodiment 3 Next, a third embodiment will be described. FIG. 6 is a configuration diagram of a feedback control device in which the present invention is applied to a position control device for an electric motor used for a machine tool or the like. Reference numeral 27 denotes a control object including a mechanical system, an electric motor, and a speed control device for the electric motor. Reference numeral 28 denotes a transfer function unit constituting the feedback control device of the present invention used as a motor position control device. Reference numeral 29 denotes a control device for performing P (proportional) calculation, and reference numeral 30 denotes a resonance control device. The transfer function device 28 is configured by connecting the control device 29 and the resonance control device 30 in series. Reference numeral 31 denotes a frequency detection unit, and reference numeral 32 denotes a command signal generation device that generates a sine wave or a periodic command signal.

Next, the operation will be described. Command signal generator 3
2 generates a sine wave or a periodic command signal, and the transfer function unit 28 controls the motor rotation angle y as a control amount and the command signal r.
Is input, and an appropriate operation is performed to output a speed command signal u as an operation amount. The control device 29 inputs the deviation between the motor rotation angle y and the command signal r and outputs the result of performing the P calculation. The resonance control device 30 receives the output of the control device 29,
Outputs the speed command signal u. The control target 7 receives the speed command signal u, and controls the motor speed to follow the speed command signal u, thereby controlling the rotation angle y of the motor.

Here, the resonance control device 30 applies the command signal r and the motor rotation angle y to the frequency component contained in the command signal r.
And has a resonance transfer characteristic Cr (s) shown in the following equation 1.

[0037]

(Equation 8)

The frequency detector 31 detects a frequency omega _d contained in the command signal r, the resonance frequency of the resonance control apparatus 30 omega _r
The by matching to the omega _d, the steady-state deviation between the command signal r and the motor rotation angle y with respect to the frequency components omega _d containing the command signal is controlled to be zero.

Also in this embodiment, since the transmission characteristic of the resonance control device 30 is configured so that the phase is not delayed by more than 0 degrees, the instability of the closed-loop transfer function is hardly caused, and the command is executed by simple adjustment. The steady-state deviation in the frequency component included in the signal can be easily reduced to zero.

Next, the effect of the third embodiment of the present invention will be described using simulation. FIG. 7 shows a simulation for a position command signal of a triangular wave when the electric motor position control device as the feedback control device of the present invention is used. From the figure, it can be seen that the steady-state error is large in the conventional control device, but is small in the feedback control device of the present invention. FIG. 8 shows a simulation result with respect to a circular trajectory command signal when the electric motor position control device as the feedback control device of the present invention is used for an XY table having friction. From the figure, it can be seen that in the method of the present invention, the command signal almost coincides with the command signal shown by the dotted line, and the steady-state error is almost eliminated.

In this case as well, the transfer characteristic expressed by the equation (3) shown in the second embodiment is similarly changed.
Can be applied to

[0042]

According to the feedback control device of the present invention, when a sine wave or periodic disturbance is present, the gain becomes infinite or maximum without delaying the phase from 0 degree at the frequency of the disturbance. Since a resonance control device having the following transfer characteristics is included, a steady deviation can be easily reduced to zero or very small, and control with excellent stability can be performed.

Further, in the feedback control device according to the present invention, when a sinusoidal or periodic command signal is used, at the frequency of the command signal, the gain is infinite or maximal without delaying the phase from 0 degree. Since a resonance control device having the following transfer characteristics is included, the steady deviation can be easily reduced to zero or minimized, and control with excellent stability can be performed.

Further, according to the present invention, by including the transfer characteristic of the resonance control device as a product element in the transfer function unit, stable adjustment can be more easily performed.

According to the present invention, since the transfer characteristic of the resonance control device is expressed by the equation (1), the steady-state deviation can be easily reduced to zero with respect to a command signal including a frequency component or a disturbance, and feedback having excellent stability can be obtained. A control device is obtained.

According to the present invention, since the transfer characteristic of the resonance control device is expressed by the equation (2), the steady-state deviation can be easily minimized with respect to a command signal including a frequency component or a disturbance, and feedback excellent in stability can be obtained. A control device is obtained.

[Brief description of the drawings]

FIG. 1 is a block diagram illustrating a configuration of a feedback control device used in Embodiment 1 of the present invention.

FIG. 2 is a Bode diagram of a loop transfer function when only the control device according to the first embodiment of the present invention is used.

FIG. 3 is a Bode diagram of the resonance control device according to the first embodiment of the present invention.

FIG. 4 is a Bode diagram of a loop transfer function according to the first embodiment of the present invention.

FIG. 5 is a time response simulation diagram showing the effect of the first embodiment of the present invention.

FIG. 6 is a block diagram illustrating a feedback control device used as a motor position control device in Embodiment 3 of the present invention.

FIG. 7 is a time response simulation diagram for a triangular wave position command showing the effect of the third embodiment of the present invention.

FIG. 8 is a time response simulation diagram of an XY table showing the effect of the second embodiment of the present invention.

FIG. 9 is a diagram of a mold liquid level control system of a steel continuous caster to be controlled in the conventional example and the first embodiment of the present invention.

FIG. 10 is a block diagram illustrating a configuration of a feedback control device according to a conventional example.

[Explanation of symbols]

Reference Signs List 21 controlled object, 22 transfer function device, 24 resonance control device, 27 controlled object, 28 transfer function device, 30 resonance control device.

Claims (5)

[Claims] A means for generating a command signal for a control target; inputting the command signal and the output of the control target to a transfer function unit; and controlling the control target with an output signal from the transfer function unit In the feedback control device that
The transfer function unit includes a resonance control device having a transfer characteristic in which the gain becomes infinite or maximal with respect to a frequency included as a component of the disturbance input to the controlled object and the phase does not lag behind 0 degree. Feedback control device. And means for generating a command signal for the controlled object, inputting the command signal and the output of the controlled object to a transfer function unit, and controlling the controlled object by an output signal from the transfer function unit. In the feedback control device that
A feedback control device including, in the transfer function unit, a resonance control device having a transfer characteristic in which a gain becomes infinite or a maximum with respect to a frequency included as a component of the command signal and the phase does not lag behind 0 degree. . 3. The feedback control device according to claim 1, wherein the transfer characteristic of the resonance control device is included as a product element in the transfer function unit. 4. The feedback control device according to claim 1, wherein the resonance control device has a transfer characteristic represented by the following equation. (Equation 1) 5. The feedback control device according to claim 1, wherein the resonance control device has a transfer characteristic represented by the following equation. (Equation 2)