JP3084675B2 - State feedback control method - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

It is well known that in an industrial application drive system, a torque transmission mechanism includes an elastic element and a resonance system is formed in relation to a motor itself and a moment of inertia of a load. Often a problem.
Applying PI control, which is often used, to such a higher-order system to improve its responsiveness, for example, causes torsional vibration of the shaft. Further, there is an adverse effect that fluctuations in load torque and system parameters greatly affect the output.

[0002] The present invention relates to a control system in which state feedback control is applied to a higher-order system, for example, a torsional system to improve torsional vibration and transient characteristics in order to solve such a problem. The idea of the equivalent disturbance observer described in detail in Japanese Patent Application Laid-Open No. Hei 3-025505, filed on Jun. 22, 2001 by the present applicant, is based on the method of determining the state feedback gain. One of the measures is to select a feedback gain element such that an input disturbance is canceled by an equivalent disturbance observer.

[0003]

2. Description of the Related Art A high-order system, for example, an induction motor directly connected to an elastic shaft as shown in FIG. 2 and a load constitute a high-order system to constitute a torsional vibration system.

[0004] Reference numerals are, _T ^{m *;} torque command T _L; load torque T _S; axial torsional torque K _t; torque constant J _m; the inertia of the motor J _L; load inertia .omega.m; motor speed ω _L; loading rate K _S; modulus axis D _m; damping constant of the axis D _L;; damping constant D S of the electric motor is a damping constant of the load, the damping constant D _m of the induction motor, the load of the damping constant D _{Since L} and the damping constant of the axis are extremely small, they will be ignored in the following description.

FIG. 3 is a block diagram of the torsion system shown in FIG. A state equation such as equation (1) is obtained from the model of FIG.

(Equation 1)

The characteristic equation becomes as S (S ² + ω ₀ ² ) (2), and the resonance frequency ω ₀ is ω ₀ = {[K _s ｛(1 / J _m ) + (1 / J _L )}]. (3)

As described above, in the torsion system, resonance occurs at a resonance frequency ω ₀ determined by K _s , J _m , and J _L , as shown in equation (3). This vibration is particularly effective for increasing the response of the speed system.
As the I gain was increased, torsional vibration of the shaft occurred at the resonance frequency ω ₀ , which became a problem, and the PI gain had to be reduced.

[0008] In addition, the speed of the load from the load torque T _L ω _L
The transfer function up to becomes a higher-order system as in the following equation. _{ω L / T L = (-} b 3 S 3 + b 2 S 2 + b 1 S + b 0) / (S 4 + a 3 S 3 + a 2 S 2 + a 1 S + a 0) (4) where, a ₀ = K _I K _t K _s / (J _m J _L ) where K _I is an integration constant. _{a 1 = K P K t K} s / (J m J L) where K _P is a proportionality constant. a ₂ = ω ₀ ² a ₃ = 0 b ₀ = 0 b ₁ = K _s / (J _m J _L ) b ₂ = 0 b ₃ = 1 / J _L

[0009] Equation (4) speed omega _L of the load from sensitive to variations in the load torque T _L, also it can be seen that likely to be dependent on the parameter variation of the control system. When torsional vibration occurs, there is a danger that the shaft is cut off, the shaft shaft is damaged, and the like. Conventionally, active torsional vibration isolation control with high responsiveness has been impossible with PI control. Conventionally, the control response frequency is set lower than the resonance frequency ω ₀ (the PI gain is reduced and the response is slowed), and the control is performed so as not to cause a sudden change. Further, the resonance frequency ω ₀ is increased by increasing the elastic coefficient K _s of one axis. As described above, active torsional vibration control cannot be performed by the conventional PI control.

[0010]

In order to suppress the torsional vibration of the shaft and improve the control response of the speed of the load, all the poles of the system must have a desired stable pole arrangement. In addition, as described above, in order not to be influenced by the fluctuation of the load torque _TL or the parameter of the control system, it is necessary to actively compensate for these effects. As a method, the problem is considered in an example in which the state feedback control of modern control theory is applied to a torsional system. The state feedback control has been described in many documents and will not be described here.

FIG. 4 shows a state feedback control applied to the general formula (1) of the aforementioned torsion system model.
Here, the matrix F of the state feedback gain is represented as follows by the elements f ₁₁ , f ₁₂ , f ₁₃ and f ₂₁ , f ₂₂ , f ₂₃ .

(Equation 2)

Here, in the case of one input and one output, the state feedback gain is generally obtained by giving a desired pole (characteristic root). However, in the case of two inputs and two outputs or more, the matrix F has many elements. Therefore, it is impossible to easily find the desired pole, and a considerable amount of time must be passed through a trial and error stage. The present invention has been made to solve this problem.

[0013]

According to the equation (6), the disturbance compensation amount T _L ′, which is a state feedback compensation element, is given by T _L ′ = f ₁₁ T _s + f ₁₂ ω _L + f ₁₃ ω _m (7) , be selected so that the load torque T _L is reduced the influence to the system can be robust processing load speed omega _L against disturbance torque T _L.

If an appropriate feedback gain f ₁₁ , f ₁₂ , f ₁₃ can be selected in the above equation (7), T _L ′ = −T _L (8) holds, and the disturbance torque T _L is applied to the system. The effect can be canceled.

Now, to simplify the block diagram in FIG.

(Equation 3) Holds. Therefore, if the feedback gain element is selected as in the following equation, equation (8) is satisfied.

(Equation 4) At this time, the equation (7) of the disturbance compensation amount T _L 'which is a state feedback compensation element is obtained by substituting the equation (12).

(Equation 5) Is obtained.

Equation (13) is generally referred to as an equivalent disturbance observer. For example, see M. Nakano, K. Ohnishi, and K. Miyachi, “A Robust Dece
nrralized Joint Control-Based Based on Interference Est
imation) Proc.IEEE Int.Conf. Robotic andAutomatio
n, Vol.1 (1987) Yasuhiko Tate "Application to Intelligent Motion Control" This control method is described in detail in T.IEE Japan Vol.109-D, No.5 (1989).

By selecting the feedback gain elements so that an equivalent disturbance observer can be constructed as described above, these gain elements can be uniquely obtained, and T _L ′ in the equation (13) is obtained by calculating only the load torque. In addition, there is an effect of canceling the influence of any variation such as a parameter variation of the control target.

Therefore, if equation (8) is satisfied, the state feedback control block diagram of FIG. 4 can be rewritten as shown in FIG. Block 12 in FIG. 5 shows a state in which the disturbance torque _TL is canceled by the equivalent disturbance observer output, and the disturbance becomes zero. FIG.
When the feedback control block diagram in the state where the load disturbance is canceled is expressed by the state equation,

(Equation 6) However,

(Equation 7)

In the open loop control system of FIG. 5, the remaining state feedback gain elements f ₂₁ and f ₂₁ are changed from the desired pole arrangement.
₂₂ and f ₂₃ can be obtained. This is a method that has been conventionally applied as a method of determining the state feedback gain.

Next, the operation of the equivalent disturbance observer will be supplemented. In the control system of FIG. 5, what can be controlled is the torque command value _Tm ^* . Therefore, it must return estimated torque T _{L 'at} the T _m. Now, and seek a positive transfer function from _{T m} to _{T L,}

(Equation 8) Is obtained. The configuration of the equivalent disturbance observer is shown in FIG. 6 as two values of the control state quantity, that is, ω _m (motor speed) and T
Blocks 5 and 6 which receive _S (shaft torsional torque) as input and a block 10 which performs a first-order lag filter on a deviation output thereof are added. The observer output is added to the torque command.

Now, to consider the observer operation of FIG. 6, consider a general observer circuit as shown in FIG. Also, for simplicity, the nominal value to be used for the observer is assumed to correspond to the actual value, the noise N is on the detected value of y ₀ as shown in FIG. 7 by the dashed line. When the transfer function of the output y ₀ is obtained for this noise N, y ₀ / N = ∞ (19) Therefore, it can be seen that this observer is a system that is unstable in practical use. The solution to this problem, it is common to put the filter on the detected value of y _0. The characteristics of the observer greatly depend on the time constant of the filter. If this time constant is selected to be small, noise cannot be removed and the system may become unstable. Conversely, when this time constant is increased, the effect as a disturbance observer is reduced, and vibration is more likely to occur due to a delay of the filter.

Therefore, here, a filter is inserted in the equivalent disturbance observer output instead of the filter in the detected value of y ₀ , and a gain K _c (<1) is inserted to reduce the loop gain. Naturally, the effect of the disturbance observer is reduced, but it is considered to be excellent in terms of stability. Selection of the gain K _c should be determined by conditions of characteristics and actual control system is used to be required. Further, the filter may be set to a detection filter time constant that can ignore the delay as compared with other elements of the system in practical use.

FIG. 1 is a block diagram from the torque command value T _m ^* including the equivalent observer to the load speed ω _L , and the elements f ₁₁ , f ₁₂ and f _{13 of the} state feedback gain.
Constitutes an equivalent disturbance observer, and f ₂₁ , f ₂₂ , f
_{In 23} , the pole position is determined so as to be stable and is fed back to T _m ^* . As defined in equation (6), T _m ′
Is a state feedback compensation amount determined from the stability of the pole arrangement, which is a state feedback compensation element.

[0024]

In a state feedback control device in which a difference between a target value u and a state feedback amount u 'obtained by multiplying a controlled state variable x by a feedback gain F is determined as a gain of a state feedback gain matrix. As a method, the disturbance T as a target value input of the controlled object
_L a, so as to cancel the disturbance T _L by applying an equivalent disturbance observer, first determines the feedback gain element _{f 11, f 12, f 13} . If f ₁₁ , f ₁₂ , and f ₁₃ are determined in this manner, the disturbance _TL is canceled (canceled) by the equivalent disturbance observer output _TL ′, and acts as an equivalent to a system in which no disturbance is input to the controlled object. Become.

Next, for the target value command input T _m ^* ,
Similar to the conventional state feedback gain determination method, the feedback gain elements f ₂₁ , f ₂₂ , f ₂₂ , f ₂₂ , f ₂₂ , f ₂₂ , f 2, f 2, f 2, f 2, f 3, f 2, f 3, and f 2 are arranged such that a desired gain is given and its pole (characteristic root) is located in a stable region in the left half plane on the S plane. three values of f ₂₃ may be determined.
That is, the constant group of f ₁₁ , f ₁₂ , and f _{13 and} the constant group of f ₂₁ , f ₂₂ , and f ₂₃ can be determined separately, so that the degree of freedom of the determination method is expanded and the handling method is easy. By determining the state feedback gain constant as described above, f ₁₁ , f ₁₂ , f
The group of ₁₃ constants contributes to the improvement of the transient characteristics, and f ₂₁ ,
The constant group of f ₂₂ and f ₂₃ acts on stabilization of characteristics.

[0026]

FIG. 8 is a block diagram showing an embodiment of a state feedback control of a higher-order system according to the present invention, in which speed control of a torsion system is performed.

As described above for the state equation, the state feedback variables u 'for the target value u include _TL ' and _Tm ', and these state feedback gains f
₁₁ , f ₁₂ , f ₁₃ and two sets of f ₂₁ , f ₂₂ , f ₂₃ ,
In the first set, we define the equivalent disturbance observer as
If the selection is made as shown in (12), the disturbance T as shown in FIG.
_L is canceled.

[0028] In FIG. 8, and estimates the disturbance T _L by the equivalent disturbance observer that inputs a variable omega _m - [omega] _L and omega _L, the torque command through the inverse function 1 / G _F and observer filter of formula (18) Feedback to T _m ^* .

The second set includes shaft torque T _s , load speed ω _L ,
Feedback gain constants f ₂₁ to motor speed omega _m,
Although over the f _22, f ₂₃ and is fed back to the torque command T _m ^*, the selection of f _21, f _22, f ₂₃ is to be determined by the pole placement as described above.

[0030]

According to the conventional control method, when there are many feedback gain elements such as state feedback control of a higher-order system, there are too few decision guidelines to determine the gain from controllability, stability, etc. The experience in classical control was useless at all.

According to the present invention, one guideline for determining the state feedback gain has been established, and it can be said that the determination method is far more theoretical and does not require trial and error as compared with the prior art.
In addition, since it is an application of the method of the equivalent disturbance observer, it can be said that this is a control method that can make the most of the effect that the robustness against disturbance is greatly improved.

Further, when there is an undetectable variable as a part of the state variables, for example, in the case of the above embodiment, the load speed ω _L
There the case of undetectable, 0 feedback gain f ₂₂ is corresponding to this state variable, so to look for stability by operating the two gains of the remainder of f _21, f _23,
It is possible to select a gain with much better controllability and responsiveness than in the conventional method, and it is possible to easily improve the disturbance response. That is, when the present invention is applied, the necessity of the load speed detector as shown in the embodiment has a great effect.

[Brief description of the drawings]

FIG. 1 is a block diagram showing the principle of the present invention.

FIG. 2 is a conceptual diagram showing a torsion system as an example of a higher-order system.

FIG. 3 is a block diagram of the torsion system of FIG. 2;

FIG. 4 is a block diagram of a state equation when state feedback control is applied to a torsional system model.

FIG. 5 is a block diagram showing a state in which disturbance T _L is canceled by an equivalent disturbance observer in state feedback control.

FIG. 6 illustrates the basics of the present invention, and is a state feedback block diagram in which an equivalent disturbance observer is incorporated in a state feedback gain element.

FIG. 7 is a block diagram for explaining an equivalent disturbance observer and explaining an observer filter.

FIG. 8 is a block diagram showing an embodiment of the present invention, in which speed control of a torsional system is performed as a higher-order system.

[Explanation of symbols]

DESCRIPTION OF SYMBOLS 1 Torque generation coefficient part 2 Motor part 3 Torsional shaft part 4 Load part 5 The part which made the constant of the torsional shaft part 6 The part which made the constant of the load part nominal and made reciprocal 7, 8, 9 State feedback gain 10 T _m ^* parts that reciprocal of a material obtained by nominal the constants of the transfer function to T _s from (equation (18)) 11 disturbance torque T _L by the primary delay filter 12 equivalent disturbance observer output for the equivalent disturbance observer Represents the state in which is canceled 13 Detection noise T _m ^* Torque command T _L Load torque T _s- axis torsion torque K _t Torque constant J _m Motor inertia J _L Load inertia ω _m Motor speed ω _L Load speed K _s axis of the elastic coefficient D _m motor damping constant D _s axis of the damping constant D _L load damping constant T _L 'disturbance compensation amount F state equation of the gain matrix _{f 11, f 12, f 13} , f 21 f _22, f ₂₃ the gain of the A matrix B equations of state of the state feedback gain A state equation is an element of the matrix F B matrix u target value u 'feedback value x is the state variable

──────────────────────────────────────────────────続 き Continuation of the front page (56) References JP-A-64-64007 (JP, A) JP-A-63-209491 (JP, A) JP-A-2-199502 (JP, A) JP-A-3-3 17703 (JP, A) JP-A-3-25505 (JP, A) JP-A-4-112690 (JP, A) JP-A-5-53603 (JP, A) (58) Fields investigated (Int. ^7, DB name) G05B 13/00 - 13/04 H02P 5/00 G05D 3/12 JICST file (JOIS)

Claims (2)

(57) [Claims] A motor speed and a shaft torsion torque among state variables of a controlled object in which an electric motor and a load are connected by an elastic element are detected, and a state feedback value corresponding to the state variable is multiplied. In the control method of feeding back the state feedback amount to the torque command,
After forming an equivalent disturbance observer that receives the two values of the detected control state quantity as input, and after determining the coefficients of some elements of the state feedback gain so as to cancel the disturbance torque using the observer, A state feedback gain is selected by determining a coefficient of a remaining element of the state feedback gain so that the state feedback control system is stabilized by the arrangement, and a state feedback amount is obtained using the state feedback gain. And control method. 2. The state feedback control method according to claim 1, wherein a first-order lag filter is added to the output of the equivalent disturbance observer, and the gain Kc is set to 0 <Kc ≦ 1.