JPH0553602A - State feedback control system - Google Patents

Abstract

PURPOSE:To improve the controllability and the responsiveness of a state feedback control system by selecting the coefficient of a state feedback gain element in order to cancel the equivalent disturbance input with use of an equivalent disturbance observer which uses the torque command input value and the control state value as its input. CONSTITUTION:A state feedback controller defines the difference between the target value mu and the state feedback value mu' obtained by multiplying the feedback gain F by a controlled state variable (x) as a manipulated variable of a controlled system. The feedback gain elements f11, f12 and f13 of a state feedback gain matrix are decided so that the disturbance TL, i.e., the target input of the controlled system is eliminated with use of an equivalent disturbance observer. Thus the disturbance TL is eliminated by the equivalent disturbance observer output TL. Then it is possible to attain a system equivalent to that where any disturbance is inputted to the controlled system.

Description

Detailed Description of the Invention

[0001]

[Industrial application] It is well known that in a drive system for industrial application, a torque transmission mechanism includes an elastic element, and a resonance system is formed in relation to the moment of inertia of the motor itself and the load, and it is necessary to control Often a problem.
When the PI control which is usually used is applied to such a high-order system and its quickness is increased, for example, torsional vibration of the shaft occurs. In addition, the adverse effect that the load torque and the parameter of the system largely change and the output is affected was accompanied.

In order to solve such a problem, the present invention relates to a control system in which state feedback control is applied to a higher-order system, for example, a torsion system to improve torsional vibration and transient characteristics. That is, the idea of the equivalent disturbance observer described in detail in Japanese Patent Laid-Open No. 025505, “Multifunctional controller”, filed on June 22, 1991 by the present applicant, is based on the method of determining the state feedback gain. One of the measures is to select the feedback gain element so that the equivalent disturbance observer cancels the input disturbance.

[0003]

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

Symbols in the figure are T _m ; torque command _TL ; load torque T _s ; shaft torsion torque K _t ; torque constant J _m ; motor inertia J _L ; load inertia ω _m ; motor speed ω _L Load speed K _s ; elastic modulus of shaft D _m ; damping constant of motor D _s ; damping constant of shaft D _L ; damping constant of load, damping constant D _m of induction motor and damping constant D _{L of} load , And the damping constants of the axes are extremely small, and these will be ignored in the following description.

FIG. 3 is a block diagram of the torsion system of FIG. From the model of FIG. 3, a state equation like the equation (1) can be obtained.

[Equation 1]

The characteristic equation becomes S (S ² + ω ₀ ² ) (2), and this 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 the resonance frequency ω ₀ determined by K _s , J _m , and J _L as shown in the equation (3). This vibration is P to increase the response of the speed system.
When the I gain is increased, torsional vibration of the shaft occurs at the resonance frequency ω ₀ , which becomes a problem, and the PI gain has to be decreased.

From the load torque T _L to the load speed ω _L
The transfer functions up to are high-order systems as shown in the following equation. ω _L / _TL = (-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 proportional 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

From the equation (4), it can be seen that the load speed ω _L is easily influenced by the fluctuation of the load torque T _{L and} is easily influenced by the parameter fluctuation of the control system. When torsional vibration occurs, there is a danger of threading of the shaft, breakage of the shaft, and the like, and in the past, active torsional antivibration control with high responsiveness was not realized by PI control. Conventionally, the control response frequency is set lower than the resonance frequency ω ₀ (the PI gain is lowered to slow the response), and the control is performed so as not to give a sudden change. Further, the elastic coefficient K _s of the one axis is increased to increase the resonance frequency ω ₀ . As described above, active torsional vibration isolation 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 load speed, all the poles of the system must have a desired stable pole arrangement. Further, as described above, in order not to be influenced by the influence of the change in the load torque T _L and the parameters of the control system, it is necessary to actively compensate for these influences, and it is necessary to satisfy these requirements. As a method, the problem is considered in the case where the state feedback control of the modern control theory is applied to the torsion system. State feedback control is described in many documents and will not be described here.

When the state feedback control is applied to the above-mentioned general formula (1) of the torsion system model, it becomes as shown in FIG.
Here, the matrix F of the state feedback gain is represented by the elements f ₁₁ , f ₁₂ , f ₁₃ and f ₂₁ , f ₂₂ , f _{23 as} follows.

[Equation 2]

Here, in the case of 1 input and 1 output, the state feedback gain is generally obtained by giving a desired pole (characteristic root), but in the case of 2 inputs and 2 outputs or more, the elements of the matrix F are many. Therefore, it is impossible to easily find a desired pole, and it takes a considerable amount of time to go through a trial and error stage. The present invention has been made to solve this.

[0013]

Since the disturbance compensation amount T _L ′, which is a state feedback compensation element, is T _L ′ = f ₁₁ T _s + f ₁₂ ω _L + f ₁₃ ω _m (7) from the equation (6). , The load speed ω _L can be made robust against the disturbance torque T _L if the load torque T _L is selected so as to reduce the influence on the system.

[0014] If it is possible to select the above equation (7) appropriate feedback gain f ₁₁ in, f _12, f ₁₃ if, T _L '= -T _L (8) is satisfied, the disturbance torque T _L is the system You can cancel the effect.

Now, to simplify the block diagram in FIG.

[Equation 3] Is established. 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 the state feedback compensation element is substituted by this equation (12) to obtain

[Equation 5] Is obtained.

Equation (13) is generally called an equivalent disturbance observer, and is described in, for example, the literature M. Nakano, K. Ohnishi, K. Miyachi "A Robust Dece.
nrralized Joint Con-trol Based on Interference Est
imation "Proc. IEEE Int. Conf. Robotic and Automatio
n, Vol.1 (1987) Yasuhiko Dote "Application to Intelligent Motion Control" T.IEE Japan Vol. 109-D, No.5 (1989).

By selecting the feedback gain elements so that the equivalent disturbance observer can be constructed as described above, these gain elements can be uniquely obtained, and T _L ′ in the equation (13) is the load torque only. It has the effect of canceling the influence of all fluctuations such as parameter fluctuations of the controlled object.

Therefore, if the 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 represents a state in which the disturbance torque _TL is canceled by the equivalent disturbance observer output and the disturbance becomes zero. Figure 5
Of the feedback control block diagram of the state of canceling the load disturbance of

[Equation 6] However,

[Equation 7]

From the desired pole placement in the open loop control system of FIG. 5, the remaining state feedback gain elements f ₂₁ , f
₂₂ and f ₂₃ can be obtained. This is a method that has been conventionally applied as a method for 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 T _m ^* . Therefore, the estimated torque T _L ′ must be returned to T _m . Now, when the forward transfer function from T _m to T _L is obtained,

[Equation 8] Is obtained. The structure of the equivalent disturbance observer is as shown in FIG.

Now, in order to consider the observer operation of FIG. 6, consider a general observer circuit as shown in FIG. Further, for simplicity, it is assumed that the nominal value used for the observer agrees with the actual value, and the noise N appears in the detected value of y ₀ as shown by the alternate long and short dash line in FIG. 7. When the transfer function of the output y ₀ is obtained with respect to this noise N, y ₀ / N = ∞ (19) Therefore, it is understood that this observer is an unstable system in practical use. As a solution to this problem, it is general to insert a filter into the detected value of y ₀ . The characteristics of the observer largely 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. On the contrary, if the time constant is increased, the effect of the disturbance observer is reduced, and further, the delay of the filter makes the vibration easily occur.

Therefore, here, instead of a filter, a filter is inserted in the equivalent disturbance observer output for the detected value of y ₀ , and a gain K _c (<1) is inserted to reduce the loop gain. As a matter of course, the effect of the disturbance observer is reduced, but it is considered to be excellent in terms of stability. The selection of the gain K _c must be decided according to the required characteristics and the situation where the control system is actually used. Further, the filter may be set to have a detection filter time constant such that the delay can be ignored in comparison 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. The elements f ₁₁ , f ₁₂ , f _{13 of the} state feedback gain are shown.
The equivalent disturbance observer is composed of f ₂₁ , f ₂₂ , and f
_The pole position of ₂₃ is determined so as to be stable and is fed back to T _m ^* .

[0024]

In the state feedback control device in which the difference between the target value u and the state feedback amount u ′ obtained by multiplying the controlled state variable x by the feedback gain F is the operation amount of the controlled object, the gain element of the state feedback gain matrix is determined. As a method, the disturbance T as the 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 thus determined, the disturbance T _L is canceled by the equivalent disturbance observer output T _L ′, 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 ^* ,
Like the determination method of the conventional state feedback gain, the pole is given the desired gain (characteristic roots) is the feedback gain element f ₂₁ so as to be positioned in a stable region in the left half on the S plane, f _22, 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, the degree of freedom of the determination method is expanded, and it becomes easy to handle. By determining the state feedback gain constant as described above, f ₁₁ , f ₁₂ , f
The constant group of ₁₃ contributes to the improvement of transient characteristics, and f ₂₁ ,
The constant group of f ₂₂ and f ₂₃ acts to stabilize the characteristics.

[0026]

FIG. 8 shows a block diagram of a state feedback control of a higher order system according to the present invention when the speed of a torsion system is controlled.

As described above regarding the state equation, the state feedback variable u'for the target value u has T _L and T _m ^* , and these state feedback gains f
For two sets of ₁₁ , f ₁₂ , f ₁₃ and f ₂₁ , f ₂₂ , f ₂₃ ,
In the first set, if the equation (12) is selected so as to form the equivalent disturbance observer, the disturbance T can be calculated as shown in FIG.
_L is canceled.

In FIG. 8, the disturbance _TL is estimated by an equivalent disturbance observer having the variables ω _m -ω _L and ω _L as inputs, and the torque command is passed through the inverse function 1 / G _{F of the} equation (18) and the observer filter. I am giving feedback to T _m ^*

The second set is the shaft torque T _s , the load speed ω _L ,
The feedback gain constant f ₂₁ , to the motor speed ω _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 the state feedback control of a higher order system, there are too few decision guidelines for determining the gain from the controllability, stability, etc. My experience with classical control was completely useless.

According to the present invention, a guideline for determining the state feedback gain has been established, and it can be said that the determination method is far more theoretical than conventional methods and does not require trial and error.
Moreover, since it is an application of the equivalent disturbance observer method, it can be said that the control method can take full advantage of the fact that robustness against disturbance is greatly improved.

Further, if some of the state variables cannot be detected, for example, in the case of the above-mentioned one embodiment, the load speed ω _L
Is not detected, the feedback gain f ₂₂ corresponding to this state variable is set to 0, and stability can be searched for by operating the remaining two gains f ₂₁ and f ₂₃ .
It is possible to select a gain having significantly better controllability and responsiveness than the conventional method, and it is possible to easily improve the disturbance response. That is, if the present invention is applied, the load speed detector is unnecessary as shown in the embodiment, which is very useful.

[Brief description of 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 twist system of FIG.

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

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

FIG. 6 is a state feedback block diagram showing the basics of the present invention and incorporating an equivalent disturbance observer in a state feedback gain element.

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

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

[Explanation of symbols]

1 Torque generation coefficient part 2 Electric motor part 3 Torsional shaft part 4 Load part 5 Part where the constant of the torsion shaft part is normalized 6 Part where the constant of the load part is normalized and reciprocated 7, 8, 9 State feedback Gain 10 T _m ^* to T _s Nominalized constant of the transfer function and reciprocal (Equation (18)) 11 First-order lag filter for equivalent disturbance observer 12 Disturbance torque _TL due to equivalent disturbance observer output Is a part where the noise is canceled. 13 Detection noise T _m ^* Torque command _TL Load torque T _s Shaft 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

Claims (2)

[Claims] 1. A detector for controlling an electric motor speed and a shaft torque, which is a controlled object in which an electric motor and a load are coupled by an elastic element, and which is a state variable of the controlled object. In a control device having a control means for performing a state feedback of a state feedback amount obtained by multiplying a value of a corresponding state feedback gain to a target value, a torque command input value of the target value and a control state amount that is an output of the detector. A state feedback control method, characterized in that an equivalent disturbance observer is configured with two values of 1 and 2 being input, and the coefficient of the element of the state feedback gain is selected so as to cancel the equivalent disturbance input using the observer. .. 2. A state feedback control system characterized in that the gain K of a first-order lag filter added to the output of the equivalent disturbance observer constructed as in claim 1 is 0 <K ≦ 1.