JPH04218719A - State observation method - Google Patents

Abstract

PURPOSE:To provide a state observation method with a less estimation error by compensating for influence which a solid friction gives to estimation of a state when performing estimation of the state of a machine mechanism which the solid friction operates. CONSTITUTION:After positive, negative, and zero code information of a speed of a machine mechanism is detected, an influence which a solid friction gives to a state estimation value is compensated for by changing values of a matrix of a state observing equipment and that of a gain according to a code information of the detected speed.

Description

[Detailed description of the invention]

0001

[Field of Industrial Application] The present invention relates to a method for observing the state of a mechanical mechanism whose motion is controlled by a servo motor or the like. This relates to a state observation method.

0002

[Prior Art] In order to achieve high-speed and precise motion control of a mechanism using a servo motor, feedback of state variables such as displacement, speed, and current of the mechanism system including the servo motor is required. However, since it is actually impossible to detect all the necessary state variables, state estimation is performed using a state observer.

[0003] Since solid friction acts on many actual mechanical mechanisms, a state observation device that takes solid friction into consideration is required. However, solid friction has the sign of velocity (positive,
Solid friction has nonlinear characteristics with different values depending on (negative, zero), etc., and is difficult to handle. Therefore, in conventional state observation instruments, solid friction is ignored or, at best, considered as a steady disturbance. there were. Although it is appropriate to regard solid friction as a steady disturbance when the motion of a mechanical mechanism is unidirectional, it cannot be applied to general motion control such as high-speed positioning control where the direction of motion is reversed.

0004

[Problems to be Solved by the Invention] As described above, there are no conventional state observation methods that fully take into account the nonlinear characteristics of solid friction. An estimation error occurred due to the influence of , and it was not possible to obtain a satisfactory state estimate.

[0005] In order to solve the above problem, the present invention uses speed sign information (positive, negative, zero) as the parameter of the state observation device.
The purpose is to compensate for the influence of solid friction on state estimation.

[0006]

[Means for Solving the Problems] A state observation method according to the present invention is a state observation method for performing high-speed positioning control of a mechanical mechanism using a servo motor as a drive source on which solid friction acts, using a state observation device. In the observation method, the positive velocity of the mechanical mechanism,
After detecting negative and zero sign information, the influence of solid friction on the state estimate is compensated by changing the values of the system matrix and gain matrix of the state observer according to the detected speed sign information. This is how it was done.

[0007]

[Function] Parameters change depending on the sign (positive, negative, zero) of the angular velocity.
, the system matrix A(x2), the gain matrix K(
By using a state observer that changes x2), state estimation that compensates for the influence of solid friction torque is realized.

[0008]

[Examples] First, the principle will be explained, and then examples will be shown.

A servo motor system on which solid friction torque Tf acts is typically represented by the block diagram of FIG. In Fig. 2, J, KT, R, L, and C are respectively servo motors.
moment of inertia, torque constant, induced voltage constant, winding resistance, winding inductance, and viscous damping coefficient, and θ,
ω, i, and e are the angular displacement, angular velocity, and servo motor, respectively.
They are current and input voltage, and s is a Laplace operator. If we express the system in Figure 2 using an equation of motion, we get

0010

[Equation 1] In addition, the nonlinear characteristics of the solid friction torque Tf can be approximated in Fig. 3 using the dynamic friction torque Tf0,

0011
]

It can be expressed as [Equation 2]. Here, the function f(ω
), g(ω),

0012

[Equation 3] and simplifying the nonlinear characteristics of the solid friction torque in Equation (2), the equation of motion in Equation (1) becomes

[0013]

[Equation 4] The treatment of solid friction torque in equations (3) and (4) is the same as in equations (1) and (2) except for a small area where ω = 0 and |KT i | > Tf0, This is considered to be appropriate as a basic formula for a servo motor system for constructing a state observation device.

Next, when the state variables of the servo motor system are selected as angular displacement θ, angular velocity ω, current i, and dynamic friction torque Tf0, and dimensionless conversion is performed using the reference angular displacement θ0 and reference time T, the following is obtained. The equation of state for is obtained.

[0015]

[Math 5] here,

[0016]

[Math 6] It is.

In general, it is clear from estimation theory that it is necessary to detect the angular displacement x1 [θ] in order to construct a servo motor system state observation device. Therefore, here we use the angular displacement x1 as a state observation device to compensate for the effect of solid friction.
[θ] and other state variables, i.e. angular velocity x2
An example of a state observation device for estimating [ω], current u[i], and dynamic friction torque γ[Tf0] is shown below. however,
Angular velocity x to compensate for the nonlinear characteristics of solid friction torque
It is assumed that the sign information (positive, negative, example) of 2 can be detected.

The solid friction torque Tf acts on the (5th
) Consider a state observation device expressed by the following equation (7) in which the value of the parameter can be changed depending on the sign of the angular velocity x2 for the servo motor system expressed by the equation (7).

[0019]

[Math 7] Estimation error ε(τ)

[0020]

[Equation 8] Then, from equations (5) and (7), the error equation becomes

[0021]

[Math. 9]

[0022]

[Formula 10]. Therefore, the state observer gain matrix K(x2
)=[k1 (x2) k2 (x2) k3
(x2 ) k4 (x2 )]′ depends on the sign of x2,

[0023]

[Equation 11] When degree x2 = 0, the characteristic equation (10) has a zero root, so the estimation of dynamic friction torque γ stops, but even in this case, the other state variables angular velocity x2 and current u It is possible to estimate

As described above, the value of the parameter, that is, the system matrix A(x2
), the gain matrix K(x2) is the (6)th and (1st
It has been theoretically shown that state estimation that compensates for the influence of solid friction torque can be realized by using a state observer that changes as shown in equation 1).

FIG. 1 is a block diagram showing the functions of one embodiment of the present invention. I indicates the side of the object to be measured, and II indicates the state observation device side according to the present invention. The corner blocks and codes correspond to the above-mentioned formulas. Each estimated value marked with ∧ is taken out and used for positioning, but its system is omitted.

In this embodiment, as shown in equation (11), the estimation error is automatically compensated by appropriately setting k4.

Next, the effects of the state observation device according to the present invention will be described. When a servo motor system on which solid friction torque is applied performs the positioning operation shown in Fig. 4, if a state observation device designed without considering solid friction torque is used, Fig. 5 is obtained.
An estimation error Δω of the angular velocity and an estimation error Δi of the current as shown in (■) and (■) occur, and a satisfactory estimated value cannot be obtained. On the other hand, when the state is estimated using the state observation method according to the present invention, the angular velocity estimation error Δω and the current estimation error Δi become considerably small, as shown by ■' and ■' in FIG. 6 indicates the estimated value Tf0 of the dynamic friction torque obtained by the state observation method of the present invention, which agrees well with the measured value Tf0 of the dynamic friction torque shown in the figure ■.

The configuration and effectiveness of the state observation device that compensates for the effects of solid friction using the sign information of the angular velocity x2 have been described above, taking as an example the state observation method when only the angular displacement x1 can be detected. The state observation method according to the invention is based on the angular displacement
It is clear that a state observation device is included when the angular velocity x2 or the current u can be detected in addition to 1. Further, although the configuration of the state observation device described above is given as a continuous time system, it goes without saying that it can be easily extended to a discrete time system.

[0029]

As explained above, the state observation method according to the present invention detects the sign information of positive, negative, and zero of the mechanical mechanism, and then detects the system matrix according to the detected speed sign information. By modifying the gain matrix and changing the parameters of the state observer, the influence of solid friction on the state estimate is compensated for, so the parameters are changed according to the sign of the velocity. Since it compensates for the nonlinear characteristics of solid friction, it has the advantage that it can be used for state estimation when performing high-speed motion control of many mechanical mechanisms where solid friction acts.

[Brief explanation of the drawing]

FIG. 1 is a block diagram showing the functions of an embodiment of the present invention.

FIG. 2 is a typical block diagram of a servo motor system.

FIG. 3 is a diagram showing linear characteristics of solid friction torque.

FIG. 4 is a diagram showing an example of positioning operation of a servo motor system in which solid friction acts.

FIG. 5 is a diagram showing the effects of the present invention.

FIG. 6 is a comparison diagram of an estimated value and an actual value of dynamic friction torque.

[Explanation of symbols]

I Measured object side II Condition observation device side ■ Curve showing estimation error of angular velocity and estimation error of current ■ Curve showing estimation error of angular velocity and estimation error of current ■ Estimated value of dynamic friction torque according to the present invention ■
Actual value

Claims (1)

[Claims] 1. A state observation method for performing high-speed positioning control of a mechanical mechanism using a servo motor as a drive source on which solid friction acts, using a state observation device, wherein the positive and negative speeds of the mechanical mechanism are , After detecting the sign information of zero, the influence of solid friction on the estimated state value is compensated for by changing the values of the system matrix and gain matrix of the state observer according to the detected sign information of the speed. A state observation method characterized by: