JPS63301303A - Control input designing method for variable structure control system - Google Patents

Abstract

PURPOSE:To clearly and properly design the gain for control input designation, the variable gain, the gradient of a sliding curve, etc., by designing the control input from the offset of the sliding curve and the position feedback of the variable gain. CONSTITUTION:The control input U is applied to satisfy the generation of a sliding mode for control of a variable structure system. In this case, the input I is designed from the offset value between a speed axis on a phase surface of a phase deviation and a sliding curve S=0 and the position feedback value of the variable gain. When the gradient of the curve S is decided, a gain constant designed for decision of the gradient and the input U is calculated from the position loop gain kp of a proportion control system, the cut-off angle frequency kv of a speed loop, the attenuation coefficient zeta and the inherent angle frequency omegan. At the same time, the maximum gradient value Cmax is set at kvmax. In this respect, a control system consists of a sliding mode controller 1, a block 2 showing the system transmission coefficient, and an integration element 3.

Description

DETAILED DESCRIPTION OF THE INVENTION [Field of Industrial Application] The present invention relates to a control input design method for improving control characteristics in a variable structure control system, particularly in sliding mode control.

[Conventional technology]

One type of control system is a variable structure control system. This is a system in which the coefficients of a plurality of parameters that determine the control input, that is, the magnitude of the gain, are switched according to the control stage.

In the control of such a variable structure system, when specifying the control input U, conventionally, the control input has been specified using the feedback amount of position deviation and speed, mainly using the method expressed by the following equation.

U = to 1xl+ to 2x20, Slgn(S)...
・・・・・・(1) S=CXl+X2
・・・・・・・・・・・・(2) However, X,=xr−X
.

X2=X.

x: Position command xI=Position feedback variable gain is "I+"2, and these are switched so as to satisfy SS<O, which is a sliding mode generation condition. Here, the sliding mode refers to the positional deviation X +
This is a mode in which the variable gain is switched so that when the position command X starts from the position command X and comes close to the straight line S=0, the variable gain converges toward the origin along the straight line S.

[Problem that the invention seeks to solve]

However, in this method, it is difficult to associate each gain "I + k2 with the speed loop cutoff angular frequency of PI control (proportional-integral control), etc.
Since it is necessary to switch 2 independently, the gain setting design becomes complicated, and the slope C and gain "I+"
Setting 2 tends to involve trial and error. Therefore, chattering of the control input is likely to occur more than necessary, and its control characteristics are difficult to predict.

On the other hand, the introduction of a smoothing function aimed at reducing chattering is basically completely equivalent to PI control, so its characteristics can be discussed in terms of PI control systems, but the inherent robustness of variable structure systems decreases. Robustness here refers to the fact that even if the dynamic characteristics of the controlled object change during operation, the basic characteristics of the control system are not affected.

In particular, when the robustness of the control system to fluctuations in the moment of inertia decreases and the moment of inertia increases, overshoot occurs at the origin of the phase plane.

The present invention has been made in view of the problems encountered with conventional variable structure systems, and aims to facilitate the design of control inputs and reduce chattering while maintaining robustness. .

[Means for solving problems]

In order to achieve this object, the present invention provides a method for controlling a variable structure system in which, when applying a control input U that satisfies the generation of a sliding mode, the velocity axis on the phase plane and the sliding curve S = 0 for positional deviation. The control input is designed based on a position feedback amount of an offset and a variable gain.

In this design, when determining the slope of the sliding curve S, the gain constant designed for determining the slope and control input U is determined by the position loop gain kv of the proportional control system, the cutoff angular frequency kv of the velocity loop, Using the damping coefficient ζ and the natural angular frequency ω7, the maximum value of the slope Cs
aw can be given as Cmax=kVsax.

[Effect]

In the present invention, the control input U for controlling the variable structure system is specified by the following equation.

U=kPS+ksx1+! l5dt・・・・・・・・・
...(3) Here, each gain constant of k, k, k, is set on the condition that SS<Q, and then 2
The state equation of the next system is equation (4). However, S is (
2) Given by Eq.

・・・・・・・・・・・・・・・(4) Here, F: Torque disturbance.

d: Viscous friction torque coefficient J: Moment of inertia of the servo motor (including load, if any).

k, two torque constants It is.

Since SS<O, each gain in equation (3) needs to satisfy the following conditions.

&, > (J/kt) (C-d/J) ・・・
・・・・・・・・・・・・(5) &, > O...
(6) Compensate the integral term for F by considering C>>d/J, which is a condition that holds in a normal control system, and parameter fluctuations in the control system. let them deal with it. Also,
In order not to impede the robustness, as shown in Figure 5, S
In the present invention, the gain constant is set using the following formula, considering that an offset δ set near 0 is effective.

&,>(J□Jkt-MX)C・・・・・・・・・・・・
(8) As can be seen from equations (8), (9), and 00, the design method of the present invention provides a clear correspondence between the parameters of the control system and each gain.

The switching gain constituting the variable structure system is 3, and α
It is only necessary to set the minimum necessary value that satisfies Equation 0, and chattering of the control input can be suppressed to a minimum. Further, there is no need to switch k, and it is sufficient to set the maximum value allowed by the control system, and the upper limit value of C that can be given can be derived from the maximum value. Set gain constant kp to P
By associating it with the I control system, its upper limit value can be obtained.

A block diagram of a variable structure control system that provides control input using equation (8) is shown in FIG. In the figure, 1 is a sliding mode controller, 2 is a block representing the system transfer function, and 3 is a sliding mode controller.
indicates an integral element. Here, in order to clarify the relationship between k and the PI control system, if k, = 0, then (X,
+X, the control system that provides negative feedback and the transfer function become equivalent, and the block diagram becomes as shown in Figure 2. When FIG. 2 is converted into a block diagram for outputting xl, FIG. 3 is obtained. FIG. 3 shows the control system itself of the second-order lag system using proportional control. FIG. 4 is a conversion of FIG. 3 into a quadratic standard form. This is a condition that holds true in a normal control system.
>> Considering d, the following relational expression is obtained from FIG.

Position loop gain: に、＝（： ・・・・・・・・・
...0υ velocity loop cutoff angular frequency: kv=#
, , /J..., has an upper limit in an actual system due to the delay of the current loop and high-order parasitic terms, and , is suppressed by kv.

k, □-””(t+v・J)/ky...
・・・・・・・・・αJ From formula (8), C<
kvmax ・・・・・・・・・・・・04)α0
The formula gives a clear upper limit for C. In PI control,
From non-vibration conditions, C< kv*ax/4...
・・・・・・0■.

As a result, under the same conditions, the slope of C is 4
Can be doubled.

Note that by setting the switching line to cL+Xz=b and appropriately giving C1b, the present invention can be applied even under conditions where xl and x2 vary in various ways over the entire region of the phase plane.

〔Example〕

Hereinafter, the present invention will be specifically described based on embodiments shown in the drawings.

Figures 6 and 7 show a comparison of the phase plane locus (a) and the response to the control input signal (b) when the control of the present invention and the conventional PI control are respectively applied to the positioning of a servo motor. be. Fig. 6 shows the case with no load, and Fig. 7 shows the case when the moment of inertia (J) increases by 100%. As shown in Fig. 6(a) and Fig. 7(a), the phase plane shows the number of output pulses of the pulse generator as the position on the horizontal axis, and the angular velocity (rad/5ec) on the vertical axis. . In this example, the output of the pulse generator was 6000 pulses per revolution (2πrad). In FIGS. 6 and 7, solid lines indicate control to which the present invention is applied, and broken lines indicate P
This shows the case where I control is applied.

Focusing on the phase plane locus in Fig. 7(a), when the moment of inertia (J) increases by 100%, overshoot is seen near the origin with conventional PI control, but with the control according to the present invention. In this case, along the straight line S=0, X converges toward the origin without overshoot.

This clearly shows the advantage of the present invention in terms of robustness against control system parameter fluctuations.

Focusing on the control input, in FIG. 7(b) where the load has a control parameter equal to the calculated value, the control according to the present invention obtains a control input whose transfer function is approximately equal to the equivalent control input, and chattering is reduced. Almost invisible.

Note that control calculations regarding variables such as these variable gains can be processed by a signal processor.

〔Effect of the invention〕

As explained above, in the present invention, the control input is designed using the offset of the sliding curve and the position feedback of the variable gain. This makes it possible to clearly and appropriately design the gain, variable gain, and slope C of the sliding curve for specifying the specified control input. Thereby, chattering can be suppressed to the necessary minimum. Since the integral term is limited by the magnitude of the offset, torque disturbances can be compensated for without impairing robustness, and steady-state deviations can be eliminated. Further, the present invention can be easily introduced into conventional PI control, and it is possible to easily change PI control performed by software to control of a variable structure system.

[Brief explanation of the drawing]

Fig. 1 is a block diagram of a control system using variable structure control according to the present invention, Fig. 2 is a block diagram when x = 0, and Fig. 3 is a conversion of Fig. 2 into a system whose output is x. FIG. 4 is a block diagram when FIG. 3 is converted into the quadratic standard form. FIG. 5 shows the relationship between the sliding curve in the phase plane and the offset δ. 6 and 7 show the application of this control method to a positioning control system using a servo motor, and show a comparison with PI control. 1 Nisliding mode controller 2: Block representing transfer function 3: Integral element Patent applicant Anyo Electric Manufacturing Co., Ltd. Agent
Masu Kobori (and 2 others) Figure 1 Figure 2 Figure 3 Figure 6 Figure 7

Claims (1)

[Claims] 1. In the control of a variable structure system, when applying a control input U that satisfies the occurrence of a sliding mode, the speed axis and sliding curve S on the phase plane regarding positional deviation
1. A method for designing a control input in a variable structure control system, characterized in that the control input is designed based on an offset from =0 and a position feedback amount of a variable gain. 2. In the control of a variable structural system, when determining the slope of the sliding curve S, the gain constant designed for determining the slope and control input U is calculated using the position loop gain k_v of the proportional control system and the cut of the speed loop. Using the off angular frequency k_v, the damping coefficient ζ and the natural angular frequency ω_n,
The maximum value of the slope C_m_a_x is calculated as C_m_a_x=k_
2. A control input design method for a variable structure control system according to claim 1, wherein the control input is given as v_m_a_x.