JP2655895B2 - Spring device - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION <Industrial Application Field> The present invention provides a drive control system including an actuator, a power amplifier for driving the actuator, a displacement sensor for measuring displacement of a rotor of the actuator, and a compensator. It relates to a stable spring device which is realized electrically.

<Prior Art> With a combination of ordinary springs, a stable negative spring that is displaced in the direction opposite to the direction of the external force cannot be realized in principle.

Conventionally, a spring electrically realized by a stable drive control system having an actuator, a power amplifier for driving the actuator, a displacement sensor for measuring the displacement of a rotor of the actuator, and a compensator, has conventionally had a compensator. Therefore, a stable negative spring in which the rotor is displaced in the direction opposite to the external force applied to the rotor cannot be realized because only the negative feedback of the displacement signal is performed.

<Problems to be Solved by the Invention> In view of the above prior art, in the present invention, a signal proportional to the output current of the power amplifier is positively fed back by the compensator as long as the entire system maintains stability, or The input signal to the power amplifier is positively fed back, so that the transfer function from the external force applied to the rotor to the rotor displacement has an unstable zero point, so that the transfer function can be obtained in a frequency band corresponding to the unstable zero point. Is set to a negative value, and an electric negative spring is realized such that the rotor is stably displaced in the direction opposite to the direction of the external force applied to the rotor.
That is, a stable negative spring is electrically realized in which the external force applied to the rotor and the displacement of the rotor have a linear relationship having a negative proportional constant in a static state or a low frequency band.

An object of the present invention is to provide a stable spring having a negative compliance constant such that it is displaced in a direction opposite to the direction of the external force,
It is to be realized electrically.

<Means and Actions for Solving the Problems> The present invention relates to a stable spring device which is realized electrically, and a compensator is provided with a signal proportional to an output current of the power amplifier or a signal to the power amplifier. By positively feeding back the input signal, the transfer function from the external force applied to the rotor to the displacement of the rotor has at least one unstable zero, and the real parts of all poles of the transfer function are negative values. The most important feature is that the rotor is displaced in a direction opposite to the direction of the external force with respect to the external force.

In the compensator of the present invention, while the conventional compensator performs only negative feedback, the signal proportional to the output current of the power amplifier is positively fed back, or the input signal to the power amplifier is positively fed back. It is possible to have at least one unstable zero in the transfer function from the applied external force to the displacement of the rotor. That is, since the numerator of the transfer function from the external force to the displacement has a zero on the right half plane of the complex plane, the constant term of the numerator polynomial becomes a negative value. On the other hand, if the system is stable, the denominator of the transfer interval, that is, the poles are all present in the left half plane of the complex plane, so that the constant term of the denominator polynomial always has a positive value. Therefore, since the zero frequency gain of the transfer function, that is, the DC gain takes a negative value, a displacement having a sign opposite to that of the external force occurs in a steady state, that is, when a sufficient time has elapsed. Therefore, the rotor is normally displaced in a direction opposite to the external force applied to the rotor.

<Example> Hereinafter, an example of the present invention will be described in detail with reference to the drawings. In the following embodiments, an example of a spring device that performs translational displacement in a direction opposite to a translational external force by using a translational drive actuator will be described. is there.

1 to 3 show an embodiment of the present invention. As shown in the figure, the spring device of this embodiment includes a translation drive actuator 1 such as a voice coil motor, a constant current type power amplifier 2, a displacement sensor 3 such as a non-contact type gap sensor, and a compensator 4. And a drive control system having The actuator 1 drives the rotor 5 by the output current i from the power amplifier 2, and the displacement x is detected by the displacement sensor 3, multiplied by the gain k _s and input to the compensator 4 as a signal y (= k _s x). Is done. The compensator 4 can have a negative compliance characteristic by positive feedback of a signal proportional to the output current i from the power amplifier 2. Even when a constant-voltage power amplifier is used, a negative compliance characteristic can be realized by selecting a control parameter in consideration of the first-order lag of current and voltage in the constant-voltage power amplifier, as described later.

Here, as shown in FIG. 3, a general block diagram of the translation drive actuator, a transfer function G _px from an external force q applied to the rotor 5 to a displacement x of the rotor 5 is represented by the following equation (1). .

Where α = D _O / M _O , β = K _O / M _O , δ = 1 / M _O
D _O is the viscosity coefficient of the actuator, M _O is the mass of the rotor 5, K _O
Is the spring constant of the actuator. In Figure 3, k _i is the force constant of the actuator, f is the force generated by the actuator, the speed of the rotor, the acceleration of the rotor, is 7,8 an integrator.

Next, as shown in FIG. 2, a block diagram of a drive control system for realizing the spring device of the present embodiment uses an integrator 6, and the following equations (2), (3) ( The relational expression of 4) is derived.

_{u = m O0 y + (m} O1 y + l 1 i) / s ... (2) i = k a u ... (3) y = k s x ... (4) where, u is a power amplifier input, l ₁ is the positive feedback gain,
m _O0, m _O1 control parameter, k _a is the gain of the power amplifier.

When the transfer function W _qx from the compensated external force q to the displacement x of the rotor is calculated from the above equations (1) to (4), it is shown by the following equation.

However, it is _{γ = k a k i k s} / M O.

Here, in order to stably displace in the opposite direction to an external force, the transfer function W _qx of the above equation (5) must be stable and a non-minimum phase transition system having an unstable zero point in the molecule. That is, the denominator of the transfer function W _qx must have a pole in the left half of the s-plane, and its numerator must have a zero in the right half of the s-plane. If the conditions for this are obtained by the method of Hurwitz, the control parameters m _O0 , m _O1 and the positive feedback gain l ₁ that satisfy the simultaneous inequalities shown below can be selected.

0 <l ₁ <α (6) β-αl ₁ -m _O0 γ> 0 (7) -βl ₁ -m _O1 γ> 0 (8) (α-l ₁ ) (β-αl ₁ -m _{O0 γ) - (- βl 1} -m O1 γ)>
0 (9) Therefore, when such a condition is satisfied, ω <l ₁ (red /
In the frequency band of (sec), Gain (W _qx ) <0, and the steady value x ′ of the rotor displacement x when a constant external force q _O > 0 is applied is as shown in the following equation, and is in the direction opposite to the external force. And the displacement is stable.

Specific numerical examples are shown below. D _O = 70N / m / s, M _O = 0.1
When kg, K _O = 0 N / m, k _a = 1 V / A, k _i = 1 N / A, and k _s = 5 V / mm, for example, m _O0 = −1.4, l ₁ = 28, m _O1 = − If a control parameter of 28.0 is selected, W _qx is as follows.

This system is clearly stable, and at zero frequency or a sufficiently low frequency band, the relation between the external force q applied to the rotor and the displacement x is x = −0.0002q (12), and −0.0002 (m / N) = A negative spring with a negative compliance constant of -0.2 (mm / N) is realized. This value can be set freely by adjusting the control parameters and the characteristics of the actuator.

FIG. 4 shows a simulation result of a displacement x of the rotor when a step-like external force q having a magnitude of 1N is applied. According to the figure, the rotor moves in the direction opposite to the external force applied constantly (1
2) It can be confirmed that it is displaced by 0.2 mm according to the formula.

In this embodiment, when there is no friction in the actuator, that is, when D _O = 0, equation (6) is not satisfied, so that a stable negative spring cannot be realized. In such a case, the characteristics of the actuator are improved by adding damping mechanically or electrically, and D _O > 0
It is good.

Next, another embodiment of the present invention will be described with reference to the block diagram shown in FIG. The translation drive actuator shown in FIG. 3 was used as the actuator in the embodiment shown in FIG. In the following, for the sake of simplicity, description will be made assuming that all constants and variables to be described are dimensionless with appropriate values. The transfer function W _qx from the external force q after compensation to the displacement x of the rotor is as follows.

_{However, α 3 = k u k d} M o, α 2 = k u k p M o + k u k d D o -M o, α 1 = k u k p
_{D o + k u k d K} o -D o -k d, α 0 = k u k p K o -K o -k p, b 1 = k
_u k _d , b ₀ = k _u k _p -1.

Here, the control parameter to satisfy the following simultaneous equations in (13) k _p, k _d, if you choose a positive feedback gain k _u, W _qx is and stable, non-minimum phase shift system with unstable zeros in the molecule Becomes

b ₁ > 0 (14) b ₀ <0 (15) α _j > 0 (j = 0,..., 3) (16) α ₂ α ₁ −α ₃ α ₀ > 0 (17) In the best frequency band of ω <b ₀ / b ₁ , Gain (W _qx )
<0, the steady-state value x 'of the displacement x of the rotor when a constant external force q ₀ > 0 is applied is as shown in the following equation, and a stable negative spring can be realized.

x ′ = (b ₀ / α ₀ ) q ₀ <0 (18) Specific numerical examples are shown below. For simplicity, D _o = 10,
M _o = K _o = time of _{k a = k i = k s} = 1 is, for example, k _u = -0.5, k
If control parameters _p = -1 and k _d = -10 are selected, W
_qx is as follows.

Therefore, this system is clearly stable, and the static relation between the constant external force q ₀ and the steady-state value x ′ of the rotor displacement x becomes as shown in the following equation (20), and the negative compliance constant of −1 is obtained. A negative spring with is realized.

x ′ = − q ₀ (20) When _Do = 0 as in the above-described embodiment, mechanical or electrical damping is added to improve the characteristics of the actuator, and _Do > 0.

<Effects of the Invention> As described in the above two embodiments, the spring device according to the present invention has a stable negative spring characteristic displaced in the direction opposite to the direction of the external force, which cannot be realized by the conventional technology. Is realized electrically. Therefore, the spring device of the present invention can be a very wide-ranging mechanical element in the field of mechatronics represented by a robot, alone or in combination with a normal spring. For example, by incorporating the present apparatus at the front stage of the end effector of the deburring robot, it becomes possible to more positively remove the unevenness of the object supported by the flexible base.

[Brief description of the drawings]

FIG. 1 is a structural view of a spring device according to an embodiment of the present invention, FIG. 2 is a block diagram of the spring device shown in FIG. 1, and FIG. FIG. 4 is a block diagram, FIG. 4 is a graph showing a result of simulating a rotor displacement when a step-like external force having a magnitude of 1N is applied, and FIG. 5 is a graph showing another embodiment of the present invention. In the drawing, 1 is a translation drive actuator, 2 is a power amplifier, 3 is a displacement sensor, 4 is a compensator, 5 is a rotor, and 6, 7, and 8 are integrators.

Claims (1)

(57) [Claims] 1. A stable spring device electrically realized by a drive control system having an actuator, a power amplifier for driving the actuator, a displacement sensor for measuring a displacement of a rotor of the actuator, and a compensator. , By causing the compensator to positively feed back a signal proportional to the output current of the power amplifier or an input signal to the power amplifier, at least one transfer function from an external force applied to the rotor to a displacement of the rotor is provided. An unstable zero point is provided, and the real parts of all poles of the transfer function are set to negative values, and the rotor is displaced in a direction opposite to the direction of the external force with respect to the external force. Spring device.