CN104821769A - Control method for stepping motor of multi-freedom-degree permanent magnet inductor type - Google Patents

Abstract

The invention discloses a control method for a stepping motor of a multi-freedom-degree permanent magnet inductor type, and the method comprises: step S1, building a dynamical model of a permanent-magnet spherical stepping motor in a rotor fixed coordinate system in a rotating manner through a Cardan angle according to an operation process of the permanent-magnet spherical stepping motor; and step S2, optimizing the control process of the operation of the permanent-magnet spherical stepping motor based on an optimal stability control theory. Through the current vector control of the permanent-magnet spherical stepping motor, an optimized self-adaption control scheme for the stepping motor of the multi-freedom-degree permanent magnet inductor type is proposed, and the effective control of all axial rotational inertias and torques of the rotor is achieved, thereby enabling the motor to adapt to the change of various environmental conditions and loads, and obtaining the optimal output control characteristics so as to achieve the optimal movement track and optimal control characteristic of a drive robot.

Description

The control method of multiple degrees of freedom permanent magnet induction stepping motor

Technical field

The present invention relates to motor control technology field, particularly relate to a kind of control method of multiple degrees of freedom permanent magnet induction stepping motor.

Background technology

As the actuator of robot and System for Joint Motion of Manipulator, it is comparatively common that one dimension controls motor.The appearance of novel three degree of freedom spherical motor, joint of robot is moved can be completed in less three dimensions, thus simplifies system configuration, reduces organization volume, and improves the dynamic property of system, static properties and positioning precision.

But, Permanent magnetsphericalsteppermotor carries out the restriction of commutation control model by Control stator coil owing to being limited by, and sphere finite discrete point can only be adopted to describe continuous print three dimensions, make this globular motor only can complete fixed-point motion, positioning precision is too low.Apparently, for Permanent magnetsphericalsteppermotor, control and positioning precision are a difficult point all the time.

Seek a kind ofly to control to stablize, the control method of Permanent magnetsphericalsteppermotor that positioning precision is high become one of those skilled in the art's technical problem urgently to be resolved hurrily.

Therefore for prior art Problems existing, this case designer is by means of being engaged in the industry experience for many years, and active research improves, so there has been the control method of a kind of multiple degrees of freedom permanent magnet induction of the present invention stepping motor.

Summary of the invention

The present invention be directed in prior art, tradition Permanent magnetsphericalsteppermotor is owing to being limited by the restriction being carried out commutation control model by Control stator coil, and sphere finite discrete point can only be adopted to describe continuous print three dimensions, the defects such as this globular motor only can complete fixed-point motion, and positioning precision is too low are made to provide a kind of control method of multiple degrees of freedom permanent magnet induction stepping motor.

For realizing the object of the present invention, the invention provides a kind of control method of multiple degrees of freedom permanent magnet induction stepping motor, the control method of described multiple degrees of freedom permanent magnet induction stepping motor, comprising:

Perform step S1: according to the running of Permanent magnetsphericalsteppermotor, and utilize Ka Erdan angle to rotate the kinetic model setting up Permanent magnetsphericalsteppermotor under rotor fixed coordinate system;

Perform step S2: based on optimal stability control theory, optimize the control procedure of Permanent magnetsphericalsteppermotor operation.

Alternatively, the control procedure optimization system of described Permanent magnetsphericalsteppermotor operation is by the Current Vector Control to Permanent magnetsphericalsteppermotor, multiple degrees of freedom permanent magnet induction stepping motor Adaptive control with optimization scheme is proposed, the each axial rotation inertia of rotor and moment are control effectively, it is made effectively to adapt to the change of various environmental condition and load, obtain optimum output control characteristic, to realize optimum movement locus and the optimal control characteristic of drive machines people.

Alternatively, the approximate error of described adaptive fuzzy system is enough little, then system keeps stable state.

Alternatively, the modeling process of the kinetic model of described Permanent magnetsphericalsteppermotor ignores friction and uncertain disturbances.

Alternatively, when described Permanent magnetsphericalsteppermotor is unloaded, the centre of sphere and the stator of rotor ball are based upon rest frame.

Alternatively, 0-x ₀y ₀z ₀kinetic coordinate system overlap with the initial position of 0-xyz system.

In sum, the present invention is by analyzing Permanent magnetsphericalsteppermotor running, establish dynamical model of rotor, and utilizing the rotation of Ka Erdan angle to set up on the basis of spherical spinner kinetic model under rotor fixed coordinate system, based on system optimal stability control theory, further optimization Permanent magnetsphericalsteppermotor runs control procedure, by the Current Vector Control to Permanent magnetsphericalsteppermotor, multiple degrees of freedom permanent magnet induction stepping motor Adaptive control with optimization scheme is proposed, the each axial rotation inertia of rotor and moment are control effectively, it is made effectively to adapt to the change of various environmental condition and load, obtain optimum output control characteristic, to realize optimum movement locus and the optimal control characteristic of drive machines people.

Accompanying drawing explanation

Figure 1 shows that the flow chart of the control method of multiple degrees of freedom permanent magnet induction stepping motor of the present invention.

Figure 2 shows that the schematic diagram that Ka Erdan angle rotates;

Figure 3 shows that the adaptive control block diagram of the control method of multiple degrees of freedom permanent magnet induction stepping motor of the present invention.

Embodiment

By describe in detail the invention technology contents, structural feature, reached object and effect, coordinate accompanying drawing to be described in detail below in conjunction with embodiment.

Refer to Fig. 1, Figure 1 shows that the flow chart of the control method of multiple degrees of freedom permanent magnet induction stepping motor of the present invention.The control method of described multiple degrees of freedom permanent magnet induction stepping motor, comprising:

Perform step S1: according to the running of Permanent magnetsphericalsteppermotor, and utilize Ka Erdan angle to rotate the kinetic model setting up Permanent magnetsphericalsteppermotor under rotor fixed coordinate system;

Perform step S2: based on optimal stability control theory, optimize the control procedure of Permanent magnetsphericalsteppermotor operation.

As those skilled in the art, easy understand ground, spherical spinner model not adopts conventional transformation matrix to carry out to the description rotating change between coordinate system, and the introducing of contravariant vector and covariant vector is not easy to the understanding to model.On the other hand, variable reluctance spherical spinner kinetic model is based upon generalized Euler and rotates on the basis of X-Y-Z, and when actual rotational angle is less, computational process easily produces singular point, is unfavorable for the introducing of angular displacement infinitesimal.

Refer to Fig. 2, Fig. 3, Figure 2 shows that the schematic diagram that Ka Erdan angle rotates.Figure 3 shows that the adaptive control block diagram of the control method of multiple degrees of freedom permanent magnet induction stepping motor of the present invention.In step sl, in order to simplify the modeling process of the kinetic model of Permanent magnetsphericalsteppermotor, ignore friction and various uncertain disturbances.When described Permanent magnetsphericalsteppermotor is unloaded, the centre of sphere and the stator of rotor ball are based upon rest frame.0-x ₀y ₀z ₀kinetic coordinate system overlap with the initial position of 0-xyz system, then the determined change in location of rotor ball can by Ka Erdan angle rotate describe.The dominant vector set up is as follows:

$\mathrm{\τ}=H\left(q\right)\stackrel{..}{q}+C(q,\stackrel{.}{q})\stackrel{.}{q}---\left(1\right)$

Wherein, $H\left(q\right)=\left[\begin{array}{ccc}I& 0& I\sin \mathrm{\β}\\ 0& I& 0\\ I\sin \mathrm{\β}& 0& I\end{array}\right]---\left(2\right)$

$C(q,\stackrel{.}{q})=\left[\begin{array}{ccc}0& \frac{1}{2}\mathrm{I\γ}\cos \mathrm{\β}& \frac{1}{2}\mathrm{I\β}\cos \mathrm{\β}\\ -\frac{1}{2}\mathrm{I\γ}\cos \mathrm{\β}& 0& -\frac{1}{2}\mathrm{I\α}\cos \mathrm{\β}\\ \frac{1}{2}\mathrm{I\β}\cos \mathrm{\β}& \frac{1}{2}\mathrm{I\α}\cos \mathrm{\β}& 0\end{array}\right]---\left(3\right)$

Q represents generalized displacement matrix multiplier.

In the present invention, when the kinetic model of described Permanent magnetsphericalsteppermotor exists uncertain parameters and load rotating inertia matrix there is disturbance term, robust controller is devised.The Theory of Stability basis of robust controller is Lyapunov's stability theorem.For deriving auto-adaptive control scheme, first provide dynamical model of rotor known time input-output stability theory control mode.Different from all kinds of control programs designed based on Lyapunov's stability theorem, after adding the control law determined, closed-loop error equation is a nonlinear equation.Consider that the situation that motion vector mouth d (f) is time variation amount expected by rotor, namely rotor does CP motion, and position deviation is:

e＝q-q _d(4)

Utilize Fuzzy Adaptive Control Scheme, the switching function in robust controller is carried out obfuscation, simultaneously by switching function serialization, to reduce the shake of described robust controller.

For the single input single output control system of n rank,

x ⁽ⁿ⁾＝f(x,t)+g(x,t)u(t)+d(t) (5)

Wherein, f (x, t) and g (x, t) > 0 is unknown nonlinear function, and x ∈ R ⁿ, u ∈ R, y ∈ R, the unknown disturbances that d (t) is bounded.

Definition switching function:

$s(x,t)=k_{1}e+k_2\stackrel{.}{e}+...+k_{n-1}{e}^{(n-2)}+e^{(n-1)}=\mathrm{ke}---\left(6\right)$

Wherein, k=[k ₁, k ₂..., k _n-1, 1] and meet Holwitz condition, then control rate can be designed to:

$u\left(t\right)=\frac{1}{g(x,t)}(-f(x,t)-\underset{i=1}{\overset{n-1}{\mathrm{\Σ}}}{k}_i{e}^{\left(i\right)}+x_d^{\left(n\right)}-\mathrm{\ηsgn}\left(s\right))---\left(7\right)$

Differential is got to switching function, then:

$\begin{array}{c}\stackrel{.}{s}(x,t)=k_1\stackrel{.}{e}+k_2\stackrel{..}{e}+...+k_{n-1}{e}^{(n-1)}+e^{\left(n\right)}\\ =\underset{i=1}{\overset{n-1}{\mathrm{\Σ}}}{k}_i{e}^{\left(i\right)}+x^{\left(n\right)}-x_d^{\left(n\right)}\\ =\underset{i=1}{\overset{n-1}{\mathrm{\Σ}}}{k}_i{e}^{\left(i\right)}+f(x,t)+g(x,t)u+d\left(t\right)-x_d^{\left(n\right)}\end{array}---\left(8\right)$

Formula (7) is updated to in, then:

$s(x,t)\·\stackrel{.}{s}(x,t)=s(x,t)\·(d\left(t\right)-\mathrm{\ηsgn}\left(s\right))---\left(9\right)$

As f (x, t), when the upper bound of g (x, t), d (t) is unknown, control rate is inapplicable.By f (x, t), g (x, t), d (t) are fuzzy to be turned to systematical control rate then after obfuscation is:

$u\left(t\right)=\frac{1}{\hat{g}(x,t)}(-\hat{f}(s,t)-\underset{i=1}{\overset{n-1}{\mathrm{\Σ}}}{k}_i{e}^{\left(i\right)}+x_d^{\left(n\right)}-\hat{h}\left(s\right))---\left(10\right)$

$\hat{f}\left(x\right|{\mathrm{\θ}}_f)={\mathrm{\θ}}_f^T\mathrm{\ξ}\left(x\right),\hat{g}\left(x\right|{\mathrm{\θ}}_g)={\mathrm{\θ}}_g^T\mathrm{\ξ}\left(x\right),\hat{h}\left(s\right|{\mathrm{\θ}}_h)={\mathrm{\θ}}_h^T\mathrm{\φ}\left(s\right)---\left(11\right)$

In formula (11), represent the output of fuzzy system, ξ (x) and φ (s) represents fuzzy vector, θ _f, θ _g, θ _hfor the adaptive change parameter of adaptive controller.

Adaptive control rate reasonable in design and should satisfy condition for:

${\stackrel{.}{\mathrm{\θ}}}_f=r_1\mathrm{s\ξ}\left(x\right)---\left(12\right)$

${\stackrel{.}{\mathrm{\θ}}}_g=r_2\mathrm{s\ξ}\left(x\right)u---\left(13\right)$

${\stackrel{.}{\mathrm{\θ}}}_h=r_3\mathrm{s\φ}\left(s\right)---\left(14\right)$

$\hat{h}\left(s\right|{\mathrm{\θ}}_h^{*})={\mathrm{\η}}_{\mathrm{\Δ}}\mathrm{sgn}\left(s\right),{\mathrm{\η}}_{\mathrm{\Δ}}=D+\mathrm{\η},\left|d\left(t\right)\right|\≤D---\left(15\right)$

Therefore formula (10) represents fuzzy control rate, formula (12), formula (13), formula (14) represent adaptive control rate.Its proof procedure is as follows:

Suppose represent the optimized parameter of adaptive controller, and have:

${\mathrm{\θ}}_f^{*}=\underset{{\mathrm{\θ}}_f\∈{\mathrm{\Ω}}_f}{\arg \min }\left[\sup \right|\underset{x\∈R^n}{\hat{f}\left(x\right|{\mathrm{\θ}}_f)-f(x,t)}\left|\right]---\left(16\right)$

${\mathrm{\θ}}_g^{*}=\underset{{\mathrm{\θ}}_g\∈{\mathrm{\Ω}}_g}{\arg \min }\left[\sup \right|\underset{x\∈R^n}{\hat{g}\left(x\right|{\mathrm{\θ}}_g)-g(x,t)}\left|\right]---\left(17\right)$

${\mathrm{\θ}}_h^{*}=\underset{{\mathrm{\θ}}_h\∈{\mathrm{\Ω}}_h}{\arg \min }\left[\sup \right|\underset{x\∈R^n}{\hat{h}\left(x\right|{\mathrm{\θ}}_h)-u_{\mathrm{sw}}}\left|\right]---\left(18\right)$

The minimal error of define system is ω, then:

$\begin{array}{c}\mathrm{\ω}=f(x,t)+g(x,t)u\left(t\right)+d\left(t\right)-\hat{f}\left(x\right|{\mathrm{\θ}}_f^{*})-\hat{g}\left(x\right|{\mathrm{\θ}}_f^{*})u\left(t\right)-d\left(t\right)\\ =f(x,t)-\hat{f}\left(x\right|{\mathrm{\θ}}_f^{*})+(g(x,t)-\hat{g}\left(x\right|{\mathrm{\θ}}_f^{*}))u\left(t\right)\end{array}---\left(19\right)$

Fuzzy control rate is substituted in the derived function of switching function, then:

In formula (20), definition Liapunov function is:

Wherein, r ₁, r ₂, r ₃for positive number.Get the derived function of liapunov function, then:

Because $\hat{h}\left(x\right|{\mathrm{\θ}}_h^{*})={\mathrm{\η}}_{\mathrm{\Δ}}\mathrm{sgn}\left(s\right),$ Then formula (22) is:

In formula (22), formula (23), formula (12), formula (13), formula (14) are substituted into formula (23), then:

Apparently, if the approximate error of adaptive fuzzy system is enough little, then system keeps stable state.

In sum, the present invention is by analyzing Permanent magnetsphericalsteppermotor running, establish dynamical model of rotor, and utilizing the rotation of Ka Erdan angle to set up on the basis of spherical spinner kinetic model under rotor fixed coordinate system, based on system optimal stability control theory, further optimization Permanent magnetsphericalsteppermotor runs control procedure, by the Current Vector Control to Permanent magnetsphericalsteppermotor, multiple degrees of freedom permanent magnet induction stepping motor Adaptive control with optimization scheme is proposed, the each axial rotation inertia of rotor and moment are control effectively, it is made effectively to adapt to the change of various environmental condition and load, obtain optimum output control characteristic, to realize optimum movement locus and the optimal control characteristic of drive machines people.

Those skilled in the art all should be appreciated that, without departing from the spirit or scope of the present invention, can carry out various modifications and variations to the present invention.Thus, if when any amendment or modification fall in the protection range of appended claims and equivalent, think that these amendment and modification are contained in the present invention.

Claims (6)

1. a control method for multiple degrees of freedom permanent magnet induction stepping motor, is characterized in that, the control method of described multiple degrees of freedom permanent magnet induction stepping motor, comprising:

Perform step S1: according to the running of Permanent magnetsphericalsteppermotor, and utilize Ka Erdan angle to rotate the kinetic model setting up Permanent magnetsphericalsteppermotor under rotor fixed coordinate system;

Perform step S2: based on optimal stability control theory, optimize the control procedure of Permanent magnetsphericalsteppermotor operation.

2. the control method of multiple degrees of freedom permanent magnet induction stepping motor as claimed in claim 1, it is characterized in that, the control procedure optimization system of described Permanent magnetsphericalsteppermotor operation is by the Current Vector Control to Permanent magnetsphericalsteppermotor, multiple degrees of freedom permanent magnet induction stepping motor Adaptive control with optimization scheme is proposed, the each axial rotation inertia of rotor and moment are control effectively, it is made effectively to adapt to the change of various environmental condition and load, obtain optimum output control characteristic, to realize optimum movement locus and the optimal control characteristic of drive machines people.

3. the control method of multiple degrees of freedom permanent magnet induction stepping motor as claimed in claim 2, it is characterized in that, the approximate error of described adaptive fuzzy system is enough little, then system keeps stable state.

4. the control method of multiple degrees of freedom permanent magnet induction stepping motor as claimed in claim 1, is characterized in that, the modeling process of the kinetic model of described Permanent magnetsphericalsteppermotor ignores friction and uncertain disturbances.

5. the control method of multiple degrees of freedom permanent magnet induction stepping motor as claimed in claim 4, is characterized in that, when described Permanent magnetsphericalsteppermotor is unloaded, the centre of sphere and the stator of rotor ball are based upon rest frame.

6. the control method of multiple degrees of freedom permanent magnet induction stepping motor as claimed in claim 5, is characterized in that, 0-x ₀y ₀z ₀kinetic coordinate system overlap with the initial position of 0-xyz system.