CN105372992A - Underactuated sliding-mode control algorithm of suspended floater follow-up system - Google Patents
Underactuated sliding-mode control algorithm of suspended floater follow-up system Download PDFInfo
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- CN105372992A CN105372992A CN201510859604.6A CN201510859604A CN105372992A CN 105372992 A CN105372992 A CN 105372992A CN 201510859604 A CN201510859604 A CN 201510859604A CN 105372992 A CN105372992 A CN 105372992A
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- G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
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Abstract
The present invention relates to an underactuated sliding-mode control algorithm of a suspended floater follow-up system. The algorithm provided by the invention comprises: establishing a kinematics formulation, simplifying the kinematics formulation according to the symmetry and the decoupling of the formulation, and designing a controller and regulating the parameters of the controller on the basis of the kinematics formulation. According to the invention, the problems the parameters of other control methods are difficult to perform mutual coordination and matching and the tracking precision cannot be ensured under the condition of changing the parameters in real time are solved; and moreover, the response quality of a closed-loop system is improved.
Description
Technical field
The invention belongs to low gravitation following control system field, relate to a kind of drive lacking sliding mode control algorithm suspending floating thing servomechanism in midair.
Background technology
The space equipment that mankind's exploration of the universe is used is in recent years increasing, in view of these space equipments necessarily require reliability and security, therefore the requisite stage is become on ground in the face of space equipment does test, how become the key of problem at ground simulation low-gravity environment, wherein suspension method ground low-gravity environment simulation system is widely applied.This system in the vertical direction provides one to act on objective body barycenter by constant tension device and the balancing force reverse greatly with objective body self gravitation etc., realizes low-gravity simulation for offsetting objective body self gravitation.Construct the servomechanism regulated based on hoist cable pivot angle in the horizontal direction, when objective body moves generation drift angle in the horizontal direction, servomechanism is followed rapidly objective body by compensation drift angle control suspension apparatus and is moved, and makes perturbed force momentum be zero, realizes the real time modelling of satellite tangential movement.
The current Research Literature for suspention floating thing horizontal servomechanism control algolithm is less, and document " suspension type gravity compensation system precision tracking method " has been set forth a kind of method utilizing nonlinear programming to provide optimum control and realized servomechanism control.The method belongs to a kind of planing method, and not only searching process is complicated, and belongs to open cycle system, cannot ensure that in motion process, objective body changes desired trajectory in real time.
Document " three-dimensional gravity compensation method and space object floating analogue experiment installation are studied ", for suspension system servo antrol problem, proposes a kind of method being planned hunting gear movement locus by measurement target body speed and displacement.The method is using control as driving item, but the corresponding torque mode of driving force precision in Electric Machine Control is not high, and therefore this method is not good enough for suspending control effects in servomechanism in midair.
Publication " a kind of suspend the acceleration compensation control method of drift servomechanism and the control method based on model selection in midair " provides a kind of by angle integration design acceleration feedback controller (PID-Acceleration, be abbreviated as PIDA) method, the closed-loop control to servomechanism is completed respectively under motor torque pattern and rotating speed pattern, but the method controls based on classical PID the innovatory algorithm that does, parameter regulates more complicated, and needs to readjust parameter when changing for Different Weight objective body and rope length.
Summary of the invention
Not high for suspention floating thing servomechanism control accuracy in order to solve existing method, difficult parameters, mutually to coordinate matching problem, now provides a kind of drive lacking sliding-mode control.The method is based on servomechanism kinematical equation, and compared to traditional PID control method, parameter regulates simple, finely tunes parameter just can realize following in real time when objective body weight, suspension rope length change.
For a drive lacking sliding-mode control for suspention floating thing servomechanism, the method comprises the following steps:
Step one: the control objectives of clear and definite servomechanism: control compliant platform and catch up with objective body rapidly, follows compliant platform and objective body after terminating and is synchronized with the movement, keep rope vertical.
Step 2: the kinematical equation providing suspention floating thing servomechanism single-degree-of-freedom:
；
Wherein,
for the quality of objective body,
for acceleration of gravity,
for sling length,
for the acceleration of objective body X-direction movement,
for X-direction augmented state amount, i.e. the X-direction margin of error,
for X-direction angle,
for X-direction angular acceleration,
for the perturbed force of objective body X-direction.
Step 3: provide drive lacking sliding mode controller form according to kinematical equation:
；
Wherein,
for X-direction Integral Convergence item,
for X-direction ratio convergent,
for the Dynamic sliding mode function of X-direction,
for the handoff gain of X-direction sliding formwork Reaching Law,
for the exponential convergence item of X-direction sliding formwork Reaching Law,
for the speed of objective body X-direction movement,
for the acceleration of objective body X-direction movement,
for X-direction quantity of state, i.e. the X-direction margin of error,
for X-direction angle,
for X-direction angular velocity,
for acceleration of gravity,
for sling length;
Regulate the parameter of X-direction in drive lacking sliding mode controller, eliminate the error in X-direction servomechanism operational process, make system reach steady state (SS), realize following in real time objective body.
The present invention is the closed-loop control system utilizing Sliding mode variable structure control to design, and the structure of this control system can make corresponding change according to the change of current system, and system is run according to projected path; This control system to external world disturbance is insensitive, has stronger robustness.The present invention is applicable to suspend floating thing servomechanism field in midair.
Accompanying drawing explanation
Fig. 1 suspends the structural representation of floating thing servomechanism in midair;
Fig. 2 suspends floating thing servomechanism X-direction coordinate system in midair;
Fig. 3 is suspention floating thing servomechanism X-direction hoist cable pivot angle curve map;
Fig. 4 is suspention floating thing servomechanism X-direction hoist cable pivot angle integrated curve figure;
Fig. 5 is suspention floating thing servomechanism X-direction speed-error curve figure;
Wherein, 1, X to drive motor, 2, Y-direction drive motor, 3, X to line slideway, 4, Y-direction line slideway, 5, compliant platform, 6, optical position Analytical system, 7, hoist cable, 8, object of experiment body, 9, sub-truss, 10, combine Ore-controlling Role.
Embodiment
embodiment one:specify the control objectives of servomechanism: control compliant platform and catch up with objective body rapidly, follow compliant platform and objective body after terminating and be synchronized with the movement, keep rope vertical.
embodiment two:this enforcement is described further a kind of drive lacking sliding-mode control of suspending floating thing servomechanism in midair, and in present embodiment, kinematical equation is:
；
Wherein,
for the quality of objective body,
for acceleration of gravity,
for sling length,
for the acceleration of objective body X-direction movement,
the acceleration of objective body Y-direction movement,
for X-direction augmented state amount, i.e. the X-direction margin of error,
for Y-direction augmented state amount, i.e. the Y-direction margin of error,
for the perturbed force in objective body X-direction,
for the perturbed force in objective body Y-direction,
for X-direction angle,
for Y-direction angle,
for X-direction angular acceleration,
for Y-direction angular acceleration.
A kind of described in present embodiment suspends in midair in the drive lacking sliding-mode control of floating thing servomechanism, the effect of suspention floating thing servomechanism is motion state in the horizontal plane under simulated target body low gravitation state, and accompanying drawing 1 and accompanying drawing 2 are shown in structure and the distribution of X-direction coordinate system of suspention floating thing servomechanism.
Observation suspention floating thing servomechanism X-direction coordinate system and kinematical equation can find
two degree of freedom equations with
,
two degree of freedom equations are symmetrical, and degree of freedom is described
,
with
,
mutual decoupling zero.So kinematical equation can be reduced to according to the symmetry of equation and decoupling:
；
Kinematical equation is rewritten as
functional form:
；
Wherein,
for the quality of objective body,
for acceleration of gravity,
for sling length,
for the acceleration of compliant platform,
for augmented state amount, the i.e. margin of error,
for angle,
for angular acceleration,
for the perturbed force of objective body;
embodiment three:this enforcement is described further a kind of drive lacking sliding-mode control of suspending floating thing servomechanism in midair, in present embodiment, designs following system equation according to the kinematical equation of single-degree-of-freedom in embodiment two:
；
Wherein,
for control inputs
, coefficient is all known,
for the quality of objective body,
for sling length,
for the perturbed force of objective body,
for acceleration of gravity;
embodiment four:this enforcement makes the derivation of equation to a kind of drive lacking sliding-mode control of suspending floating thing servomechanism in midair, and derivation is as follows:
Get error equation:
;
Sliding formwork control law is set:
,
>0,
=1,2;
Equivalent control:
;
Switch and control:
;
Control law:
;
Stability and convergence:
Design error equation:
；
When
time, have
;
Get
,
for Hurwitz.Get
, then have
, get
, due to
for Hurwitz, then there is Lyapunov equation
, its solution is
; Get Lyapunov function
, then
Wherein,
for positively definite matrix
minimal eigenvalue,
；
Will
substitute into:
；
Get
,
,
; Get Lyapunov function
;
The control law obtained
for:
；
In this enforcement,
for Integral Convergence item,
for ratio convergent,
for the gain of sliding formwork Reaching Law,
for the exponential convergence item of sliding formwork Reaching Law,
for the acceleration of compliant platform.
Obtaining X-direction through above-mentioned derivation based on the controller of speed and acceleration is:
；
Wherein,
for acceleration of gravity,
for sling length,
for X-direction Integral Convergence item,
for X-direction ratio convergent,
for the Dynamic sliding mode function of X-direction,
for the gain of X-direction sliding formwork Reaching Law,
for the exponential convergence item of X-direction sliding formwork Reaching Law,
for the speed of objective body X-direction movement,
for the acceleration of objective body X-direction movement;
embodiment five:present embodiment is described further a kind of drive lacking sliding-mode control of suspending floating thing servomechanism in midair, regulates the method for X-direction parameter as follows described in present embodiment respectively:
Regulate switching control parameter
with
, make systematic error have convergent tendency; Regulate equivalent control parameter
with
, system state is remained on sliding-mode surface; Accurate adjustment switch controller exponential term parameter
with
, make systematic error converge to zero, in order to ensure error Fast Convergent and prevent vibration, should in increase
while reduce
;
In present embodiment, by adjustment control parameter, Sliding Mode Controller is played a role, ensure servomechanism accurate tracking.In order to test Sliding Mode Controller to suspention floating thing control performance in the horizontal direction, do following experiment.This experiment control target is that the real time kinematics speed of requirement objective body and desired speed deviation are no more than ± 1mm/s.Experiment start time objective body be subject to an X to
momentum, experiment duration 20
s.Getting controller relevant parameters is
,
,
,
,
,
.
Claims (4)
1. suspend a drive lacking sliding-mode control for floating thing servomechanism in midair, it is characterized in that, the method comprises the following steps:
Step one: the control objectives of clear and definite servomechanism: control compliant platform and catch up with objective body rapidly, follows compliant platform and objective body after terminating and is synchronized with the movement, keep rope vertical;
Step 2: under the state that objective body pendulum angle is very little, the kinematical equation according to suspention floating thing servomechanism simplifies, and the kinematical equation after simplification is:
；
Step 3: the drive lacking sliding mode controller according to the kinematical equation design simplified with exponential convergence performance:
；
This controller is only based on kinematical equation, simplify design cycle, control law is as the acceleration of motor, directly motor speed is controlled after integrable, controller using hoist cable pivot angle to the integration of time as tracking error, and make angle and angle differential be zero simultaneously, improve the control accuracy of low-gravity simulation equipment;
Step 4: adjustment control parameter: regulate switching control parameter, systematic error is restrained; Regulate equivalent control parameter, system state is remained on sliding-mode surface; Accurate adjustment switching control parameter, ensures that error convergence is 0 and prevents vibration.
2. a kind of drive lacking sliding-mode control of suspending floating thing servomechanism in midair according to claim 1, it is characterized in that, the kinematical equation described in step 2 is:
；
Wherein,
for the quality of objective body,
for acceleration of gravity,
for sling length,
for the acceleration of objective body X-direction movement,
the acceleration of objective body Y-direction movement,
for X-direction augmented state amount, i.e. the X-direction margin of error,
for Y-direction augmented state amount, i.e. the Y-direction margin of error,
for the perturbed force in objective body X-direction,
for the perturbed force in objective body Y-direction,
for X-direction angle,
for Y-direction angle,
for X-direction angular acceleration,
for Y-direction angular acceleration;
Can be found by suspention floating thing servomechanism X-direction coordinate system and kinematical equation
,
two degree of freedom equations with
,
two degree of freedom equations are symmetrical, and degree of freedom is described
,
with
,
mutual decoupling zero; So kinematical equation can be reduced to according to the symmetry of equation and decoupling:
；
Wherein,
for the quality of objective body,
for acceleration of gravity,
for sling length,
for the acceleration of compliant platform,
for augmented state amount, the i.e. margin of error,
for X-direction angle,
for angular acceleration in X-direction.
3. a kind of drive lacking sliding-mode control of suspending floating thing servomechanism in midair according to claim 1, it is characterized in that, step 3 provides drive lacking sliding mode controller according to kinematical equation:
Kinematical equation is rewritten as
with
functional form:
；
Then, the drive lacking sliding mode controller with exponential convergence performance is obtained according to above formula:
；
Wherein,
for X-direction Integral Convergence item,
for X-direction ratio convergent,
for the Dynamic sliding mode function of X-direction,
for the handoff gain of X-direction sliding formwork Reaching Law,
for the exponential convergence item of X-direction sliding formwork Reaching Law,
for the speed of objective body X-direction movement,
for the acceleration of objective body X-direction movement,
for X-direction quantity of state, i.e. the X-direction margin of error,
for X-direction angle,
for X-direction angular velocity,
for acceleration of gravity,
for sling length;
This controller is based on kinematical equation, and compared to traditional PID control method, parameter regulates simple, finely tunes parameter just can realize following in real time when objective body weight, suspension rope length change; Control law, as the acceleration of motor, directly controls motor speed after integration; Using hoist cable pivot angle to the integration of time as tracking error, and make angle and angle differential be zero simultaneously, improve the control accuracy of low-gravity simulation equipment; Add exponential convergence item in controller, make system response time faster and weaken shake.
4. a kind of drive lacking sliding-mode control of suspending floating thing servomechanism in midair according to claim 1, is characterized in that, step 4 adjustment control parameter:
Regulate switching control parameter
with
, make systematic error have convergent tendency; Regulate equivalent control parameter
with
, system state is remained on sliding-mode surface; Accurate adjustment switch controller exponential term parameter
with
, make systematic error converge to zero, in order to ensure error Fast Convergent and prevent vibration, should in increase
while reduce
.
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107458630A (en) * | 2017-06-07 | 2017-12-12 | 北京航空航天大学 | Across the yardstick tracking of suspension type active gravity compensation system hangs point |
| CN112817328A (en) * | 2020-12-31 | 2021-05-18 | 青岛理工大学 | Path planning and swing reduction control method of four-rotor variable-rope-length hanging system |
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| CN104460722A (en) * | 2014-09-19 | 2015-03-25 | 哈尔滨理工大学 | Acceleration compensation control method of suspension floating object follow-up system and mode-selection-based control method of suspension floating object follow-up system |
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| CN104460722A (en) * | 2014-09-19 | 2015-03-25 | 哈尔滨理工大学 | Acceleration compensation control method of suspension floating object follow-up system and mode-selection-based control method of suspension floating object follow-up system |
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Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107458630A (en) * | 2017-06-07 | 2017-12-12 | 北京航空航天大学 | Across the yardstick tracking of suspension type active gravity compensation system hangs point |
| CN107458630B (en) * | 2017-06-07 | 2020-06-30 | 北京航空航天大学 | Suspension point cross-scale tracking method for suspension type active gravity compensation system |
| CN112817328A (en) * | 2020-12-31 | 2021-05-18 | 青岛理工大学 | Path planning and swing reduction control method of four-rotor variable-rope-length hanging system |
| CN112817328B (en) * | 2020-12-31 | 2022-08-02 | 青岛理工大学 | Path planning and swing reduction control method of four-rotor variable-rope-length hanging system |
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Denomination of invention: An Underactuated Sliding mode control Control Method for Suspended Floating Object Servo System Effective date of registration: 20230526 Granted publication date: 20180731 Pledgee: Industrial Bank Limited by Share Ltd. Hefei branch Pledgor: Strict scientific and Technological Innovation Industry Development Group Hefei Co.,Ltd. Registration number: Y2023980041849 |