CN107643760A - A kind of coaxial two wheels robot balance controller based on LQR algorithms - Google Patents
A kind of coaxial two wheels robot balance controller based on LQR algorithms Download PDFInfo
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- 239000011159 matrix material Substances 0.000 claims 4
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Abstract
The present invention devises a kind of coaxial two wheels robot balance controller based on LQR algorithms, establishes coaxial two wheels robot nonlinear model according to Newtonian mechanics analytic approach first, and then linearizes and decouple the model, finally designs balance controller according to inearized model；It is characterized in that：Described coaxial two wheels robot is that one kind is rigidly connected in being studied herein, i.e., the car body of robot and wheel are independent；The balance controller of described coaxial two wheels robot is to be based on feedback of status Method of Pole Placement, i.e., using the characteristic of controlled system arbitrary disposition limit in the case of controllable, coaxial two wheels robot is reached plateau within the short time in the case of initial interference；The balance controller of described coaxial two wheels robot introduces LQR algorithms, when controlled system be it is linear or linearisation, can take into account multinomial performance index with optimum control, coaxial two wheels robot is reached plateau within the short time in the case of initial interference.
Description
Technical field
The present invention relates to a kind of coaxial two wheels robot balance controller based on LQR algorithms, specifically controller is base
Designed in the thought of feedback of status with Method of Pole Placement and LQR algorithms, then by MATLAB simulation analysis control performances,
Mainly solve the balance control problem of coaxial two wheels robot, belong to robot technology research field.
Background technology
With the fast development of society, the mankind are also improving to the demand of intelligence degree, and the appearance of robot is when drawing
Generation, it according to the thought of people, can assist or substitute the work of human work, such as production industry, manufacturing industry or dangerous work；
And coaxial two wheels robot is because of its unique texture, efficient and convenient, flexibility and the characteristic such as easily controllable, be widely used in industrial production,
Civilian or show business, has research on theory and practice meaning, and the present invention is namely based on coaxial two wheels robot extensively using property and spirit
On the basis of activity, then data collection and first pertinent literature balance control problem to solve it.
The content of the invention
The present invention designs a kind of coaxial two wheels robot balance controller based on LQR algorithms.
The present invention is achieved by the following technical solutions：A kind of coaxial two wheels robot balance controller based on LQR algorithms,
Coaxial two wheels robot nonlinear model is established according to Newtonian mechanics analytic approach first, and then linearizes and decouples the model, finally
Balance controller is designed according to inearized model.
Described coaxial two wheels robot is that one kind is rigidly connected in being studied herein, i.e., the car body of robot and wheel are independent
's.
The balance controller of described coaxial two wheels robot is to be based on feedback of status Method of Pole Placement, i.e., is existed using controlled system
The characteristic of arbitrary disposition limit in the case of controllable, finally makes coaxial two wheels robot reach steady within the short time in the case of initial interference
State.
The balance controller of described coaxial two wheels robot introduces LQR algorithms, when controlled system be it is linear or linearisation, fortune
Multinomial performance index can be taken into account with optimum control, coaxial two wheels robot is reached steady within the short time in the case of initial interference
State.
The usefulness of the invention is, for coaxial two wheels robot moving equilibrium problem, to be balanced setting for controller herein
Meter, the controller using the quantity of state that system export as research point of penetration, using feedback of status thought, introducing Method of Pole Placement with
LQR algorithms, design is simple, and control performance is good, and LQR controllers can make robot reach plateau, stability in the short time again
More preferably, this is exactly the coaxial two wheels robot target to be reached.
Brief description of the drawings
Accompanying drawing 1 is coaxial two wheels robot stress diagram
In figure：M is car body weight, and m is wheel weight, JωIt is wheel to wheel shaft rotary inertia, JθZ-axis is rotated for wheel used
Amount, JθIt is wheel to y-axis rotary inertia, R is radius of wheel, and D is wheel spacing, and L is the distance that Z axis arrives car body barycenter, and C is defeated
Enter torque, f is to smear frictional force.
Accompanying drawing 2 is POLE PLACEMENT USING simulating schematic diagram
In figure：Subsystem is coaxial two wheels robot nonlinear model.
Accompanying drawing 3 is pitch angle control curve map
In figure：1 is rate curve, and 2 be inclination angle rate curve, and 3 be displacement curve, and 4 be tilt curves.
Accompanying drawing 4 is Bit andits control curve map
In figure：1 is inclination angle rate curve, and 2 be rate curve, and 3 be tilt curves, and 4 be displacement curve.
Accompanying drawing 5 is LQR simulating schematic diagrams
Accompanying drawing 6 is pitch angle control curve map
In figure：1 is rate curve, and 2 be displacement curve, and 3 be tilt curves, and 4 be inclination angle rate curve.
Accompanying drawing 7 is Bit andits control curve map
In figure：1 is tilt curves, and 2 be displacement curve, and 3 be rate curve, and 4 be inclination angle rate curve.
For the ordinary skill in the art, according to the teachings of the present invention, do not depart from the principle of the present invention with
In the case of spirit, the changes, modifications, replacement and the modification that are carried out to embodiment still fall within protection scope of the present invention it
It is interior.
Claims (4)
1. a kind of coaxial two wheels robot balance controller based on LQR algorithms, comprises the following steps：Analyzed according to Newton classic mechanics
The nonlinear model that method establishes coaxial two wheels robot is as follows：
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Due to non-linear factor be present, control degree-of-difficulty factor greatly compared with, therefore herein for robot nonlinear model carry out it is linear
Change is handled, and model is as follows：
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Lienarized equation is converted into matrix form again：
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<mtr>
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</mrow>
Wherein, M is car body weight, and m is wheel weight, JωIt is wheel to wheel shaft rotary inertia, JθIt is wheel to z-axis rotary inertia,
JθIt is wheel to y-axis rotary inertia, R is radius of wheel, and D is wheel spacing, and L is the distance that Z axis arrives car body barycenter, and C is inputs
Torque.
Found out according to matrix form, it will be seen that coefficient matrices A is block diagonal matrix, that is, is shown on balancing 4 with speed control
Individual state variable is unrelated with 2 state variables on course changing control, therefore for the ease of theory analysis, utilizes decoupling side herein
Method carries out decoupling processing to the matrix form of lienarized equation, and substitutes into relevant parameter and obtain following two subsystems：
Balance and forward system：
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<mtd>
<mover>
<mi>&theta;</mi>
<mo>&CenterDot;</mo>
</mover>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>+</mo>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>1.8332</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>-</mo>
<mn>4.9798</mn>
</mtd>
</mtr>
</mtable>
</mfenced>
<msub>
<mi>C</mi>
<mi>&theta;</mi>
</msub>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>7</mn>
<mo>)</mo>
</mrow>
</mrow>
Steering：
<mrow>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mover>
<mi>&delta;</mi>
<mo>&CenterDot;</mo>
</mover>
</mtd>
</mtr>
<mtr>
<mtd>
<mover>
<mi>&delta;</mi>
<mo>&CenterDot;&CenterDot;</mo>
</mover>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>=</mo>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>1</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
</mtable>
</mfenced>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mi>&delta;</mi>
</mtd>
</mtr>
<mtr>
<mtd>
<mover>
<mi>&delta;</mi>
<mo>&CenterDot;</mo>
</mover>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>+</mo>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>5.1519</mn>
</mtd>
</mtr>
</mtable>
</mfenced>
<msub>
<mi>C</mi>
<mi>&delta;</mi>
</msub>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>8</mn>
<mo>)</mo>
</mrow>
</mrow>
The balance control problem of this paper primary study coaxial two wheels robots, i.e., balance controller is designed according to above-mentioned formula (7), recycled
The effect of MATLAB simulation analysis balance control.
2. the coaxial two wheels robot balance controller according to claim 1 based on LQR algorithms, it is characterised in that：Described
Coaxial two wheels robot is that one kind is rigidly connected in being studied herein, i.e., the car body of robot and wheel are independent.
3. the coaxial two wheels robot balance controller according to claim 1 based on LQR algorithms, it is characterised in that：Described
The balance controller of coaxial two wheels robot is to be based on feedback of status Method of Pole Placement, i.e., using controlled system in the case of controllable it is any
The characteristic of assigned pole, coaxial two wheels robot is finally set to reach plateau within the short time in the case of initial interference.
4. the coaxial two wheels robot balance controller according to claim 1 based on LQR algorithms, it is characterised in that：Described
The balance controller of coaxial two wheels robot introduces LQR algorithms, can be simultaneous with optimum control when controlled system is linear or linearisation
Multinomial performance index is cared for, coaxial two wheels robot is reached plateau within the short time in the case of initial interference.
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| US20100292840A1 (en) * | 2009-05-15 | 2010-11-18 | Beijing University Of Technology | Flexible two-wheeled self-balancing robot system and its motion control method |
| CN104298113A (en) * | 2014-10-22 | 2015-01-21 | 五邑大学 | Self-adaptive fuzzy balance controller for two-wheeled robot |
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2017
- 2017-08-24 CN CN201710732832.6A patent/CN107643760A/en active Pending
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|---|---|---|---|---|
| US20100292840A1 (en) * | 2009-05-15 | 2010-11-18 | Beijing University Of Technology | Flexible two-wheeled self-balancing robot system and its motion control method |
| CN104298113A (en) * | 2014-10-22 | 2015-01-21 | 五邑大学 | Self-adaptive fuzzy balance controller for two-wheeled robot |
| CN106078744A (en) * | 2016-06-30 | 2016-11-09 | 杭州电子科技大学 | A kind of double-wheel self-balancing robot Sliding Mode Adaptive Control system |
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| GAO X S等: "Two typesTwo types of coaxial self-balancing robots of coaxial self-balancing robots" * |
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