CN107368081A - A kind of double-wheel self-balancing robot adaptive sliding mode variable structure control system - Google Patents

A kind of double-wheel self-balancing robot adaptive sliding mode variable structure control system Download PDF

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CN107368081A
CN107368081A CN201710790443.9A CN201710790443A CN107368081A CN 107368081 A CN107368081 A CN 107368081A CN 201710790443 A CN201710790443 A CN 201710790443A CN 107368081 A CN107368081 A CN 107368081A
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mrow
sliding mode
speed
mode controller
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CN107368081B (en
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陈龙
张志辉
满志红
吴龙飞
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Hangzhou Dianzi University
Hangzhou Electronic Science and Technology University
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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
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
    • G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance

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Abstract

The invention discloses a kind of double-wheel self-balancing robot adaptive sliding mode variable structure control system, models the kinetics equation of following double-wheel self-balancing robot according to classical mechanics analytic approach and the Lagrange algorithms based on energy spectrometer and designs Sliding Mode Controller according to the kinetics equation；Sliding Mode Controller includes speed Sliding Mode Controller and angle Sliding Mode Controller, and speed Sliding Mode Controller and angle Sliding Mode Controller phase mutual feedback, its back analysis equations are：θr=β V；Self Adaptive Control is carried out to system using based on function approximation mode.Using technical scheme, make modeling process more simplify and comprehensively, the robustness of strengthening system, the response speed for improving system；Simultaneously because there is mutual feedback relationship in the speed and angle of system, when the inclination angle of system is excessive, system can automatic reduction of speed, while speed reduces, equilbrium position can be automatically returned to, in the case of in face of different pavement conditions, system can adaptively external environment condition and the change loaded on a large scale, so as to ensure the safety and stablization of system.

Description

A kind of double-wheel self-balancing robot adaptive sliding mode variable structure control system
The application is the divisional application of the patent application of Application No. 2015105060910, and the applying date of female case is 2015 On August 17, it is entitled：A kind of double-wheel self-balancing robot adaptive sliding mode variable structure control method and system.
Technical field
The present invention relates to robot control field, more particularly to a kind of double-wheel self-balancing robot adaptive sliding moding structure Control system.
Background technology
In recent years, as mobile robot research deepens continuously, application field is more extensive, the environment and task faced Also become increasingly complex.Robot is frequently encountered that some are narrow, and has the workplace of many big corners, how at this Execution task in the more complicated environment of sample flexibly and fast, turn into the problem that people are rather concerned about.Double-wheel self-balancing machine Device people's concept is exactly to put forward in this context.Double-wheel self-balancing robot technology is a kind of across the comprehensive of multiple subjects Conjunction technology, its system model are the kinetic models of a considerably complicated nonlinear instability, and double-wheel self-balancing machine People's system architecture is special, and adaptation to the ground changing capability is strong, and motion is flexible, the work that can be competent in some more complicated environment, So being received much concern in control theory and engineering field, knowwhy associated with it includes:1. point of physical architecture Analysis；2. kinematics analysis and the structure of kinetic model, include the analysis of dynamics and drive lacking；3. simulation and emulation point Analysis；4. attitude detection technology and space orientation technique, including overcome zero point or the temperature drift of inertial sensor, filtering algorithm Design and theory analysis, multisensor Data Fusion technology etc.；5. the theory of motion control and balance control and control method Research.
Simulation process is carried out to two-wheel self-balance robot system, it is necessary first to know the mathematical modeling of system, then Be possible to simulate system, the modeling pattern of double-wheel self-balancing robot is built using system mostly in the prior art The one of which of classical mechanics analytic approach or the Lagrange methods based on energy spectrometer in mould mode, individually using classical mechanics The consequence of analytic approach modeling is that mechanical analysis process is excessively complicated；And when individually using the Lagrange methods based on energy spectrometer It has ignored the situation of change of energy in system.The control algolithm of prior art double-wheel self-balancing robot is mostly PID controls simultaneously Algorithm processed, LQR control algolithms, optimal control algorithm, FUZZY ALGORITHMS FOR CONTROL etc., these control algolithms are in double-wheel self-balancing robot This non-linear, natural time-dependent system is difficult to reach satisfied control effect, and robustness is not good enough, and response speed is not fast enough, During in face of larger disturbance, system is unstable, when outside pavement conditions change, it is impossible to adaptive more complicated external rings Border and the change loaded on a large scale, it is impossible to which whether is the addition of automatic detection load；It is not intelligent enough on data processing method； Speed control method is only excessively single by the change at inclination angle, mode；The buffeting of system is very big.
Therefore for drawbacks described above present in currently available technology, it is necessary to be studied in fact, to provide a kind of scheme, Solves defect present in prior art.
The content of the invention
The purpose of the present invention is a kind of double-wheel self-balancing robot adaptive sliding mode variable structure control system, makes modeling process More simplify and comprehensively, the robustness of strengthening system, improve system response speed；Cope with larger external disturbance；Energy Enough adaptive external environment conditions and the change loaded on a large scale；It is capable of the addition of automatic detection load；The value of system parameters is more Add accurate；Speed control method variation.
In order to overcome the shortcomings of the prior art, the technical scheme is that：
A kind of double-wheel self-balancing robot adaptive sliding mode variable structure control system, including power module, gyroscope, acceleration Degree meter, turn to potentiometer, control unit, the first motor drive module, the second motor drive module, the first motor, the second motor, First encoder and second encoder, wherein,
The power module is used for system power supply；
The gyroscope is used to detect self-balance robot car body drift angle information, and it is single to send that information to the control Member；
The accelerometer is used for the acceleration information for detecting self-balance robot, and sends that information to the control Unit；
The direction information for turning to potentiometer and being used to detect self-balance robot, and send that information to the control Unit；
First encoder and the second encoder are used for the velocity information for detecting self-balance robot, and this is believed Breath is sent to described control unit；
Described control unit calculates output according to drift angle information, acceleration information, direction information and the velocity information Control signal, and it is sent to first motor drive module and second motor drive module；
First motor drive module and second motor drive module output PWM drive signal make first electricity Machine and second motor rotate；
Described control unit includes Kalman's data fusion module, speed Sliding Mode Controller and angle sliding formwork and becomes knot Structure controller, wherein,
Kalman's data fusion module is used to the drift angle information and the acceleration information carrying out data fusion, And fuse information is sent to the angle Sliding Mode Controller；
The fuse information and institute that the angle Sliding Mode Controller exports according to Kalman's data fusion module State the feedback information output control signal of speed Sliding Mode Controller；
The feedback information is determined by following back analysis equations：
θr=β V, wherein, θrThe feedback letter of angle Sliding Mode Controller is fed back to for speed Sliding Mode Controller Breath, V are present speed, and β is constant, between the value range -0.15 of its value to 0.15；
The output control signal of the angle Sliding Mode Controller is determined by following output equation：
Wherein Δ T is the sampling time, Y=β b2, Z=b1-βc2b2,For adaptive item；s2For angle sliding variable, ε2For system perspective error constant item, λ2For Speed real constant item, sat (s2) it is ramp function, eθFor angular error,For the first derivative of car body drift angle,For angular error First derivative；
The speed Sliding Mode Controller is according to the output control of the velocity information and the angle Sliding Mode Controller Signal processed, the feedback information is exported, its output quantity U is determined by below equation Wherein, s1For speed sliding variable, VrFor reference velocity,For the first derivative of reference velocity, evFor velocity error, ε1For system Velocity-error constant, λ1For angle real constant item.
Preferably, the speed Sliding Mode Controller and angle Sliding Mode Controller are analyzed according to classical mechanics Method and Lagrange algorithms based on energy spectrometer are simultaneously established the kinetics equation (1) of following double-wheel self-balancing robot and designed Out：
Wherein, U is the output control signal of Sliding Mode Controller, and θ is the car body drift angle of double-wheel self-balancing robot, ev=V-VrFor present speed V and reference velocity VrSpeed difference, a1、b1、c1、d1、a2、b2、c2、d2For double-wheel self-balancing robot Model parameter.
Preferably, described angle Sliding Mode Controller uses self-adaptive controlled to carry out based on function approximation mode System, its adaptive item are：Wherein To draw Lid that basic function,For the every parameter sets of orthogonal family of function Laguerre polynomials,For the coefficient of each,For Laguerre basic function multinomial.
Preferably, in described angle Sliding Mode Controller and the speed Sliding Mode Controller, using oblique Slope functionWherein, Δ is referred to as boundary layer.
Preferably, the β value is -0.14.
Preferably, a1、b1、c1、d1、a2、b2、c2、d2Value determined by below equation：
Wherein,M is the quality of double-wheel self-balancing robot, and g is acceleration of gravity, and L is matter The heart from wheel center with a distance from, J be self-balance robot car body rotary inertia, VrFor reference velocity, KtIt is normal for motor torque Number, KeFor back EMF coefficient, RaFor armature both ends resistance.
Compared with prior art, the Lagrange side present invention incorporates classical mechanics analytic approach and based on energy spectrometer Method, avoids the mechanical analysis process of complexity, and in view of the change of energy in system, modeling process is more simplified and entirely Face；Meanwhile the output control signal of Sliding Mode Controller, it is contemplated that the relational expression θ between angle and speedr=β V, lead to The value for choosing β is crossed, so that the speed and angle of system can influence each other, when the inclination angle of system is excessive, system can be automatic Reduction of speed, while speed reduces, equilbrium position can be automatically returned to, so as to ensure the safety and stablization of system.
Figure of description
Fig. 1 is the design cycle block diagram of double-wheel self-balancing robot adaptive sliding mode variable structure control system of the present invention；
Fig. 2 is the integral mechanical structure block diagram of double-wheel self-balancing robot；
Fig. 3-a are double-wheel self-balancing robot three-dimensional force diagram；
Fig. 3-b are double-wheel self-balancing robot two dimension force diagram；
Fig. 3-c are double-wheel self-balancing robot two dimension force simplified figure；
Fig. 4 is the hardware block diagram of double-wheel self-balancing robot control system；
Fig. 5 is the schematic diagram of control signal in double-wheel self-balancing robot control system；
Fig. 6 is the analogous diagram of β value under different double-wheel self-balancing robot model parameters；
Fig. 7 is the analogous diagram of the β value under particular model parameter；
Fig. 8-a are speed of the double-wheel self-balancing robot in the case where speed reference signal is the adaptive sliding-mode observer of sinusoidal signal Spend aircraft pursuit course；
Fig. 8-b are double-wheel self-balancing robot speed in the case where speed reference signal is the adaptive sliding-mode observer of sinusoidal signal Error curve；
Fig. 8-c are angle of the double-wheel self-balancing robot in the case where speed reference signal is the adaptive sliding-mode observer of sinusoidal signal Spend error curve；
Fig. 8-d are that double-wheel self-balancing robot exports song in the adaptive sliding-mode observer that speed reference signal is sinusoidal signal Line；
Fig. 9-a are speed tracing of the double-wheel self-balancing robot in the case where speed reference signal is the PID control of sinusoidal signal Curve；
Fig. 9-b are velocity error of the double-wheel self-balancing robot in the case where speed reference signal is the PID control of sinusoidal signal Curve；
Fig. 9-c are angular error of the double-wheel self-balancing robot in the case where speed reference signal is the PID control of sinusoidal signal Curve；
It is that controller under the PID control of sinusoidal signal is defeated that Fig. 9-d, which are double-wheel self-balancing robot in speed reference signal, Go out curve.
Figure 10-a are double-wheel self-balancing robot in the case where speed reference signal is the adaptive sliding-mode observer of square-wave signal Speed tracing curve；
Figure 10-b are that double-wheel self-balancing robot is fast in the case where speed reference signal is the adaptive sliding-mode observer of square-wave signal Spend error curve；
Figure 10-c are double-wheel self-balancing robot in the case where speed reference signal is the adaptive sliding-mode observer of square-wave signal Angular error curve；
Figure 10-d are double-wheel self-balancing robot in the adaptive sliding-mode observer output that speed reference signal is square-wave signal Curve；
Figure 11-a are speed tracing of the double-wheel self-balancing robot in the case where speed reference signal is the PID control of square-wave signal Curve；
Figure 11-b are velocity error of the double-wheel self-balancing robot in the case where speed reference signal is the PID control of square-wave signal Curve；
Figure 11-c are angular error of the double-wheel self-balancing robot in the case where speed reference signal is the PID control of square-wave signal Curve；
It is that controller under the PID control of square-wave signal is defeated that Figure 11-d, which are double-wheel self-balancing robot in speed reference signal, Go out curve.
Embodiment
Referring to Fig. 1, a kind of setting for double-wheel self-balancing robot adaptive sliding mode variable structure control system of the invention is shown FB(flow block) is counted, is comprised the following steps：
Step 101：Following two-wheeled is modeled certainly according to classical mechanics analytic approach and the Lagrange algorithms based on energy spectrometer The kinetics equation of balanced robot：
Step 102：And Sliding Mode Controller is designed according to above-mentioned kinetics equation；
Wherein, in kinetics equation, U is the output control signal of Sliding Mode Controller, and θ is double-wheel self-balancing machine The car body drift angle of people, ev=V-VrFor present speed V and reference velocity VrSpeed difference, a1、b1、c1、d1、a2、b2、c2、d2For two Take turns the model parameter of self-balance robot, d1And d2For system interference.
Step 103：Gather transducing signal and in this, as the input parameter of Sliding Mode Controller, wherein, two-wheeled is certainly The present speed information of balanced robot is one of input parameter of Sliding Mode Controller.
Step 104：Sliding Mode Controller is according to its input parameter output control signal；
Step 105：Transported according to Sliding Mode Controller output control signal and potentiometer signal co- controlling motor It is dynamic；According to Sliding Mode Controller output control signal, system is balanced and speed control, and using turning to electricity Position device signal, course changing control is carried out to system；
Step 106：The present speed information of double-wheel self-balancing robot is detected, and is fed back to Sliding mode variable structure control One of the input of device, the input parameter as Sliding Mode Controller；
Repeat step 103 is real according to transducing signal parameter and feedback signal, Sliding Mode Controller to step 106 When adjust output control signal driving double-wheel self-balancing robot motion.
In above-mentioned steps 101, to the mathematical modeling of double-wheel self-balancing robot control system control system research In have considerable status, to improve the performance of system, it is necessary first to know the mathematical modeling of system, be then possible to Simulation process is carried out to system, and then framework real system carries out simulation test.Referring to Fig. 2, double-wheel self-balancing machine is shown The integral mechanical structure block diagram of people, the mechanical structure of two-wheel self-balance robot system mainly by car body, two driving wheels in left and right, Motor, encoder and sensor group are into sensor further comprises gyroscope, accelerometer, turns to potentiometer, speed Sensor etc. is spent, controls driving wheel to move according to sensor signal, the movement locus of robot is relevant with the two driving wheels.It is left Right two-wheeled is independently driven by respective motor and two-wheeled shaft axis are on same straight line, and robot car body can be around two-wheeled rotating shaft certainly By rotating.When gyroscope detects that car body produces inclination, control system produces a corresponding torque according to the inclination angle measured, Two wheels are driven to be moved towards the direction to be fallen down of vehicle body by controlled motor, to keep the dynamic of double-wheel self-balancing robot itself State balances.Mainly the rotating torque as caused by the motor that two wheels of driving rotate is controlled for the motion of double-wheel self-balancing robot System.
In the prior art, it is certainly flat to two-wheeled only with classical mechanics analytic approach or the Lagrange methods based on energy spectrometer Weighing apparatus robot system is modeled, and the present invention by the force analysis to double-wheel self-balancing robot, is then used and is based on first The Lagrange methods of energy spectrometer establish the whole mathematical model of double-wheel self-balancing robot, and double-wheel self-balancing robot is overall Three-dimensional force analysis as shown in Fig. 3-a, it is contemplated that the motion of double-wheel self-balancing robot is realized by vehicle wheel rotation, this hair Bright technical scheme is co-axially mounted using a pair and parameter identical tire, so the model of left and right wheels is the same, therefore only The two-dimentional stressing conditions of double-wheel self-balancing robot are considered, as shown in Fig. 3-b, for the ease of mathematical derivation, by its further letter It is melted into the form as shown in Fig. 3-c.The parameter declaration being related in Fig. 3-a, Fig. 3-b and Fig. 3-c is as shown in table 1 below.
The symbol description of the double-wheel self-balancing robot model of table 1
The kinetics equation derivation of double-wheel self-balancing robot of the invention described in detail below, wherein, the present invention In used other symbol descriptions it is as shown in table 2.
The symbol description of the double-wheel self-balancing robot model of table 2
First, according to principle of conservation of momentum, equation (2) of the double-wheel self-balancing robot on momentum is obtained, according to energy Conservation principle is measured, obtains equation (3) of the double-wheel self-balancing robot on energy.
(2) in formula and (3) formula：P0Represent the initial momentum (Kgm/s) of double-wheel self-balancing robot, E0It is certainly flat for two-wheeled The primary power (J) of weighing apparatus robot, J are the rotary inertia (Kgm of car body2)。
Derivation is carried out to (2) formula and (3) formula respectively and obtains equation (4) formula on the F that makes a concerted effort and the equation (5) on power Formula：
(4) formula is substituted into (5) formula, obtains (6) formula:
When controlling the balance of double-wheel self-balancing robot and motion, controlled quentity controlled variable is the rotating torque of wheel, so needing Know the output torque of motor, the output torque expression formula in DC motor model is (7) formula：
K in formula (7)tFor the torque constant (NmA) of motor, KeFor back EMF coefficient (Vs), UaInputted for armature Voltage (V), w are motor Output speed (rad/s), RaFor armature resistance (Ω).
By the form of output torque expression formula chemical conversion (8) formula in (7) formula motor model：
F=CuU-CvV (8)
Wherein：
(8) formula is updated to (4) formula and obtains (9) formula：
Because θ and w are smaller, so there is (10) formula：
Definition：
ev=V-Vr (11)
Wherein VrFor V reference velocity.
With reference to (5), (8), (9) and (10) formula, finally show that double-wheel self-balancing robot equation is：
Wherein
In a step 102, become according to above-mentioned kinetics equation (formula 12) to design the sliding formwork of double-wheel self-balancing robot Structure controller, detailed process are as follows：
Define first：
eθ=θ-θr (13)
Wherein θrFor θ reference angle.
According to kinetics equation (12) formula that double-wheel self-balancing robot is overall, Sliding Mode Controller is designed, by cunning Moding amount s equation is defined as (14) formula：
WhereinMeet Hurwitz stability criterion conditions.
Sliding Mode Controller is designed using above-mentioned technical proposal, the sliding variable of entirety is designed to that speed sliding formwork becomes The matrix form of amount and angle sliding variable composition, and speed sliding variable is designed to band integrated form, reduced so as to play The effect of buffeting.
Definition lyapunov energy function is (15) formula：
Among formula (15)
To ensure that whole two-wheel self-balance robot system is stable, i.e., v derivative is less than zero.Ensure double-wheel self-balancing simultaneously Robot speed and it is upright on Simultaneous Stabilization, i.e. v1And v2Derivative be both less than zero.
v1Derivative be (16) formula.
Order
Constant ε in formula (17)1＞ 0, represent that the motor point of system levels off to diverter surface s=0 speed.ε1It is smaller, convergence speed Degree is slow；ε1It is bigger, then there is larger speed when motor point reaches diverter surface, caused shake is also larger.
In a preferred embodiment, the expression formula of ramp function is (18) formula in formula (17).Ramp function conduct A kind of method of quasisliding mode control, its essence is outside boundary layer, using switching control, in boundary layer, using line Property feedback control, the buffeting of system is reduced, so that system is more stable.
(17) formula is updated to (16) formula and obtains (19) formula.
Formula (19) shows to slide variable s1It is asymptotically stability, meets Lyapunov stability condition.
Rate of change (20) formula on speed is obtained by (17) formula.
Because the speed among system and angle signal have certain contact, in a preferred embodiment, angle is defined Spend reference signal θrRelational expression with speed V is (21) formula.
θr=β V (21)
Derivation is carried out to (21) formula and secondary derivation obtains (22) formula and (23) formula.
Derivation is carried out to angular error (13) formula and secondary derivation obtains (24) formula and (25) formula.
Order
(26) formula is updated in (25) formula (27) formula that obtains.
(13) formula equation and (24) formula equation are arranged to obtain (28) formula and (29) formula.
eθ=θ-θr=θ-β (ev+Vr) (28)
(20) formula is updated to (29) formula and obtains (30) formula.
U is the laststate of double-wheel self-balancing robot controller in formula (30).
v2Derivative be (31) formula.
Order
Constant ε in formula (32)2＞ 0, and ε1Effect as, β value must is fulfilled for (33) formula.
The value that β is obtained with reference to (26) formula is (34) formula.
The final Sliding Mode Controller that double-wheel self-balancing robot is obtained by (32) formula is (35) formula.
In formula (35),
Y=β b3,
Z=b2-βa33b3.Its adaptive item isWherein For Laguerre Ball curve.
(32) formula is updated in (31) formula (36) formula that obtains.
Formula (36) shows to slide variable s2It is asymptotically stability, meets Lyapunov stability condition.In formula (35) Sliding Mode Controller U be correct in theory.
In a preferred embodiment, in a step 102, by the defeated of the output control signal of Sliding Mode Controller Go out equation to be set as：
Wherein, Δ T is the sampling time, Y=β b2, Z=b1-βc2b2,For adaptive item.
In step 103, transducing signal includes gathering drift angle information by gyroscope and added by what accelerometer gathered Velocity information, in a preferred embodiment, the drift angle information and the acceleration are believed by Kalman filtering algorithm Breath carries out data fusion.Data fusion is carried out using Kalman filtering algorithm and mainly uses below equation, so that system controls It is more accurate.
X (k | k-1)=AX (k-1 | k-1)+BU (k) (37)
P (k | k-1)=AP (k-1 | k-1) A'+Q (38)
X (k | k)=X (k | k-1)+Kg (k) (Z (k)-HX (k | k-1)) (39)
Kg (k)=P (k | k-1) H'/(HP (k | k-1) H'+R) (40)
P (k | k)=(I-Kg (k) H) P (k | k-1) (41)
Referring to Fig. 4, the hardware principle frame for the double-wheel self-balancing robot control system for realizing above-mentioned control method is shown Figure, including power module, gyroscope, accelerometer, steering potentiometer, control unit, the first motor drive module, the second motor Drive module, the first motor, the second motor, the first encoder and second encoder, other modules such as key-press module, display screen Etc. will not be repeated here.
Within the system, power module is used for whole system offer supply voltage；
Gyroscope is used to detect self-balance robot car body drift angle information, and sends that information to control unit；Gyro The drift angle information of instrument is important parameter, and control unit controls output control signal as benchmark.
Accelerometer is used for the acceleration information for detecting self-balance robot, and sends that information to control unit；
The direction information that potentiometer is used to detect self-balance robot is turned to, and sends that information to control unit；
First encoder and second encoder are used for the velocity information for detecting self-balance robot, and send that information to Control unit；First encoder and second encoder are separately mounted on the first driving wheel and the second driving wheel, and detection first is driven The rotating speed of driving wheel and the second driving wheel.
Control unit calculates output control signal according to drift angle information, acceleration information, direction information and velocity information, And it is sent to the first motor drive module and the second motor drive module；
First motor drive module and the second motor drive module export PWM drive signal according to above-mentioned output control signal Rotate the first motor and the second motor.
In a preferred embodiment, referring to Fig. 5, it show control signal in double-wheel self-balancing robot control system Schematic diagram, control unit further comprises Kalman's data fusion module and Sliding Mode Controller, sliding moding structure control Device processed includes speed Sliding Mode Controller and angle Sliding Mode Controller, wherein,
Kalman's data fusion module is used to drift angle information and acceleration information carrying out data fusion, and by fuse information It is sent to angle Sliding Mode Controller；
The fuse information and speed sliding formwork that angle Sliding Mode Controller exports according to Kalman's data fusion module become The feedback information output control signal of structure controller；
In a preferred embodiment, the feedback information of speed Sliding Mode Controller output is by following back analysis equations It is determined that：
θr=β V, wherein, θrThe feedback letter of angle Sliding Mode Controller is fed back to for speed Sliding Mode Controller Breath, V is present speed, and β is constant, by choosing β value, so that the speed and angle of system can influence each other, when being When the inclination angle of system is excessive, system can automatic reduction of speed, speed reduce while, equilbrium position can be automatically returned to, so as to ensure system Safety and stablization.
β is the stable important parameter of system, and (partial parameters in table 1, table 2), β value are determined by two wheel robot model parameters Selection by solving equationAnd obtain, while it must is fulfilled for conditionIt is so finalThe present invention tries to achieve the scope of β value by way of emulation.Referring to Fig. 6, it show The analogous diagram of β value under different double-wheel self-balancing robot model parameters, between the value range -0.15 of β value to 0.15.
In a preferred embodiment, the output control signal of angle Sliding Mode Controller is by following output equation It is determined that：
Wherein, Δ T is the sampling time, Y=β b2, Z=b1-βc2b2,For adaptive item.
In a preferred embodiment, speed Sliding Mode Controller is according to velocity information and angle sliding moding structure The output control signal of controller, export feedback information.
In a preferred embodiment, in addition to speed regulating handle, throttle signal is exported by speed regulating handle, and this is believed Number it is sent to control unit.Throttle signal and reference velocity VrProportion relation, therefore made by throttle signal with reference to speed Spend VrValue change.Technical solution of the present invention is only compared with existing by drift angle information control speed mode, adds one Kind control mode so that the speed control method variation of system, while increase the safety coefficient of system.
In a preferred embodiment, in addition to self-adapting load detection module, there is load detecting function.Load inspection Module is surveyed using sluggish function, determines whether to load by given threshold, i.e., indicator lamp when people station is got on Can be bright, threshold value is set according to the output quantity of encoder and motor.
In a preferred embodiment, in addition to wireless communication module, it is connected with control unit, is used for and host computer End is communicated, and data are handled and analyzed by wireless communication module, to improve the accuracy and intelligence of system control Can property.Wireless data receipt modules and sending module in wireless communication module use chip NRF24L01, RXF2401 radio frequency work( Rate amplifier.
In a preferred embodiment, control unit uses 32 microcontroller MK60DN512ZVLQ10 of Freescale, speed Degree sensor selects photoelectric encoder, the full bridge driving circuit that motor driving is built using BTN7971B half-bridge driven chips, electricity Source module uses 24V, 14Ah chargeable nickel-cadmium cell.LPR510AL and MMA7260 is respectively adopted in gyroscope and accelerometer.
In a preferred embodiment, the motor of two-wheel self-balance robot system of the invention is watched using direct current The servomotor of motor, specifically EC90M485500RGOL models is taken, because DC servo motor has excellent speed Control performance, it exports larger torque, directly drags load running, while the direct control of its suspension control signal again is turned Velocity modulation section.The technical parameter of the direct current generator is as shown in table 3 below.
The technical parameter of the EC90M485500RGOL direct current generators of table 3
With reference to upper table 3, further according to UaIa=EaIa+Ia 2Ra, PI=PM+PCuaTwo equations and double-wheel self-balancing robot are consolidated There is the resistance R that technical parameter measures armature both ends in systema, inductance La, time constant of electric motors Kt, it is viscous damping coefficient B, anti- Power coefficient Ke, rotor rotary inertia J, go out armature both ends inductance L in system by apparatus measuresaAnd machine The weight M of people.Finally by below equation Calculate the parameter in two-wheel self-balance robot system kinetics equation and sliding mode controller so that The control of system is more accurate.
System emulation is carried out to β value according to above-mentioned model parameter, referring to Fig. 7, show the β value under particular model parameter Analogous diagram；From figure 7 it can be seen that when β value is -0.14, system tends towards stability, and the relation between desired angle and speed meets The value of setting.
In order to further verify technique effect that technical solution of the present invention can reach, in same double-wheel self-balancing robot Under system model parameter, data are carried out to Sliding Mode Controller of the present invention and prior art pid algorithm controller respectively and imitated Very.Referring to Fig. 8-a, it show and is emulated in the case where speed reference signal is sine wave using the speed tracing of adaptive sliding-mode observer Figure, Fig. 8-b are the sliding formwork control velocity error analogous diagram in the case where speed reference signal is sine wave, and Fig. 8-c are to believe in speed reference Number be sine wave under sliding formwork pilot angle degree error analogous diagram, Fig. 8-d be in the case where speed reference signal is sine wave sliding mode controller Output quantity, as can be seen that actual speed and angle error in tracking very little from analogous diagram, tracking effect well can be reached Fruit, the response speed of system is very fast, due to automatically controlling central balance moving principle, occurs when speed tracing Phase shift phenomenon, Fig. 9 a-d are that double-wheel self-balancing robot uses prior art PID control in the case where speed reference signal is sine wave The performance curve of algorithm, from Fig. 8 and Fig. 9 contrast as can be seen that the adaptive sliding-mode observer of the design can respond system Faster, robustness is stronger for speed, be can be seen that from speed and angular error due to phase shift phenomenon, so using adaptive sliding mode Control, the speed tracing error of system is slightly bigger, but when equilbrium position, using PID control, system occurs gently Micro- jitter phenomenon, positive effect are not so good as the effect using adaptive sliding mode controller, and using the angleonly tracking of PID control Error is bigger, be can be seen that in addition from controller output quantity using adaptive sliding mode controller, and system is more stable, with the obvious advantage, In order to further verify the advantage of the sliding mode controller of the design, due to have among square-wave signal from 0 change to immediately 1 when Carve, can preferably verify the characteristics such as system robustness and response speed, Figure 10 a-d are in the case where speed reference signal is square wave Using the performance curve of adaptive sliding-mode observer, Figure 11 a-d are the performance that PID control is used in the case where speed reference signal is square wave Curve, as can be seen that system by 0 when changing to 1 from Figure 10 and 11, system uses the response speed of adaptive sliding-mode observer more It hurry up, speed tracing effect is more preferable, and robustness is stronger.
The explanation of above example is only intended to help the method and its core concept for understanding the present invention.It should be pointed out that pair For those skilled in the art, under the premise without departing from the principles of the invention, the present invention can also be carried out Some improvement and modification, these are improved and modification is also fallen into the protection domain of the claims in the present invention.
The foregoing description of the disclosed embodiments, professional and technical personnel in the field are enable to realize or using the present invention. A variety of modifications to these embodiments will be apparent for those skilled in the art, defined in the present invention General Principle can realize in other embodiments without departing from the spirit or scope of the present invention.Therefore, this hair Bright these embodiments being not intended to be limited to shown in the present invention, and be to fit to special with principles of this disclosure and novelty The consistent most wide scope of point.

Claims (6)

1. a kind of double-wheel self-balancing robot adaptive sliding mode variable structure control system, it is characterised in that including power module, top Spiral shell instrument, accelerometer, turn to potentiometer, control unit, the first motor drive module, the second motor drive module, the first motor, Second motor, the first encoder and second encoder, wherein,
The power module is used for system power supply；
The gyroscope is used to detect self-balance robot car body drift angle information, and sends that information to described control unit；
The accelerometer is used for the acceleration information for detecting self-balance robot, and it is single to send that information to the control Member；
The direction information for turning to potentiometer and being used to detect self-balance robot, and it is single to send that information to the control Member；
First encoder and the second encoder are used for the velocity information for detecting self-balance robot, and the information is sent out Give described control unit；
Described control unit calculates output control according to drift angle information, acceleration information, direction information and the velocity information Signal, and it is sent to first motor drive module and second motor drive module；
First motor drive module and second motor drive module output PWM drive signal make first motor and Second motor rotates；
Described control unit includes Kalman's data fusion module, speed Sliding Mode Controller and angle sliding moding structure control Device processed, wherein,
Kalman's data fusion module is used to the drift angle information and the acceleration information carrying out data fusion, and will Fuse information is sent to the angle Sliding Mode Controller；
The fuse information and the speed that the angle Sliding Mode Controller exports according to Kalman's data fusion module Spend the feedback information output control signal of Sliding Mode Controller；
The feedback information is determined by following back analysis equations：
θr=β V, wherein, θrThe feedback information of angle Sliding Mode Controller, V are fed back to for speed Sliding Mode Controller For present speed, β is constant, between the value range -0.15 of its value to 0.15；
The output control signal of the angle Sliding Mode Controller is determined by following output equation：
Wherein Δ T is the sampling time, Y=β b2, Z=b1-βc2b2,For adaptive item；s2For angle sliding variable, ε2For system perspective error constant item, λ2For Speed real constant item, sat (s2) it is ramp function, eθFor angular error,For the first derivative of car body drift angle,For angular error First derivative；
The speed Sliding Mode Controller is according to the velocity information and the output control of the angle Sliding Mode Controller Signal, the feedback information is exported, its output quantity U is determined by below equation Wherein, s1For speed sliding variable, VrFor reference velocity,For the first derivative of reference velocity, evFor velocity error, ε1For system Velocity-error constant, λ1For angle real constant item.
2. double-wheel self-balancing robot adaptive sliding mode variable structure control system according to claim 1, it is characterised in that The speed Sliding Mode Controller and angle Sliding Mode Controller are according to classical mechanics analytic approach and based on energy point The Lagrange algorithms of analysis are simultaneously established the kinetics equation (1) of following double-wheel self-balancing robot and designed：
<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mover> <mi>&amp;theta;</mi> <mo>&amp;CenterDot;&amp;CenterDot;</mo> </mover> <mo>=</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> <mi>&amp;theta;</mi> <mo>+</mo> <msub> <mi>b</mi> <mn>1</mn> </msub> <mi>U</mi> <mo>+</mo> <msub> <mi>c</mi> <mn>1</mn> </msub> <msub> <mi>e</mi> <mi>v</mi> </msub> <mo>+</mo> <msub> <mi>d</mi> <mn>1</mn> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mover> <mi>e</mi> <mo>&amp;CenterDot;</mo> </mover> <mi>v</mi> </msub> <mo>=</mo> <msub> <mi>a</mi> <mn>2</mn> </msub> <mi>&amp;theta;</mi> <mo>+</mo> <msub> <mi>b</mi> <mn>2</mn> </msub> <mi>U</mi> <mo>+</mo> <msub> <mi>c</mi> <mn>2</mn> </msub> <msub> <mi>e</mi> <mi>v</mi> </msub> <mo>+</mo> <msub> <mi>d</mi> <mn>2</mn> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow>
Wherein, U be Sliding Mode Controller output control signal, θ be double-wheel self-balancing robot car body drift angle, ev= V-VrFor present speed V and reference velocity VrSpeed difference, a1、b1、c1、d1、a2、b2、c2、d2For double-wheel self-balancing robot Model parameter.
3. double-wheel self-balancing robot adaptive sliding mode variable structure control system according to claim 1 or 2, its feature exist In described angle Sliding Mode Controller is used based on function approximation mode to carry out Self Adaptive Control, its adaptive item For：Wherein For Laguerre basic function,For The every parameter sets of orthogonal family of function Laguerre polynomials,For the coefficient of each, For Laguerre basic function multinomial.
4. double-wheel self-balancing robot adaptive sliding mode variable structure control system according to claim 1 or 2, its feature exist In in described angle Sliding Mode Controller and the speed Sliding Mode Controller, using ramp functionWherein, Δ is referred to as boundary layer.
5. double-wheel self-balancing robot adaptive sliding mode variable structure control system according to claim 1 or 2, its feature exist In the β value is -0.14.
6. double-wheel self-balancing robot adaptive sliding mode variable structure control system according to claim 2, it is characterised in that a1、b1、c1、d1、a2、b2、c2、d2Value determined by below equation：
<mrow> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>=</mo> <mfrac> <mrow> <mi>M</mi> <mi>g</mi> <mi>L</mi> </mrow> <mi>J</mi> </mfrac> <mo>,</mo> <msub> <mi>b</mi> <mn>1</mn> </msub> <mo>=</mo> <mo>-</mo> <mfrac> <mrow> <msub> <mi>C</mi> <mi>u</mi> </msub> <mi>L</mi> </mrow> <mi>J</mi> </mfrac> <mo>,</mo> <msub> <mi>c</mi> <mn>1</mn> </msub> <mo>=</mo> <mfrac> <mrow> <msub> <mi>C</mi> <mi>v</mi> </msub> <mi>L</mi> </mrow> <mi>J</mi> </mfrac> <mo>,</mo> <msub> <mi>d</mi> <mn>1</mn> </msub> <mo>=</mo> <mfrac> <mrow> <msub> <mi>C</mi> <mi>v</mi> </msub> <mi>L</mi> </mrow> <mi>J</mi> </mfrac> <msub> <mi>V</mi> <mi>r</mi> </msub> <mo>,</mo> <msub> <mi>d</mi> <mn>1</mn> </msub> <mo>=</mo> <mfrac> <mrow> <msub> <mi>C</mi> <mi>v</mi> </msub> <mi>L</mi> </mrow> <mi>J</mi> </mfrac> <msub> <mi>V</mi> <mi>r</mi> </msub> <mo>,</mo> <msub> <mi>d</mi> <mn>1</mn> </msub> <mo>=</mo> <mfrac> <mrow> <msub> <mi>C</mi> <mi>v</mi> </msub> <mi>L</mi> </mrow> <mi>J</mi> </mfrac> <msub> <mi>V</mi> <mi>r</mi> </msub> <mo>,</mo> <msub> <mi>a</mi> <mn>2</mn> </msub> <mo>=</mo> <mo>-</mo> <mfrac> <mrow> <msup> <mi>MgL</mi> <mn>2</mn> </msup> </mrow> <mi>J</mi> </mfrac> <mo>,</mo> </mrow> <mrow> <msub> <mi>b</mi> <mn>2</mn> </msub> <mo>=</mo> <mfrac> <mrow> <mo>(</mo> <mi>J</mi> <mo>+</mo> <msup> <mi>ML</mi> <mn>2</mn> </msup> <mo>)</mo> <msub> <mi>C</mi> <mi>u</mi> </msub> </mrow> <mrow> <mi>J</mi> <mi>M</mi> </mrow> </mfrac> <mo>,</mo> <msub> <mi>c</mi> <mn>2</mn> </msub> <mo>=</mo> <mo>-</mo> <mfrac> <mrow> <mo>(</mo> <mi>J</mi> <mo>+</mo> <msup> <mi>ML</mi> <mn>2</mn> </msup> <mo>)</mo> <msub> <mi>C</mi> <mi>v</mi> </msub> </mrow> <mrow> <mi>J</mi> <mi>M</mi> </mrow> </mfrac> <mo>,</mo> <msub> <mi>d</mi> <mn>2</mn> </msub> <mo>=</mo> <mo>-</mo> <msub> <mover> <mi>V</mi> <mo>&amp;CenterDot;</mo> </mover> <mi>r</mi> </msub> <mo>-</mo> <mfrac> <mrow> <mo>(</mo> <mi>J</mi> <mo>+</mo> <msup> <mi>ML</mi> <mn>2</mn> </msup> <mo>)</mo> <msub> <mi>C</mi> <mi>v</mi> </msub> </mrow> <mrow> <mi>J</mi> <mi>M</mi> </mrow> </mfrac> <msub> <mi>V</mi> <mi>r</mi> </msub> <mo>;</mo> </mrow>
Wherein,M is the quality of double-wheel self-balancing robot, and g is acceleration of gravity, and L is barycenter from car The distance at wheel center, J be self-balance robot car body rotary inertia, VrFor reference velocity, KtFor motor torque constant, KeFor Back EMF coefficient, RaFor armature both ends resistance.
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