CN109067264B - Balance car system and control method thereof - Google Patents
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P6/00—Arrangements for controlling synchronous motors or other dynamo-electric motors using electronic commutation dependent on the rotor position; Electronic commutators therefor
- H02P6/04—Arrangements for controlling or regulating the speed or torque of more than one motor
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B62—LAND VEHICLES FOR TRAVELLING OTHERWISE THAN ON RAILS
- B62K—CYCLES; CYCLE FRAMES; CYCLE STEERING DEVICES; RIDER-OPERATED TERMINAL CONTROLS SPECIALLY ADAPTED FOR CYCLES; CYCLE AXLE SUSPENSIONS; CYCLE SIDE-CARS, FORECARS, OR THE LIKE
- B62K11/00—Motorcycles, engine-assisted cycles or motor scooters with one or two wheels
- B62K11/007—Automatic balancing machines with single main ground engaging wheel or coaxial wheels supporting a rider
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P6/00—Arrangements for controlling synchronous motors or other dynamo-electric motors using electronic commutation dependent on the rotor position; Electronic commutators therefor
- H02P6/006—Controlling linear motors
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P6/00—Arrangements for controlling synchronous motors or other dynamo-electric motors using electronic commutation dependent on the rotor position; Electronic commutators therefor
- H02P6/10—Arrangements for controlling torque ripple, e.g. providing reduced torque ripple
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P6/00—Arrangements for controlling synchronous motors or other dynamo-electric motors using electronic commutation dependent on the rotor position; Electronic commutators therefor
- H02P6/34—Modelling or simulation for control purposes
Abstract
The invention discloses a balance car system and a control method thereof.A state equation of extended Kalman filtering and a mathematical model of a permanent magnet linear motor are established according to a difference equation model and a drift error model of an attitude signal of the balance car system; driving the permanent magnet synchronous motor by using a second-order dynamic Terminal sliding film; and simultaneously optimizing parameters of a tracking controller, a synchronous controller, an anti-backlash controller and a switching function in the dual-motor system by using a particle swarm algorithm. The invention realizes that the signals acquired by the sensor of the balance car have larger noise and zero drift error; the robustness is poor; the brush motor has the advantages of complex structure, more faults, large maintenance workload, short service life, easy generation of electromagnetic interference by reversing sparks, and the problems of jitter, overlarge deviation, low safety and the like in the running process of the balance car.
Description
Technical Field
The invention belongs to the technical field of balance car control, and particularly relates to a balance car system and a control method thereof.
Background
The two-wheel balance car gradually enters the life of people due to the characteristics of low price, small volume, light weight, convenience in moving and carrying and the like. At present, the related technology of the balance car is continuously updated, the control of a balance system is more flexible and sensitive, and a human-computer interaction system tends to be delicate and humanized. However, in the driving mode, most of the balance vehicle brands in the current market are direct current brush motors, and electric energy enters an armature winding through a brush and a commutator to drive the motor. Due to the existence of the electric brush and the commutator, the brush motor has the characteristics of complex structure, more faults, large maintenance workload, short service life, easy generation of electromagnetic interference by commutation sparks and the like, and the production cost and the maintenance cost are increased to a certain extent. The traditional balance car has the defects of weak endurance, low precision of a control system, single function and the like.
Although balance cars on the market are various in product types, most of the product motors are insufficient in control design, and the traditional control method is easy to cause balance accidents due to the defects of the traditional control method. PID control, based on T _ S fuzzy control, self-adaptive control and the like have the following defects: the control variable armature voltage indirectly controls the balance of the vehicle body, so that the dynamic performance of the electric vehicle is difficult to ensure; the signal collected by the sensor has larger noise and zero drift error; the robustness is poor, and the method is not suitable for the application of a nonlinear system. The sliding mode control design is simple, the control precision is high, the sliding mode has complete robustness to perturbation and external disturbance of a system, and the method is an important method for solving the nonlinear problem. However, in general sliding mode control, a linear switching function is generally selected, and although system stability can be ensured, in theory, infinite time is required for a system state (or error) to converge to a balance origin. The Terminal sliding mode constructs a switching surface by a nonlinear function and can converge to a balance point within a limited time, which is inspired by an attractor concept in a neural network. But the problem of buffeting exists, and the application and the control effect of the sliding mode control in engineering are seriously influenced by the buffeting. Although effective in removing buffeting, methods such as saturation functions may degrade control performance.
In summary, the existing balance car driving control method does not comprehensively consider the tracking and monitoring of the controller on various performances of the permanent magnet synchronous motor, and the problems of jitter, overlarge deviation, low safety and the like often occur in the implementation process of the method. Therefore, the novel balance car control method has great practical engineering value.
Disclosure of Invention
The invention aims to solve the technical problem of providing a balance car system and a control method thereof aiming at the defects in the prior art, and the balance car system converges at a balance origin within a limited time on the basis of a permanent magnet synchronous motor based on a second-order dynamic Terminal sliding mode of Kalman filtering and a particle swarm algorithm, so that buffeting is eliminated, and the stability and durability of the balance car are improved.
The invention adopts the following technical scheme:
a balance car system comprises a control part, a sensor part, a man-machine interaction part, a power supply part, a main circuit part and an upper computer part; the control part adopts a microcontroller and is respectively connected with the sensor part, the man-machine interaction part, the power supply part and the main circuit part; the upper computer part is connected with the human-computer interaction part, and the human-computer interaction part is powered by the power supply part;
the sensor part comprises a gyroscope for acquiring the angular speed of the offset of the vehicle body, an accelerometer for acquiring the acceleration of the vehicle, a speed sensor for acquiring the actual speed, a corner sensor for acquiring the direction angle of the joystick, an infrared sensor for detecting the road condition, and a voltage and current sensor for acquiring related data of the inverter;
the man-machine interaction part comprises an L CD display screen used for displaying vehicle speed information, electric quantity information, battery temperature information and system running state feedback, a wireless Bluetooth used for transmitting data to a mobile phone APP and sending instructions to a controller, an upper computer communication module used for communicating with a PC, keys used for power switch control, mode selection and information inquiry, a L ED lamp and a buzzer used for prompting vehicle alarm information, and a power supply module used for supplying power to the mobile phone APP;
the power supply part comprises a charging module and a storage battery, wherein the charging module is used for charging batteries and supplying power to all parts of the system;
the main circuit part comprises two permanent magnet synchronous motors and a three-phase arm inverter capable of driving the two permanent magnet synchronous motors, and is used for realizing independent control and cooperative operation of the motors;
the upper computer part comprises a mobile phone for transmitting information and transmitting instructions through wireless Bluetooth and a PC (personal computer) end for communicating through a serial port.
A balance car system control method comprises the steps of establishing a state equation of extended Kalman filtering and a mathematical model of a permanent magnet linear motor according to a difference equation model and a drift error model of an attitude signal of a balance car system; driving the permanent magnet synchronous motor by using a second-order dynamic Terminal sliding film; and simultaneously optimizing parameters of a tracking controller, a synchronous controller, an anti-backlash controller and a switching function in the dual-motor system by using a particle swarm algorithm.
Specifically, the state equation of the extended kalman filter is as follows:
wherein the content of the first and second substances,
is the output value of the gyroscope,
the actual angular velocity measured by the gyroscope is represented by k, scale error and drift error, v (n-1) is white Gaussian noise with the mean value of zero, and T is a period.
Further, the difference equation model of the attitude signal of the balance car is as follows:
wherein, ω is0For initial angle values of the gyroscope, κ is the scale error, α is the drift error, and the first order autoregressive AR model for the gyroscope drift error is as follows:
wherein the content of the first and second substances,
is an autoregressive model parameter; v (n) is measurement white noise with a mean value of zero;
the variance of gaussian white noise is as follows:
wherein, Ci、CgInclinometer and gyroscope noise covariance, respectively;1is the standard deviation of the tilt angle;2is the gyroscope gaussian noise density standard deviation;3is the standard deviation of the noise in the gyro drift error AR model.
Specifically, the mechanical motion equation of the permanent magnet linear motor is as follows:
wherein s is mover displacement; v is the mover speed; m is the total mass of the rotor and the load carried by the rotor; b isvIs the viscous friction factor; f∑Is the total disturbance force.
Further, the total disturbance force F∑The following were used:
F∑＝Frip+Fload+Ffric
wherein, FloadIs the load resistance; fripEquivalent resistance to the end effect; fMThe end effect thrust fluctuation amplitude; tau is a polar distance;
is the initial phase electrical angle; ffricIs a friction force; f. ofcIs the coulomb friction coefficient; f. ofsIs the static friction coefficient; v is the mover speed; v. ofsIs the critical friction speed.
Specifically, driving the permanent magnet synchronous motor by using a second-order dynamic Terminal slip film specifically comprises the following steps:
let x be [ x ]1,x2]T＝[s,v]TIs a change of state of the systemQuantity, input control quantity u ═ iqThe equation of state is as follows:
wherein k is1,k2,k3For unknown parameters, kfIs a coefficient of resistance, BvIs viscous friction factor, F∑M is total disturbance force, and M is total mass of the rotor and the load carried by the rotor;
let the system tracking error be e ═ x1 *-x1Wherein x is1 *Is x1Defining the second-order nonsingular fast terminal sliding mode variable of the system as follows:
wherein, 0<α<1，β∈R+P, q ∈ N are odd numbers, lambda is more than p/q, and p/q is more than 1 and less than 2;
when the system state is close to the balance point, the high-order term of the tracking error e (t) approaches to 0, and the convergence speed of the tracking error e (t) is approximate to that of a nonsingular terminal sliding mode; when the system is far away from a balance point, the high-order terms of the tracking error e (t) play a main role, and the convergence speed of the tracking error e (t) is higher than that of a nonsingular terminal sliding mode; the sliding mode control system meets the sliding mode variable sigma and the first derivative thereof
Converging to zero.
Further, the first derivative of the synovial variable
The following were used:
the synovial membrane control law is as follows:
wherein: r is a position command, ce is an error, f (t) is a function designed to achieve a global sliding mode surface, f (t) is s (0) exp (- λ t), λ >0, s (0) is an initial time s (t), sgn(s) is a step function, and B is a friction coefficient; k (t) is a switching gain, k (t) max (| e (t) |) + ρ, ρ > 0; when the system input ss <0, the synovium is present; if the system input ss >0, the switching gain K (t) should be increased; if the system input ss <0, the switching gain K (t) should be reduced.
Specifically, a performance index function F of a parameter set by using a particle swarm algorithm is as follows:
wherein, the smaller the first term of the performance index is, the smaller the steady-state error of the system is; the smaller the second term is, the smaller the energy consumption of the system is; t is time, e1(t) is a constraint term, u1,u2Is a comprehensive control law.
Further, the method comprises the following specific steps:
s401, initializing each parameter value of a particle swarm, calculating a fitness function of each particle, and calculating the performance index size of each group of parameters in a weighting mode;
updating the adaptation value with the new particle if the adaptation value of the new particle is smaller than that of the previous one; otherwise, the adaptation value remains unchanged.
Where pbest (t) is the best adaptation value at time t, f (-) is the objective function of the performance indicator, and X (t) is the position of each particle; pbest records the optimal solution searched by an individual, and gbest is used for recording the optimal solution searched by the whole group in one iteration;
the updated equations for velocity and particle position are as follows:
V[i]＝w×v[i]+c1×rand()×(pbest[i]-present[i])+c2×rand()×(gbest-present[i])
wherein v [ i ] represents the velocity of the ith particle, w represents an inertia weight, c1 and c2 represent learning parameters, rand () represents a random number between 0 and 1, pbest [ i ] represents the optimal value searched by the ith particle, gbest represents the optimal value searched by the whole cluster, and present [ i ] represents the current position of the ith particle;
s402, when the minimum adaptive value in pbest is smaller than the global adaptive value, updating the global adaptive value by using the position of the corresponding minimum adaptive value; otherwise, the global adaptation value remains unchanged;
gbest(t+1)＝argmin{f(pbest1(t)),f(pbest2(t)),...,f(pbestn(t))}
wherein gbest (t) is the global optimal adaptive value at the time t, and n is the total number of particles;
s403, updating the control parameter value according to the following formula
Xi'j(t+1)＝Xi'j(t)+Vi'j(t+1)
Wherein Vi' j (t) is the speed of the ith population iteration particle of the jth dimension particle; xi ' j (t) is the position of the ith ' group iteration particle of the jth dimension particle, and i ' is taken as 20; omega is inertia weight, and is taken as 0.7; c. C1And c2To obtain the learning rate, take c1＝c2＝2；
S404, the current position of the particle exceeds the set maximum value and the set minimum value, and the particles beyond the range are re-assigned, namely
When the maximum velocity of the particle is exceeded, the velocity of the particle is reassigned to
Wherein, xmin (j) and xmax (j) are respectively the minimum position and the maximum position of the j dimension; vmin (j) and Vmax (j) are respectively the minimum speed and the maximum speed of the j dimension;
s405, when the iteration times are smaller than the maximum set times, turning to the step S403; otherwise, ending.
Compared with the prior art, the invention has at least the following beneficial effects:
the invention relates to a balance car system which comprises a control part, a sensor part, a man-machine interaction part, a power supply part, a main circuit part and an upper computer part, wherein a permanent magnet synchronous motor is adopted as a motor. The design of the five-bridge arm inverter improves the dynamic performance of the two-motor system, reduces torque fluctuation and can effectively reduce the energy loss rate. Under the condition of the same battery capacity, the endurance of a balance car system driven by the five-bridge-arm inverter is obviously stronger.
The invention also discloses a balance car system control method, which optimizes the parameters of the designed controller by utilizing the particle swarm algorithm, reduces the energy consumption of the system on the premise of ensuring the tracking performance, needs to minimize the value of the controlled variable to achieve the energy-saving effect, obtains the unknown parameters in the control law and the optimal value of β in the switching function by adopting the particle swarm algorithm to simultaneously meet the aims of tracking precision and energy saving, combines the second-order dynamic sliding mode with the Terminal sliding mode, effectively removes the sliding mode buffeting while quickly and highly accurately tracking the command signals, and simulates to show the effectiveness of the method.
Further, using kalman filtering, well-founded predictions are made of the next step of the system, which always indicates what is actually happening, even with various disturbances. The use of kalman filtering is highly desirable in continuously varying systems, has the advantage of small memory usage, (no need to retain historical data other than the previous state quantity) and is fast and well suited for real-time problem and embedded systems.
Furthermore, the permanent magnet synchronous linear motor has the advantages of no need of electromagnetism, high thrust density, high efficiency and the like. The simulation method overcomes the defects of the prior art, provides the running state of the linear motor, realizes the simulation of the permanent magnet linear synchronous motor, and provides great help for the research of the running state of the permanent magnet linear synchronous motor.
Further, when the second-order dynamic Terminal sliding mode traditional sliding mode is designed, in order to keep the system motion on the sliding mode surface, the system input is switched back and forth between different controllers, so that the system has buffeting. High order sliding modes and dynamic sliding modes can overcome this problem well. The high-order sliding mode selection controller not only enables the switching function to be equal to zero, but also enables the first-order derivative of the switching function to be equal to zero until the r-1-order derivative, and the control item only acts on the r-order derivative of the switching function, which is called r-order sliding mode control. The dynamic sliding mode embeds the discontinuous term into the derivative term of the controller.
Furthermore, the method for setting the parameters of the PID controller by using the particle swarm optimization algorithm gives specific design steps for each parameter and an adaptive function, selects a permanent magnet type direct current servo motor commonly used in control engineering design as a research object, and has certain practical value. Compared with the genetic algorithm, the simulation result has certain improvement. The optimal parameters obtained by the simulation result under different adaptive functions can be applied to actual servo motor speed control.
In conclusion, the invention realizes that the signals acquired by the sensor of the balance car have larger noise and zero drift error; the robustness is poor; the brush motor has the advantages of complex structure, more faults, large maintenance workload, short service life, easy generation of electromagnetic interference by reversing sparks, and the problems of jitter, overlarge deviation, low safety and the like in the running process of the balance car.
The technical solution of the present invention is further described in detail by the accompanying drawings and embodiments.
Drawings
FIG. 1 is a general block diagram of a novel balance car system;
FIG. 2 is a functional block diagram of the present invention;
FIG. 3 is a control flow diagram of the present invention;
FIG. 4 is a block diagram of a particle swarm algorithm of the present invention.
Detailed Description
Referring to fig. 1, the invention provides a balance car system, which adopts a second-order dynamic Terminal sliding mode and a particle swarm algorithm based on kalman filtering, and comprises a control part, a sensor part, a man-machine interaction part, a power supply part, a main circuit part and an upper computer part; the control part adopts a microcontroller and is respectively connected with the sensor part, the man-machine interaction part, the power supply part and the main circuit part; the upper computer part is connected with the human-computer interaction part, and the human-computer interaction part is powered by the power supply part.
The control part: STM32F103ZET6 control of selection ST company is as main control chip, and this chip has two senior timers and 512K's storage capacity, has 5 kinds of IO mouths, a plurality of serial ports communication interface, fine satisfying the design requirement.
A sensor portion: the gyroscope, the external sensor, the current sensor, the voltage sensor, the rotation angle sensor and the speed sensor are arranged. The gyroscope is used for acquiring angular velocity of vehicle body deviation, the accelerometer is used for acquiring acceleration of a vehicle, the speed sensor is used for acquiring actual speed, the corner sensor is used for acquiring a direction angle of the operating lever, the infrared sensor is used for detecting road conditions, and the voltage and current sensors are used for acquiring relevant data of the inverter.
The man-machine interaction part comprises an L CD display screen, a wireless Bluetooth, an upper computer communication module, a key, a L ED lamp and a buzzer.
The L CD display screen can display vehicle speed information, electric quantity information, battery temperature information and system running state feedback, the wireless Bluetooth is mainly used for transmitting data to the mobile phone APP and sending instructions to the controller, the upper computer communication module is used for communicating with the PC, the keys are used for power switch control, mode selection and information inquiry, and the L ED lamp and the buzzer are used for prompting vehicle alarm information.
A power supply section: the charging device comprises a charging module and a storage battery.
For battery charging and for powering the various parts of the system.
A main circuit part: there are power driver and two permanent magnet synchronous motors.
The power driver is a five-bridge arm inverter, can simultaneously drive two motors, and can realize independent control and cooperative operation of the motors.
The upper computer part: the system is divided into a mobile phone end and a PC end.
The mobile phone mainly transmits information and transmits instructions through wireless Bluetooth; the PC terminal is communicated through a serial port and is mainly used for programming and debugging a system.
The function module comprises a rotor interval calculation module, a speed calculation module, an angle subdivision module, a phase adjustment module, a speed control module, a current limiting control module, a waveform modulation module, a three-phase inverter and a motor starting module. As shown in fig. 2.
Referring to fig. 3, the method for controlling a balance car according to the present invention optimizes parameters of a designed controller by using a particle swarm algorithm, reduces energy consumption of a system on the premise of ensuring tracking performance, minimizes a value of a control quantity ui for achieving an energy saving effect, obtains optimal values of unknown parameters k1, k2, k3, k4 in a control law and β in a switching function for simultaneously satisfying tracking accuracy and energy saving, and specifically integrates tracking accuracy and energy consumption into a target function E, wherein the final objective of optimization is to obtain the minimum value of the target function E under the condition of satisfying constraint conditions.
The balance car works as follows:
the method comprises the following steps: starting, initializing the system;
step two: information interaction is carried out through a wireless communication Bluetooth module;
step three: acquiring a video shot by a vehicle bottom camera, and compressing, encoding and storing the video signal;
step four: keyboard key scanning;
step five: scanning obstacles; acquiring obstacle avoidance sensor signals and calculating a route through an obstacle avoidance algorithm;
step six: road condition scanning;
(1) the infrared sensor is used for detecting the distance from the vehicle bottom to the ground to acquire the ground flatness information, the road condition parameters are calculated through a road condition detection algorithm, and the road condition of the road which is running at present is acquired through further analyzing data, so that the road condition is judged.
(2) The method comprises the steps that the angle and the angular speed of a vehicle body are obtained through an accelerometer and a gyroscope sensor, the angle and the angular speed are input into a Kalman filter, the second-order dynamic Terminal sliding mode is used for calculating, and a group of output signals are output to a motor to control the adjustment of the angle of the vehicle body, so that the vehicle body can be stably kept upright;
(3) acquiring a signal of a speed sensor, acquiring an actual speed, and completing closed-loop control on the speed through a speed PID;
(4) sampling a voltage signal of the operating rod, comparing the voltage signal with a reference voltage to judge the direction and the angle of steering, generating a corresponding motor control signal to a control part, and controlling the left motor and the right motor to run at different speeds to complete steering;
(5) detecting the position of an obstacle by an obstacle avoidance sensor and acquiring the surrounding situation of the obstacle by an infrared sensor, firstly selecting all positions without the obstacle within a certain range, calculating and comparing routes corresponding to the positions according to the detected surrounding characteristics of the obstacle, and finding out an obstacle avoidance route with the shortest bypassing radius so as to avoid the obstacle;
(6) collecting motor voltage and winding current through a voltage and current sensor, calculating torque and flux linkage by using the motor winding current and voltage, generating PWM (pulse width modulation) of required 12 paths through a torque and flux linkage regulator and an existing and disclosed vector table, performing direct torque control, and outputting the PWM to a direct current brushless motor;
controlling a buzzer and L ED, displaying on a display screen, judging whether the operation is finished, if so, entering the step eight, if not, returning to the step two;
step eight: and (6) ending.
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. The components of the embodiments of the present invention generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations. Thus, the following detailed description of the embodiments of the present invention, presented in the figures, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The control method of the balance car comprises the following steps:
s1 Kalman signal fusion filtering
In the sensor system, the inclination angle and speed of the balance car body are measured by a gyroscope, the measurement result has errors which are mainly drift error and scale error, and the output characteristic is
In the formula:
is the output value of the gyroscope,
for the true angular velocity of the gyroscope measurements, κ is the scale error and α is the drift error.
If the equation (1) is subjected to differential operation, the model of the differential equation of the attitude signal of the balance car in one period T is
ω0For initial angle values of the gyroscope, a first-order Autoregressive (AR) model of the drift error of the gyroscope can be established according to an AR estimation method of the drift error of the gyroscope:
in the formula:
the values are 0.9185 for the autoregressive model parameters; v (n) is measurement white noise with a mean value of zero.
Establishing a state equation of the extended Kalman filtering according to a difference equation model and a drift error model of the attitude signal of the balance car:
in the formula: v (n-1) is white Gaussian noise with a mean value of zero.
Variance of Gaussian white noise of
In the formula: ci、CgInclinometer and gyroscope noise covariance, respectively;1is the standard deviation of the tilt angle;2is the gyroscope gaussian noise density standard deviation;3is the standard deviation of the noise in the model of the gyroscope drift error AR (1).
S2 mathematical model of permanent magnet linear motor
The electromagnetic thrust expression of the permanent magnet linear motor is
The mechanical equation of motion for PM L SM is:
wherein s is mover displacement; v is the mover speed; m is the total mass of the rotor and the load carried by the rotor; b isvIs the viscous friction factor; f∑Is the total disturbance force F∑＝Frip+Fload+Ffric；FloadIs the load resistance; fripEquivalent resistance to the end effect;
wherein, FMThe end effect thrust fluctuation amplitude; tau is a polar distance;
is the initial phase electrical angle; ffricIs a friction force;
fcis the coulomb friction coefficient; f. ofsIs the static friction coefficient; v is the mover speed; v. ofsIs the critical friction speed.
S3, second-order dynamic Terminal sliding mode control
The permanent magnet synchronous motor is used as a control object, a magnetic circuit is not saturated, a space magnetic field is in sinusoidal distribution, hysteresis and eddy current loss influence are not counted, and a voltage equation is
The torque equation is
Tm＝p(ψd*iq-ψq*id) (10)
The mechanical equation of motion is
In the formula ud、uqIs the stator voltage dq axis component; i.e. id、iqIs stator current component, omega is rotor angular velocity Ld、LqEquivalent inductance of a dq axis of a stator winding; rsIs a stator resistor; psifFor each pair of magnetic pole flux linkage; t isLIs the load torque; j is moment of inertia; b is a friction coefficient; p is the rotor stage logarithm.
Let the speed given signal be ω, define the error state emThe rotation speed error system is obtained as
According to the properties of the high-order slip film, the system buffeting-free slip film control is realized through the slip film with two or more stages.
For convenience of description, let x ═ x1,x2]T＝[s,v]TAs a state variable of the system, the input control quantity is u-iq。
The equation of state for the system (3) is then in the form:
wherein the content of the first and second substances,
let the system tracking error be e ═ x1 *-x1Wherein x is1 *Is x1Given values of (a).
Defining a second-order nonsingular fast terminal sliding mode variable of the system as follows:
wherein, 0<α<1，β∈R+P, q ∈ N are odd numbers, λ > p/q, 1 < p/q <2 to satisfy the nonsingularity of the slide film surface.
According to the sliding mode surface, when the system state is close to a balance point, the high-order term of the tracking error e (t) approaches to 0 and can be ignored, and the convergence speed of the tracking error e (t) is similar to that of a nonsingular terminal sliding mode; when the system is far away from the balance point, the high-order terms of the tracking error e (t) play a main role, so the convergence speed of the system is faster than that of a nonsingular terminal sliding mode.
The sliding mode variable sigma and the first derivative thereof must be satisfied according to the design requirement of the sliding mode control system
Converging to zero.
First derivative of synovial variable
Is composed of
Assuming that the sliding mode variable σ designed in equation (14) is the output variable of the uncertain system, and the relative order of the second-order sliding mode control system is 1 as known from equation (15), u is selected to make the output variable σ and its derivative be appropriate
Convergence to zero within a finite time.
The equation of state for the sliding-mode variable of equation (15) can be written as
Wherein, r is the position instruction, through fuzzy synovial membrane algorithm, sets up error e to: e-r- θ.
The overall dynamic slide film surface is additionally arranged as follows:
s＝e+ce-F(t) (17)
where f (t) is a function for achieving the global sliding mode surface design, s (0) exp (- λ t), λ >0, and s (0) is s (t) at the initial time.
Define L yapunov function as
Then:
the synovial membrane control law is therefore:
wherein: k (t) is a switching gain, and k (t) max (| e (t) |) + ρ, ρ > 0.
Bringing formula (19) into formula (18):
V＝-K(t)|s|-E(t)s (20)
wherein V is less than or equal to- η | s | is less than or equal to 0.
From the above, the stability theorem of Liya Punuo Fu can be used
When ss<0, the slip film is present.
Fuzzy rules:
1. if ss >0, K (t) should be increased.
2. ss <0, K (t) should decrease.
Let ss be the system input and Δ K (t) be the system output, according to the fuzzy rule, the fuzzy is defined as follows:
ss＝{NB NM ZO PM PB}
ΔK＝{NB NM ZO PM PB} (21)
wherein NB, NM, ZO, PM, PB are respectively negative big, negative middle, zero, middle and positive big.
Estimating the upper limit of K (t) by adopting an integral method:
wherein: g is a proportionality coefficient, G > 0. Carrying in formula (19) to obtain:
wherein the content of the first and second substances,
r(t,x1,x2) Is an uncertain function and satisfies the following boundary conditions:
the state trajectory can be set to converge spirally around the origin to the origin within a finite time on the sigma-sigma plane using a supercoiling algorithm. The specific algorithm is as follows:
wherein M is1、M2Satisfies the following conditions:
for the system (13), a nonlinear sliding mode variable (14) is selected, a condition (24) is met, and under the action of a superspiral control law (25), if the condition (26) is met, the system converges in a limited time.
S4, simultaneously optimizing parameters of the tracking controller, the synchronous controller, the anti-backlash controller and the switching function in the dual-motor system by using a particle swarm optimization, as shown in figure 4.
And selecting a particle swarm algorithm-based setting parameter. In order to guarantee two conditions of minimum tracking performance and energy consumption, the following performance index functions are designed:
smaller first term of the performance index indicates smaller steady state error of the system; the smaller the second term, the smaller the power consumption of the system. The constraints are to ensure that the tracking accuracy is within 10% and that the total energy consumed by the system is minimal. And integrating the tracking precision and the energy consumption into an objective function E, wherein the final objective of the optimization is to obtain the minimum value of the objective function E under the condition of meeting the constraint condition.
S401, initializing each parameter value of the particle swarm, and calculating a fitness function of each particle. And calculating the size of the performance index (target function adaptive value) of each group of parameters in a weighted mode.
Updating the adaptation value with the new particle if the adaptation value of the new particle is smaller than that of the previous one; otherwise, the adaptation value remains unchanged.
Where pbest (t) is the best fit at time t, f (-) is usually an objective function of the performance metric, i.e., a weighting of multiple significant metrics, and x (t) is the position of each particle.
pbest is used for recording the optimal solution searched by the individual, and gbest is used for recording the optimal solution searched by the whole population in one iteration.
The updated equations for velocity and particle position are as follows:
V[i]＝w×v[i]+c1×rand()×(pbest[i]-present[i])+c2×rand()×(gbest-present[i]) (29)
where v [ i ] represents the velocity of the ith particle, w represents the inertia weight, c1 and c2 represent the learning parameters, rand () represents a random number between 0 and 1, pbest [ i ] represents the optimum value searched for by the ith particle, gbest represents the optimum value searched for by the entire cluster, and present [ i ] represents the current position of the ith particle.
S402, when the minimum adaptive value in pbest is smaller than the global adaptive value, updating the global adaptive value by using the position of the corresponding minimum adaptive value; otherwise, the global adaptation value remains unchanged.
gbest(t+1)＝argmin{f(pbest1(t)),f(pbest2(t)),...,f(pbestn(t))} (30)
Wherein, gbest (t) is the global optimum adaptive value at time t, and n is the total number of particles.
S403, updating the control parameter value according to the following formula
Xi'j(t+1)＝Xi'j(t)+Vi'j(t+1) (31)
Wherein Vi' j (t) is the speed of the ith population iteration particle of the jth dimension particle; xi ' j (t) is the position of the ith ' group iteration particle of the jth dimension particle, and i ' is taken as 20; omega is inertia weight, and is taken as 0.7; c1 and c2 are learning rates, and c1 is equal to c2 is equal to 2.
S404, the current position of the particle exceeds the set maximum value and the set minimum value, and the particles beyond the range are re-assigned, namely
Similarly, for the current velocity of the particle, when the maximum velocity of the particle is exceeded, the velocity of the particle is reassigned to
Wherein, xmin (j) and xmax (j) are respectively the minimum position and the maximum position of the j dimension; vmin (j) and Vmax (j) are the minimum and maximum speeds, respectively, for dimension j.
S405, when the iteration times are smaller than the maximum set times, turning to the step S3; otherwise, the procedure is terminated.
In the control of the motor of the balance car, under the condition that the particle swarm algorithm finds the optimal parameters, not only the tracking error of the system does not generate tremble, but also the two motors only eliminate backlash when backlash occurs, and keep synchronous operation under other conditions, thereby realizing the comprehensive control target of tracking, synchronization and backlash elimination. And the two motors alternately pass through the tooth gaps, and when one motor passes through the tooth gaps, the other motor drags the load, so that the function of offsetting moment backlash elimination is achieved. Therefore, the integrated controller designed by the embodiment can eliminate the nonlinear influence of the backlash and ensure the synchronization of the two motors on the premise of ensuring the load tracking performance.
The above-mentioned contents are only for illustrating the technical idea of the present invention, and the protection scope of the present invention is not limited thereby, and any modification made on the basis of the technical idea of the present invention falls within the protection scope of the claims of the present invention.
Claims (2)
1. A control method of a balance car system is characterized in that the balance car system comprises a control part, a sensor part, a man-machine interaction part, a power supply part, a main circuit part and an upper computer part, wherein the control part adopts a microcontroller which is respectively connected with the sensor part, the man-machine interaction part, the power supply part and the main circuit part, the upper computer part is connected with the man-machine interaction part, the man-machine interaction part provides electric energy by the power supply part, the sensor part comprises a gyroscope for acquiring the angular velocity of the deviation of a car body, an accelerometer for acquiring the acceleration of the car, a speed sensor for acquiring the actual speed, a corner sensor for acquiring the direction angle of a control lever, an infrared sensor for detecting the road condition, a voltage sensor and a current sensor for acquiring relevant data of an inverter, the man-machine interaction part comprises an L CD display screen for displaying the speed information, the electric quantity information, the battery temperature information and the system running state feedback, a wireless Bluetooth module for transmitting the data to a mobile phone and sending instructions to the controller, the upper computer communication module for communicating with the PC, a power supply module for controlling the power switch, a mode selection, a key for prompting the vehicle alarm information, a L and a buzzer for prompting the vehicle alarm information, a battery, a power supply part, a battery, a charging system, a permanent magnet motor, a battery, a charging system, a permanent magnet motor and a permanent;
establishing a state equation of extended Kalman filtering and a mathematical model of the permanent magnet synchronous motor according to a difference equation model and a drift error model of an attitude signal of a balance car system; driving the permanent magnet synchronous motor by using a second-order dynamic Terminal sliding film; simultaneously optimizing parameters of a tracking controller, a synchronous controller, an anti-backlash controller and a switching function in a dual-motor system by using a particle swarm algorithm, wherein the state equation of the extended Kalman filtering is as follows:
wherein, k is a scale error and is a drift error, v (n-1) is white gaussian noise with a mean value of zero, T is a period, and a difference equation model of the attitude signal of the balance car is as follows:
wherein, ω is0The initial angle value of the gyroscope, κ is the scale error, and drift error, and the first-order Autoregressive (AR) model of the gyroscope drift error is as follows:
wherein the content of the first and second substances,
is an autoregressive model parameter; v (n) is white Gaussian noise with the mean value of zero;
the variance of gaussian white noise is as follows:
wherein, Ci、CgInclinometer and gyroscope noise covariance, respectively;1is the standard deviation of the tilt angle;2the mechanical motion equation of the permanent magnet synchronous motor is the standard deviation of the Gaussian noise density of the gyroscope as follows:
wherein s is mover displacement; v is the mover speed; m is the total mass of the rotor and the load carried by the rotor; b isvIs the viscous friction factor; f∑Total disturbance force is total disturbance force F∑The following were used:
F∑＝Frip+Fload+Ffric
wherein, FloadIs the load resistance; fripEquivalent resistance to the end effect; fMThe end effect thrust fluctuation amplitude; tau is a polar distance;
is the initial phase electrical angle; ffricIs a friction force;
the driving of the permanent magnet synchronous motor by utilizing the second-order dynamic Terminal sliding film is specifically as follows:
let x be [ x ]1,x2]T＝[s,v]TAs a state variable of the system, the input control quantity is u-iqThe equation of state is as follows:
wherein k is1,k2,k3For unknown parameters, kfIs a coefficient of resistance, BvIs viscous friction factor, F∑M is total disturbance force, and M is total mass of the rotor and the load carried by the rotor;
let the system tracking error be e ═ x1 *-x1Wherein x is1 *Is x1Defining the second-order nonsingular fast terminal sliding mode variable of the system as follows:
wherein, 0<α<1，β∈R+P, q ∈ N are odd numbers, lambda is more than p/q, and p/q is more than 1 and less than 2;
when the system state is close to the balance point, the high-order term of the tracking error e (t) approaches to 0, and the convergence speed of the tracking error e (t) is approximate to that of a nonsingular terminal sliding mode; when the system is far away from a balance point, the high-order terms of the tracking error e (t) play a main role, and the convergence speed of the tracking error e (t) is higher than that of a nonsingular terminal sliding mode; the sliding mode control system meets the sliding mode variable sigma and the first derivative thereof
Convergence to zero, first derivative of synovial variable
The following were used:
the synovial membrane control law is as follows:
wherein: r is a position command, ce is an error, f (t) is a function for achieving global sliding mode surface design, f (t) is s (0) exp (- λ t), λ >0, s (0) is an initial time of s (t), sgn(s) is a step function, and B is a friction coefficient; k (t) is a switching gain, k (t) max (| e (t) |) + ρ, ρ > 0; when the system input ss <0, the synovium is present; if the system input ss >0, the switching gain K (t) should be increased; if the system input ss <0, the switching gain K (t) should be reduced;
the performance index function F of the parameter setting by using the particle swarm optimization is as follows:
wherein, the smaller the first term of the performance index is, the smaller the steady-state error of the system is; the smaller the second term is, the smaller the energy consumption of the system is; t is time, e1(t) is a constraint term, u1,u2Is a comprehensive control law.
2. The balance car system control method according to claim 1, characterized by comprising the following specific steps:
s401, initializing each parameter value of a particle swarm, calculating a fitness function of each particle, and calculating the performance index size of each group of parameters in a weighting mode;
updating the adaptation value with the new particle if the adaptation value of the new particle is smaller than that of the previous one; otherwise, the adaptation value remains unchanged;
where pbest (t) is the best adaptation value at time t, f (-) is the objective function of the performance indicator, and X (t) is the position of each particle; pbest records the optimal solution searched by an individual, and gbest is used for recording the optimal solution searched by the whole group in one iteration;
the updated equations for velocity and particle position are as follows:
V[i]＝w×v[i]+c1×rand()×(pbest[i]-present[i])+c2×rand()×(gbest-present[i])
wherein v [ i ] represents the velocity of the ith particle, w represents an inertia weight, c1 and c2 represent learning parameters, rand () represents a random number between 0 and 1, pbest [ i ] represents the optimal value searched by the ith particle, gbest represents the optimal value searched by the whole cluster, and present [ i ] represents the current position of the ith particle;
s402, when the minimum adaptive value in pbest is smaller than the global adaptive value, updating the global adaptive value by using the position of the corresponding minimum adaptive value; otherwise, the global adaptation value remains unchanged;
gbest(t+1)＝argmin{f(pbest1(t)),f(pbest2(t)),...,f(pbestn(t))}
wherein gbest (t) is the global optimal adaptive value at the time t, and n is the total number of particles;
s403, updating the control parameter value according to the following formula
Xi'j(t+1)＝Xi'j(t)+Vi'j(t+1)
Wherein Vi' j (t) is the speed of the ith population iteration particle of the jth dimension particle; xi ' j (t) is the position of the ith ' group iteration particle of the jth dimension particle, and i ' is taken as 20; omega is inertia weight, and is taken as 0.7; c. C1And c2To obtain the learning rate, take c1＝c2＝2；
S404, the current position of the particle exceeds the set maximum value and the set minimum value, and the particles beyond the range are re-assigned, namely
When the maximum velocity of the particle is exceeded, the velocity of the particle is reassigned to
Wherein, xmin (j) and xmax (j) are respectively the minimum position and the maximum position of the j dimension; vmin (j) and Vmax (j) are respectively the minimum speed and the maximum speed of the j dimension;
s405, when the iteration times are smaller than the maximum set times, turning to the step S403; otherwise, ending.
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