CN113830166A - Intelligent networking automobile line control chassis integrated control method - Google Patents
Intelligent networking automobile line control chassis integrated control method Download PDFInfo
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- CN113830166A CN113830166A CN202110860242.8A CN202110860242A CN113830166A CN 113830166 A CN113830166 A CN 113830166A CN 202110860242 A CN202110860242 A CN 202110860242A CN 113830166 A CN113830166 A CN 113830166A
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B62—LAND VEHICLES FOR TRAVELLING OTHERWISE THAN ON RAILS
- B62D—MOTOR VEHICLES; TRAILERS
- B62D5/00—Power-assisted or power-driven steering
- B62D5/04—Power-assisted or power-driven steering electrical, e.g. using an electric servo-motor connected to, or forming part of, the steering gear
- B62D5/0457—Power-assisted or power-driven steering electrical, e.g. using an electric servo-motor connected to, or forming part of, the steering gear characterised by control features of the drive means as such
- B62D5/046—Controlling the motor
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B62—LAND VEHICLES FOR TRAVELLING OTHERWISE THAN ON RAILS
- B62D—MOTOR VEHICLES; TRAILERS
- B62D5/00—Power-assisted or power-driven steering
- B62D5/06—Power-assisted or power-driven steering fluid, i.e. using a pressurised fluid for most or all the force required for steering a vehicle
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B62—LAND VEHICLES FOR TRAVELLING OTHERWISE THAN ON RAILS
- B62D—MOTOR VEHICLES; TRAILERS
- B62D5/00—Power-assisted or power-driven steering
- B62D5/06—Power-assisted or power-driven steering fluid, i.e. using a pressurised fluid for most or all the force required for steering a vehicle
- B62D5/20—Power-assisted or power-driven steering fluid, i.e. using a pressurised fluid for most or all the force required for steering a vehicle specially adapted for particular type of steering gear or particular application
- B62D5/22—Power-assisted or power-driven steering fluid, i.e. using a pressurised fluid for most or all the force required for steering a vehicle specially adapted for particular type of steering gear or particular application for rack-and-pinion type
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Abstract
The invention discloses an intelligent networking automobile drive-by-wire chassis integrated control method. The invention aims to provide an intelligent networking automobile drive-by-wire chassis integrated control method, which aims to solve the problems of overhigh energy consumption, poor operation stability and the like in the prior art. The invention is based on a motor efficiency MAP graph of a double-execution mechanism, considers the constraint condition of electro-hydraulic braking, takes the lowest energy consumption as a control target, and realizes the power-assisted distribution calculation of chassis-related mechanisms. The invention designs the power-assisted characteristic curve of the electro-hydraulic compound power-assisted steering system by dividing the power-assisted characteristic curve into a low-speed section and a middle-high speed section, takes influence factors of three aspects of vehicle speed, lateral acceleration and steering wheel hand force into consideration, adopts a BP neural network method to fit the power-assisted characteristic curve, and the designed power-assisted characteristic curve meets the power-assisted requirement, can be coordinated with the electro-hydraulic braking system to match driving feeling, and meets driving portability and operation sensitivity.
Description
Technical Field
The invention relates to the technical field of automobile chassis integration, in particular to an intelligent networking automobile drive-by-wire chassis integrated control method.
Background
In recent years, the automobile holding capacity of China is greatly improved, the requirements on driving safety and energy conservation are continuously improved, meanwhile, a large amount of attention of researchers is paid to a drive-by-wire chassis based on a novel electro-hydraulic composite steering system and an electro-hydraulic braking system, and the drive-by-wire chassis is suitable for relevant technical requirements of intelligent networked vehicles. The electro-hydraulic compound steering system is provided with the power-assisted motor and the speed reducing mechanism thereof on the basis of the EHPS system, so that the system can switch modes according to different working conditions and respectively work in three working modes: respectively an electric power-assisted mode, a hydraulic power-assisted mode and a compound power-assisted mode. The electro-hydraulic brake system can greatly improve the energy recovery efficiency and improve the brake response time. Therefore, on the basis of meeting basic power-assisted requirements and providing good road feel, the conventional chassis cannot be integrated with an electro-hydraulic compound steering and brake-by-wire system for control.
Disclosure of Invention
Aiming at the defects of the prior art, the invention aims to provide an intelligent networking automobile drive-by-wire chassis integrated control method to solve the problems of overhigh energy consumption, poor operation stability and the like in the prior art. The invention is based on a motor efficiency MAP graph of a double-execution mechanism, considers the constraint condition of electro-hydraulic braking, takes the lowest energy consumption as a control target, and realizes the power-assisted distribution calculation of chassis-related mechanisms.
The invention adopts the following technical scheme for solving the technical problems:
the invention provides an intelligent networking automobile drive-by-wire chassis integrated control method, which comprises the following steps:
(1) designing a power-assisted characteristic curve of the electro-hydraulic composite steering system, selecting a driving speed, a lateral acceleration and a steering wheel corner as steering hand force influence factors, determining the width between a low-speed section and a high-speed section based on intelligent network connection road data, solving the maximum power-assisted moment under different speeds, and optimally designing the power-assisted characteristic curve;
(2) according to the intelligent network connection data signals, the vehicle speed sensor and the steering wheel torque sensor acquire the driving vehicle speed and the steering wheel hand force of the automobile and transmit data to the upper controller. The input of the upper layer controller is the current running speed of the vehicle and the torque of a steering wheel, the current required power-assisted torque is obtained by looking up a table through low-speed section and high-speed section power-assisted steering characteristic curves, and then the optimal mixing ratio solving controller is used for performing power-assisted distribution on the total power-assisted with the lowest energy consumption as a control target to obtain the ideal rotating speed of the motors of the two actuating mechanisms. Meanwhile, when the intelligent networked automobile brakes, the displacement of the brake pedal is also transmitted to the upper controller to be used as the constraint of the steering boosting characteristic.
(3) The lower layer controller controls the motor rotating speed in the electro-hydraulic composite steering system, the input of the lower layer controller is the ideal rotating speed of the motors of the two actuating mechanisms, the actual rotating speed of the motors follows the ideal rotating speed through the double closed loop PID control of the motors, and the power-assisted torque of the two actuating mechanisms is output.
(4) And the lower layer controller is used for controlling the rack displacement, and a sliding mode controller is designed by adopting a nominal model control method to control the rack displacement based on a gear and rack system dynamic model.
Further, the power assisting characteristic curve fitting in the step (1) adopts a BP neural network to perform fitting of a nonlinear curve. The input layer neuron of the neural network model is the vehicle speed, and the output neuron is the maximum power-assisted moment under the vehicle speed. Input layer to hidden layer uses tansig as transfer function, hidden layer to output layer uses purelin as transfer function. The maximum number of convergence was set to 5000; convergence error is set to 106; the learning rate is set to 0.05.
Further, the dynamic solving step of the optimal allocation ratio of the double actuators of the upper layer controller in the step (2) is as follows:
(2.1) defining the distribution ratio of the double actuating mechanisms as the ratio of the power-assisted torque of the electric power-assisted actuating mechanism to the total power-assisted torque, wherein the expression is as follows:
where x is the defined division ratio of the two actuators, TelecFor assisting the torque of electric power-assisted actuators, TassitIs the total assisting torque.
Thus:
Telec＝xTassit
Thydra＝(1-x)Tassit
(2.2) calculating total energy consumption according to the distributed torque of the double actuators, wherein the total energy consumption of the double actuators is as follows:
in the formula, nelecIs the motor speed, ηelecFor electric actuator efficiency, nhydraIs the rotational speed of the hydraulic pump, ηhydraEfficiency of the hydraulic actuator; beta is the loss coefficient of the electro-hydraulic module, and the loss coefficient is 1.2 because torque loss exists between the motor and the oil pump.
And (2.3) the value range of the distribution ratio of the double actuators is [0,1], traversing the [0,1] interval by x at a change rate of 0.01, obtaining power corresponding to different distribution ratios, obtaining a distribution ratio-power curve, obtaining the lowest point of the curve, and obtaining the optimal distribution ratio corresponding to the lowest energy consumption of the double actuators under the conditions of the current vehicle speed and the torque of the steering wheel.
And (3) further, the lower layer controller controls the motor by adopting double closed-loop PID control, wherein an outer ring is a speed ring, and an inner ring is a current ring. The input of the outer ring controller is the difference between the ideal rotating speed and the actual rotating speed of the motor, the output control current is used as the set value of the inner ring (current ring) controller, and the output of the inner ring controller is the control voltage for controlling the rotating speed of the motor.
Further, the rack displacement control of the lower controller in the step (4) comprises the following steps:
(4.1) establishment of dynamic model of rack and pinion system
The equivalent force dynamic equation of the rack part is as follows:
in the formula igIs a transmission ratio of a recirculating ball type power-assisted steering gear rwIs the sector radius, x, of a recirculating ball-type power-assisted steering gearctIs rack displacement, mlmFor steering nut mass, JlgTo the moment of inertia of the steering screw, JcsTo the moment of inertia of the steering gear sector, rxclIs the gear radius, MctFor rack mass, P is the lead of the steering screw, l is the pitch of the steering screw, BlgIs the viscous damping coefficient of a screw rod of the recirculating ball type power-assisted steering gear, the viscous damping coefficient of a nut of the recirculating ball type power-assisted steering gear, BcsIs the viscous damping coefficient of the sector of the recirculating ball type power-assisted steering gear, BctIs the rack viscous damping coefficient im2For worm-gear reduction ratio, TEPSFor electric power-assisted torque, TsFor steering hand torque, TEHPSFor electro-hydraulic assistance torque, TrIs the steering drag torque.
The transfer function between the front wheel corner and the rack force is:
in the formula IwIs inertia, delta is front wheel angle, CWTo equivalent stiffness, K1For front wheel stiffness, e is wheel offset.
The transfer function between rack displacement and rack force is:
the rack module dynamic model is as follows:
in the formula, M is the equivalent mass of the model, and B is the equivalent viscous damping coefficient of the model.
Is provided with
For system input, the system can be described as:
wherein u is a control input; d is interference.
Then one can get:
where e is the tracking error of the nominal model, xdTo an ideal position, MnAs model equivalent mass, BnThe model equivalent viscous damping coefficient is denoted as μ, the difference between the control input and the disturbance.
(4.2) carrying out control law design on the rack displacement by adopting a nominal model control method;
the control law for the nominal model is designed as follows:
where σ is the Laplace operator, i.e.
h1＝k2H can be realized by taking the value of k1And h2。
(4.3) design of sliding mode controller according to control law
Suppose | d | ≦ dMGet en＝x-xnDefining a sliding mode function as:
the design control law is as follows:
compared with the prior art, the invention adopting the technical scheme has the following technical effects:
1. designing a power-assisted characteristic curve of the electro-hydraulic compound power-assisted steering system by dividing the power-assisted characteristic curve into a low-speed section and a middle-high speed section, fitting the power-assisted characteristic curve by adopting a BP neural network method by considering three influence factors of vehicle speed, lateral acceleration and hand force of a steering wheel, wherein the designed power-assisted characteristic curve meets the power-assisted requirement, can be matched with an electro-hydraulic braking system in a coordinated manner to achieve driving feeling, and meets driving portability and control sensitivity;
2. based on a motor efficiency MAP graph, the optimal distribution ratio under the constraint of electro-hydraulic braking can be obtained by taking the lowest energy consumption of the system as a control target, so that the energy consumption of the chassis is reduced, and the fuel economy of the system is improved;
3. a double-closed-loop PID controller is designed for motors of two actuating mechanisms, a sliding mode controller based on a nominal model is designed for rack displacement, the chassis control stability is improved, and the adverse effects of road surface impact and mixed interference signals of a mechanical structure are effectively reduced.
Drawings
FIG. 1 is a control strategy diagram of the present invention.
Fig. 2 is a sliding mode control module structure of a nominal model.
Detailed Description
The technical scheme of the invention is further explained in detail by combining the attached drawings:
the present invention may be embodied in many different forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art.
The invention discloses an intelligent networking automobile drive-by-wire chassis integrated control method, which aims to solve the problems of overhigh energy consumption, poor operation stability and the like in the prior art. The invention is based on a motor efficiency MAP graph of a double-execution mechanism, considers the constraint condition of electro-hydraulic braking, takes the lowest energy consumption as a control target, and realizes the power-assisted distribution calculation of chassis-related mechanisms. Comprises the following steps:
(1) designing a power-assisted characteristic curve of the electro-hydraulic composite steering system, selecting a driving speed, a lateral acceleration and a steering wheel corner as steering hand force influence factors, determining the width between a low-speed section and a high-speed section based on intelligent network connection road data, solving the maximum power-assisted moment under different speeds, and optimally designing the power-assisted characteristic curve;
(2) according to the intelligent network connection data signals, the vehicle speed sensor and the steering wheel torque sensor acquire the driving vehicle speed and the steering wheel hand force of the automobile and transmit data to the upper controller. The input of the upper layer controller is the current running speed of the vehicle and the torque of a steering wheel, the current required power-assisted torque is obtained by looking up a table through low-speed section and high-speed section power-assisted steering characteristic curves, and then the optimal mixing ratio solving controller is used for performing power-assisted distribution on the total power-assisted with the lowest energy consumption as a control target to obtain the ideal rotating speed of the motors of the two actuating mechanisms. Meanwhile, when the intelligent networked automobile brakes, the displacement of the brake pedal is also transmitted to the upper controller to be used as the constraint of the steering boosting characteristic.
(3) The lower layer controller controls the motor rotating speed in the electro-hydraulic composite steering system, the input of the lower layer controller is the ideal rotating speed of the motors of the two actuating mechanisms, the actual rotating speed of the motors follows the ideal rotating speed through the double closed loop PID control of the motors, and the power-assisted torque of the two actuating mechanisms is output.
(4) And the lower layer controller is used for controlling the rack displacement, and a sliding mode controller is designed by adopting a nominal model control method to control the rack displacement based on a gear and rack system dynamic model.
Further, the power assisting characteristic curve fitting in the step (1) adopts a BP neural network to perform fitting of a nonlinear curve. The input layer neuron of the neural network model is the vehicle speed, and the output neuron is the maximum power-assisted moment under the vehicle speed. Input layer to hidden layer uses tansig as transfer function, hidden layer to output layer uses purelin as transfer function. The maximum number of convergence was set to 5000; convergence error is set to 106; the learning rate is set to 0.05.
Further, the dynamic solving step of the optimal allocation ratio of the double actuators of the upper layer controller in the step (2) is as follows:
(2.1) defining the distribution ratio of the double actuating mechanisms as the ratio of the power-assisted torque of the electric power-assisted actuating mechanism to the total power-assisted torque, wherein the expression is as follows:
where x is the defined division ratio of the two actuators, TelecFor assisting the torque of electric power-assisted actuators, TassitIs the total assisting torque.
Thus:
Telec＝xTassit
Thydra＝(1-x)Tassit
(2.2) calculating total energy consumption according to the distributed torque of the double actuators, wherein the total energy consumption of the double actuators is as follows:
in the formula, nelecIs the motor speed, ηelecFor electric actuator efficiency, nhydraIs the rotational speed of the hydraulic pump, ηhydraEfficiency of the hydraulic actuator; beta is the loss coefficient of the electro-hydraulic module, and the loss coefficient is 1.2 because torque loss exists between the motor and the oil pump.
And (2.3) the value range of the distribution ratio of the double actuators is [0,1], traversing the [0,1] interval by x at a change rate of 0.01, obtaining power corresponding to different distribution ratios, obtaining a distribution ratio-power curve, obtaining the lowest point of the curve, and obtaining the optimal distribution ratio corresponding to the lowest energy consumption of the double actuators under the conditions of the current vehicle speed and the torque of the steering wheel.
And (3) further, the lower layer controller controls the motor by adopting double closed-loop PID control, wherein an outer ring is a speed ring, and an inner ring is a current ring. The input of the outer ring controller is the difference between the ideal rotating speed and the actual rotating speed of the motor, the output control current is used as the set value of the inner ring (current ring) controller, and the output of the inner ring controller is the control voltage for controlling the rotating speed of the motor.
Further, the rack displacement control of the lower controller in the step (4) comprises the following steps:
(4.1) establishment of dynamic model of rack and pinion system
The equivalent force dynamic equation of the rack part is as follows:
in the formula igIs a circulating ball type boosterSteering gear ratio, rwIs the sector radius, x, of a recirculating ball-type power-assisted steering gearctIs rack displacement, mlmFor steering nut mass, JlgTo the moment of inertia of the steering screw, JcsTo the moment of inertia of the steering gear sector, rxclIs the gear radius, MctFor rack mass, P is the lead of the steering screw, l is the pitch of the steering screw, BlgIs the viscous damping coefficient of a screw rod of the recirculating ball type power-assisted steering gear, the viscous damping coefficient of a nut of the recirculating ball type power-assisted steering gear, BcsIs the viscous damping coefficient of the sector of the recirculating ball type power-assisted steering gear, BctIs the rack viscous damping coefficient im2For worm-gear reduction ratio, TEPSFor electric power-assisted torque, TsFor steering hand torque, TEHPSFor electro-hydraulic assistance torque, TrIs the steering drag torque.
The transfer function between the front wheel corner and the rack force is:
in the formula IwIs inertia, delta is front wheel angle, CWTo equivalent stiffness, K1For front wheel stiffness, e is wheel offset.
The transfer function between rack displacement and rack force is:
the rack module dynamic model is as follows:
in the formula, M is the equivalent mass of the model, and B is the equivalent viscous damping coefficient of the model.
Is provided with
For system input, the system can be described as:
wherein u is a control input; d is interference.
Then one can get:
where e is the tracking error of the nominal model, xdTo an ideal position, MnAs model equivalent mass, BnThe model equivalent viscous damping coefficient is denoted as μ, the difference between the control input and the disturbance.
(4.2) carrying out control law design on the rack displacement by adopting a nominal model control method;
the control law for the nominal model is designed as follows:
where σ is the Laplace operator, i.e.
h1＝k2H can be realized by taking the value of k1And h2。
(4.3) design of sliding mode controller according to control law
Suppose | d | ≦ dMGet en＝x-xnDefining a sliding mode function as:
the design control law is as follows:
the above-mentioned embodiments, objects, technical solutions and advantages of the present invention are further described in detail, it should be understood that the above-mentioned embodiments are only illustrative of the present invention and are not intended to limit the present invention, and any modifications, equivalents, improvements and the like made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (5)
1. An intelligent networking automobile drive-by-wire chassis integrated control method is characterized by comprising the following steps:
(1) designing a power-assisted characteristic curve of the electro-hydraulic composite steering system, selecting a driving speed, a lateral acceleration and a steering wheel corner as steering hand force influence factors, determining the width between a low-speed section and a high-speed section based on intelligent network connection road data, solving the maximum power-assisted moment under different speeds, and optimally designing the power-assisted characteristic curve;
(2) according to the intelligent network connection data signal, a vehicle speed sensor and a steering wheel torque sensor acquire the driving vehicle speed and the steering wheel hand force of the automobile and transmit data to an upper controller; the input of the upper controller is the current running speed of the vehicle and the torque of a steering wheel, the current required power-assisted torque is obtained by looking up a table through low-speed section and high-speed section power-assisted steering characteristic curves, and then the optimal mixing proportion solving controller is used for performing power-assisted distribution on the total power-assisted with the lowest energy consumption as a control target to obtain the ideal rotating speed of the motors of the two actuating mechanisms; meanwhile, when the intelligent networked automobile brakes, the displacement of the brake pedal is also transmitted to the upper controller to be used as the constraint of the steering boosting characteristic;
(3) the lower layer controller controls the motor rotating speed in the electro-hydraulic composite steering system, the input of the lower layer controller is the ideal rotating speed of the motors of the two actuating mechanisms, the actual rotating speed of the motors follows the ideal rotating speed through the double closed loop PID control of the motors, and the power-assisted torque of the two actuating mechanisms is output;
(4) and the lower layer controller is used for controlling the rack displacement, and a sliding mode controller is designed by adopting a nominal model control method to control the rack displacement based on a gear and rack system dynamic model.
2. The intelligent networked automobile drive-by-wire chassis integrated control method according to claim 1, wherein the power-assisted characteristic curve fitting in the step (1) adopts a BP neural network to perform fitting of a nonlinear curve; the input layer neuron of the neural network model is the vehicle speed, and the output neuron is the maximum power-assisted moment under the vehicle speed; tansig is adopted from the input layer to the hidden layer as a transfer function, and purelin is adopted from the hidden layer to the output layer as a transfer function; the maximum convergence number was set to 5000 and the convergence error was set to 10-6The learning rate is set to 0.05.
3. The intelligent networked automobile drive-by-wire chassis integrated control method according to claim 1, wherein the dynamic solution of the optimal distribution ratio of the double actuators of the upper controller in the step (2) comprises the following steps:
(2.1) defining the distribution ratio of the double actuating mechanisms as the ratio of the power-assisted torque of the electric power-assisted actuating mechanism to the total power-assisted torque, wherein the expression is as follows:
where x is the defined division ratio of the two actuators, TelecFor assisting the torque of electric power-assisted actuators, TassitThe total assistance torque is the total assistance torque,
thus:
Telec＝xTassit
Thydra＝(1-x)Tassit
(2.2) calculating total energy consumption according to the distributed torque of the double actuators, wherein the total energy consumption of the double actuators is as follows:
in the formula, nelecIs the motor speed, ηelecFor electric actuator efficiency, nhydraIs the rotational speed of the hydraulic pump, ηhydraEfficiency of the hydraulic actuator; beta is the loss coefficient of the electro-hydraulic module, and the loss coefficient is 1.2 because torque loss exists between the motor and the oil pump,
and (2.3) the value range of the distribution ratio of the double actuators is [0,1], traversing the [0,1] interval by x at a change rate of 0.01, obtaining power corresponding to different distribution ratios, obtaining a distribution ratio-power curve, obtaining the lowest point of the curve, and obtaining the optimal distribution ratio corresponding to the lowest energy consumption of the double actuators under the conditions of the current vehicle speed and the torque of the steering wheel.
4. The intelligent networked automobile drive-by-wire chassis integrated control method according to claim 1, wherein the lower layer controller in the step (3) adopts double closed loop PID control for motor control, an outer loop is a speed loop, and an inner loop is a current loop; the input of the outer ring controller is the difference between the ideal rotating speed and the actual rotating speed of the motor, the output control current is used as the set value of the inner ring (current ring) controller, and the output of the inner ring controller is the control voltage for controlling the rotating speed of the motor.
5. The intelligent networked automobile drive-by-wire chassis integrated control method according to claim 1, wherein the rack displacement control of the lower controller in the step (4) comprises the following steps:
(4.1) establishment of dynamic model of rack and pinion system
The equivalent force dynamic equation of the rack part is as follows:
in the formula igIs a transmission ratio of a recirculating ball type power-assisted steering gear rwIs the sector radius, x, of a recirculating ball-type power-assisted steering gearctIs rack displacement, mlmFor steering nut mass, JlgTo the moment of inertia of the steering screw, JcsTo the moment of inertia of the steering gear sector, rxclIs the gear radius, MctFor rack mass, P is the lead of the steering screw, l is the pitch of the steering screw, BlgIs the viscous damping coefficient of a screw rod of the recirculating ball type power-assisted steering gear, the viscous damping coefficient of a nut of the recirculating ball type power-assisted steering gear, BcsIs the viscous damping coefficient of the sector of the recirculating ball type power-assisted steering gear, BctIs the rack viscous damping coefficient im2For worm-gear reduction ratio, TEPSFor electric power-assisted torque, TsFor steering hand torque, TEHPSFor electro-hydraulic assistance torque, TrIs the steering drag torque;
the transfer function between the front wheel corner and the rack force is:
in the formula IwIs inertia, delta is front wheel angle, CWTo equivalent stiffness, K1Front wheel stiffness, e wheel offset;
the transfer function between rack displacement and rack force is:
the rack module dynamic model is as follows:
in the formula, M is the equivalent mass of the model, and B is the equivalent viscous damping coefficient of the model;
is provided with
For system input, the system can be described as:
wherein u is a control input; d is interference;
then one can get:
where e is the tracking error of the nominal model, xdTo an ideal position, MnAs model equivalent mass, BnIs the model equivalent viscous damping coefficient, mu is the difference between the control input and the interference;
(4.2) carrying out control law design on the rack displacement by adopting a nominal model control method;
the control law for the nominal model is designed as follows:
where σ is the Laplace operator, i.e.
h1＝k2H can be realized by taking the value of k1And h2；
(4.3) design of sliding mode controller according to control law
Suppose | d | ≦ dMGet en＝x-xnDefining a sliding mode function as:
the design control law is as follows:
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