CN115833676A - Sliding speed controller of automobile electric skylight and design method thereof - Google Patents
Sliding speed controller of automobile electric skylight and design method thereof Download PDFInfo
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Abstract
The invention discloses an automobile electric skylight sliding speed controller and a design method thereof, belonging to the technical field of skylight sliding speed control, wherein an extended state observer is improved, a novel nonlinear function is designed, the problem of system buffeting caused by discontinuity of a traditional nonlinear function near an original point is solved, and the anti-interference capability of a system is improved; secondly, a nonlinear error feedback control law is designed by combining sliding mode control and fractional order control, the degree of freedom of the system can be increased by utilizing the fractional order calculus control, the anti-interference performance is enhanced, the buffeting of the system can be well weakened, meanwhile, the traditional sliding mode surface is improved by adopting a hyperbolic tanh(s) function, the buffeting of the system is further reduced, and the response speed and the anti-interference performance of the system are improved.
Description
Technical Field
The invention relates to the technical field of skylight sliding speed control, in particular to an automobile electric skylight sliding speed controller and a design method thereof.
Background
The electric skylight is an important part in the car, can improve the light intensity in the car and provides a bright environment for people; but also can strengthen the convection of the air inside the automobile and the air outside the automobile, and effectively improve the comfort level of the driver and passengers. The motion actuator of the skylight consists of three main components: motor, two flexible axles and mechanical assembly. Most of the prior automobile skylights adopt built-in skylights, namely skylights with sliding assemblies arranged between an inner decoration and a roof, and the working principle is as follows: the motor is equivalent to a sliding rod, a round turbine is arranged in the hose, and the hose is connected with the mechanical group of the skylight. When the motor is started, the worm wheel in the hose is pushed to rotate forwards or backwards through the operation between the gears, so that the skylight is pushed to be opened or closed. Fig. 1 is a structural view of a conventional sunroof machine. Fig. 2 shows a sliding control system of the whole conventional sunroof, a sunroof control module processes a switching signal, a hall signal detects the operating speed of a motor, and an SCU controls the operation of an anti-pinch system through the acquired motor speed.
Although the traditional ADRC control strategy has a better control effect than the PID controller, when the motor is subjected to sudden disturbance under the control of the traditional ADRC control strategy, the speed of the motor cannot be recovered in time by the traditional active disturbance control method, the interference resistance is poor, skylight glass cannot run stably enough, and an anti-pinch system is easily opened mistakenly. In order to ensure the safety protection function of the skylight and the control of the sliding speed of the skylight glass, it is necessary to adopt an improved active disturbance rejection control strategy to control the skylight glass to slide at a constant speed. Therefore, the sliding speed controller of the automobile electric skylight is provided.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: how to solve the problems that the traditional active-disturbance-rejection control method cannot recover the speed of a motor in time, the disturbance rejection is poor, the operation of a sunroof is not stable enough, and the mistaken opening of an anti-pinch system is easily caused, and the sliding speed controller of the automobile power sunroof is provided.
The invention solves the technical problems through the following technical scheme, and the invention comprises the following steps:
the tracking differentiator is used for extracting an input skylight glass opening or closing signal, arranging signal transition and realizing rapid tracking;
the extended state observer is used for estimating uncertain factors and external disturbance of the skylight glass of the controlled object and compensating the uncertain factors and the external disturbance;
the fractional order synovial nonlinear error feedback control law is used for processing the error value of the signal extracted by the tracking differentiator and the observation signal of the state observer and compensating the total disturbance of observation, so that the control of the speed of the skylight glass has better response speed and anti-interference performance;
in the extended state observer, replacing a traditional nonlinear function fal (-) with glan (-);
in the fractional order slip film nonlinear error feedback control law, the nonlinear error feedback control law is designed by combining slip film control and fractional order control, the fractional order calculus is utilized to not only increase the degree of freedom of the system and enhance the anti-interference performance, but also well weaken the buffeting of the system, and meanwhile, a hyperbolic tanh(s) function is adopted to improve the traditional slip film surface, so that the buffeting of the system is further reduced.
Further, the algorithm expression of the tracking differentiator is as follows:
where v is a given input signal, v 1 Is a tracking signal of a given input signal v, v 2 Is that the given input signal v tracks the differential signal, epsilon is the tracking error, l is the sampling step size 0 Is a filter factor, r 0 Is the velocity factor, fhan (v) 1 ,v 2 ,r 0 ,l 0 ) Is the fastest control synthesis function.
Further, the arithmetic expression of the extended state observer is as follows:
wherein x is 1 For observation errors, y outputs a signal, z 1 、z 2 、z 3 Is the state x of the system 1 、x 2 、x 3 (ii) an observed output of (d); parameter beta 1 、β 2 、β 3 Is the gain coefficient of the extended state observer; b 0 Is a parameter of the system gain, glan (-) is a nonlinear function, u is the control output, a 1 ,a 2 ,a 3 For the tunable parameter, it is the linear interval width of the glan (·) function.
Further, the expression of the nonlinear function is as follows:
where x is the difference between the given input signal and the output signal, and a is an adjustable parameter, which is the width of the linear interval of the glan (·) function.
Further, the arithmetic expression of the fractional synovial nonlinear error feedback control law is as follows:
wherein e is 1 ，e 2 Respectively, error signal and error difference signal of the tracking differentiator and the extended state observer, c 1 Is a parameter of the slip film surface,
fractional calculus operator, t is the upper limit of the fractional calculus operator, beta, lambda is the order of the fractional calculus operator, b 0 Is a parameter of the system gain, v 2 Is a given signal, z 1 、z 2 、z 3 Is the state x of the system 1 、x 2 、x 3 Observed output of (a), k 1 ,k 3 Is a constant coefficient and u is the compensated control signal.
The invention also provides a design method of the sliding speed controller of the automobile electric skylight, which is used for designing the controller and comprises the following steps:
s1: according to the actual physical model of the skylight, establishing a kinematic equation of the skylight and simplifying the kinematic equation;
s2: analyzing the motor and establishing a motor rotating speed mathematical model;
s3: the structure of the traditional ADRC controller is optimally designed, and an improved ADRC controller, namely an automobile electric skylight sliding speed controller, is obtained.
Further, in the step S1, the kinematic equation of the sunroof is as follows:
wherein, F L The clamping force is prevented; f h Representing the friction force during the running of the skylight glass; u represents the motor operating voltage; k t Representing a motor torque coefficient; r a Representing the rotor electrical drive resistance, i representing the turbine gear ratio; w is the motor angular velocity, λ represents the motor efficiency; l represents the gear radius; m represents the weight of the moving part of the skylight glass driven by the motor; j denotes the rotor moment of inertia.
Further, in the step S1, within a sampling period satisfying the set small, will be
Neglect, by simplification yields:
order to
Obtaining the variation delta w of the angular speed of the motor and the anti-pinch force F L Is in direct proportion.
Further, in the step S2, the motor rotation speed mathematical model is as follows:
where w is the angular velocity of the motor, B is the coefficient of viscous friction, k 1 Is the PWM amplification factor, k 2 Is the motor torque coefficient, i is the armature current, J is the equivalent moment of inertia, ce is the back-emf, U a Is the motor terminal voltage and L is the armature inductance.
Still further, the step S3 includes the following sub-steps:
s31: make the external load moment T L =0,w = x, the mathematical model of the rotating speed of the motor is obtained by arranging:
considering the armature current i as an internal disturbance, let
Obtaining:
s32: designing an improved ADRC controller according to the step S31, namely designing a tracking differentiator, an extended state observer and a fractional order synovial membrane nonlinear error feedback control law in the improved ADRC controller;
in step S32, the tracking differentiator in the improved ADRC controller adopts a tracking differentiator of a conventional ADRC, and an algorithm expression is as follows:
where v is a given input signal, v 1 Is a tracking signal given an input signal v 2 Is given an input signal v Tracking differential signal,. Epsilon.is tracking error,. L is sampling step size,. L 0 Is a filter factor, r 0 Is the velocity factor, fhan (v) 1 ,v 2 ,r 0 ,l 0 ) Is the fastest control synthesis function;
the algorithm expression of the extended state observer in the improved ADRC controller is as follows:
wherein x is 1 For observation errors, y outputs a signal, z 1 、z 2 、z 3 Is the state x of the system 1 、x 2 、x 3 (ii) an observed output of (d); parameter beta 1 、β 2 、β 3 Is the gain coefficient of the extended state observer; b is a mixture of 0 Is a parameter of the system gain, glan (-) is a non-linear function, u is the control output, a 1 ,a 2 ,a 3 Is a tunable parameter, is the linear interval width of the glan (·) function;
the algorithm expression of the fractional synovial membrane nonlinear error feedback control law in the improved ADRC controller is as follows:
wherein e is 1 ，e 2 Respectively, error signal and error difference signal of the tracking differentiator and the extended state observer, c 1 Is a parameter of the slip film surface,
fractional calculus operator, t 0 Is the upper limit of the fractional calculus operator, beta, lambda are the fractional calculus operator order, b 0 Is a parameter of the system gain, v 2 Is a given signal, z 1 、z 2 、z 3 Is the state x of the system 1 、x 2 、x 3 Observed output of (a), k 1 ,k 3 Is a constant coefficient and u is the compensated control signal.
Compared with the prior art, the invention has the following advantages: according to the sliding speed controller of the automobile electric skylight, the extended state observer is improved, a novel nonlinear function is designed, the problem of system buffeting caused by discontinuity of the traditional nonlinear function near an original point is solved, and the anti-interference capacity of a system is improved; secondly, a nonlinear error feedback control law is designed by combining sliding mode control and fractional order control, the degree of freedom of the system can be increased by utilizing fractional order calculus, the anti-interference performance is enhanced, the buffeting of the system can be well weakened, meanwhile, the traditional sliding film surface is improved by adopting a hyperbolic tanh(s) function, the buffeting of the system is further reduced, and the response speed and the anti-interference performance of the system are improved.
Drawings
FIG. 1 is a schematic view of a mechanical structure of a prior art skylight;
FIG. 2 is a block diagram of a sliding control model of a conventional sunroof;
FIG. 3 is a block diagram of a brushless DC motor servo system in an embodiment of the present invention;
FIG. 4 is a schematic diagram of an improved ADRC controller according to an embodiment of the present invention;
FIG. 5 is a graph comparing the glan (x, a) and fal (x, a, b) functions in an embodiment of the present invention;
FIG. 6 is a graph comparing error gains of glan (x, a) and fal (x, a, b) functions in an embodiment of the present invention;
figure 7 is a graph comparing waveforms of step signals for the improved ADRC control strategy of the present invention and a conventional ADRC control strategy in accordance with an embodiment of the present invention;
figure 8 is a graph comparing the waveforms of the response plots of square wave signals for the improved ADRC control strategy of the present invention and the conventional ADRC control strategy in accordance with an embodiment of the present invention;
FIG. 9 is a graph comparing waveforms of response curves of the improved ADRC control strategy and the conventional ADRC control strategy under the external 50rad/s step value interference in the embodiment of the present invention.
In fig. 1:
1. a motor; 2. a gear; 3. a hose; 4. a turbine; 5. a skylight glass; 6. a track;
in fig. 2:
10. BCM; 12. a turbine; 15. a Hall sensor A; 16. a Hall sensor B; 17. a mechanical group; 18. a roof window glass.
Detailed Description
The following examples are given for the detailed implementation and specific operation of the present invention, but the scope of the present invention is not limited to the following examples.
The embodiment provides a technical scheme: a design process of an automobile electric skylight sliding speed controller based on an improved active disturbance rejection control strategy comprises the following steps:
the first step is as follows: firstly, establishing a motion mechanics equation of the skylight glass according to an actual physical model of the skylight glass:
force balance equation:
torque balance equation:
and the acceleration and turning torque equations:
the combination of the above formulas (1), (2) and (3) can obtain:
wherein, F L The clamping force is prevented; f m Is the motor rotation torque; f h Representing the friction force during the running of the skylight glass; u represents the motor operating voltage; k t Representing a motor torque coefficient; r a Representing the rotor electrical drive resistance, w being the motor angular velocity, i representing the turbine gear ratio; λ represents the motor efficiency; l represents the gear radius; m represents the weight of the moving part of the skylight glass driven by the motor; j denotes the rotor moment of inertia.
When one period of sampling is very small, comparing and comparing
The value of (a) is small and negligible, and can be obtained by simplification:
The variation delta w of the angular speed of the motor and the anti-clamping force F can be obtained from the formula (5) L Is a direct proportional relationship. And calculating the clamping force of the skylight according to the change of the rotating speed. If the variation delta w of the angular speed of the motor is continuously changed due to the change of the load characteristic or the influence of the external environment in the running process of the skylight glass, the anti-pinch force F is generated L Greater than the anti-pinch threshold, may cause the anti-pinch system to be erroneously turned on. No matter to the detection of motor speed variation, still set for the threshold value to the anti-pinch force, the control of motor speed plays the key role to the operation of whole anti-pinch system and the operation of sky window glass are stable.
The second step is that: in order to make the skylight glass run stably even if being interfered, the motor (brushless direct current motor) is analyzed, and a motor rotating speed mathematical model is established as follows:
according to the KVL voltage equation, the phase voltage equation of the motor (brushless dc motor) is:
wherein, U a To terminal voltage of the machine, E a Is back electromotive force, R is armature resistance, L is armature inductance, i armature current;
back electromotive force:
E a ＝C e w (7)
wherein E is a Is a back electromotive force, C e Is the back electromotive force constant; w is the motor angular velocity (rad/s);
electromagnetic torque equation:
T e ＝pk 2 i (8)
wherein, T e Is the electromagnetic torque, pk 2 For a torque constant, p is the number of pole pairs of the motor, and for a fully excited motor, neglecting the coil reaction, consider k to be 2 Is a constant;
the motion equation of the motor is as follows:
wherein w is the angular velocity of the motor, T L An external load moment (n.m);
the mathematical model of the whole motor rotating speed obtained by integrating the steps (6), (7), (8) and (9) is as follows:
the movement of the skylight mainly comprises the steps that a motor provides power for the skylight glass to slide, and then the skylight glass is opened and closed through the transmission of a mechanical structure, so that the speed of the skylight glass is mainly controlled by the motor, the motor is controlled by the improved ADRC controller, and the structural diagram of the improved ADRC controller is shown in figure 4.
The third step: the structure of the traditional ADRC controller is optimally designed to obtain an improved ADRC controller
The controller is designed by the above equation (10):
let T L =0,w = x, finishing formula (10) to formula (11)
Considering the armature current i as an internal disturbance, let
Obtaining:
the improved ADRC controller is designed by the following formula (13):
1) TD (tracking differentiator)
With the tracking differentiator TD of the conventional ADRC, the algorithm expression is as follows:
where v is a given input signal, v 1 Is a tracking signal given an input signal v 2 Is that the given input signal v tracks the differential signal, epsilon is the tracking error, l is the sampling step size 0 Is a filter factor, r 0 Is the velocity factor, fhan (v) 1 ,v 2 ,r 0 ,l 0 ) Is the fastest control synthesis function;
2) ESO (extended state observer)
Design of the nonlinear function:
the conventional nonlinear function is expressed as follows:
the novel nonlinear function expression designed by the invention is as follows:
where x is the difference between the given input signal and the output signal, and a is an adjustable parameter, which is the width of the linear interval of the glan (·) function.
The traditional nonlinear function fal (x, a, b) and the novel nonlinear function glan (x, a) are simulated, a =0.01, b =0.5 is taken, and compared with the image of the fal (x, a, b) and the glan (x, a) function in the figure 5, the problem that the slope is large due to the fact that an inflection point exists in the traditional function near the origin can be effectively solved, and the fact that the function of the glan (x, a) has better convergence and smoothness can be seen near the origin. As can be seen from the functional error curve of fig. 6, when the input error is small, the glan (x, a) output gain is higher than the fal (x, a, b) function; when the input error is larger, the output gain of the glan (x, a) function is obviously lower than that of the fal (x, a, b) function. The glan (x, a) function fully embodies' small error, large gain; large error, small gain ". The problem that the increment of the fal (x, a, b) function at the origin is too large is avoided, and the problem of system jitter is effectively solved.
The Extended State Observer (ESO) algorithm expression designed in this embodiment is as follows:
wherein: x is the number of 1 For observation errors, y outputs a signal, z 1 、z 2 、z 3 Is the state x of the system 1 、x 2 、x 3 (ii) an observed output of; parameter beta 1 、β 2 、β 3 Is the gain coefficient of the extended state observer; b 0 Is a parameter of the system gain.
3) FOSMC-NLSEF (fractional synovial nonlinear error feedback control law)
The expression of the fractional synovial nonlinear error feedback control law algorithm preliminarily designed in this embodiment is as follows:
wherein e is 1 ，e 2 Error signals and error difference signals of TD and ESO respectively; u. u 0 Is the disturbance compensation control signal, u is the compensated control signal,
is the compensation of the total disturbance of the skylight glass,
is the optimal control function.
When improved ESO is stabilized, z 2 Is close to x 2 ，z 3 Is close to x 3 And glan (x, a) is close to 0, therefore, it is assumed that glan (x, a) =0 while
It is possible to obtain:
in order to design an optimal control function
Based on the error feedback equation, the fractional order synovial surfaces were chosen as follows:
wherein, c 1 Is a constant number c 1 Greater than 0,0 < beta < 1,t is the fractional calculus upper limit and beta is the fractional calculus operator order.
The derivation of equation (20) yields:
fractional synovial membrane control rates were chosen as follows:
wherein k is 1 ,k 3 Is a constant coefficient, λ is a fractional order integral order, k 1 ＞0,k 3 ＞0,0＜λ＜1。
Substituting hyperbolic tanh(s) function for sign(s) function, and deforming equation (22) according to calculus definition and property to obtain:
the combined formulas (18), (19), (21) and (23) are as follows:
the algorithm expression of the obtained final FOSMC-NLSEF is as follows:
the speed control of the skylight is simulated by combining the improved active disturbance rejection control strategy, and in order to illustrate the advantages of the improved active disturbance rejection control strategy, the simulation is compared with the traditional ADRC control strategy. Through simulation verification, skylight glass controlled by the improved active disturbance rejection control strategy can slide more stably, and an anti-pinch system is more reliable. In order to verify the performance gap under the same conditions, the parameters of the conventional ADRC control strategy are selected as the parameters of the improved ADRC control strategy, and the parameters are selected as shown in table 1.
TABLE 1 simulation parameters Table
The following description is combined with a simulation diagram: as can be seen from fig. 7 and 8, the settling time of the improved ADRC control strategy is 1.657s, the settling time of the conventional ADRC control strategy is 1.678s, the response speed of the improved ADRC control strategy is faster than that of the conventional ADRC control strategy, and the response curve of the improved ADRC control strategy is smooth without overshoot. Compared with the simulation graph of the control of the traditional ADRC control strategy under the condition of adding interference in the graph of FIG. 9, the simulation graph of the control of the improved ADRC control strategy and the simulation graph of the control of the traditional ADRC control strategy show that when the motor is subjected to external interference, the recovery time of the improved ADRC control strategy on the rotating speed is faster than that of the traditional ADRC control strategy, the fluctuation of the improved ADRC control strategy is smaller than that of the traditional ADRC control strategy, and the anti-interference performance of the improved ADRC control strategy is stronger.
In summary, the sliding speed controller of the automotive electric sunroof according to the embodiment improves the extended state observer, designs a novel nonlinear function, improves the problem that the conventional nonlinear function is discontinuous near the origin to cause system buffeting, and improves the anti-interference capability of the system; secondly, a nonlinear error feedback control law is designed by combining sliding mode control and fractional order control, the degree of freedom of the system can be increased by utilizing fractional order calculus, the anti-interference performance is enhanced, the buffeting of the system can be well weakened, meanwhile, the traditional sliding film surface is improved by adopting a hyperbolic tanh(s) function, the buffeting of the system is further reduced, and the response speed and the anti-interference performance of the system are improved.
Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention, and that variations, modifications, substitutions and alterations can be made to the above embodiments by those of ordinary skill in the art within the scope of the present invention.
Claims (10)
1. An automobile electric sunroof sliding speed controller, comprising:
a tracking differentiator for solving extraction of an input skylight glass opening or closing signal and arranging signal transition;
the extended state observer is used for estimating uncertain factors and external disturbance of the skylight glass of the controlled object and compensating the uncertain factors and the external disturbance;
the fractional order slip film nonlinear error feedback control law is used for processing the error values of the signals extracted by the tracking differentiator and the observation signals of the state observer and compensating the total observed disturbance;
in the extended state observer, replacing a traditional nonlinear function fal (-) with glan (-);
in the fractional order slip film nonlinear error feedback control law, the nonlinear error feedback control law is designed by combining slip film control and fractional order control, and meanwhile, a hyperbolic tanh(s) function is adopted to improve the traditional slip film surface.
2. The sliding speed controller of an automobile power sunroof according to claim 1, wherein: the algorithm expression of the tracking differentiator is as follows:
where v is a given input signal, v 1 Is a tracking signal of a given input signal v, v 2 Is that the given input signal v tracks the differential signal, epsilon is the tracking error, l is the sampling step size 0 Is a filter factor, r 0 Is the velocity factor, fhan (v) 1 ,v 2 ,r 0 ,l 0 ) Is the steepest control synthesis function.
3. The sliding speed controller of an automobile power sunroof according to claim 2, wherein: the algorithm expression of the extended state observer is as follows:
wherein x is 1 For the observation error, y outputs a signal, z 1 、z 2 、z 3 Is the state x of the system 1 、x 2 、x 3 (ii) an observed output of (d); parameter beta 1 、β 2 、β 3 Is the gain coefficient of the extended state observer; b 0 Is a parameter of the system gain, glan (-) is a non-linear function, u is the control output, a 1 ,a 2 ,a 3 For the tunable parameter, it is the linear interval width of the glan (·) function.
4. The sliding speed controller of an automobile power sunroof according to claim 3, wherein: the expression of the nonlinear function is as follows:
where x is the difference between the given input signal and the output signal, and a is an adjustable parameter, which is the width of the linear interval of the glan (-) function.
5. The sliding speed controller of an automobile power sunroof according to claim 4, wherein: the algorithm expression of the fractional order synovial membrane nonlinear error feedback control law is as follows:
wherein e is 1 ，e 2 Respectively error signal and error difference signal of tracking differentiator and extended state observer, c 1 Is a parameter of the slip film surface,
fractional calculus operator, t is the upper limit of the fractional calculus operator, beta, lambda is the order of the fractional calculus operator, b 0 Is a parameter of the system gain, v 2 Is a given signal, z 1 、z 2 、z 3 Is the state x of the system 1 、x 2 、x 3 Observed output of (a), k 1 ,k 3 Is a constant coefficient and u is the compensated control signal.
6. A method for designing a sliding speed controller of a power sunroof for an automobile, the method being used for designing the controller according to any one of claims 1 to 5, and comprising the steps of:
s1: according to the actual physical model of the skylight, establishing a kinematic equation of the skylight and simplifying the kinematic equation;
s2: analyzing the motor and establishing a motor rotating speed mathematical model;
s3: the structure of the traditional ADRC controller is optimally designed, and an improved ADRC controller, namely an automobile electric skylight sliding speed controller, is obtained.
7. The design method of the sliding speed controller of the automobile power sunroof according to claim 6, wherein the method comprises the following steps: in step S1, the kinematic equation of the sunroof is as follows:
wherein, F L The clamping force is prevented; f h Representing the friction force during the operation of the skylight glass; u represents the motor operating voltage; k t Representing a motor torque coefficient; r a Representing the rotor electrical drive resistance, i representing the turbine gear ratio; w is the motor angular velocity, λ represents the motor efficiency; l represents the gear radius; m represents the weight of the part of the motor driving the skylight glass to move; j denotes the rotor moment of inertia.
8. The design method of the sliding speed controller of the electric skylight of the automobile of claim 7, characterized in that: in the step S1, within one sampling period satisfying the set small value, the sampling period is set to be short
Neglect, by simplification yields:
order to
Obtaining the variation delta w of the angular speed of the motor and the anti-pinch force F L Is in direct proportion.
9. The design method of the sliding speed controller of the automobile power sunroof according to claim 8, wherein the method comprises the following steps: in step S2, the motor rotation speed mathematical model is as follows:
where w is the angular velocity of the motor, B is the coefficient of viscous friction, k 1 Is the PWM amplification factor, k 2 Is the motor torque coefficient, i is the armature current, J is the equivalent moment of inertia, ce is the back electromotive force, U a Is the motor terminal voltage, and L is the armature inductance.
10. The design method of the sliding speed controller of the automobile power sunroof according to claim 9, wherein the method comprises the following steps: the step S3 includes the following substeps:
s31: make the external load moment T L And (5) finishing a motor rotating speed mathematical model to obtain:
considering the armature current i as an internal disturbance, let
Obtaining:
s32: designing an improved ADRC controller according to the step S31, namely designing a tracking differentiator, an extended state observer and a fractional order synovial membrane nonlinear error feedback control law in the improved ADRC controller;
in the step S32, the tracking differentiator in the modified ADRC controller adopts a tracking differentiator of the conventional ADRC, and the algorithm expression is as follows:
where v is a given input signal, v 1 Is a tracking signal of a given input signal v, v 2 Is that the given input signal v tracks the differential signal,. Epsilon.is the tracking error,. Is the sampling step size,. L 0 Is a filter factor, r 0 Is the velocity factor, fhan (v) 1 ,v 2 ,r 0 ,l 0 ) Is the fastest control synthesis function;
the algorithm expression of the extended state observer in the improved ADRC controller is as follows:
wherein x is 1 For observation errors, y outputs a signal, z 1 、z 2 、z 3 Is a systemState x of 1 、x 2 、x 3 (ii) an observed output of (d); parameter beta 1 、β 2 、β 3 Is the gain coefficient of the extended state observer; b 0 Is a parameter of the system gain, glan (-) is a non-linear function, u is the control output, a 1 ,a 2 ,a 3 Is a tunable parameter, is the linear interval width of the glan (·) function;
the algorithm expression of the fractional order synovial membrane nonlinear error feedback control law in the improved ADRC controller is as follows:
wherein e is 1 ，e 2 Respectively error signal and error difference signal of tracking differentiator and extended state observer, c 1 Is a parameter of the slip film surface,
fractional calculus operator, t is the upper limit of the fractional calculus operator, beta, lambda is the order of the fractional calculus operator, b o Is a parameter of the system gain, v 2 Is a given signal, z 1 、z 2 、z 3 Is the state x of the system 1 、x 2 、x 3 Observed output of (a), k 1 ,k 3 Is a constant coefficient and u is the compensated control signal.
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| CN116248003A (en) * | 2023-05-06 | 2023-06-09 | 四川省产品质量监督检验检测院 | Sliding mode control-based method and system for controlling active disturbance rejection speed of switched reluctance motor |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN116248003A (en) * | 2023-05-06 | 2023-06-09 | 四川省产品质量监督检验检测院 | Sliding mode control-based method and system for controlling active disturbance rejection speed of switched reluctance motor |
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