CN110908288A - Unmanned aerial vehicle ground speed constraint disturbance rejection control method based on obstacle Lyapunov function - Google Patents

Unmanned aerial vehicle ground speed constraint disturbance rejection control method based on obstacle Lyapunov function Download PDF

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CN110908288A
CN110908288A CN201911364832.0A CN201911364832A CN110908288A CN 110908288 A CN110908288 A CN 110908288A CN 201911364832 A CN201911364832 A CN 201911364832A CN 110908288 A CN110908288 A CN 110908288A
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ground speed
airplane
disturbance
angle
lyapunov function
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苏子康
李春涛
解明扬
李雪兵
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Nanjing University of Aeronautics and Astronautics
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Nanjing University of Aeronautics and Astronautics
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    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
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Abstract

The invention discloses an unmanned aerial vehicle ground speed constraint anti-interference control method based on a barrier Lyapunov function, which mainly comprises the following steps: firstly, establishing a dynamic model of an airplane ground speed nonlinear subsystem, and processing the dynamic model into an affine nonlinear form; on the basis, aiming at a ground speed affine nonlinear model, a finite time high-order sliding mode disturbance observer is designed to estimate uncertain disturbance caused by perturbation of system parameters; and then, with the unknown disturbance obtained by estimation as feedforward compensation, designing a nonlinear constrained disturbance rejection tracking controller of the ground speed subsystem to realize accurate tracking of the expected ground speed under the given ground speed constraint condition. The invention can be used for ground speed constrained accurate control in the fields of airplane air refueling docking, air-based recovery docking, ultra-low-altitude air drop, complex terrain obstacle avoidance and the like, and can effectively improve the ground speed flight control accuracy and flight safety of airplanes.

Description

Unmanned aerial vehicle ground speed constraint disturbance rejection control method based on obstacle Lyapunov function
Technical Field
The invention relates to an unmanned aerial vehicle ground speed constraint anti-interference control method based on a Lyapunov (Lyapunov) function, and belongs to the technical field of unmanned aerial vehicle navigation guidance and control.
Background
Unmanned aerial vehicles have been widely used and developed in many fields with their advantages of low loss, low cost, zero casualties, reusability, high maneuverability, and the like. The ground speed of the airplane is an important motion parameter, which is the premise of the stability and track control of the unmanned aerial vehicle. Fixed wing drones generally fly at a certain altitude according to a designed cruising speed, but often have to change the flying speed when performing complex tasks. With the rapid development of unmanned aerial vehicles, many application scenes provide new higher requirements for ground speed control of the unmanned aerial vehicles, and the unmanned aerial vehicles automatically track moving targets, automatically form flying, automatically refuel in the air, automatically recover in the air, automatically land on ships, and throw at ultra-low altitude, etc.
In the special application scenario, the airplane ground speed controller not only has higher control precision, but also needs to have anti-interference capability and ground speed constrained control capability. The existing airplane ground speed control method, such as PID control, adaptive control, robust control, sliding film control and the like, is rarely considered from the perspective of anti-interference and constrained control capability. How to ensure that aircraft ground speed control has sufficient interference killing feature simultaneously, can make ground speed be in the scope of expectation by strict constraint control simultaneously, be the problem that makes it to adapt to some to have special demand tasks to ground speed control and must solve, can show the task execution ability and the flight safety that improve fixed wing unmanned aerial vehicle.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the ground speed constraint disturbance rejection control method of the unmanned aerial vehicle based on the obstacle Lyapunov function is provided, the control precision and the disturbance rejection capability of the ground speed controller of the aircraft are effectively improved on the premise of ensuring that the ground speed is strictly constrained and controlled within an expected range, and technical support can be provided for improving the task execution capability and the flight safety of the unmanned aerial vehicle.
The invention adopts the following technical scheme for solving the technical problems:
an unmanned aerial vehicle ground speed constraint disturbance rejection control method based on a barrier Lyapunov function comprises the following steps:
step 1, setting an airplane ground speed instruction
Figure BDA0002338128140000021
Ground speed instruction upper bound
Figure BDA0002338128140000022
And lower bound
Figure BDA0002338128140000023
And ground speed constraint range Kc；
Step 2, establishing a dynamic model of the airplane ground speed nonlinear subsystem to describe the ground speed motion state;
step 3, converting the airplane ground speed nonlinear subsystem dynamic model established in the step 2 into an airplane ground speed affine nonlinear model;
step 4, neutralizing the opening delta of the control throttle valve in the airplane ground speed affine nonlinear modelTTaking the linearly independent terms as system lumped disturbance terms, and designing a finite time convergence high-order sliding mode disturbance observer to observe and estimate the lumped disturbance;
step 5, using the lumped disturbance obtained by observation and estimation in the step 4 as a feedforward compensation term, and combining with ground speed constrained conditions to design a ground speed constrained anti-interference controller based on a barrier Lyapunov function; the specific process is as follows:
step 51, defining the tracking error of ground speed
Figure BDA0002338128140000024
VkIn order to determine the ground speed of the airplane,
Figure BDA0002338128140000025
for the aircraft ground speed command, and defining a constant A0> 0 so that
Figure BDA0002338128140000026
Step 52, selecting is based on
Figure BDA0002338128140000027
The asymmetric barrier Lyapunov function of (1); the method comprises the following specific steps:
Figure BDA0002338128140000028
wherein L represents the Lyapunov function of the asymmetric barrier,
Figure BDA0002338128140000029
p is a positive integer, p is more than or equal to 1,
Figure BDA00023381281400000210
step 53, designing an airplane ground speed constrained tracking controller; the method comprises the following specific steps:
Figure BDA00023381281400000211
wherein the content of the first and second substances,
Figure BDA00023381281400000212
Tmaxto maximize engine thrust, σ is the engine mount angle, α and β are the angle of attack and sideslip angle, respectively, m is the aircraft mass,
Figure BDA00023381281400000213
in order to aggregate the perturbation term,
Figure BDA00023381281400000214
controlling gain for ground speed feedback;
step 54, using the lumped disturbance observed estimation obtained by the observer in step 4
Figure BDA0002338128140000031
Instead of in step 53
Figure BDA0002338128140000032
Obtaining an aircraft ground speed constrained disturbance rejection tracking controller, and completing the design of the controller; the method comprises the following specific steps:
Figure BDA0002338128140000033
as a preferable scheme of the present invention, the dynamic model of the ground speed non-linear subsystem of the aircraft in step 2 is:
Figure BDA0002338128140000034
wherein, VkTaking the ground speed of the airplane, m is the mass of the airplane, g is the gravity acceleration, T is the thrust of an engine, D, L, C is the aerodynamic drag, the lift force and the lateral force respectively, sigma is the installation angle of the engine, gamma is the inclination angle of a track, α and β are the attack angle and the sideslip angle respectively, αwAnd βwRespectively the additional quantities of the attack angle and the sideslip angle caused by the airflow disturbance.
As a preferred embodiment of the present invention, the specific process of step 3 is:
step 31, separating the dynamic model of the airplane ground speed nonlinear subsystem established in the step 2 into two parts:
Figure BDA0002338128140000035
wherein, VkIs the ground speed of the airplane, m is the mass of the airplane, g is the acceleration of gravity, TmaxD, L, C is aerodynamic drag, lift force and side force respectively for the maximum thrust of the engine, sigma is the installation angle of the engine, gamma is the track inclination angle, α and β are the attack angle and the sideslip angle respectively, αwAnd βwAdding quantities, delta, to the angle of attack and sideslip angle respectively caused by disturbance of the air flowTOpening the throttle of the engine;
step 32, converting the model in the step 31 into an airplane ground speed affine nonlinear model:
Figure BDA0002338128140000036
wherein the content of the first and second substances,
Figure BDA0002338128140000037
as a preferred embodiment of the present invention, the specific process of step 4 is:
step 41, performing neutralization control on the ground speed affine nonlinear model of the airplaneThrottle opening deltaTLinearly independent terms
Figure BDA0002338128140000038
And (3) regarding the system as a lumped disturbance term, and amplifying the airplane ground speed affine nonlinear model to obtain a ground speed amplification system:
Figure BDA0002338128140000039
wherein, VkIn order to determine the ground speed of the airplane,
Figure BDA00023381281400000310
is that
Figure BDA00023381281400000311
The derivative of (a) of (b),
Figure BDA00023381281400000312
Tmaxfor maximum engine thrust, σ is the engine mount angle, α and β are the angle of attack and sideslip angle, respectively, m is the aircraft mass, δTOpening the throttle of the engine;
step 42, designing a finite time convergence high-order sliding mode disturbance observer aiming at a ground speed augmentation system; the method comprises the following specific steps:
Figure BDA0002338128140000041
wherein the content of the first and second substances,
Figure BDA0002338128140000042
is a VkIs determined by the estimated value of (c),
Figure BDA0002338128140000043
Figure BDA0002338128140000044
for observer parameters to be designed;
Figure BDA0002338128140000045
to the lumped disturbance term
Figure BDA0002338128140000046
Is observed.
Compared with the prior art, the invention adopting the technical scheme has the following technical effects:
1. the unmanned aerial vehicle ground speed constraint disturbance rejection control method based on the obstacle Lyapunov function can realize accurate observation and estimation of unmeasured lumped disturbance induced by uncertainty including parameter perturbation and the like.
2. The unmanned aerial vehicle ground speed constraint disturbance rejection control method based on the obstacle Lyapunov function can obviously ensure that the ground speed of the aircraft is strictly constrained and controlled within an expected range.
3. The unmanned aerial vehicle ground speed constraint anti-interference control method based on the obstacle Lyapunov function can realize constrained anti-interference accurate control of the ground speed under perturbation of a certain parameter and obviously improve the control accuracy.
Drawings
FIG. 1 is a block diagram of an unmanned aerial vehicle ground speed constraint disturbance rejection control method based on a barrier Lyapunov function.
FIG. 2 shows the tracking results of the ground speed of the perturbation aircraft with and without aerodynamic parameters in the embodiment of the invention.
FIG. 3 shows the results of the perturbation of the ground speed tracking error of the airplane by the aerodynamic parameters in the embodiment of the invention.
FIG. 4 shows the results of perturbation of the throttle opening of the aircraft engine by the aerodynamic parameters in the embodiment of the invention.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings. The embodiments described below with reference to the accompanying drawings are illustrative only for the purpose of explaining the present invention, and are not to be construed as limiting the present invention.
The invention relates to an unmanned aerial vehicle ground speed constraint disturbance rejection control method based on a barrier Lyapunov function, which comprises the steps of firstly establishing a dynamic model of an airplane ground speed nonlinear subsystem, and processing the dynamic model into an affine nonlinear form; further, aiming at a ground speed affine nonlinear model, a finite-time high-order sliding mode disturbance observer is designed to estimate uncertain disturbance caused by perturbation of system parameters; on the basis, an unknown disturbance obtained by estimation is used as feedforward compensation, and a nonlinear constrained disturbance rejection tracking controller of the ground speed subsystem is designed to realize accurate tracking of the expected ground speed under the given ground speed constraint condition.
In this embodiment, the aircraft flying height is set to 7010 m.
As shown in fig. 1, an unmanned aerial vehicle ground speed constraint disturbance rejection control method based on a barrier Lyapunov function specifically includes the following steps:
step one, setting an airplane ground speed instruction
Figure BDA0002338128140000051
Upper and lower bounds of ground speed instruction
Figure BDA0002338128140000052
And
Figure BDA0002338128140000053
and ground speed constraint range S ═ { V ═ Vk||Vk|≤Kc}。
In this step, the ground speed command of the airplane is selected
Figure BDA0002338128140000054
The upper and lower boundaries of the ground speed command are
Figure BDA0002338128140000055
And
Figure BDA0002338128140000056
meanwhile, the ground speed constraint range K is selected in the stepc＝202.2m/s。
And step two, establishing a dynamic model of the airplane ground speed nonlinear subsystem to describe the ground speed motion state.
Figure BDA0002338128140000057
In the formula, c(·)＝cos(·),s(·)Sin (·), m is the aircraft mass, g is the gravitational acceleration, T is the engine thrust, D, L and C are the aerodynamic drag, lift and side forces, σ is the engine mount angle, γ is the track pitch angle, α and β are the attack and sideslip angles, αwAnd βwAdding an additional amount to the angle of attack and sideslip angle caused by the airflow disturbance.
In this step:
Figure BDA0002338128140000058
T＝TmaxδT,ρ＝ρ0e-k|z|,Q＝0.5ρV2
in the formula (I), the compound is shown in the specification,
Figure BDA0002338128140000059
rho, V and Q are respectively atmospheric density, airspeed and dynamic pressure, rho0Is the standard atmospheric density, k is the calculation parameter of the atmospheric density, z is the flying height, S is the pneumatic sectional area,
Figure BDA00023381281400000510
is the aerodynamic chord length, q is the pitch angle rate, δeFor elevator rudder deflection angle, deltarIs the rudder deflection angle.
And selecting the following physical and pneumatic parameters of the airplane: t ismax244647.2N、m＝88380kg、S＝226.03m2、cL,0＝0、
Figure BDA0002338128140000062
cD,0＝0.028、
Figure BDA0002338128140000063
cC,0＝0、
Figure BDA0002338128140000064
And step three, converting the ground speed subsystem dynamic model established in the step two into an affine nonlinear form so as to facilitate the design of a nonlinear controller.
The method comprises the following specific steps:
step 31, separating the ground speed subsystem dynamic model established in the second step into: the ground speed subsystem dynamic model and other items established in the second step; the method comprises the following specific steps:
Figure BDA0002338128140000065
in the formula, deltaTIs the engine throttle opening degree, unit: percent; t ismaxThe maximum thrust of the engine.
Step 32, writing the formula (2) in the step 31 into an affine nonlinear form described by the formula (3); the method comprises the following specific steps:
Figure BDA0002338128140000066
in the formula (I), the compound is shown in the specification,
Figure BDA0002338128140000067
fourthly, the opening delta of the throttle opening is subjected to neutralization control in the airplane ground speed affine nonlinear modelTLinearly independent terms
Figure BDA0002338128140000068
And (3) as the system lumped disturbance, designing a finite time convergence high-order sliding mode disturbance observer to accurately observe and estimate the disturbance.
The method comprises the following specific steps:
step 41, adding the compound of formula (3) in step 32
Figure BDA0002338128140000069
The augmentation is a new state of the system, and a ground speed augmentation system is obtained; the method comprises the following specific steps:
Figure BDA00023381281400000610
in the formula (I), the compound is shown in the specification,
Figure BDA00023381281400000611
Figure BDA00023381281400000612
is that
Figure BDA00023381281400000613
A derivative of (a);
step 42, designing a finite time convergence high-order sliding mode disturbance observer for the ground speed augmentation system described in the formula (4) in the step 41; the method comprises the following specific steps:
Figure BDA00023381281400000614
in the formula (I), the compound is shown in the specification,
Figure BDA0002338128140000071
Figure BDA0002338128140000072
for observer parameters to be designed;
Figure BDA0002338128140000073
i.e. to the lumped disturbance term
Figure BDA0002338128140000074
Is observed.
In this step, the parameters of the finite time convergence high-order sliding mode observer are selected as follows:
Figure BDA0002338128140000075
and step five, taking the disturbance obtained by observation and estimation in the step four as a feedforward compensation term, and designing a ground speed constrained anti-interference controller based on the barrier Lyapunov function by combining the ground speed constrained condition.
The method comprises the following specific steps:
step 51, defining the tracking error of ground speed
Figure BDA0002338128140000076
And defines a constant A0If greater than 0, then
Figure BDA0002338128140000077
Step 52, selecting is based on
Figure BDA0002338128140000078
The asymmetric barrier Lyapunov function of (1); the method comprises the following specific steps:
Figure BDA0002338128140000079
in the formula (I), the compound is shown in the specification,
Figure BDA00023381281400000710
p is more than or equal to 1 and is a positive integer,
Figure BDA00023381281400000711
step 53, designing an airplane ground speed constrained tracking controller; the method comprises the following specific steps:
Figure BDA00023381281400000712
in the formula (I), the compound is shown in the specification,
Figure BDA00023381281400000713
the gain is feedback controlled for ground speed.
Step 54, obtaining the lumped disturbance estimate using the observer in step four
Figure BDA00023381281400000714
Instead of in formula (7) in step 53
Figure BDA00023381281400000715
Obtaining an aircraft ground speed constrained disturbance rejection tracking controller, and completing the design of the controller; the method comprises the following specific steps:
Figure BDA00023381281400000716
in this step, the selected control parameters are:
Figure BDA00023381281400000717
p＝2。
by adopting the unmanned aerial vehicle ground speed constraint disturbance rejection control method based on the barrier Lyapunov function, and combining the given flight and ground speed constraint conditions, the result graphs of the ground speed, the ground speed error and the accelerator opening of the aircraft are obtained in a simulation mode respectively without the pneumatic parameter perturbation of-20% and + 20% respectively.
As shown in FIG. 2, the results of tracking the ground speed of the airplane without the aerodynamic parameter perturbation, the aerodynamic parameter perturbation of-20% and the aerodynamic parameter perturbation of + 20% in the present embodiment are shown. The method has the advantages that the ground speed controller well controls the ground speed to accurately track the command under the condition of the perturbation of the aerodynamic parameters, and the ground speed tracking results under the three conditions tend to be coincident, so that the method fully shows that the aircraft ground speed controller provided by the invention has excellent anti-interference capability and can better resist the perturbation influence of the aerodynamic parameters of +/-20%; on the other hand, the ground speed tracking result does not exceed the given ground speed constraint range K in all three conditionsC202.2m/s, which shows that the method of the present invention can accurately restrict the ground speed within the given restriction range.
As shown in FIG. 3, the results of the tracking errors of the ground speed of the airplane without the aerodynamic parameter perturbation, the aerodynamic parameter perturbation of-20% and the aerodynamic parameter perturbation of + 20% in the embodiment are shown. It can be seen that under the condition of existence or nonexistence of the perturbation of the pneumatic parameters, the tracking errors are slightly different at the initial stage, but quickly tend to coincide, and the controller can better resist the influence of +/-20% perturbation of the pneumatic parameters, thereby keeping higher tracking accuracy; on the other hand, the tracking error result of the ground speed does not exceed the given ground speed error constraint range of [ -0.20.2] m/s in all three cases, which also proves that the method of the invention can have accurate ground speed constraint control capability.
As shown in FIG. 4, the results are shown without aerodynamic parameter perturbation, -20% aerodynamic parameter perturbation and + 20% aerodynamic parameter perturbation for throttle opening. It can be seen that with the introduction of the perturbation of the pneumatic parameters, the opening degree of the accelerator has obvious difference in amplitude, but the overall change trend tends to be consistent. When the perturbation of the aerodynamic parameter is increased (such as + 20%), a larger throttle opening is required to achieve the desired ground speed constrained anti-interference control effect; conversely, when the aerodynamic parameter perturbation is reduced (e.g., -20%), a smaller throttle opening is required to achieve the desired ground speed constrained immunity control effect.
By combining the analysis and the simulation verification, the effectiveness of the unmanned aerial vehicle ground speed constraint anti-interference control method based on the barrier Lyapunov function in the aspect of the constrained anti-interference precise control of the ground speed of the airplane is fully proved.
The above embodiments 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 modifications made on the basis of the technical scheme according to the technical idea of the present invention fall within the protection scope of the present invention.

Claims (4)

1. An unmanned aerial vehicle ground speed constraint disturbance rejection control method based on a barrier Lyapunov function is characterized by comprising the following steps:
step 1, setting an airplane ground speed instruction
Figure FDA0002338128130000011
Ground speed instruction upper bound
Figure FDA0002338128130000012
And lower bound
Figure FDA0002338128130000013
And ground speed constraint range Kc；
Step 2, establishing a dynamic model of the airplane ground speed nonlinear subsystem to describe the ground speed motion state;
step 3, converting the airplane ground speed nonlinear subsystem dynamic model established in the step 2 into an airplane ground speed affine nonlinear model;
step 4, neutralizing the opening delta of the control throttle valve in the airplane ground speed affine nonlinear modelTTaking the linearly independent terms as system lumped disturbance terms, and designing a finite time convergence high-order sliding mode disturbance observer to observe and estimate the lumped disturbance;
step 5, using the lumped disturbance obtained by observation and estimation in the step 4 as a feedforward compensation term, and combining with ground speed constrained conditions to design a ground speed constrained anti-interference controller based on a barrier Lyapunov function; the specific process is as follows:
step 51, defining the tracking error of ground speed
Figure FDA0002338128130000014
VkIn order to determine the ground speed of the airplane,
Figure FDA0002338128130000015
for the aircraft ground speed command, and defining a constant A0> 0 such that
Figure FDA0002338128130000016
Step 52, selecting is based on
Figure FDA0002338128130000017
The asymmetric barrier Lyapunov function of (1); the method comprises the following specific steps:
Figure FDA0002338128130000018
wherein L represents the Lyapunov function of the asymmetric barrier,
Figure FDA0002338128130000019
p is a positive integer, p is more than or equal to 1,
Figure FDA00023381281300000110
step 53, designing an airplane ground speed constrained tracking controller; the method comprises the following specific steps:
Figure FDA00023381281300000111
wherein the content of the first and second substances,
Figure FDA00023381281300000112
Tmaxto maximize engine thrust, σ is the engine mount angle, α and β are the angle of attack and sideslip angle, respectively, m is the aircraft mass,
Figure FDA00023381281300000113
in order to aggregate the perturbation term,
Figure FDA00023381281300000114
controlling gain for ground speed feedback;
step 54, using the lumped disturbance observed estimation obtained by the observer in step 4
Figure FDA0002338128130000021
Instead of in step 53
Figure FDA0002338128130000022
Obtaining an aircraft ground speed constrained disturbance rejection tracking controller, and completing the design of the controller; the method comprises the following specific steps:
Figure FDA0002338128130000023
2. the obstacle Lyapunov function-based unmanned aerial vehicle ground speed constraint disturbance rejection control method according to claim 1, wherein the aircraft ground speed nonlinear subsystem dynamic model in the step 2 is as follows:
Figure FDA0002338128130000024
wherein, VkIs the ground speed of the airplane, m is the mass of the airplane, g is the gravity acceleration, and T is the thrust of the engineThe forces, D, L, C, are aerodynamic drag, lift, and side forces, respectively, σ is the engine mount angle, γ is the track inclination angle, α and β are the attack angle and the sideslip angle, respectively, αwAnd βwRespectively the additional quantities of the attack angle and the sideslip angle caused by the airflow disturbance.
3. The unmanned aerial vehicle ground speed constraint disturbance rejection control method based on the barrier Lyapunov function according to claim 1, wherein the specific process of the step 3 is as follows:
step 31, separating the dynamic model of the airplane ground speed nonlinear subsystem established in the step 2 into two parts:
Figure FDA0002338128130000025
wherein, VkIs the ground speed of the airplane, m is the mass of the airplane, g is the acceleration of gravity, TmaxD, L, C is aerodynamic drag, lift force and side force respectively for the maximum thrust of the engine, sigma is the installation angle of the engine, gamma is the track inclination angle, α and β are the attack angle and the sideslip angle respectively, αwAnd βwAdding quantities, delta, to the angle of attack and sideslip angle respectively caused by disturbance of the air flowTOpening the throttle of the engine;
step 32, converting the model in the step 31 into an airplane ground speed affine nonlinear model:
Figure FDA0002338128130000026
wherein the content of the first and second substances,
Figure FDA0002338128130000027
4. the unmanned aerial vehicle ground speed constraint disturbance rejection control method based on the barrier Lyapunov function according to claim 1, wherein the specific process of the step 4 is as follows:
step 41, comparing the opening delta of the control throttle valve in the airplane ground speed affine nonlinear modelTLinearly independent terms
Figure FDA0002338128130000028
And (3) regarding the system as a lumped disturbance term, and amplifying the airplane ground speed affine nonlinear model to obtain a ground speed amplification system:
Figure FDA0002338128130000031
wherein, VkIn order to determine the ground speed of the airplane,
Figure FDA0002338128130000032
is that
Figure FDA0002338128130000033
The derivative of (a) of (b),
Figure FDA0002338128130000034
Tmaxfor maximum engine thrust, σ is the engine mount angle, α and β are the angle of attack and sideslip angle, respectively, m is the aircraft mass, δTOpening the throttle of the engine;
step 42, designing a finite time convergence high-order sliding mode disturbance observer aiming at a ground speed augmentation system; the method comprises the following specific steps:
Figure FDA0002338128130000035
wherein the content of the first and second substances,
Figure FDA0002338128130000036
is a VkIs determined by the estimated value of (c),
Figure FDA0002338128130000037
Figure FDA0002338128130000038
for observer parameters to be designed;
Figure FDA0002338128130000039
to the lumped disturbance term
Figure FDA00023381281300000310
Is observed.
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