CN110829933A - Neural network output feedback self-adaptive robust control method based on transmitting platform - Google Patents

Neural network output feedback self-adaptive robust control method based on transmitting platform Download PDF

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CN110829933A
CN110829933A CN201911096543.7A CN201911096543A CN110829933A CN 110829933 A CN110829933 A CN 110829933A CN 201911096543 A CN201911096543 A CN 201911096543A CN 110829933 A CN110829933 A CN 110829933A
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neural network
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theta
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CN110829933B (en
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胡健
沈旭亮
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Nanjing University of Science and Technology
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P23/00—Arrangements or methods for the control of AC motors characterised by a control method other than vector control
    • H02P23/0004—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control
    • H02P23/0018—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control using neural networks
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/0003—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control
    • H02P21/0014—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control using neural networks
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/13—Observer control, e.g. using Luenberger observers or Kalman filters
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P23/00—Arrangements or methods for the control of AC motors characterised by a control method other than vector control
    • H02P23/12—Observer control, e.g. using Luenberger observers or Kalman filters

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Abstract

The invention discloses a neural network output feedback self-adaptive robust control method based on a transmitting platform, which comprises the following steps: firstly, establishing a mathematical model of an emission platform, secondly designing a neural network state observer and a neural network output feedback self-adaptive robust controller based on the neural network state observer; and finally, carrying out stability verification on the neural network state observer and the neural network output feedback self-adaptive robust controller by applying the Lyapunov stability theory. The invention solves the problem that the actual value of the state quantity in the motor servo system of the launching platform is difficult to obtain.

Description

Neural network output feedback self-adaptive robust control method based on transmitting platform
Technical Field
The invention relates to the field of launching platform motor servo control, in particular to a neural network output feedback self-adaptive robust control method based on a launching platform.
Background
The launching platform is widely applied to air defense weapons and consists of a position servo system and a pitching servo system, and the mathematical models of the position servo system and the pitching servo system are consistent, so that the invention can be used for researching the position servo system.
High precision motion control has become the main development direction of modern dc motors. In a motor servo system, due to the variation of working conditions, external interference and modeling errors, when designing a controller, many model uncertainties, especially uncertainties and nonlinearities are encountered, which severely deteriorate the achievable control performance, thereby causing low control accuracy, limit cycle oscillation and even system instability. For known non-linearities, this can be handled by feedback linearization techniques. However, an accurate model of an actual industrial process is difficult to obtain, and the non-linearity is more unknown, so that it is extremely difficult to design a high-performance controller.
The traditional control mode is difficult to meet the requirement of uncertain nonlinear tracking precision, so that a control method which is simple and practical and meets the requirement of system performance needs to be researched. In recent years, various advanced control strategies are applied to servo systems, such as sliding mode variable structure control, robust adaptive control, adaptive robustness and the like. However, the speed of the conventional system is not easy to obtain. The sensor is high in price and large in error, the position signal differentiation inevitably amplifies the measured noise, so that the obtained signal is not ideal or even can not be used, but if the signal is filtered, the signal delay and the speed signal acquisition lag can be caused. Therefore, the traditional adaptive robust method has great defects and limitations.
Disclosure of Invention
The invention aims to provide a neural network output feedback self-adaptive robust control method based on a launching platform, and solves the problem that the actual value of the state quantity in a motor servo system of the launching platform is difficult to obtain.
The technical solution for realizing the aim of the invention is as follows: the neural network output feedback self-adaptive robust control method based on the transmitting platform comprises the following specific steps:
step 1, establishing a mathematical model of a transmitting platform, and turning to step 2;
step 2, designing a neural network state observer and a neural network output feedback self-adaptive robust controller based on the neural network state observer;
and 3, performing stability certification on the neural network state observer and the neural network output feedback self-adaptive robust controller by applying the Lyapunov stability theory.
Compared with the prior art, the invention has the following remarkable advantages:
(1) the invention effectively observes the system speed by utilizing the neural network observer, thereby solving the problem that the system speed is not easy to obtain in the traditional method and ensuring the excellent control performance of the launching platform.
(2) The coupling moment between the two shaft systems is effectively compensated.
(3) Parameter self-adaptation enables accurate system parameters during system operation not to be acquired, and engineering practice is facilitated.
(4) The self-adaption and the robust control are combined, so that the unknown interference can be processed, and the robustness of the controller is improved.
Drawings
Fig. 1 is a control schematic diagram of a launch pad motor servo system.
FIG. 2 is a diagram of an adaptive robust control flow and strategy based on neural network output feedback.
Fig. 3 is a graph of the input voltage u of the controller under the interference of f (t) equal to 0.5sin (0.5 pi t) (N · m), and the input voltage of the controller satisfies the input range of-15V to +15V, which is suitable for practical application.
Fig. 4 is a diagram of the process of tracking system output versus command under the action of the output feedback ARC controller under the action of disturbance f (t) 0.5sin (0.5 tt) (N · m).
Fig. 5 is a graph of system tracking error over time with disturbance f (t) 0.5sin (0.5 tt) (n.m) by the output feedback ARC controller.
Fig. 6 is a graph of the neural network state observer versus system velocity estimate under the influence of the disturbance f (t) 0.5sin (0.5 tt) (n.m).
Fig. 7 is a graph of the estimation of the system speed error by the neural network state observer under the effect of the disturbance f (t) of 0.5sin (0.5 pi t) (N · m).
FIG. 8 output feedback ARC controller with estimation of θ3Graph is shown.
FIG. 9 output feedback ARC controller effects estimate θ4Graph is shown.
FIG. 10 output feedback ARC controller with estimation of θ5Graph is shown.
FIG. 11 is a graph of error under the effect of a conventional ARC controller.
Detailed Description
The invention concerns a launch platform in which the azimuth servo is a torque-controlled servo motor driven by a servo drive, linked to the load by a reducer. The objective is to make the inertial load follow as much as possible an arbitrarily specified smooth curve Xd, as shown in connection with fig. 1.
With reference to fig. 2, a method for controlling an emission platform based on neural network output feedback adaptive robustness includes the following steps:
step 1, establishing a motor position servo system model:
according to Newton's second law, the dynamic model equation of the inertia load of the motor is as follows:
Figure BDA0002268507780000031
the dynamic model of the inertia load of the motor considers other unmodeled interference tau and viscous frictionBiaxial coupling torque
Figure BDA0002268507780000033
In the formula JeqRepresenting an inertial load parameter, kuRepresenting the torque amplification factor at the output of the machine, u being the system control input, dnIs a constant interference, wherein BeqRepresenting the viscous coefficient of friction, y representing the displacement of the inertial load, ω and
Figure BDA0002268507780000034
is the angular velocity and angular acceleration of the pitch servo system, c1And c2Is corresponding to ω andthe coupling coefficient of (2).
The formula (1) is abbreviated as follows
Figure BDA0002268507780000036
Wherein the intermediate variableIntermediate variables
Figure BDA0002268507780000038
Intermediate variables
Figure BDA0002268507780000039
Intermediate variablesIntermediate variables
Figure BDA00022685077800000311
Intermediate variables
Figure BDA00022685077800000312
Writing the formula (2) into a state space form, namely a mathematical model of the transmitting platform:
Figure BDA00022685077800000313
wherein
Figure BDA00022685077800000314
x＝[x1，x2]TState vector representing position and velocity, typically due to system parameter Jeq、ku、Beq、dnUnknown, system parameters are uncertain, nominal values of which can be determined; furthermore, the non-linearity of the system
Figure BDA00022685077800000315
Also not explicitly modelled, but
Figure BDA00022685077800000316
Is always bounded, thus, the following assumptions are always true:
assume that 1: the parameter theta satisfies:
wherein theta ismin＝[θ3min，θ4min，θ5min]T，θmax＝[θ3max，θ4max，θ5max]TAll of which are known as θT＝[θ3，θ4，θ5]Has an upper bound value of thetaM。
Assume 2: τ (x, t) is bounded and differentiable to the first order, i.e.
|τ(x，t)|≤δd(5)
Wherein deltadAre known.
Step 2, designing a neural network state observer and a neural network output feedback self-adaptive robust controller based on the neural network state observer, and specifically comprising the following steps:
step 2-1, constructing a neural network state observer of the motor according to the formula (3)
Equation (3) is written as follows:
Figure BDA0002268507780000041
wherein D (x, t) ═ theta1-θ1n)x1-(θ2-θ2n)x2-d (x, t) is a generalized disturbance representing the deviation of the nominal system, θ1nAnd theta2nIs theta1And theta2Nominal value of (D)1(x，t)＝(θ1-θ1n)u-(θ2-θ2n)x2-ho(x, t) and hypothesis 2 know D1(x, t) is also bounded to the first differentiable.
Since the neural network can approximate any non-linear function, equation (6) exists
Figure BDA0002268507780000042
Wherein ω isoIs the output layer weight, σoFor the excitation function, x is the state variable of the input layer of the neural network, εoIs the error of the network bounded by the actual function, i.e. | εo|≤εo，M
Figure BDA0002268507780000043
Wherein epsilono，MIs epsilonoAn upper limit value of (d);
Figure BDA0002268507780000044
is omegaoAn estimated value of (d);
Figure BDA0002268507780000045
is omegaoError of the estimated value of (c); in the formula (7), the estimated value of the weight of the neural network
Figure BDA0002268507780000046
Provided by a tuning algorithm, as in formula (8)
Figure BDA0002268507780000047
Wherein
Figure BDA0002268507780000048
Is composed of
Figure BDA0002268507780000049
Derivative of (F), matrix F ═ FT＞0，koIs a sufficiently large design parameter.
The neural network observer is of the formula (9)
Figure BDA00022685077800000410
Figure BDA00022685077800000411
Representing the estimated value of the state observer of the neural network,
Figure BDA00022685077800000412
observer estimation for representing neural network states
Figure BDA00022685077800000413
The derivative of (a) of (b),observer estimation for representing neural network states
Figure BDA00022685077800000415
The derivative of (c).
Design parameter kdIf the parameter k is more than 0, the state observer of the neural network and the state estimation of the system are performed
Figure BDA0002268507780000051
The relationship exists as follows:
Figure BDA0002268507780000052
Figure BDA0002268507780000053
design parameter kp> 0, the stability of the neural network state observer is guaranteed by a Lyapunov function L, as shown in formula (11)
Guarantee
Figure BDA0002268507780000055
And is
Figure BDA0002268507780000056
Wherein the content of the first and second substances,
Figure BDA0002268507780000057
is a basis function
Figure BDA0002268507780000058
Upper limit of (a), ωMRepresents | ω | non-calculationFThe upper limit of (3).
Figure BDA0002268507780000059
Taking design parameters
Figure BDA00022685077800000510
koIs more than 1; the observer can be guaranteed to be bounded in the global state estimate, and equation (12) is expressed as:
Figure BDA00022685077800000511
and design parameters k, kp，koWhen the appropriate value is taken, the state estimation can converge to a sufficiently small value; wherein ζ1、ζ2、ζ3、
Figure BDA00022685077800000512
And λ are intermediate variables.
Step 2-2, designing a neural network output feedback self-adaptive robust controller based on a neural network state observer:
the state equation of the system is rewritten as follows:
Figure BDA00022685077800000513
definition e1＝x1-x1dAs a tracking error of the system, x1dIs that the system expects to track position instructions that are continuously differentiable in the second order,is the speed that the system is expected to track,
Figure BDA00022685077800000515
is the acceleration the system is expected to track; let x2eqFor desired values of virtual control, x2eqAnd the true state x2Error e2＝x2-x2eqTo e is aligned with1The derivation can be:
Figure BDA00022685077800000516
is provided with
Figure BDA00022685077800000517
Wherein k is1For an adjustable parameter greater than 0, then
Figure BDA0002268507780000061
After laplace transform of equation (14), transfer function g(s) ═ 1/(s + k) is known1) For a stable transfer function, s is the sign of the variable in the frequency domain, when e2When going to 0, e1Also inevitably tends to be 0, to e2＝x2-x2eqThe differential can be found as:
Figure BDA0002268507780000062
the input quantity is expressed as u-ua+usWherein u isaIs the feedforward compensation of the model, usAs a feedback term
Figure BDA0002268507780000063
us＝us1+us2(17)
θ1nAnd theta2nIs theta1And theta2Nominal value of (u)s1Is a linear feedback term，us2For non-linear robust feedback terms
us1＝-k2e2(18)
Figure BDA0002268507780000064
Is a parameter thetaT＝[θ3，θ4，θ5]Estimated value of, adaptive rateThe definition is as follows:
Figure BDA0002268507780000066
wherein gamma is a positive definite diagonal matrix,
Figure BDA0002268507780000067
is an adaptive parameter regressor.
To ensure that the tuned parameter is a controlled process and the parameter cannot exceed a predefined parameter range, a discontinuity map is defined as follows:
since the design observer state error in step 2-1 is bounded, there is a constant δjSo that the error j
Figure BDA0002268507780000069
Figure BDA00022685077800000610
Figure BDA00022685077800000611
An error value representing a parameter estimate; epsilonsIs any normal number; to satisfy the condition in equation (21), the nonlinear robust feedback term u is applieds2The design is as follows:
Figure BDA0002268507780000071
wherein, | θM||||ψ||+δd+|θ2-θ1k1|δ2≤hs，
Wherein, thetaMRepresenting the parameter thetaTUpper bound value of hsIs | | | thetaM||||ψ||+δd+|θ2-θ1k1|δ2The upper bound value of (1).
And 3, performing stability certification on the neural network state observer and the neural network output feedback self-adaptive robust controller by applying the Lyapunov stability theory:
the stability of the neural network state observer is represented by the following Lyapunov function L1Warranty of certification
Figure BDA0002268507780000073
For the above formula Lyapunov function L1Derivation, the following equation can be obtained
Figure BDA0002268507780000074
Due to design parameters
Figure BDA0002268507780000075
koIs more than 1; i.e. the observer is guaranteed to be bounded in the global state estimate, the above equation can be expressed as:
wherein ζ1、ζ2、ζ3、And λ are intermediate variables, and k, kp，koTaking the appropriate value, the state estimate can converge to a sufficiently small value.
Adaptive robust control controller definition Lyapunov function
Figure BDA0002268507780000078
Then to L2Derivation, e.g. formula (23)
Figure BDA0002268507780000079
Therefore, the designed controller outputs a tracking error to be bounded and stably adjusts the u gain parameter in the robust controller based on the state estimation of the neural network, and the control performance index is met.
The invention has the beneficial effects that: aiming at the characteristics of an azimuth position servo system of a launching platform, a motor position servo system model is established; the robust controller based on the output feedback state estimation estimates the state and adjusts the state in real time, can well estimate the state through the parameter adjustment of the control law, can effectively solve the problem of uncertain nonlinearity of a motor servo system, and meets the performance index of the system control precision under the interference condition; the invention relates to the design of an observer and an adaptive robust controller, and the simulation result shows the effectiveness of the observer and the adaptive robust controller.
Example (b):
the simulation parameters are as follows: inertial load parameter Jeq＝0.01kg·m2Coefficient of moment amplification kuCoefficient of viscous friction B ═ 5eq1.025N s/m, constant disturbance dn1.525n.m, pitch azimuth coupling coefficient c1＝0.14N.m(rad/s)，c20.13n.m (rad/s), and 0.6N · m is an upper bound δ of time-varying interference;
Figure BDA0002268507780000081
upper bound delta of2＝0.3N.m；θmin＝[0，0.002，0.22]T；θmax＝[0.215，0.01，0.3]T(ii) a Time-varying interference f (t) of 0.5sin (0)5 π t) (N · m); position equation of motion in pitch direction theta is 0.1sin (pi t) [1-exp (-0.01t)](rad); position angle input signalTaking observer parameters kd as 20, k as 400, kp as 200 and ko as 1.1; f ═ diag [10, 10]Controller parameter k1＝50，k2＝1，，λ0＝200，λ1＝1500，λ2＝2000；θ1n＝300；θ2nThe nominal value of θ is chosen to be far from the true value of the parameter, 20, to assess the effectiveness of the adaptive control law.
As can be seen from fig. 4 to 11, the present invention utilizes the neural network observer to effectively observe the system velocity amount, thereby solving the problem that the system velocity amount is not easy to obtain in the conventional method, ensuring the excellent control performance of the launch platform, and effectively compensating the coupling torque between the two axis systems. Parameter self-adaptation enables accurate system parameters during system operation not to be acquired, and engineering practice is facilitated. The self-adaption and the robust control are combined, so that the unknown interference can be processed, and the robustness of the controller is improved.
The algorithm provided by the invention can accurately estimate the interference value in a simulation environment, and compared with the traditional ARC control, the controller designed by the invention can greatly improve the parameter uncertainty and the control precision of an interference system. Research results show that under the influence of uncertain nonlinearity and parameter uncertainty, the method provided by the invention can meet performance indexes.

Claims (4)

1. A neural network output feedback self-adaptive robust control method based on a transmitting platform is characterized in that: the method comprises the following steps:
step 1, establishing a mathematical model of a transmitting platform, and turning to step 2;
step 2, designing a neural network state observer and a neural network output feedback self-adaptive robust controller based on the neural network state observer;
and 3, performing stability certification on the neural network state observer and the neural network output feedback self-adaptive robust controller by applying the Lyapunov stability theory.
2. The neural network output feedback adaptive robust control method based on the transmitting platform as claimed in claim 1, wherein:
step 1, establishing a mathematical model of a transmitting platform, which comprises the following specific steps:
according to Newton's second law, the dynamic model equation of the inertia load of the motor is as follows:
Figure FDA0002268507770000011
in the formula JeqRepresenting an inertial load parameter, kuRepresenting the torque amplification factor at the output of the machine, u being the system control input, dnFor constant interference, tau for other unmodeled interference,
Figure FDA0002268507770000012
in order to achieve the viscous friction,is a biaxial coupling torque, wherein BeqRepresenting the viscous coefficient of friction, y representing the displacement of the inertial load, ω and
Figure FDA0002268507770000014
is the angular velocity and angular acceleration of the pitch servo system, c1And c2Is corresponding to ω and
Figure FDA0002268507770000015
the coupling coefficient of (a);
the formula (1) is abbreviated as follows
Wherein the intermediate variableIntermediate variablesIntermediate variables
Figure FDA0002268507770000019
Intermediate variables
Figure FDA00022685077700000110
Intermediate variables
Figure FDA00022685077700000111
Intermediate variables
Writing the formula (2) into a state space form, namely a mathematical model of the transmitting platform:
Figure FDA00022685077700000113
wherein
Figure FDA00022685077700000114
x＝[x1,x2]TState vector representing position and velocity, typically due to system parameter Jeq、ku、Beq、dnUnknown, system parameters are uncertain, nominal values of which can be determined; furthermore, the non-linearity of the system
Figure FDA0002268507770000021
Also not explicitly modelled, but
Figure FDA0002268507770000022
Is always bounded, thus, the following assumptions are always true:
assume that 1: the parameter theta satisfies:
Figure FDA0002268507770000023
wherein theta ismin＝[θ3min,θ4min,θ5min]T，θmax＝[θ3max,θ4max,θ5max]TAll of which are known as θT＝[θ3,θ4,θ5]Has an upper bound value of thetaM；
Assume 2: τ (x, t) is bounded and differentiable to the first order, i.e.
|τ(x,t)|≤δd(5)
Wherein deltadThe method comprises the following steps of (1) knowing;
and (5) transferring to the step 2.
3. The neural network output feedback adaptive robust control method based on the transmitting platform as claimed in claim 2, wherein:
step 2, designing a neural network state observer and a neural network output feedback self-adaptive robust controller based on the neural network state observer, and specifically comprising the following steps:
step 2-1, constructing a neural network state observer of the motor according to the formula (3),
equation (3) is written as follows:
Figure FDA0002268507770000024
wherein D (x, t) ═ theta1-θ1n)x1-(θ2-θ2n)x2-d (x, t) is a generalized disturbance representing the deviation of the nominal system, θ1nAnd theta2nIs theta1And theta2Nominal value of (D)1(x,t)＝(θ1-θ1n)u-(θ2-θ2n)x2-ho(x, t) and hypothesis 2 know D1(x, t) is also bounded first order differentiable;
since the neural network can approximate any non-linear function, equation (6) exists
Figure FDA0002268507770000025
Wherein ω isoIs the output layer weight, σoFor the excitation function, x is the state variable of the input layer of the neural network, εoIs the error of the network bounded by the actual function, i.e. | εo|≤εo,M
Figure FDA0002268507770000026
Wherein epsilono,MIs epsilonoAn upper limit value of (d);
Figure FDA0002268507770000031
is omegaoAn estimated value of (d); is omegaoError of the estimated value of (c); in the formula (7), the estimated value of the weight of the neural network
Figure FDA0002268507770000034
Provided by a tuning algorithm, as in formula (8)
Figure FDA0002268507770000035
Wherein
Figure FDA0002268507770000036
Is composed ofDerivative of (F), matrix F ═ FT＞0，koIs a sufficiently large design parameter;
the neural network observer is of the formula (9)
Figure FDA0002268507770000038
Figure FDA0002268507770000039
Representing the estimated value of the state observer of the neural network,
Figure FDA00022685077700000310
observer estimation for representing neural network states
Figure FDA00022685077700000311
The derivative of (a) of (b),
Figure FDA00022685077700000312
observer estimation for representing neural network states
Figure FDA00022685077700000313
A derivative of (a);
design parameter kdIf the parameter k is more than 0, the state observer of the neural network and the state estimation of the system are performed
Figure FDA00022685077700000314
The existence relationship is as follows
Figure FDA00022685077700000315
Design parameter kp> 0, the stability of the neural network state observer is guaranteed by a Lyapunov function L, as shown in formula (11)
Figure FDA00022685077700000317
Guarantee
Figure FDA00022685077700000318
And is
Figure FDA00022685077700000319
Wherein the content of the first and second substances,
Figure FDA00022685077700000320
is a basis function
Figure FDA00022685077700000321
Upper limit of (1), ωMRepresents | ω | non-calculationFThe upper limit of (d);
Figure FDA00022685077700000322
taking design parameterskoIs more than 1; the observer can be guaranteed to be bounded in the global state estimate, and equation (12) is expressed as:
Figure FDA00022685077700000324
and design parameters k, kp,koWhen the appropriate value is taken, the state estimation can converge to a sufficiently small value; wherein ζ1、ζ2、ζ3、
Figure FDA00022685077700000325
Figure FDA0002268507770000041
And λ are intermediate variables;
step 2-2, designing a neural network output feedback self-adaptive robust controller based on a neural network state observer:
the state equation of the system is rewritten as follows:
Figure FDA0002268507770000042
definition e1＝x1-x1dAs a tracking error of the system, x1dIs that the system expects to track position instructions that are continuously differentiable in the second order,
Figure FDA0002268507770000043
is the speed that the system is expected to track,
Figure FDA0002268507770000044
is the acceleration the system is expected to track; let x2eqFor desired values of virtual control, x2eqAnd the true state x2Error e2＝x2-x2eqTo e is aligned with1The derivation can be:
Figure FDA0002268507770000045
is provided withWherein k is1For an adjustable parameter greater than 0, then
Figure FDA0002268507770000047
After laplace transform of equation (14), transfer function g(s) ═ 1/(s + k) is known1) For a stable transfer function, s is the sign of the variable in the frequency domain, when e2When going to 0, e1Also inevitably tends to be 0, to e2＝x2-x2eqThe differential can be found as:
Figure FDA0002268507770000048
the input quantity is expressed as u-ua+usWherein u isaIs the feedforward compensation of the model, usAs a feedback term
Figure FDA0002268507770000049
us＝us1+us2(17)
θ1nAnd theta2nIs theta1And theta2Nominal value of (u)s1For linear feedback terms, us2For non-linear robust feedback terms
us1＝-k2e2(18)
Figure FDA00022685077700000410
Is a parameter thetaT＝[θ3,θ4,θ5]Estimated value of, adaptive rate
Figure FDA00022685077700000411
The definition is as follows:
Figure FDA00022685077700000412
wherein gamma is a positive definite diagonal matrix,
Figure FDA00022685077700000413
is an adaptive parameter regressor;
to ensure that the tuned parameter is a controlled process and the parameter cannot exceed a predefined parameter range, a discontinuity map is defined as follows:
Figure FDA0002268507770000051
since the design observer state error in step 2-1 is bounded, there is a constant δjMake an error
Figure FDA0002268507770000052
Figure FDA0002268507770000053
Figure FDA0002268507770000054
An error value representing a parameter estimate; epsilonsIs any normal number; to satisfy the condition in equation (21), the nonlinear robust feedback term u is applieds2The design is as follows:
wherein, | θM||||ψ||+δd+|θ2-θ1k1|δ2≤hs，
Figure FDA0002268507770000057
Wherein, thetaMRepresenting the parameter thetaTUpper bound value of hsIs | | | thetaM||||ψ||+δd+|θ2-θ1k1|δ2The upper bound value of (d);
and (5) turning to the step 3.
4. The neural network output feedback adaptive robust control method based on the launch platform as claimed in claim 3, wherein the stability of the neural network state observer and the neural network output feedback adaptive robust controller is proved by applying Lyapunov stability theory, so as to prove the convergence of the neural network output feedback adaptive robust control method based on the launch platform; through designing a discontinuous projection type parameter adaptive rule formula (8) and a weight adaptive rule formula (20), stability verification is carried out on a motor servo system by utilizing the Lyapunov stability theory, and the tracking performance of the system can be ensured by using a controller formula (16) and a controller formula (17).
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