CN116203847A - Motion control method of nonlinear electromechanical servo system - Google Patents
Motion control method of nonlinear electromechanical servo system Download PDFInfo
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Abstract
The invention discloses a motion control method of a nonlinear electromechanical servo system, and relates to the technical field of electromechanical system management; establishing a dynamic model of the nonlinear electromechanical servo system, and simplifying the electrical dynamic of a motor current loop corresponding to the nonlinear electromechanical servo system into a proportional link; performing approximate fitting on uncertainty of a dynamic model of the nonlinear electromechanical servo system by using a radial basis function neural network; estimating strong external time-varying disturbance of the nonlinear electromechanical servo system by using an extended state observer in combination with a dynamics model; and feeding back the expected motion trail of the nonlinear electromechanical servo system by adopting an error sign robust integral control method according to the estimation result, and controlling the actual motion trail of the nonlinear electromechanical servo system.
Description
Technical Field
The invention discloses a method, relates to the technical field of electromechanical system management, and particularly relates to a motion control method of a nonlinear electromechanical servo system.
Background
At present, the existing nonlinear electromechanical servo system control method mainly comprises calculation torque control, self-adaptive robust control, synovial membrane control, active disturbance rejection control and the like. However, the calculation of torque control requires obtaining a dynamic model of a precise nonlinear system to realize control, and in practical application, the dynamic model is difficult to control precisely. The adaptive robust control performs adaptive design on parameters of model uncertainty in a system, but other disturbance exists in model parameter estimation, and particularly when the system faces strong external disturbance, the control effect is deteriorated, and even the system is unstable. The sliding mode control has a strong suppression capability on the bounded interference of the system, but the buffeting problem caused by discontinuous control input is a defect which cannot be solved in the prior art. The active disturbance rejection control estimates the external disturbance of the system through a state observer, but the overall design parameters are more, the debugging is complicated, and the wide application is not facilitated.
Disclosure of Invention
Aiming at the problems that the control accuracy of a nonlinear electromechanical servo system is affected by nonlinear uncertainty dynamic influences such as uncertainty of system dynamics model parameters and external time-varying interference in the prior art, the invention provides a motion control method of the nonlinear electromechanical servo system, which ensures that the nonlinear electromechanical servo system can accurately track an expected motion track to move and avoids system instability.
The specific scheme provided by the invention is as follows:
the invention provides a motion control method of a nonlinear electromechanical servo system, which comprises the following steps:
step S1: establishing a dynamic model of the nonlinear electromechanical servo system, and simplifying the electrical dynamic of a motor current loop corresponding to the nonlinear electromechanical servo system into a proportional link;
step S2: performing approximate fitting on uncertainty of a dynamic model of the nonlinear electromechanical servo system by using a radial basis function neural network;
step S3: estimating strong external time-varying disturbance of the nonlinear electromechanical servo system by using an extended state observer in combination with a dynamics model;
step S4: and feeding back the expected motion trail of the nonlinear electromechanical servo system by adopting an error sign robust integral control method according to the estimation result, and controlling the actual motion trail of the nonlinear electromechanical servo system.
Further, in the motion control method of a nonlinear electromechanical servo system, the nonlinear electromechanical servo system in the step S1 is a nonlinear biaxial electromechanical servo system, a dynamic model of the nonlinear biaxial electromechanical servo system is established by using a lagrangian second class equation, nominal parameters of the nonlinear biaxial electromechanical servo system are obtained according to the dynamic model, and an uncertainty term caused by nonlinear factors, a set function of the uncertainty term and an uncertainty term set including external unknown interference are determined according to the nominal parameters.
Further, in the motion control method of a nonlinear electromechanical servo system, the following formula is used in the step S2:
and performing approximate fitting of the radial basis function to the uncertainty of the dynamic model of the nonlinear electromechanical servo system, wherein epsilon is a neural network fitting error, f is the output of the multi-layer neural network, W is the weight between the hidden layer and the output layer of the multi-layer neural network, sigma is an activation function of the multi-layer neural network, and the radial basis function is selected as the activation function.
Further, in the motion control method of a nonlinear electromechanical servo system, in the step S3, an expansion state and a change rate of interference are defined according to an estimation error of uncertainty of a dynamics model, a state equation of the nonlinear electromechanical servo system after expansion is obtained according to the estimation error and the change rate of interference, and an observation error dynamic equation is obtained according to the state equation and a bandwidth of an expansion state observer and is used for estimating the error.
Further, in the step S4, the error sign robust integral control method is used to control the actual motion trajectory of the nonlinear electromechanical servo system according to the adjustable control gain, the feedforward compensation control term of the dynamics model, the radial basis function neural network estimation term, the observation term of the extended state observer, and the robust control term.
The invention also provides a motion control device of the nonlinear electromechanical servo system, which comprises a control module, wherein the control module comprises a model control module, a radial basis function neural network module and an expansion state observation module,
the model control module establishes a dynamic model of the nonlinear electromechanical servo system, and simplifies the electrical dynamic of a motor current loop corresponding to the nonlinear electromechanical servo system to be a proportional link;
the radial basis function neural network module approximately fits uncertainty of a dynamic model of the nonlinear electromechanical servo system by using the radial basis function neural network;
the extended state observation module is combined with the dynamic model to estimate strong external time-varying disturbance of the nonlinear electromechanical servo system by using an extended state observer;
and the control module feeds back the expected motion trail of the nonlinear electromechanical servo system by adopting an error sign robust integral control method according to the estimation result, and controls the actual motion trail of the nonlinear electromechanical servo system.
Further, in the motion control device of the nonlinear electromechanical servo system, the nonlinear electromechanical servo system in the model control module is a nonlinear biaxial electromechanical servo system, a dynamic model of the nonlinear biaxial electromechanical servo system is established by using a Lagrange second class equation, nominal parameters of the nonlinear biaxial electromechanical servo system are obtained according to the dynamic model, and an uncertainty term caused by nonlinear factors, a set function of the uncertainty term and an uncertainty term set including external unknown interference are determined according to the nominal parameters.
Further, in the motion control device of a nonlinear electromechanical servo system, the radial basis function neural network module uses the following formula:
and performing approximate fitting of the radial basis function to the uncertainty of the dynamic model of the nonlinear electromechanical servo system, wherein epsilon is a neural network fitting error, f is the output of the multi-layer neural network, W is the weight between the hidden layer and the output layer of the multi-layer neural network, sigma is an activation function of the multi-layer neural network, and the radial basis function is selected as the activation function.
Further, in the motion control device of a nonlinear electromechanical servo system, the extended state observation module defines an extended state and a change rate of interference according to an estimated error of uncertainty of a dynamic model, obtains a state equation of the extended nonlinear electromechanical servo system according to the estimated error and the change rate of the interference, and obtains an observation error dynamic equation according to the state equation and a bandwidth of an extended state observer, wherein the observation error dynamic equation is used for estimating the error.
Further, in the motion control device of the nonlinear electromechanical servo system, the control module feeds back the expected motion track of the nonlinear electromechanical servo system by using an error sign robust integral control method according to the adjustable control gain, a feedforward compensation control item of a dynamics model, a radial basis neural network estimation item, an observation item of an extended state observer and a robust control item, and controls the actual motion track of the nonlinear electromechanical servo system.
The invention has the advantages that:
the invention provides a motion control method of a nonlinear electromechanical servo system, which utilizes uncertainty of a radial basis function neural network approximation servo system model, adopts an extended state observer to estimate approximation error of the radial basis function neural network and system external interference, and adopts a robust feedback method to further reduce feedforward compensation error and improve system robustness. The method can accurately track the expected motion trail under the nonlinear dynamic influence of model uncertainty, strong external time-varying disturbance and the like, and control the actual motion trail of the nonlinear electromechanical servo system.
Drawings
FIG. 1 is a schematic diagram of a closed loop control framework for a nonlinear electro-mechanical servo system in accordance with the present invention.
FIG. 2 is a schematic diagram of the motion control flow of the method of the present invention.
FIG. 3 is a schematic diagram of the tracking performance of a method of controlling a nonlinear electro-mechanical servo system according to the present invention.
FIG. 4 is a schematic diagram of tracking error compared with other methods.
FIG. 5 is a graph showing the tracking error of the method of the present invention compared to other methods at 50s to 60 s.
FIG. 6 is a schematic diagram of the estimated performance of the uncertainty of the system dynamics model involved in the method of the present invention.
Fig. 7 is a schematic diagram of the estimated performance of the system under strong external time-varying interference involved in the method of the present invention.
FIG. 8 is a schematic waveform of the input voltage of the method of the present invention.
Detailed Description
The present invention will be further described with reference to the accompanying drawings and specific examples, which are not intended to be limiting, so that those skilled in the art will better understand the invention and practice it.
The invention provides a motion control method of a nonlinear electromechanical servo system, which comprises the following steps:
step S1: establishing a dynamic model of the nonlinear electromechanical servo system, and simplifying the electrical dynamic of a motor current loop corresponding to the nonlinear electromechanical servo system into a proportional link;
step S2: performing approximate fitting on uncertainty of a dynamic model of the nonlinear electromechanical servo system by using a radial basis function neural network;
step S3: estimating strong external time-varying disturbance of the nonlinear electromechanical servo system by using an extended state observer in combination with a dynamics model;
step S4: and feeding back the expected motion trail of the nonlinear electromechanical servo system by adopting an error sign robust integral control method according to the estimation result, and controlling the actual motion trail of the nonlinear electromechanical servo system.
In specific applications, based on the technical scheme of the method, in some embodiments of the method, the nonlinear electromechanical servo system in step S1 is a nonlinear biaxial electromechanical servo system, and a dynamic model of the nonlinear biaxial electromechanical servo system is established by using a lagrangian second class equation:
in the formula, q= [ alpha beta ]] T As a state vector for the system,
positive definite matrix for inertial symmetry,>
is a Coriolis force centrifugal matrix->
The gravity term matrix is specifically expressed as follows:
nominal parameters of the kinetic model are denoted as M a0 (q),M b0 (q),M g0 (q) thus, the actual kinetic model terms are expressed as:
wherein DeltaM a (q),
ΔM g (q) is an uncertainty term caused by a nonlinear factor.
Defining state variables of a system
The nonlinear state space equation of the system can be written as:
wherein, the liquid crystal display device comprises a liquid crystal display device,
d (t) is a set function of the system model uncertainty term, and d (t) is a set of uncertainty terms including external unknown disturbances.
In addition, the motor current loop is approximated as a proportional link, and the output and input of the motor are assumed to be in proportional relation, T u Can be expressed as:
T u ＝n i k ui u i ,i＝1,2
wherein n is i The transmission ratios, k, of the directional axis and the pitch axis, respectively ui The moment amplification coefficients of the servo motor with the direction axis and the pitching axis are respectively u i The control voltage inputs of the servo motors are the directional axis and the pitch axis, respectively. Wherein nominal parameters M of the kinetic model a0 (q),M b0 (q),M g0 (q) by calculation, other unmodeled parts of the system related to the system state are also attributed to system model uncertainty
Setting a given desired trajectory x 1d And its first derivative>
Second derivative
Are all continuous and bounded, and x 1 ,x 2 All can be measured; />
And d (t) is sufficiently smooth and bounded, and
θ 1 ,θ 2 ,υ 1 ,υ 2 are all unknown normal numbers.
In the step 2, the radial basis function network approximately fits the model uncertainty of the nonlinear electromechanical servo system, has good nonlinear function approximation capability, can approximate any nonlinear function, and has strong self-learning capability and fault tolerance capability. Being able to sense the dynamics of an uncertain system, thus, combining the specificity of RISE control design, letting
Wherein epsilon is a neural network fitting error, f is the output of the multi-layer neural network, W is the weight between the hidden layer and the output layer of the multi-layer neural network, sigma is an activation function of the multi-layer neural network, and a radial basis function is selected as the activation function, which is specifically expressed as follows:
the neural network fitting error ε is set to be bounded, and
In the step 3, an extended state observer is designed by combining a radial basis function neural network to estimate strong external time-varying disturbance of a nonlinear electromechanical servo system;
uncertainty of dynamic model
Estimation by a multi-layer neural network can be provided
Defining the expansion state of the system for the estimation error of the model uncertainty in the system
And x is e ＝[x e1 x e2 ] T H (t) is the rate of change of the disturbance, i.e.>
And assuming h (t) is an unknown but bounded function. Based on the equation, the system state equation after expansion can be obtained:
the following extended state observation model can be obtained:
in the method, in the process of the invention,
for system state x 1 ,x 2 ,x e Omega, estimation of omega 0 The bandwidth of the extended state observer is the only parameter to be adjusted in the observer.
Combining the equations, the observed error dynamic equation can be obtained:
wherein, the liquid crystal display device comprises a liquid crystal display device,
to estimate the error.
Definition of the definition
The formula can be written as:
wherein:
from matrix A o It is known from the definition of (a) that it meets the Hulvitz criterion, so that there is a positive and symmetrical matrix
In the step 4, the expected motion trail of the nonlinear electromechanical servo system is fed back by adopting an error sign robust integral control method according to the estimation result, specifically:
defining a system output angle error:
z 1 ＝x 1 -x 1d
let alpha 1 Is x 2 Defining alpha 1 And x 2 The error between them is:
z 2 ＝x 2 -α 1
and because of
Virtual control input alpha 1 Is that
Wherein k is 1 ＝diag([k 11 ,k 12 ]) K is an adjustable control gain 11 ，k 12 All are positive numbers.
Due to
In->
Is a stable transfer function, when z 2 When the value goes to 0, z 1 Also necessarily tends to 0;
defining an auxiliary error signal r:
further develop r:
the following is shown:
u＝u a +u s ；u s ＝u s1 +u s2
u s1 ＝-k 2 M a0 (x 1 )z 2 -k r z 2 ；
wherein k is r ＝diag([k r1 ,k r2 ]) K is an adjustable control gain r1 ,k r2 All are positive numbers. u (u) a Feedforward compensation control term based on system model, wherein
Estimating terms for a multi-layer neural network,/->
Is an observation item of the extended state observer. u (u) s Is a robust control term, where u s1 To suppress the linear robust term of the nominal model of the system, u s2 Is a nonlinear robust term for suppressing unmodeled disturbances. And (3) making: />
The weight self-adaptive law of the multilayer neural network is as follows:
further analysis may yield:
to handle the remaining disturbances of the system, the following formula is used for the nonlinear integration robustness term:
deriving the following steps:
wherein, the liquid crystal display device comprises a liquid crystal display device,
defining an error parameter z= [ Z ] 1 ,z 2 ,r] T By the following constitution
It is structurally known that there must be a globally reversible non-decreasing normal function ρ, such that +.>
According to the pre-setting, it is possible to:
wherein mu 1 ,μ 2 ,μ 3 ,μ 4 All are normal numbers.
Defining an auxiliary function L (t), L (t) =r [ N ] d +N b -βsign(z 2 )]+z 2 N b
If beta satisfies
The function P (t) defined as follows is constant at a positive value,
and (3) proving:
the above steps are integrated in parts to obtain:
further can be obtained:
if β satisfies the above equation, the function P (t) is always positive.
Verifying system stability, and defining a Lyapunov function:
the derivation of the above is available:
from Young inequality:
further can obtain
Wherein:
is->
Less than 0, it is necessary to satisfy C as a positive number, i.e. +.>
According to the formula, V (t) is less than or equal to V (0) and V E L in any time (t is more than or equal to 0) ∞
Thus z 1 ,z 2 R are all bounded.
The method can be proved to be capable of stably controlling the motion trail of the nonlinear biaxial electromechanical servo system.
The verification process can refer to the electromechanical servo system parameter size selection in the simulation as follows:
the inertial tensor matrix parameters are:
J o1yy ＝2547kg·m 2 ,J o2xx ＝5400kg·m 2 ,J o2yy ＝5443kg·m 2 ,x o2 ＝0.367
J o2zz ＝224kg·m 2 ,J o2xy ＝2.8kg·m 2 ,m 2 ＝2000kg
the desired motion profile for a given system is
The time-varying disturbance of the simulation becomes d 2 =2000 sin (t) (N/M), model uncertainty takes Δm a (q)＝0.2M a (q),
ΔM g (q)＝0.2M g (q)
RBFESORISE, which represents the high performance control method designed by the invention, the control parameters are selected as
k 11 ＝69,k 12 ＝60,k 21 ＝66,k 22 ＝60,k r1 ＝150,k r2 ＝10,β 1 ＝8,β 1 ＝10,c＝[-1,-0.5,0,0.5,1] T ,b＝3,Γ＝[2×10 6 ,8×10 5 ] T ,ω＝[400,500] T
RBFRISE represents the method of the invention but has no state observer, and the comparison is mainly set for verifying the disturbance compensation performance of the method of the invention on strong external time-varying disturbance, and the control parameters selected for the method of the invention are identical to those of RBFESORISE for fair comparison.
RISE is a representation of the method of the invention but without RBF neural network and ESO, and the comparison is mainly set for verifying the compensation performance of the high-performance controller designed by the invention on strong external time-varying disturbance and uncertain model, and the selected control parameters are identical to RBFESORISE for fair comparison.
The method has the following effects: fig. 3 is a graph of tracking performance of an actual track under the action of the method of the present invention, fig. 4 is a graph of tracking error under the action of the method of the present invention compared with other controllers, fig. 5 is a graph of tracking error under the action of the method of the present invention compared with other controllers at 50s to 60s, and it can be seen with reference to fig. 3, fig. 4 and fig. 5 that steady-state tracking error is smaller and error curve is smoother under the action of the method of the present invention, thereby verifying effectiveness of RBFESO control performance. Fig. 5 is an estimated performance diagram of uncertainty of a system model under the action of the method, and fig. 6 is an estimated performance diagram of strong external time-varying interference of the system under the action of the method, and it can be seen from the diagram that the estimated performance diagrams finally approach true values respectively, so that disturbance in the system can be estimated effectively. Fig. 7 shows the magnitude of the input voltage of the controller under the action of the method of the invention, and it can be seen from the figure that the magnitude of the input voltage of the controller obtained by the method is continuously conductive and bounded, which is beneficial to practical engineering application.
The invention also provides a motion control device of the nonlinear electromechanical servo system, which comprises a control module, wherein the control module comprises a model control module, a radial basis function neural network module and an expansion state observation module,
the model control module establishes a dynamic model of the nonlinear electromechanical servo system, and simplifies the electrical dynamic of a motor current loop corresponding to the nonlinear electromechanical servo system to be a proportional link;
the radial basis function neural network module approximately fits uncertainty of a dynamic model of the nonlinear electromechanical servo system by using the radial basis function neural network;
the extended state observation module is combined with the dynamic model to estimate strong external time-varying disturbance of the nonlinear electromechanical servo system by using an extended state observer;
and the control module feeds back the expected motion trail of the nonlinear electromechanical servo system by adopting an error sign robust integral control method according to the estimation result, and controls the actual motion trail of the nonlinear electromechanical servo system.
The content of information interaction and execution process between the modules in the device is based on the same conception as the embodiment of the method of the present invention, and specific content can be referred to the description in the embodiment of the method of the present invention, which is not repeated here.
Similarly, the device utilizes the uncertainty of the radial basis function neural network approximation servo system model, adopts the extended state observer to estimate the approximation error of the radial basis function neural network and the external interference of the system, and adopts the robust feedback method to further reduce the error of feedforward compensation and improve the robustness of the system. The device can accurately track the expected motion trail under the nonlinear dynamic influence of model uncertainty, strong external time-varying disturbance and the like, and control the actual motion trail of the nonlinear electromechanical servo system.
It should be noted that not all the steps and modules in the above processes and the structures of the devices are necessary, and some steps or modules may be omitted according to actual needs. The execution sequence of the steps is not fixed and can be adjusted as required. The system structure described in the above embodiments may be a physical structure or a logical structure, that is, some modules may be implemented by the same physical entity, or some modules may be implemented by multiple physical entities, or may be implemented jointly by some components in multiple independent devices.
The above-described embodiments are merely preferred embodiments for fully explaining the present invention, and the scope of the present invention is not limited thereto. Equivalent substitutions and modifications will occur to those skilled in the art based on the present invention, and are intended to be within the scope of the present invention. The protection scope of the invention is subject to the claims.
Claims (10)
1. A motion control method of a nonlinear electromechanical servo system is characterized by comprising the following steps of S1: establishing a dynamic model of the nonlinear electromechanical servo system, and simplifying the electrical dynamic of a motor current loop corresponding to the nonlinear electromechanical servo system into a proportional link;
step S2: performing approximate fitting on uncertainty of a dynamic model of the nonlinear electromechanical servo system by using a radial basis function neural network;
step S3: estimating strong external time-varying disturbance of the nonlinear electromechanical servo system by using an extended state observer in combination with a dynamics model;
step S4: and feeding back the expected motion trail of the nonlinear electromechanical servo system by adopting an error sign robust integral control method according to the estimation result, and controlling the actual motion trail of the nonlinear electromechanical servo system.
2. The motion control method of a nonlinear electromechanical servo system according to claim 1, wherein the nonlinear electromechanical servo system in the step S1 is a nonlinear biaxial electromechanical servo system, a dynamic model of the nonlinear biaxial electromechanical servo system is established by using a lagrangian second class equation, nominal parameters of the nonlinear biaxial electromechanical servo system are obtained according to the dynamic model, and an uncertainty term set including an uncertainty term caused by nonlinear factors, a set function of the uncertainty term and external unknown interference is determined according to the nominal parameters.
3. The method for controlling motion of a nonlinear electromechanical servo system according to claim 1 or 2, wherein the following formula is used in the step S2:
and performing approximate fitting of the radial basis function to the uncertainty of the dynamic model of the nonlinear electromechanical servo system, wherein epsilon is a neural network fitting error, f is the output of the multi-layer neural network, W is the weight between the hidden layer and the output layer of the multi-layer neural network, sigma is an activation function of the multi-layer neural network, and the radial basis function is selected as the activation function.
4. The method according to claim 1, wherein in the step S3, the expansion state and the disturbance change rate are defined according to the estimation error of the uncertainty of the dynamics model, the state equation of the expanded nonlinear electromechanical servo system is obtained according to the estimation error and the disturbance change rate, and the observation error dynamic equation is obtained according to the state equation and the bandwidth of the expansion state observer for error estimation.
5. The motion control method of a nonlinear electromechanical servo system according to claim 1, wherein in the step S4, the actual motion trajectory of the nonlinear electromechanical servo system is controlled by feeding back the desired motion trajectory of the nonlinear electromechanical servo system according to an adjustable control gain, a feedforward compensation control term of a dynamics model, a radial basis neural network estimation term, an observation term of an extended state observer, and a robust control term by using an error sign robust integral control method.
6. The motion control device of the nonlinear electromechanical servo system is characterized by comprising a control module, wherein the control module comprises a model control module, a radial basis function neural network module and an expansion state observation module,
the model control module establishes a dynamic model of the nonlinear electromechanical servo system, and simplifies the electrical dynamic of a motor current loop corresponding to the nonlinear electromechanical servo system to be a proportional link;
the radial basis function neural network module approximately fits uncertainty of a dynamic model of the nonlinear electromechanical servo system by using the radial basis function neural network;
the extended state observation module is combined with the dynamic model to estimate strong external time-varying disturbance of the nonlinear electromechanical servo system by using an extended state observer;
and the control module feeds back the expected motion trail of the nonlinear electromechanical servo system by adopting an error sign robust integral control method according to the estimation result, and controls the actual motion trail of the nonlinear electromechanical servo system.
7. The motion control device of a nonlinear electromechanical servo system according to claim 6, wherein the nonlinear electromechanical servo system in the model control module is a nonlinear biaxial electromechanical servo system, a dynamic model of the nonlinear biaxial electromechanical servo system is established by using a lagrangian second class equation, nominal parameters of the nonlinear biaxial electromechanical servo system are obtained according to the dynamic model, and an uncertainty term set including an uncertainty term caused by nonlinear factors, a set function of the uncertainty term and external unknown interference is determined according to the nominal parameters.
8. A motion control device for a nonlinear electro-mechanical servo system in accordance with claim 6 or 7, wherein said radial basis function neural network module utilizes the following formula:
and performing approximate fitting of the radial basis function to the uncertainty of the dynamic model of the nonlinear electromechanical servo system, wherein epsilon is a neural network fitting error, f is the output of the multi-layer neural network, W is the weight between the hidden layer and the output layer of the multi-layer neural network, sigma is an activation function of the multi-layer neural network, and the radial basis function is selected as the activation function.
9. The motion control device of a nonlinear electro-mechanical servo system according to claim 6, wherein the extended state observation module defines an extended state and a change rate of disturbance according to an estimated error of uncertainty of a dynamics model, obtains a state equation of the extended nonlinear electro-mechanical servo system according to the estimated error and the change rate of disturbance, and obtains an observation error dynamic equation according to the state equation and a bandwidth of an extended state observer for error estimation.
10. The motion control device of the nonlinear electro-mechanical servo system according to claim 6, wherein the control module uses an error sign robust integral control method to control an actual motion trajectory of the nonlinear electro-mechanical servo system according to an adjustable control gain, a feedforward compensation control term of a dynamics model, a radial basis neural network estimation term, an observation term of an extended state observer, and a robust control term to feed back an expected motion trajectory of the nonlinear electro-mechanical servo system.
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