RSLQR tracking control method based on model LESO

Abstract

The invention discloses an RSLQR tracking control method based on a model LESO, and the method comprises the steps: enabling the information of a controlled object model to be integrated into a parameter setting process of an extended state observer, reducing the observation burden of the observer, improving the anti-interference inhibition capability of a system, and achieving the estimation and compensation of the disturbance of the system; a robust servo linear quadratic optimal control method RSLQR is adopted to replace a PD controller in a traditional linear extended state observer LESO architecture, a tracking error is added to RSLQR control output to a quantity fed back by a system state, the dynamic response performance of a system is improved, and the RSLQR is obtained on the basis of an LQR method. The system deviation is adjusted to zero by introducing a system error integral term, so that a system state variable can accurately track an input command. According to the method disclosed by the invention, the dynamic response performance such as rise time and adjustment time and the anti-interference suppression capability of the system are remarkably improved.

Description

Technical Field

[0001] The present invention relates to the field of disturbance suppression. A proposed RSLQR tracking control method based on model LESO aims to improve the dynamic response performance of the system, such as rise time and adjustment time, and the disturbance suppression capability of the system. Background Art

[0002] In actual engineering applications, the system is often affected by external disturbances and its own internal uncertainties, which seriously affect the stability and control effect of the system. At present, the main popular methods in the control community are measurement-based direct feedforward methods (Xue W, Bai W, Yang S, et al. ADRC with adaptive extended state observer and its application to air-fuel ratio control in gasoline engines [J]. IEEE Transactions on Industrial Electronics, 2015, 62 (9): 5847-5857.), multi-closed-loop control loop methods (Tian J, Yang W, Peng Z, et al. Application of MEMS accelerometers and gyroscopes in fast steering mirror control systems [J]. Sensors, 2016, 16 (4): 440.), system type improvement methods (Liu C, Duan QW, Zhang C, et al. Extending the LQR to the design of PID type-ii and type-iii control loops [J]. IET Control Theory & Applications, 2023, 17 (6): 713-743.), and disturbance observer (DOB) compensation methods (Tang T, Niu S, Chen X,et al.Disturbance observer-based control of tip-tilt mirror formitigating telescope vibrations[J].IEEE Transactions on Instrumentation and Measurement,2018,68(8):2785-2791.) and automatic disturbance rejection control method (Liu Chao,Wang Hao Lin,QiuXiao Xia,et al.The RSLQR control method based on the linear extended stateobserver in the electro optical tracking system[J].IEEE Photonics Journal,2024.) to improve the disturbance suppression ability of the system. The direct feedforward method based on measurement needs to accurately measure and identify the disturbance transfer characteristics of the system, which is limited by the performance of the sensor. In the multi-closed-loop control loop method, the total disturbance suppression ability of the system is the superposition of the effects of each loop, but this method requires the installation of additional inertial sensors on the system, which is not conducive to the requirements of system rapidity and small inertia, and increases the space and cost of the experimental platform. Although the method of improving the system type can effectively suppress the disturbance of the system, the improvement of the system type will reduce the stability margin of the system and cause the stability problem of the system. Therefore, the high-type system is prone to instability in the actual working process. In the compensation method based on the disturbance observer, the compensation disturbance can be estimated by the observer, but this method requires accurate measurement of the characteristics of the controlled object, and the design of the compensator is often limited by this. The self-disturbance rejection control method does not require an accurate model of the controlled object. Its internal extended state observer classifies the external disturbance and the internal uncertainty of the system as the total disturbance of the system, and expands it into a state variable for observation and compensation. In actual engineering applications, as the frequency of external disturbances increases, the accuracy of the traditional extended state observer will decrease on the basis of a certain observer bandwidth, that is, the disturbance suppression ability of the system will decrease. In addition, the dynamic response performance of the traditional LESO system, such as system rise time, adjustment time, overshoot, etc., has not achieved satisfactory results. Summary of the invention

[0003] In view of the above problems existing in the prior art, the present invention provides a RSLQR tracking control method based on model LESO, which integrates the model information of the controlled object into the parameter setting work of the extended state observer, reduces the observation burden of the observer, and improves the anti-disturbance suppression ability of the system; as for the improvement of the dynamic response performance of the system, the present invention adopts the RSLQR control method to replace the traditional PD controller in the self-disturbance rejection control framework, and adds the tracking error to the amount of system state feedback in the RSLQR control output. This can further improve the response speed of the system. The RSLQR control method is based on the LQR method, and adjusts the system deviation to zero by introducing the system error integral term, so that the system state variable can accurately track the input command. The optimal control law obtained by the LQR method has many excellent characteristics, including closed-loop stability and when the system process is single-input and single-output, the system phase margin under the control of the LQR method is at least 60°, and the system amplitude margin is infinite. In addition, the balance between the state adjustment requirement and the control energy consumption can be controlled by adjusting the weighting matrix in the LQR control method. The present invention not only solves the problem of selecting the criterion of the weighted matrix in the RSLQR control method, but also significantly improves the dynamic response performance of the system such as the rise time and the adjustment time, as well as the anti-interference suppression capability of the system.

[0004] To achieve the above object, the present invention provides the following technical solutions:

[0005] A RSLQR tracking control method based on model LESO integrates the model information of the controlled object into the parameter tuning process of the extended state observer, reduces the observation burden of the observer and improves the anti-disturbance suppression capability of the system while realizing system disturbance estimation and compensation; adopts the robust servo linear quadratic optimal control method RSLQR to replace the PD controller in the traditional linear extended state observer LESO architecture, and adds the tracking error to the system state feedback in the RSLQR control output to improve the system dynamic response performance. The RSLQR is based on the LQR method, and adjusts the system deviation to zero by introducing the system error integral term, so that the system state variable can accurately track the input command.

[0006] Furthermore, the method comprises the following steps:

[0007] Step 1: Obtain the position transfer function of the controlled object, establish the differential equation of the controlled object in the transfer function, select the system state and transform the position transfer function of the controlled object into the form of an extended state space equation;

[0008] Step 2: Design a linear extended state observer LESO based on the model information of the controlled object according to the extended state space equation;

[0009] Step 3: Design a gain matrix of the model-based extended state observer within a predetermined frequency range to estimate and compensate for uncertain disturbances through the extended state;

[0010] Step 4: Based on the LQR method, a system error integral term that can adjust the system deviation to zero is introduced to design the controller RSLQR, and the tracking error is added to the system state feedback in the output of the controller RSLQR to achieve system control after disturbance compensation.

[0011] Furthermore, in step 1, a frequency response curve of the controlled object is obtained through a frequency response test, and a position transfer function of the controlled object is obtained through fitting.

[0012] Furthermore, in step 1, the expanded state space equation is:

[0013]

[0014] Among them, x represents the system state; y represents the output of the system; A represents the state transfer matrix; B represents the control matrix; C represents the system output matrix; h represents the differential of the total disturbance of the system; u represents the control signal; E is the coefficient matrix before the differential term of the total disturbance of the system; Represents the differential of the system state.

[0015] Further, in step 2, the linear extended state observer LESO based on the controlled object model information is:

[0016]

[0017] in, is the differential of the observer state; A represents the state transfer matrix; B represents the control matrix; C represents the system output matrix; y c is the output of the extended state observer; z is the observer state vector; L is the observer gain matrix that needs to be determined; u c is the observer input combination.

[0018] Furthermore, in step 3, the gain matrix of the model-based extended state observer is:

[0019] β1=3ω o -a, β2=3ω o 2 -3aω o -b+a 2 , β3=ω o 3

[0020] Where a = 2ζ ol ω ol , ζ ol ,ω ol are the damping ratio and natural frequency of the open loop system respectively; ω o is the observer bandwidth.

[0021] Furthermore, in step 4, the controller RSLQR is finally expressed as:

[0022] u(t)=-K(x+Nr)-K I x I

[0023] Where K represents the gain coefficient before the position state of the controlled object; x represents the system state; N represents the gain matrix; r is the system reference input; K I Represents the tracking error integral state x I The previous gain factor.

[0024] Compared with the prior art, the present invention has the following beneficial effects:

[0025] 1. Compared with the traditional extended state observer method, the dynamic response performance and anti-interference suppression ability of the system under the method of the present invention are significantly improved;

[0026] 2. Compared with the RSLQR method, the method of the present invention adds the tracking error to the system state feedback in the RSLQR control output, improving the dynamic response performance of the system such as the rise time and adjustment time;

[0027] 3. Compared with the RSLQR method based on LESO, the dynamic response performance and anti-interference suppression ability of the system are improved under the method of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 The block diagram of RSLQR tracking control based on model LESO;

[0029] Figure 2 It is the control block diagram of model-based LESO;

[0030] Figure 3 It is the RSLQR tracking control block diagram;

[0031] Figure 4 This is a comparison chart of step responses of different control methods under 5sin(5t) sinusoidal disturbance;

[0032] Figure 5 This is a comparison chart of step responses of different control methods under step disturbance. DETAILED DESCRIPTION

[0033] The present invention will be further described in detail below in conjunction with the accompanying drawings.

[0034] A RSLQR tracking control method based on model LESO is implemented in the following steps:

[0035] The optimal control design of RSLQR based on model LESO in the following fast mirror model is mainly divided into the model LESO observer design part and the RSLQR controller design part.

[0036]

[0037] where a = 2ζ ol ω ol , ζ ol ,ω ol are the damping ratio and natural frequency of the system open loop respectively; b0 is the open loop gain of the system.

[0038] Step 1: Establish the differential equation of the fast mirror controlled object in formula 1 as follows:

[0039]

[0040] in Indicates part of the model information identified; because the system parameters a and b are not accurately identified in practical applications, f x represents the part where the modeling is inaccurate and the part where the internal dynamics change; f w represents external disturbance; is the combined effect of known model dynamics and unknown disturbances.

[0041] Select system state x1=y, x3=f′=f x +f w Respectively represent the deflection angle, angular velocity and total disturbance of the fast mirror, and transform the above differential equation into the following expanded state space equation form:

[0042]

[0043] in C=[1 0 0],

[0044] Step 2: Design the continuous extended state observer LESO based on the model information according to the system extended state space equation as shown below:

[0045]

[0046] where z = [z1 z2 z3] T is the observer state vector; L = [β1β2β3] T is the observer gain matrix that needs to be determined; u c =[uy] T is the observer input combination; y c is the output of the extended state observer.

[0047] Step 3: Within a certain frequency range, the extended state observer based on model information accurately estimates the uncertain disturbance f′ and compensates the extended state z3, as Figure 2 As shown. The control signal u is:

[0048] u=u0-z3 / b0≈u0-(f x +f w ) / b0 (5)

[0049] Substituting formula 5 into formula 2, the differential equation of the fast mirror system can be further transformed into

[0050]

[0051] Therefore, after eliminating unnecessary interference, the system becomes

[0052]

[0053] The system in Equation 7 can be reformulated as the following transfer function:

[0054]

[0055] It can be seen that the system transfer function in Formula 8 contains the same model information as the model in Formula 1. Assuming that the system observation error state variable e(t) = x(t) - z(t), subtract Formula 4 from Formula 3, the observer error matrix equation is

[0056]

[0057] From the above formula, we can see that (A-LC) in the observer error matrix equation determines the eigenvalue of the closed-loop system. The characteristic equation corresponding to the observer error matrix equation is as follows:

[0058] |sI-(A-LC)|=s 3 +(a+β1)s 2 +(b+β2+aβ1)s+β3 (10)

[0059] According to the conclusion of the literature (Chen Z, Jia H. Design of flight control system for a novel tilt-rotor UAV [J]. Complexity, 2020, 2020.), after parameterization of LESO based on model information, the poles of the corresponding characteristic equation can be placed in the same position (-w0, w0 is the observer bandwidth), as shown below:

[0060] |sI-(A-LC)|=(s+ω o ) 3 =s 3 +3ω o s 2 +3ω o 2 s+ω o 3 (11)

[0061] Comparing the coefficients before the same variables on the right side of Formula 10 and Formula 11, the parameters of the observer gain matrix L are

[0062] β1=3ω o -a, β2=3ω o 2 -3aω o -b+a 2 , β3=ω o 3 (12)

[0063] Step 4: Design the RSLQR controller for the fast-reflection mirror controlled object model in Formula 1. Its linear state space equation is expressed as follows:

[0064]

[0065] Where A1, B1, x represent the state transfer matrix, control matrix and system state respectively; y represents the output of the system; C1 is the system output matrix.

[0066] Select the system position state x1(t) and speed state x2(t), then A1, B1, and C1 in formula 13 are modeled as follows:

[0067]

[0068] The RSLQR method is based on the LQR method by introducing a new variable x I To the system, x I satisfy This adjusts the system deviation to zero, allowing the system state variables to accurately track the input command. Therefore, the state space equation of the augmented system is expressed as follows:

[0069]

[0070] in Respectively represent the state variables of the system and the integral term of the tracking error;

[0071]

[0072] The quadratic optimal cost function of the above augmented system is as follows:

[0073]

[0074] Where R xx , R uu are the system state weighting matrix and the control weighting matrix respectively. By selecting the weighting matrix R xx and R uu To meet the performance requirements of control design, the matrix R is generally selected uu As the identity matrix, choose the matrix R xx as a diagonal matrix.

[0075] The traditional RSLQR controller in Equation 16 is expressed as follows:

[0076]

[0077] in represents the RSLQR controller gain; K1, K2, K IThey represent the gain coefficients before the position state, velocity state and tracking error integration state of the controlled object respectively; P is the symmetric positive definite solution of the following Riccati equation.

[0078]

[0079] It can be seen from formula 15 that the response of the traditional RSLQR control method (Liu Chao, Wang Hao Lin, Qiu XiaoXia, et al. The RSLQR control method based on the linear extended state observer in the electro optical tracking system [J]. IEEE Photonics Journal, 2024.) to the system reference input is driven by the error integral and the system state, ignoring the direct impact of the reference input on the system drive. This may reduce the response speed of the system, thereby affecting the performance requirements of the system. Therefore, this patent adds the tracking error to the system state feedback in the RSLQR control output, Figure 3 The RSLQR controller in is expressed as follows:

[0080]

[0081] in represents the irrelevant part of the system state; N represents the gain matrix.

[0082] Substituting y in Formula 13 into Formula 19, the RSLQR controller in this patent can be further expressed as

[0083]

[0084] Assume that the system state x can be divided into the tracking part Tx that we are interested in (the output y is directly available) and the part that we are not interested in Among them, T and represents a selection matrix with 1s and 0s on the diagonal and satisfies If NC = -T, then The RSLQR controller is finally expressed as

[0085] u(t)=-K(x+Nr)-K I x I (twenty one)

[0086] Where N = -λC T ,λ<1.

[0087] Step 5: Determine the system state weighting matrix R xx, control weight matrix R uu and the parameters of the matrix P; assuming that the system state weighting matrix R xx , control weight matrix R uu And the matrix P is designed as follows

[0088]

[0089] Substituting formula 15 and 22 into formula 17, we can get

[0090] u(t)=-b0σ -1 (p 12 x1(t) p 22 x2(t) p 23 x3(t)) (23)

[0091] Therefore, the RSLQR controller gain is

[0092]

[0093] Substituting the improved RSLQR control u(t) in the above formula 21 into the augmented system state equation of formula 15, the state space equation of the closed-loop system is as follows:

[0094]

[0095] in

[0096]

[0097] The corresponding closed-loop system characteristic equation is as follows:

[0098]

[0099] Since the system matrix A F Since there is no time delay in the system, the pole placement method can be directly applied to obtain the desired closed-loop performance of the system, that is, by establishing the characteristic equation of the closed-loop system Δ(s) equal to the required closed-loop equation.

[0100] When the system matrix A F When it is a 2×2 matrix, the closed-loop system characteristic equation Δ(s) is as follows:

[0101]

[0102] in ζ cl ,ω cl are the damping ratio and natural frequency of the desired system.

[0103] When the system matrix A FWhen it is a 3×3 matrix, using the dominant pole placement method, the closed-loop system characteristic equation Δ(s) is as follows:

[0104]

[0105] The non-dominant pole p3 should be far away from the real part of the other two complex (conjugate) closed-loop main poles p1 and p2, so as to meet the requirements of the controller pole configuration. According to the results of relevant literature (He JB, Wang QG, Lee T H. PI / PID controller tuning via LQR approach [J]. Chemical Engineering Science, 2000, 55 (13): 2429-2439. and Liu C, Duan QW, Zhang C, et al. Extending the LQR to the design of PID type-ii and type-iii control loops [J]. IET Control Theory & Applications, 2023, 17 (6): 713-743.), the value of the relative dominance m should be 3 times or more of the real part of the closed-loop main pole.

[0106] Comparing the coefficients before the same state variable on the right side of Formula 26 and Formula 28, we can get

[0107]

[0108] Solve the Riccati equation in Equation 18, the remaining elements of the P matrix and R xx The elements of the matrix are as follows:

[0109]

[0110] The specific implementation steps of the present invention are described in detail below in conjunction with the specific parameters of the fast-reflection mirror system:

[0111] Step 1: The fast mirror system operates at a sampling frequency of 5000 Hz. The frequency response curve of the controlled object is obtained through frequency response testing, and the position transfer function of the controlled object is obtained through fitting:

[0112]

[0113] Select system state x1=y, x3=f′=f x +f w They represent the deflection angle, angular velocity and total disturbance of the fast mirror respectively, and the position transfer function of the controlled object is transformed into the following extended state space equation form:

[0114]

[0115] in C=[1 0 0],

[0116] Step 2: Design a model-based continuous extended state observer based on the extended state space equation as shown below:

[0117]

[0118] where z = [z1 z2 z3] T is the observer state vector; L = [β1β2β3] T is the observer gain matrix that needs to be determined; u c =[uy] T is the observer input combination; y c is the output of the extended state observer.

[0119] Step 3: According to formula 12, the gain matrix L of the model-based extended state observer is designed as:

[0120] β1=3ω o -25.6, β2=3ω o 2 -76.8ω o -765.84, β3 = ω o 3 (34)

[0121] where ω o is the observer bandwidth.

[0122] Step 4: Based on the model-based extended state observer, design the RSLQR controller to achieve system control after disturbance compensation, such as Figure 1 As shown. Selecting the system position state x1(t), velocity state x2(t) and the integral of the system error x3(t), the state space equation of the RSLQR augmented system of the fast mirror controlled object model in formula 31 is expressed as follows:

[0123]

[0124] in

[0125]

[0126] The quadratic optimal cost function of the above augmented system is as follows:

[0127]

[0128] Where Rxx , R uu are the system state weighting matrix and the control weighting matrix respectively. By selecting the weighting matrix R xx and R uu To meet the performance requirements of control design, the matrix R is generally selected uu As the identity matrix, choose the matrix R xx as a diagonal matrix.

[0129] like Figure 3 As shown in the RSLQR controller in FIG. 1 , the present invention adds the tracking error to the system state feedback in the RSLQR control output:

[0130] u(t)=-K(x+Nr)-K I x I (37)

[0131] Where r is the system reference input; N = -λC T represents the gain matrix and λ<1, λ=0.5 in the simulation of the present invention; K and K I They represent the state of the controlled object and the tracking error integral state x I The previous gain factor.

[0132] In order to verify the effectiveness of the RSLQR method in the present invention, a traditional RSLQR controller as shown below is designed for comparison:

[0133]

[0134] in represents the RSLQR controller gain; K1, K2, K I They represent the gain coefficients before the position state, velocity state and tracking error integration state of the controlled object respectively; P is the symmetric positive definite solution of the following Riccati equation.

[0135]

[0136] Similarly, in order to ensure fairness in comparison with different control methods, the observer bandwidth ω in the simulation is o All are set to 40Hz. In addition, according to the literature (Liu Chao, Wang Hao Lin, Qiu Xiao Xia, et al. The RSLQR control method based on the linear extended state observer in the electro-optical tracking system [J]. IEEE Photonics Journal, 2024.) uuAll take the unit matrix; the system expected damping ratio ζ cl , natural frequency ω cl and the relative advantage m are both ζ cl =1.25,ω cl =17,m=100.

[0137] By using formula 24, the RSLQR controller gain parameters adjusted by the method of the present invention are as follows:

[0138]

[0139] Through formulas 29 and 30, the P matrix elements and R xx The elements of the matrix are calculated as follows:

[0140]

[0141] It can be seen that the system state weight matrix R xx The eigenvalues ​​of are all greater than zero, which meets the prerequisite requirement of using the LQR method.

[0142] Figure 4 The system step response of different control methods under the sinusoidal disturbance 5sin(5t) is given. It can be seen that compared with the traditional LESO method and the RSLQR method based on LESO, the dynamic response performance of the system such as the rise time and adjustment time and the disturbance suppression ability of the system under the method of the present invention are significantly improved; compared with the RSLQR method based on model LESO, the disturbance suppression ability of the system under the method of the present invention is consistent with that under the RSLQR method based on model LESO, but the dynamic response performance of the system such as the rise time and adjustment time is significantly improved. This is because the method of the present invention adds the tracking error to the system state feedback in the RSLQR control output, which can play a role in accelerating and improving the dynamic response performance of the system. Compared with the RSLQR method based on LESO, the dynamic response performance of the system such as the rise time and adjustment time and the disturbance suppression ability of the system are improved in the RSLQR method based on model LESO. This shows that after the introduction of the controlled object model information in the design of the extended state observer, the observation burden of the observer is reduced, the observation accuracy of the observer is improved, and the disturbance suppression ability of the system is improved. At the same time, the dynamic response performance of the system such as the rise time and adjustment time is also indirectly improved. The method of the present invention combines the advantages of the LESO design of the model and adds the tracking error to the system state feedback in the RSLQR control output to improve the system dynamic response performance and disturbance suppression capability.

[0143] In order to further illustrate the effectiveness of the method of the present invention, Figure 5A 5-fold unit step disturbance was applied at 8 seconds of simulation time, and the step responses of different control methods were compared. Compared with the traditional LESO method, the RSLQR method based on LESO, and the RSLQR method based on model LESO, it can be obtained that Figure 4 The same conclusion is reached in .

[0144] In summary, the present invention provides a RSLQR tracking control method based on model LESO, the steps of which include: designing linear extended state observer parameters based on the model information of the controlled object, estimating and compensating the system disturbance; in order to improve the dynamic response performance such as the system rise time and adjustment time, the present invention adopts the robust servo linear quadratic optimal control (RSLQR) method to replace the PD controller in the traditional linear extended state observer (LESO) architecture. The response of the traditional RSLQR control method to the system reference input is driven by the error integral and the system state, ignoring the direct influence of the reference input on the system drive, which may reduce the response speed of the system and thus affect the performance requirements of the system. Therefore, the RSLQR controller of the present invention adds the amount of tracking error to the system state feedback. The present invention takes the second-order optoelectronic tracking system as an example to illustrate the effectiveness of the method of the present invention. Compared with the traditional LESO method and the RSLQR tracking control method based on LESO, the dynamic response performance of the system rise time, adjustment time and the system anti-interference ability under the design method of the present invention are significantly improved.

[0145] The specific implementation methods, processes and effects of the present invention are described in detail above with reference to the accompanying drawings and examples, but the described content is only an embodiment of the present method and cannot limit the implementation scope of the method.

Claims

1. A RSLQR tracking control method based on model LESO, characterized in that: By incorporating the controlled object model information into the extended state observer parameter tuning process, the observation burden of the observer is reduced and the system's anti-interference ability is improved while achieving system disturbance estimation and compensation; by adopting the robust servo linear quadratic optimal control method RSLQR to replace the PD controller in the traditional linear extended state observer LESO architecture, and adding the tracking error to the system state feedback in the RSLQR control output, the dynamic response performance of the system is improved. The RSLQR is based on the LQR method and introduces a system error integral term to adjust the system deviation to zero, so that the system state variables can accurately track the input command.

2. The RSLQR tracking control method based on model LESO according to claim 1 is characterized in that: The steps include: Step 1: Obtain the position transfer function of the controlled object, establish the differential equation of the controlled object in the transfer function, select the system state and transform the position transfer function of the controlled object into the form of an extended state space equation; Step 2: Design a linear extended state observer LESO based on the model information of the controlled object according to the extended state space equation; Step 3: Design the gain matrix of the model-based extended state observer within the predetermined frequency range, and estimate and compensate for the uncertain disturbance through the extended state; Step 4: Based on the LQR method, a system error integral term that can adjust the system deviation to zero is introduced to design the controller RSLQR, and the tracking error is added to the system state feedback in the output of the controller RSLQR to achieve system control after disturbance compensation.

3. The RSLQR tracking control method based on model LESO according to claim 2 is characterized in that: In step 1, the frequency response curve of the controlled object is obtained through frequency response testing, and the position transfer function of the controlled object is obtained through fitting.

4. The RSLQR tracking control method based on model LESO according to claim 2 is characterized in that: In step 1, the expanded state space equation is: Among them, x represents the system state; y represents the output of the system; A represents the state transfer matrix; B represents the control matrix; C represents the system output matrix; h represents the differential of the total disturbance of the system; u represents the control signal; E is the coefficient matrix before the differential term of the total disturbance of the system; Represents the differential of the system state.

5. The RSLQR tracking control method based on model LESO according to claim 2 is characterized in that: In step 2, the linear extended state observer LESO based on the controlled object model information is: in, represents the differential of the observer state vector, A represents the state transfer matrix; B represents the control matrix; C represents the system output matrix; y c is the output of the extended state observer; z is the observer state vector; L is the observer gain matrix that needs to be determined; u c is the observer input combination.

6. The RSLQR tracking control method based on model LESO according to claim 2 is characterized in that: In step 3, the gain matrix of the model-based extended state observer is: β1=3ω o -a, β2=3ω o 2 -3aoh o -b+a 2 ,β3=ω o 3 Where a = 2ζ ol ω ol , ζ ol ,ω ol are the damping ratio and natural frequency of the open loop system respectively; ω o is the observer bandwidth.

7. The RSLQR tracking control method based on model LESO according to claim 2 is characterized in that: In step 4, the controller RSLQR is finally expressed as: u(t)=-K(x+Nr)-K I x I Where K represents the gain coefficient before the position state of the controlled object; x represents the system state; N represents the gain matrix; r is the system reference input; K I Represents the tracking error integral state x I The previous gain factor.

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