A remote servo motor tracking control method based on backstepping

Abstract

The present invention relates to the establishment of a remote servo motor system model containing external disturbances and the design of a remote servo motor system tracking algorithm. The present invention discloses a remote servo motor system modeling considering external disturbances and a remote servo motor system backstepping tracking algorithm design. Its technology includes remote servo motor system modeling considering external disturbances, quasi-state observer design, external disturbance estimation, event trigger mechanism design, backstepping tracking controller design and system stability proof. The present invention establishes a gear transmission system model with dead zone nonlinear characteristics for a remote servo motor system with external interference, and estimates the disturbance. According to its system characteristics, a backstepping tracking controller based on an event trigger mechanism is designed, and the stability of its control is analyzed and proved. The present invention can effectively solve the problem of the remote servo motor system stably tracking a reference signal when the system model exists with external disturbances.

Description

Technical Field

[0001] The present invention designs a tracking control method involving a remote servo motor by establishing a remote servo motor system model under external disturbance. Background Art

[0002] Servo motor systems have the advantages of remote control, ease of use, high tracking performance, and high work efficiency, making them a hot topic for scholars and widely used in various fields, including automated factories, robots, electric vehicles, etc. With the development of network technology and artificial intelligence, remote control and networked control of servo motor systems have gradually become emerging hotspots. Among them, the external disturbance problem involved in remote control is still a challenge, so it is crucial to establish a remote servo motor model considering external disturbances and design a robust tracking control algorithm. In response to the external disturbance problem, the literature [“Robust position anti-interference control for PMSM servo system with uncertain disturbance” (L. Li et al, CES Transactions on Electrical Machines and Systems, 2020, 4 (2): 151-160)] studied a nonlinear disturbance observer, and realized robust control of the permanent magnet synchronous motor servo system by compensating the system based on the observation results of the disturbance observer. However, the problem of network resource waste in the control process was not considered. The literature [“Dynamic event-triggered smc of multi-agent systems for consensus tracking” (R. Nie, W. He, W. Du, Z. Lang and S. He, IEEE Transactions on Circuits and Systems II: Express Briefs, 69(3): 1188-1192)] studied the event trigger mechanism and adopted a dynamic threshold trigger control strategy to reduce the pressure of data transmission during the control process. However, it did not consider the impact of external disturbances on the control accuracy of the system. Summary of the invention

[0003] The problem solved by the present invention is to establish a remote servo motor system model under external disturbance and design a robust tracking control algorithm based on backstepping.

[0004] The algorithm adopted by the present invention to solve the above-mentioned problem is as follows: for a remote servo motor system with external interference, a fourth-order remote servo motor model taking the interference into consideration is established; for the external interference problem, a state-like observer is designed and the interference is estimated based on the observer result combined with the superhelical control rate; for its system characteristics, an event triggering mechanism and a robust tracking control strategy of the interference observation result are designed, and its stability and the possible Zeno phenomenon are analyzed.

[0005] Modeling of remote servo motor system under external disturbances and tracking control algorithm based on backstepping, including establishment of remote servo motor system model under external disturbances, design of quasi-state observer, external disturbance estimation, design of event trigger mechanism, design of robust tracking controller and stability proof.

[0006] The remote servo motor system model under the external disturbance is established, and a fourth-order servo motor model is established by setting the gear angle and gear speed of the motor gear and the driven gear as state variables. The dead zone nonlinear characteristics of the system are described by a nonlinear function, and the external disturbance is used as a modeling reference factor.

[0007] The class state observer design uses two interference estimates for the state variables x2 and x4. and Substituting actual interference to obtain class state variables and

[0008] The estimation of the external disturbance is based on the observation results of the state observer and combined with the superhelical control rate to estimate the disturbance in the system. Since the external random disturbance is bounded, the obtained disturbance estimation value is also bounded. The disturbance estimation value is and Among them, n1, m1, n2 and m2 are parameters that need to be adjusted, and e1(t) and e2(t) are the errors between the two state variables and the class state observation values.

[0009] The event trigger strategy design, the triggering conditions are: k+1 = inf{t>t k ||e(t)|>Ω}, where t k+1 is the triggering moment, t k is the time of the last trigger, e(t) is the difference between the real-time control input and the control input signal transmitted at the last trigger, and Ω is the trigger threshold.

[0010] The tracking controller design uses backstepping control technology to continuously design the virtual control input Ψ iThe Lyapunov equations at each stage ensure that the selected state variables at each stage converge to the virtual control input value. At the same time, the recursive relationship is used to design the linear sliding surface in the final stage of the backstepping control to obtain the real control input.

[0011] The stability proof analyzes the convergence of disturbance estimation error, the discussion of event-triggered Zeno characteristics, and the convergence of the robust tracking algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] Figure 1 The structural diagram of the control system of the present invention is DETAILED DESCRIPTION

[0013] The technical solution of the present invention is described in detail below with reference to the accompanying drawings.

[0014] like Figure 1 As shown, the present invention relates to the modeling of a remote servo motor system under external disturbance and the design of a tracking control algorithm based on backstepping, including the establishment of a remote servo motor system model under external disturbance, the design of a state observer, external disturbance estimation, the design of an event trigger mechanism, the design of a robust tracking controller and stability proof.

[0015] Model building

[0016] Considering the working state space equation of the DC motor system can be expressed as:

[0017]

[0018] and Where x1 represents the angle of the load gear, x2 represents the angular velocity of the load gear, x3 represents the angle of the motor gear, and x4 represents the angular velocity of the motor gear. u is the control input, y=x1 represents the output of the system, d1 and d2 are the injected external disturbances. N0 represents the reduction ratio of the servo motor transmission system, K represents the stiffness coefficient, J l , g l Represent the inertia moment and viscous friction coefficient of the load end, J m , g m Represent the inertia moment and viscous friction coefficient of the motor end respectively. R is the softness coefficient, which is used to represent the approximation degree between the nonlinear dead zone model used in the system and the traditional non-differentiable dead zone model (2), θ = x3-N0x1, and

[0019]

[0020] Design of state-like observer

[0021] In order to assist interference estimation, the following state-like observer is designed:

[0022]

[0023] in and is the interference estimate.

[0024] Interference Estimator Design

[0025] The deviations e1(t) and e2(t) between the class state observation value and the corresponding state actual value are defined as:

[0026]

[0027] The design interference estimates are as follows:

[0028]

[0029] The disturbances d1 and d2 to be observed are continuously differentiable and their first-order and second-order derivatives are bounded, that is: According to (4), real-time estimation of external disturbances can be achieved, and the estimation error will converge to a small neighborhood near 0 within a finite time.

[0030] Event trigger mechanism design

[0031] In order to reduce the network resource consumption during the control of the remote servo motor, the following event trigger mechanism is designed:

[0032] Define the control signal calculated in real time by the control end as Θ(t), and the control signal actually involved in the control is u k (t), e(t) = Θ(t) - u k (t) is the difference between the real-time control input and the control input signal transmitted during the last trigger.

[0033] t k+1 = inf{t>t k ||e(t)|>Ω} (6)

[0034] where t k+1 is the triggering moment, t k is the time of the last trigger, and Ω is the fixed trigger threshold. Once the trigger condition (5) is met, the control signal is updated to the calculated control signal Θ(t) of the control end at the trigger moment, that is, u k (t) = Θ(t k ) and u k (t) k ,t k+1 ) during the period.

[0035] Backstepping tracking algorithm design:

[0036] In order to achieve robust tracking control of the remote servo motor system, a backstepping tracking algorithm combined with disturbance estimation is designed as follows:

[0037] Step 1: Define the output tracking error as follows:

[0038] e1=y d -x1 (7)

[0039] where y d is the output reference signal, the derivative of formula (6) is

[0040]

[0041] The designed virtual control quantity is:

[0042]

[0043] The error between the actual control amount and the virtual control amount Ψ1 is defined as follows:

[0044] e2=Ψ1-x2 (10)

[0045] The Lyapunov equation selected for this stage is:

[0046]

[0047] By taking the derivative of formula (9) and substituting it into formula (8) and formula (9), we can obtain:

[0048]

[0049] Step 2: The derivative of formula (9) is:

[0050]

[0051] The designed virtual control quantity is:

[0052]

[0053] The error between the actual control amount and the virtual control amount Ψ2 is defined as follows:

[0054] e3=Ψ2-N0Kx3 / J l (15)

[0055] The Lyapunov equation selected for this stage is:

[0056]

[0057] Deriving equation (15) and substituting it into equation (13) and equation (14) yields:

[0058]

[0059] Step 3: The derivative of formula (14) is:

[0060]

[0061] where ζ(θ)=tanh(R(θ-β))-tanh(R(θ+β)).

[0062] The designed virtual control quantity is:

[0063]

[0064] The error between the actual control amount and the virtual control amount Ψ3 is defined as follows:

[0065]

[0066] The Lyapunov equation selected for this stage is:

[0067]

[0068] Deriving equation (20) and substituting it into equation (18) and equation (19) yields:

[0069]

[0070] Step 4: Design the linear sliding surface as follows:

[0071] s=k m e3+e4 (23)

[0072] The derivative of formula (22) is:

[0073]

[0074] in ω i The description of (i=1...5) is as follows:

[0075]

[0076] Based on this, the control signal of the system can be designed as follows:

[0077]

[0078] Proof of stability

[0079] In [t k+1 ,t k+2 ) in the process, there is u k (t) = Θ(t) + ηΩ (|η| < 1), when the trigger condition is met, |η| = 1. Since Θ(t) described in the event trigger part is equivalent to the control input u in the controller design part, for any time:

[0080] u k (t)=u+ηΩ|η|≤1 (27)

[0081] The Lyapunov equation is:

[0082]

[0083] Deriving equation (27) and substituting it into equation (21), equation (22), and equation (26) yields:

[0084]

[0085] Pick Then there is

[0086]

[0087] The designed robust control algorithm based on event trigger mechanism satisfies equation (29), that is, all signals in the closed-loop system are bounded and the system is stable.

[0088] The following will prove that the event triggering mechanism adopted can avoid Zeno's phenomenon:

[0089] From e(t) = Θ(t) - u k (t), have

[0090]

[0091] Also because Then there is

[0092]

[0093] And because the above proof shows that all signals in the closed-loop system are bounded, that is, there exists a positive real number satisfy From the trigger strategy point of view, there is a minimum trigger time It can ensure that the event trigger interval t k+1 -t k ≥t min , thus proving that the event triggering strategy used can avoid the Zeno phenomenon.

Claims

1. A remote servo motor system model considering external disturbances and a remote servo motor system tracking algorithm, characterized in that: This includes the establishment of a remote servo motor system model considering external disturbances, the design of a state observer, the estimation of external disturbances, the design of an event trigger mechanism, the design of a backstepping tracking controller, and the proof of system stability. The establishment of the remote servo motor system model considering external disturbances includes the description of the servo motor transmission system with disturbance and nonlinear characteristics and the establishment of a fourth-order servo motor model; the design of the state-like observer specifically includes the design of the state-like variable; the estimation of the external disturbance specifically includes the estimation of bounded random disturbances by using the observation results of the state-like observer and combining the superhelical control rate; the design of the event trigger mechanism specifically includes the realization of the event trigger mechanism by setting a fixed threshold trigger condition; the design of the backstepping tracking controller specifically includes the derivation of the control input for robust tracking control by combining the backstepping control technology and the sliding mode control algorithm; the system stability proof includes the analysis from the convergence of the disturbance estimation error, the discussion of the Zeno characteristics of event triggering, and the convergence of the robust tracking algorithm based on backstepping; Only the disturbance of the angular velocity state variables of the motor gear and the driven gear is considered in the system, and it is assumed that the disturbances d1 and d2 are continuously differentiable and their first-order and second-order derivatives are bounded. The gear angle and gear speed of the motor gear and the driven gear are used as state variables to establish a fourth-order servo motor model, in which the dead zone nonlinear characteristics in the model are described as follows: Where K is the stiffness coefficient and R is the softness coefficient; The constructed fourth-order servo motor model is: and Where x1 represents the angle of the load gear, x2 represents the angular velocity of the load gear, x3 represents the angle of the motor gear, x4 represents the angular velocity of the motor gear, u is the control input, x1 represents the output of the system, d1 and d2 are the injected external disturbances, N0 represents the reduction ratio of the servo motor transmission system, K represents the stiffness coefficient, J l , g l Represent the inertia moment and viscous friction coefficient of the load end, J m , g m Respectively represent the inertia moment and viscous friction coefficient of the motor end, R is the softness coefficient, which is used to represent the approximation degree between the nonlinear dead zone model used in the system and the traditional non-differentiable dead zone model, θ=x3-N0x1, The design class state observer is as follows: and and e1(t) and e2(t) are the state variables x2, x4 and their corresponding class state variables respectively. The error between Set fixed trigger condition t k+1 = inf{t>t k ||e(t)|>Ω}, where t k+1 is the triggering moment, t k is the time of the last trigger, e(t) is the difference between the real-time control input and the control input signal transmitted at the last trigger, and Ω is the fixed trigger threshold; Using the disturbance estimation and backstepping control technology, the virtual control input Ψ is designed iteratively. i As well as the Lyapunov equations of each step, it is ensured that the selected state variables in each stage converge to the virtual control input value. In the final stage of backstepping control, a linear sliding surface is designed, and a threshold trigger strategy is introduced to obtain the real control input.

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