Fault-tolerant control method of electric scooter system under actuator fault and input dead zone, terminal and medium

Abstract

The invention relates to the technical field of fault-tolerant control, and discloses a fault-tolerant control method for an electric scooter system in an actuator fault and input dead zone, a terminal and a medium. The method comprises the following steps: establishing a differential equation model and a state space model of the electric scooter system by utilizing a kinetic equation of the electric scooter system; according to the differential equation model, constructing a nonlinear model considering an input dead zone of the electric scooter system and an actuator fault; establishing an extended sliding-mode observer according to the state space model to reconstruct an actuator fault; designing a fault-tolerant control strategy according to a fault reconstruction result to realize fault-tolerant control; wherein an event triggering mechanism and a fuzzy logic system are introduced when a fault-tolerant control strategy is designed, and an obstacle Lyapunov function is introduced in the process of deducing a control law according to the nonlinear model. The reliability and the control performance of the electric scooter system are effectively improved.

Description

Technical Field

[0001] The present invention relates to the technical field of fault-tolerant control, and in particular to a fault-tolerant control method, terminal and medium for an electric scooter system under actuator failure and input dead zone. Background Art

[0002] As a convenient means of transportation, primarily targeting the elderly, electric scooters have seen continued growth in market share in recent years. However, with this increased adoption, safety risks exposed during operation are also gaining increasing attention. Currently, most electric scooter manufacturers have not fully considered the potential for failures caused by the high integration of components such as sensors and actuators in complex road conditions.

[0003] Given that electric scooters are primarily used by the elderly, system failures during use are highly likely to cause personal injury and property damage. Therefore, research on fault-tolerant control technologies for electric scooters is of great practical significance. Existing fault-tolerant control technologies primarily include passive and active approaches. Passive fault-tolerant control improves system robustness through conservative controller design, ensuring that the system maintains a certain level of operational capability even in the event of a fault. However, this approach typically results in low resource utilization. Active fault-tolerant control uses online fault estimation to identify and compensate for faults, achieving more flexible and efficient fault tolerance.

[0004] Furthermore, actuator dead-band effects are a common nonlinear effect in the electromechanical systems of electric scooters. Failure to implement effective compensation methods can lead to a degradation of system control performance and even more serious safety issues. In particular, in the event of partial or complete actuator failure, the lack of an effective fault-tolerant control strategy can easily lead to vehicle loss of control, posing a serious risk to personnel safety. Therefore, a fault-tolerant control solution for electric scooters in the presence of actuator failures and input dead-band is urgently needed to improve the reliability and control performance of the electric scooter system. Summary of the Invention

[0005] To solve the technical problems existing in the prior art, the present invention provides a fault-tolerant control method, terminal and medium for an electric scooter system under actuator failure and input dead zone, which effectively improves the reliability and control performance of the electric scooter system.

[0006] To achieve the above object, the present invention provides the following technical solutions:

[0007] The present invention discloses a fault-tolerant control method for an electric scooter system under actuator failure and input dead zone, comprising:

[0008] Using the dynamic equations of the electric scooter system, a differential equation model and a state space model of the electric scooter system are established;

[0009] Based on the differential equation model, a nonlinear model is constructed that takes into account the input dead zone and actuator failure of the electric scooter system;

[0010] Establishing an extended sliding mode observer based on the state space model to reconstruct actuator faults;

[0011] A fault-tolerant control strategy is designed according to the fault reconstruction result to achieve fault-tolerant control; wherein, an event trigger mechanism and a fuzzy logic system are introduced in the design of the fault-tolerant control strategy, and an obstacle Lyapunov function is introduced in the process of deriving the control law according to the nonlinear model.

[0012] As a further improvement to the above solution, the dynamic equation is obtained by analyzing the mechanical structure of the electric scooter system; wherein the mechanical structure includes: a DC motor driver, a DC motor, a rear wheel, a body, and a front wheel; the dynamic equation is expressed as follows:

[0013]

[0014]

[0015] Where u(t) is the input voltage of the motor driver, K1 is the voltage-to-current conversion ratio of the DC motor driver, K2 is the current-torque conversion ratio of the DC motor, K3 is the reduction ratio of the reducer, K4 is the wheel radius, J1 is the motor moment of inertia, J2 is the rear wheel moment of inertia, J3 is the front wheel moment of inertia, and K f is the motor viscous friction coefficient, is the rear wheel viscous friction coefficient, is the front wheel viscous friction coefficient, F u is the Coulomb friction torque of the motor, is the Coulomb friction torque of the rear wheel, is the Coulomb friction torque of the front wheel, N1 is the rear axle stiffness, N2 is the front axle stiffness, m is the mass of the electric scooter, θ1 is the rear wheel angular displacement, s is the linear displacement of the electric scooter body, θ2 is the front wheel angular displacement, and They represent the first and second derivatives of (), respectively, and sign(·) is the sign function.

[0016] As a further improvement of the above solution, the differential equation model is expressed as follows:

[0017]

[0018] Where x1 is the rear wheel angular displacement, x2 is the rear wheel angular velocity, d(x1,x2) represents the unknown system disturbance, and

[0019]

[0020] make is the system state variable, u(t) is the system input, and the state space model of the electric scooter system is expressed as follows:

[0021]

[0022] in,

[0023]

[0024] Where, superscript T is the transposition symbol; t is time; in matrix A,

[0025] ω1 and ω2 are the rear wheel angular displacement and rear wheel angular velocity, respectively.

[0026] As a further improvement of the above solution, the construction process of the nonlinear model is as follows:

[0027] According to the input dead zone characteristics of the electric scooter system, the following electric scooter dead zone model is established:

[0028]

[0029] Where v is the dead zone input, u(v) is the dead zone output, β r (t), β l (t) is an unknown positive variable; the electric scooter actuator fault is modeled as:

[0030]

[0031] Among them, u p (t) is the nominal control input generated by the controller, is a multiplicative fault, β f (t) is an additive fault;

[0032] Reconstruct the above relationship as:

[0033]

[0034] Where,

[0035]

[0036] The nonlinear model is constructed as follows:

[0037]

[0038] As a further improvement to the above solution, the specific process of establishing a sliding mode observer based on the state space model to reconstruct the actuator fault includes:

[0039] Considering the actuator failure of the electric scooter, a new set of state space models is constructed:

[0040]

[0041] Where, f a (t) is the actuator failure; according to the state space model, a new state variable x3(t)=f a , thus rewriting the state space model of the electric scooter system as follows:

[0042]

[0043] Where, u f (t) is the fault-tolerant control law; Q is the matrix describing the nonlinear term; is a nonlinear term; Ψ(x,t) is a lumped perturbation; σ(t) is a term used to represent f a (t) is an unknown function; Based on the above rewritten state space model, the extended sliding mode observer of the electric scooter system is obtained:

[0044]

[0045] Where, for estimated value of; is the estimated value of x(t); for estimated value of; is the estimated value of y(t); L is the linear gain matrix; v is the discontinuity, defined as:

[0046]

[0047] In the formula, κ is a positive constant, and ‖·‖ is the L2 norm;

[0048] Use the continuous function v e To replace v to handle jitter, v e Defined as:

[0049]

[0050] Where δ is a positive constant less than 1.

[0051] As a further improvement to the above scheme, the specific process of introducing event trigger mechanism and fuzzy logic system in designing fault-tolerant control strategy is as follows:

[0052] Definition of interval type-2 fuzzy system It is expressed as follows:

[0053]

[0054] Where x f ∈X, X is the main variable x f The number set of u is the second variable, is each x f ∈2 main membership, is the secondary membership function; The uncertainty trajectory FOU is expressed as the union of all main members as follows:

[0055]

[0056] Design a zero-order type-2 Takagi-SugenoKang fuzzy logic system, where the antecedent is IT 2FS, the consequent is a crisp number, and the jth IF-THEN rule R (j) Expressed as:

[0057]

[0058] Where x i ∈X i is the i-th input variable, the antecedent For IT2FS, post-processing For clear numbers;

[0059] Consider the following state errors:

[0060]

[0061] In the formula, e1=y(t)-y d (t), α2 is the virtual control law, and the switching function k(t) is defined as follows:

[0062]

[0063] Where, t k For a positive number, the following event triggering mechanism is designed:

[0064] u(t)=u b (t k ),t∈[t k ,t k +1)

[0065]

[0066] In the formula, inf represents the lower bound; ι is a constant greater than 0 and less than 1, c and n are positive constants; e t (t) is the event triggering error; t k is a positive constant; u b (t k ) is the control law at t k The value at the moment; at t1 = 0, e t (t) = u b (t)-u b (t k ).

[0067] As a further improvement to the above solution, the specific process of introducing the barrier Lyapunov function in the process of deriving the control law according to the nonlinear model includes:

[0068] Step 1: Design the virtual control law α2 as follows:

[0069]

[0070] Where, η1,∈,ρ are positive constants; is the estimated value of the unknown normal number b; η1 is a normal number;

[0071] Design control law u b for:

[0072]

[0073] Where, H=[1,|u b1 |] T ; is the estimated result of the unknown parameter vector W; when hour, Among them, y d is the reference value, is the upper bound of the second-order reference value derivative; ω is the approximation error of the fuzzy logic system; Approximate the upper bound of the error for the fuzzy logic system; and They are The upper and lower bounds of for The lower bound of and They are The upper and lower bounds of and They are The upper and lower bounds of is the upper bound of β; β f The upper bound of β l The upper bound of β r The upper bound of

[0074] Design b1 for:

[0075]

[0076] Where x and θ *T ξ(x) are the input and output of the fuzzy logic system; θ *T is the optimal parameter vector; η2>1 is a positive constant;

[0077] The designed adaptive law is:

[0078]

[0079]

[0080]

[0081] Where, γ1, γ2, γ3, σ1, σ2, σ3 are all positive constants; θ is the fuzzy logic system parameter vector; for Adaptive law output; is the estimated value of b; the adaptive law ensures and is non-negative;

[0082] Step 2: Consider the barrier Lyapunov function Where ρ is the predefined boundary of z1;

[0083] Consider the following Lyapunov function V:

[0084]

[0085] Where, is the estimation error of θ; t c is a positive constant, k(t c ) is the switching function at t c The value of the moment;

[0086] Step 3: Combining the adaptive law designed in step 1 and the Lyapunov function in step 2, when a judgment condition is met, verify that the electric scooter system is semi-globally asymptotically stable under the designed control law, that is, fault-tolerant control is achieved; the judgment condition is expressed as follows:

[0087]

[0088] In the formula, τ1=min[2η1,2η2,σ1,σ2,σ3],

[0089] As a further improvement to the above solution, the specific process of designing a fault-tolerant control strategy based on the fault reconstruction results to achieve fault-tolerant control includes:

[0090] Consider the case of an electric scooter actuator failure. When the actuator fails, the system input u(t) is expressed as:

[0091] u(t)=u f (t)+f a (t)

[0092] Where u f (t) is the fault-tolerant control law, which is designed as follows:

[0093]

[0094] Where u p (t) is the nominal control input generated by the controller, Reconstructed actuator fault signals for the extended sliding mode observer;

[0095] This yields the following relationship:

[0096]

[0097] Where, is the actuator fault estimation error that converges to zero in finite time.

[0098] The present invention also discloses a computer terminal, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, the steps of the fault-tolerant control method for an electric scooter system under actuator failure and input dead zone are implemented as described above.

[0099] The present invention also discloses a computer-readable storage medium having a computer program stored thereon, wherein when the program is executed by a processor, the steps of the fault-tolerant control method of the electric scooter system under actuator failure and input dead zone are implemented as described above.

[0100] Compared with the prior art, the present invention has the following beneficial effects:

[0101] The present invention improves the backstepping control algorithm by introducing an obstacle Lyapunov function, and uses a composite obstacle Lyapunov function to complete predefined performance control; the present invention proposes an active fault-tolerant control strategy for electric scooters, and based on the designed fault reconstruction link and controller link, completes the function of active fault-tolerant control; the present invention introduces a fuzzy system to deal with the influence of dead zone and parameter uncertainty, effectively improving the reliability and control performance of the electric scooter system. BRIEF DESCRIPTION OF THE DRAWINGS

[0102] Figure 1 This is a flow chart of the fault-tolerant control method of the electric scooter system under actuator failure and input dead zone in Example 1 of the present invention.

[0103] Figure 2 This is a fault-tolerant control logic block diagram in Example 1 of the present invention.

[0104] Figure 3 This is the fault reconstruction result of the extended sliding mode observer for a single fault type in Example 1 of the present invention.

[0105] Figure 4 This is the fault reconstruction result of multiple fault types using the extended sliding mode observer in Example 1 of the present invention.

[0106] Figure 5 This is the single fault type fault tolerance control effect in Example 1 of the present invention.

[0107] Figure 6 It is the single fault type fault-tolerant control tracking error in embodiment 1 of the present invention.

[0108] Figure 7 This is the multi-fault type fault tolerance control effect in Example 1 of the present invention.

[0109] Figure 8 It is the tracking error of the multi-fault type fault-tolerant control in embodiment 1 of the present invention.

[0110] Figure 9 This is a schematic diagram of the computer terminal structure in Example 2 of the present invention. DETAILED DESCRIPTION

[0111] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0112] Example 1

[0113] See also Figure 1 This embodiment provides a fault-tolerant control method for an electric scooter system under actuator failure and input dead zone, including the following steps, namely S1 to S5.

[0114] S1. Using the dynamic equations of the electric scooter system, a differential equation model and a state space model of the electric scooter system are established; based on the differential equation model, a nonlinear model that considers input dead zones and actuator failures of the electric scooter system is constructed.

[0115] See also Figure 2 A predefined performance controller uses vehicle speed data collected by sensors as input to form a closed loop, thereby controlling the angular velocity of the electric scooter's rear wheels. Based on this, ESMO reconstructs the electric scooter's actuator faults and uses this reconstruction to correct the actuator faults, achieving the correct state of the electric scooter system. Finally, using adaptive laws and RBFNNs, the system addresses parameter uncertainty and nonlinear effects, achieving satisfactory tracking performance for the electric scooter.

[0116] Step S1 includes the following specific steps:

[0117] S11. The dynamic equation is obtained by analyzing the mechanical structure of the electric scooter system; wherein the mechanical structure includes: a DC motor drive, a DC motor, a rear wheel, a body, and a front wheel; the dynamic equation is expressed as follows:

[0118]

[0119]

[0120]

[0121] Where u(t) is the input voltage of the motor driver, K1 is the voltage-to-current conversion ratio of the DC motor driver, K2 is the current-torque conversion ratio of the DC motor, K3 is the reduction ratio of the reducer, K4 is the wheel radius, J1 is the motor moment of inertia, J2 is the rear wheel moment of inertia, J3 is the front wheel moment of inertia, and K f is the motor viscous friction coefficient, is the rear wheel viscous friction coefficient, is the front wheel viscous friction coefficient, F u is the Coulomb friction torque of the motor, is the Coulomb friction torque of the rear wheel, is the Coulomb friction torque of the front wheel, N1 is the rear axle stiffness, N2 is the front axle stiffness, m is the mass of the electric scooter, θ1 is the rear wheel angular displacement, s is the linear displacement of the electric scooter body, θ2 is the front wheel angular displacement, and They represent the first and second derivatives of (), respectively, and sign(·) is the sign function.

[0122] S12. Simultaneously establish the dynamic equations. Based on the dynamic equations of the electric scooter system, establish the state space model and differential equation model of the electric scooter system. The differential equation model is as follows:

[0123]

[0124] Where x1 is the rear wheel angular displacement, x2 is the rear wheel angular velocity, d(x1,x2) represents the unknown system disturbance, and

[0125]

[0126] S13. Order is the system state variable, u(t) is the system input, and the state space model of the electric scooter system is expressed as follows:

[0127]

[0128] in,

[0129]

[0130]

[0131] Where, superscript T is the transposition symbol; t is time; in matrix A,

[0132] ω1 and ω2 are the rear wheel angular displacement and rear wheel angular velocity, respectively.

[0133] S14. Based on the input dead zone characteristics of the electric scooter system, the following electric scooter dead zone model is established:

[0134]

[0135] Where v is the dead zone input, u(v) is the dead zone output, β r (t), β l (t) is an unknown positive variable; the electric scooter actuator fault is modeled as:

[0136]

[0137] Among them, u p (t) is the nominal control input generated by the controller, is a multiplicative fault, β f (t) is an additive fault;

[0138] S15. On this basis, rewrite the above relationship as follows:

[0139]

[0140] Where,

[0141]

[0142] The nonlinear model is constructed as follows:

[0143]

[0144] In this embodiment, in the modeling, the nominal values of the relevant parameters of the electric scooter system are shown in Table 1:

[0145] Table 1: Nominal values of relevant parameters of electric scooter system

[0146] parameter Nominal value parameter Nominal value <![CDATA[K1]]> 0.2A / V <![CDATA[J2]]> <![CDATA[4.87×10 -3 kgm 2 ]]> <![CDATA[K2]]> 1Nm / A <![CDATA[J3]]> <![CDATA[6.97×10 -3 kgm 2 ]]> <![CDATA[K3]]> 1 / 18 <![CDATA[N1]]> 10rad / Nm <![CDATA[K4]]> 1 / 0.105m <![CDATA[N2]]> 10rad / Nm <![CDATA[K f ]]> <![CDATA[1.72×10 -3 Nms / rad]]> <![CDATA[K f2 ]]> <h2 style=";text-align:left;direction:ltr"><![CDATA[1.86×10 <h2 style=";text-align:left;direction:ltr"> -3 <h2 style=";text-align:left;direction:ltr"> Nm / rad]]><h2 style=";text-align:left;direction:ltr"> <![CDATA[F u ]]> <![CDATA[5.63×10 -2 Nm]]> <![CDATA[F u2 ]]> <![CDATA[1×10 -3 Nm]]> <![CDATA[K f1 ]]> <![CDATA[3.55×10 -2 Nms / rad]]> m 20.7kg <![CDATA[J1]]> <![CDATA[5.03×10 -4 kgm 2 ]]> <![CDATA[F u1 ]]> <![CDATA[6.05×10 -2 Nm]]>

[0147] S2. Establish an extended sliding mode observer based on the state space model to reconstruct the actuator fault. The specific process includes:

[0148] Considering the actuator failure of the electric scooter, a new set of state space models is constructed:

[0149]

[0150] Where, f a (t) is the actuator failure; according to the state space model, a new state variable x3(t)=f a , thus rewriting the state space model of the electric scooter system as follows:

[0151]

[0152] Where, u f (t) is the fault-tolerant control law; Q is the matrix describing the nonlinear term; is a nonlinear term; Ψ(x,t) is a lumped perturbation; σ(t) is a term used to represent f a (t) is an unknown function; Based on the above rewritten state space model, the extended sliding mode observer of the electric scooter system is obtained:

[0153]

[0154] Where, for estimated value of; is the estimated value of x(t); for estimated value of; is the estimated value of y(t); L is the linear gain matrix; v is the discontinuity, defined as:

[0155]

[0156] In the formula, κ is a positive constant, and ‖·‖ is the L2 norm;

[0157] Use the continuous function v e To replace v to handle jitter, v e Defined as:

[0158]

[0159] Where δ is a positive constant less than 1. The state variables of the extended sliding mode observer can be approximated to the state variables of the electric scooter system in the rewritten state space equation.

[0160] S3. Considering the limited communication bandwidth and parameter uncertainty of the electric scooter system, an event trigger mechanism and fuzzy logic system are introduced to solve their impact. The specific process is as follows:

[0161] S31. Define interval type-2 fuzzy system It is expressed as follows:

[0162]

[0163] Where x f ∈X, X is the main variable x f The number set of u is the second variable, is each x f ∈X’s principal membership, is the secondary membership function; The uncertainty trajectory FOU is expressed as the union of all main members as follows:

[0164]

[0165] Considering the simplicity of calculation, a zero-order type-two Takagi-SugenoKang fuzzy logic system is designed, in which the antecedent is IT 2FS, the consequent is a clear number, and the jth IF-THEN rule R (j) Expressed as:

[0166]

[0167] Where x i ∈X i is the i-th input variable, the antecedent For IT2FS, post-processing is a clear number; the approximation property of IT2 fuzzy least squares with bounded approximation error can only hold in a convex region, which means that when the initial state of the system is in a bounded set, the stability result of this design method is semi-globally asymptotically stable under the condition that all signals of the closed-loop system are bounded.

[0168] S32. Consider the following state errors:

[0169]

[0170] In the formula, e1=y(t)-y d (t), α2 is the virtual control law, and the switching function k(t) is defined as follows:

[0171]

[0172] Where, t k For a positive number, the following event triggering mechanism is designed:

[0173] u(t)=u b (t k ),t∈[t k ,t k +1)

[0174]

[0175] In the formula, inf represents the lower bound; ι is a constant greater than 0 and less than 1, c and n are positive constants; e t (t) is the event triggering error; t k is a positive constant; u b (t k ) is the control law at t k The value at the moment; at t1 = 0, e t (t) = u b (t)-u b (t k ).

[0176] S4. Considering the error subsystem of the electric scooter, we introduce the obstacle Lyapunov function to derive the backstepping control law and achieve predefined performance control. The specific process includes:

[0177] S41. Design the virtual control law α2 as follows:

[0178]

[0179] Where, η1,∈,ρ are positive constants; is the estimated value of the unknown normal number b; η1 is a normal number;

[0180] Design control law u b for:

[0181]

[0182] Where, N=[1,|u b1 |] T ; is the estimated result of the unknown parameter vector W; when hour, Among them, y d is the reference value, is the upper bound of the second-order reference value derivative; ω is the approximation error of the fuzzy logic system; Approximate the upper bound of the error for the fuzzy logic system; and They are The upper and lower bounds of for The lower bound of and They are The upper and lower bounds of and They are The upper and lower bounds of is the upper bound of β; β f The upper bound of β l The upper bound of β r The upper bound of

[0183] Design b1 for:

[0184]

[0185] Where x and θ *T ξ(x) are the input and output of the fuzzy logic system; θ *T is the optimal parameter vector; η2>1 is a positive constant;

[0186] The designed adaptive law is:

[0187]

[0188]

[0189]

[0190] Where, γ1, γ2, γ3, σ1, σ2, σ3 are all positive constants; θ is the fuzzy logic system parameter vector; for Adaptive law output; is the estimated value of b; the adaptive law ensures and is non-negative;

[0191] S42. Consider the barrier Lyapunov function Where ρ is the predefined boundary of z1, and the derivative of the barrier Lyapunov function can be obtained:

[0192]

[0193] This process produces together with b0:

[0194]

[0195] in, Then, we can get:

[0196]

[0197] There exists b0 such that Then, we get a moment 0 <t c <t k So that:

[0198]

[0199] The definition of b can be obtained as:

[0200]

[0201] t c is a positive constant, k(t c ) is the switching function at t c The value of the moment;

[0202] Under the above conditions, there exists an unknown positive constant τ0 such that:

[0203]

[0204] Consider t∈[0,t c ) when k(t c )-k(t)>0,t∈[t c ,+∞) when k(t c )-k(t)≤0, we can get:

[0205]

[0206] The simultaneous differential equations can be obtained:

[0207]

[0208] It can be found that there is i=1,2 so that Therefore, the following relationship is obtained:

[0209]

[0210] In summary, we can get:

[0211]

[0212] in, Then we can get:

[0213]

[0214] in, Consider the following Lyapunov function:

[0215]

[0216] in, Based on t∈[0,t c ) can be obtained by:

[0217]

[0218] consider You can get:

[0219]

[0220] Combining the adaptive law designed above with the above formula, we can get:

[0221]

[0222] According to Young's inequality, we can get:

[0223]

[0224] Then, the derivative of the Lyapunov function can be rewritten as:

[0225]

[0226] Among them, τ1=min[2η1, 2η2, σ1, σ2, σ3], Consider the condition t∈[t c ,+∞), we can get the following conditions:

[0227]

[0228] In summary, we can get:

[0229]

[0230] When the above judgment conditions are met, it is verified that the electric scooter system is semi-globally asymptotically stable under the designed control law, that is, fault-tolerant control is achieved.

[0231] S5. Based on the predefined performance control and fault reconstruction results, design a fault-tolerant control strategy to implement fault-tolerant control. The specific process includes:

[0232] Consider the case of an electric scooter actuator failure. When the actuator fails, the system input u(t) can be expressed as:

[0233] u(t)=u f (t)+f a (t)

[0234] Where u f (t) is the fault-tolerant control law, f a (t) represents the actuator failure. Based on the extended sliding mode observer designed in the previous article, the actuator failure can be reconstructed. On this basis, an active fault-tolerant control method is developed to compensate for the actuator failure and ensure reliable rear wheel angular velocity tracking performance of the electric scooter. The specific fault-tolerant control law is designed as follows:

[0235]

[0236] Where u p (t) is the nominal control input generated by the controller, The actuator fault signal reconstructed by the extended sliding mode observer. The following relationship can be obtained:

[0237]

[0238] Where, is the actuator fault estimation error that converges to zero in finite time.

[0239] See also Figures 3 to 8 , Figure 3 This is the fault reconstruction effect of ESMO of the electric scooter system under a single fault type. Obviously, ESMO under a single fault type can effectively reproduce the actuator fault and provide a basis for subsequent fault-tolerant control design. Figure 4This is the fault reconstruction effect of ESMO of the electric scooter system under multiple fault types. Obviously, ESMO under multiple fault types can also effectively reproduce the actuator failures that occur and provide a basis for subsequent fault-tolerant control design. Figure 5 The figure shows the rear wheel angular velocity tracking effect of the electric scooter under the designed fault-tolerant control method under a single fault type. Obviously, in the face of a single fault type, the designed fault-tolerant control method can keep the rear wheel angular velocity of the electric scooter within a satisfactory range. Figure 6 is the rear wheel angular velocity tracking error of the electric scooter under the designed fault-tolerant control method under single fault type. The tracking error can further prove Figure 5 conclusion. Figure 7 This figure shows the rear wheel angular velocity tracking effect of the electric scooter under the designed fault-tolerant control method under multiple fault types. Obviously, in the face of multiple fault types, the designed fault-tolerant control method can still keep the rear wheel angular velocity of the electric scooter within a satisfactory range. Figure 8 The tracking error of the rear wheel angular velocity of the electric scooter under the designed fault-tolerant control method under multiple fault types can be further proved. Figure 7 conclusion.

[0240] Example 2

[0241] This embodiment provides a computer terminal, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the steps of the fault-tolerant control method for an electric scooter system under actuator failure and input dead zone as described in Example 1 are implemented.

[0242] like Figure 9 As shown, the computer terminal provided in this embodiment includes: at least one processor 101, and a memory 102 connected to the at least one processor 101. The specific connection medium between the processor 101 and the memory 102 is not limited in this embodiment. Figure 9 In the example, the processor 101 and the memory 102 are connected via the bus 100. Figure 9 The bus 100 can be divided into an address bus, a data bus, a control bus, etc. For ease of representation, Figure 9 The bus is represented by only one thick line, but it does not mean that there is only one bus or one type of bus. Alternatively, the processor 101 can also be called a controller, and there is no limitation on the name.

[0243] In this embodiment, the memory 102 stores instructions that can be executed by at least one processor 101 , and the at least one processor 101 can perform the aforementioned method by executing the instructions stored in the memory 102 .

[0244] Among them, the processor 101 is the control center of the device, which can use various interfaces and lines to connect the various parts of the entire control device, and monitor the device as a whole by running or executing instructions stored in the memory 102 and calling data stored in the memory 102, the various functions of the device and processing data.

[0245] In one possible design, processor 101 may include one or more processing units. Processor 101 may integrate an application processor and a modem processor. The application processor primarily processes the operating system, user interface, and application programs, while the modem processor primarily handles wireless communications. It is understood that the modem processor may not be integrated into processor 101. In some embodiments, processor 101 and memory 102 may be implemented on the same chip. In some embodiments, they may also be implemented on separate chips.

[0246] The processor 101 can be a general-purpose processor, such as a central processing unit (CPU), a digital signal processor, an application-specific integrated circuit, a field programmable gate array or other programmable logic device, a discrete gate or transistor logic device, or a discrete hardware component, and can implement or execute the various methods, steps, and logic block diagrams disclosed in the embodiments. The general-purpose processor can be a microprocessor or any conventional processor. The steps of the fault-tolerant control method for the electric scooter system under actuator failure and input dead zone disclosed in Example 1 can be directly implemented as a hardware processor, or can be implemented using a combination of hardware and software modules in the processor 101.

[0247] The memory 102 is a non-volatile computer-readable storage medium that can be used to store non-volatile software programs, non-volatile computer executable programs and modules. The memory 102 may include at least one type of storage medium, such as a flash memory, a hard disk, a multimedia card, a card-type memory, a random access memory (RAM), a static random access memory (SRAM), a programmable read-only memory (PROM), a read-only memory (ROM), an electrically erasable programmable read-only memory (EEPROM), a magnetic memory, a magnetic disk, an optical disk, etc. The memory 102 is any other medium that can be used to carry or store desired program code in the form of instructions or data structures and can be accessed by a computer, but is not limited thereto. The memory 102 in this embodiment can also be a circuit or any other device that can implement a storage function, for storing program instructions and / or data.

[0248] By programming the processor 101, the code corresponding to the security verification method described in the above embodiment can be fixed into the chip, so that the chip can execute the security verification method when it is running. Figure 1 The steps of the fault-tolerant control method for the electric scooter system under actuator failure and input dead band are shown. How to design and program the processor 101 is well known to those skilled in the art and will not be described in detail here.

[0249] Example 3

[0250] This embodiment provides a computer-readable storage medium having a computer program stored thereon. When the program is executed by a processor, the steps of the fault-tolerant control method for the electric scooter system under actuator failure and input dead zone as described in Example 1 are implemented.

[0251] The computer-readable storage medium may include flash memory, a hard disk, a multimedia card, a card-type memory (e.g., SD or DX memory), random access memory (RAM), static random access memory (SRAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), programmable read-only memory (PROM), magnetic memory, a magnetic disk, an optical disk, etc. In some embodiments, the storage medium may be an internal storage unit of a computer device, such as the hard disk or memory of the computer device. In other embodiments, the storage medium may also be an external storage device of the computer device, such as a plug-in hard disk equipped on the computer device, a smart media card (SMC), a secure digital (SD) card, a flash memory card, etc. Of course, the storage medium may also include both the internal storage unit of the computer device and its external storage device. In this embodiment, the memory is generally used to store the operating system and various application software installed on the computer device. In addition, the memory may also be used to temporarily store various types of data that have been output or are about to be output.

[0252] The above description is only a preferred specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any technician familiar with the technical field, within the technical scope disclosed by the present invention, who makes equivalent replacements or changes based on the technical solution and inventive concept of the present invention, should be covered by the scope of protection of the present invention.

Claims

1. A fault-tolerant control method for an electric scooter system under actuator failure and input dead zone, characterized in that: include: Using the dynamic equations of the electric scooter system, a differential equation model and a state space model of the electric scooter system are established; Based on the differential equation model, a nonlinear model is constructed that takes into account the input dead zone and actuator failure of the electric scooter system; Establishing an extended sliding mode observer based on the state space model to reconstruct actuator faults; A fault-tolerant control strategy is designed according to the fault reconstruction result to achieve fault-tolerant control; wherein, an event trigger mechanism and a fuzzy logic system are introduced in the design of the fault-tolerant control strategy, and an obstacle Lyapunov function is introduced in the process of deriving the control law according to the nonlinear model.

2. The fault-tolerant control method for an electric scooter system under actuator failure and input dead zone according to claim 1, characterized in that: The dynamic equation is obtained by analyzing the mechanical structure of the electric scooter system. The mechanical structure includes a DC motor driver, a DC motor, rear wheels, a vehicle body, and front wheels. The dynamic equation is expressed as follows: Where u(t) is the input voltage of the motor driver, K1 is the voltage-to-current conversion ratio of the DC motor driver, K2 is the current-torque conversion ratio of the DC motor, K3 is the reduction ratio of the reducer, K4 is the wheel radius, J1 is the motor moment of inertia, J2 is the rear wheel moment of inertia, J3 is the front wheel moment of inertia, and K f is the motor viscous friction coefficient, is the rear wheel viscous friction coefficient, is the front wheel viscous friction coefficient, F u is the Coulomb friction torque of the motor, is the Coulomb friction torque of the rear wheel, is the Coulomb friction torque of the front wheel, N1 is the rear axle stiffness, N2 is the front axle stiffness, m is the mass of the electric scooter, θ1 is the rear wheel angular displacement, s is the linear displacement of the electric scooter body, θ2 is the front wheel angular displacement, and They represent the first and second derivatives of (), respectively, and sign(·) is the sign function.

3. The fault-tolerant control method for an electric scooter system under actuator failure and input dead zone according to claim 2, characterized in that: The differential equation model is expressed as follows: Where x1 is the rear wheel angular displacement, x2 is the rear wheel angular velocity, d(x1,x2) represents the unknown system disturbance, and make is the system state variable, u(t) is the system input, and the state space model of the electric scooter system is expressed as follows: in, Where, superscript T is the transposition symbol; t is time; in matrix A, ω1 and ω2 are the rear wheel angular displacement and rear wheel angular velocity, respectively.

4. The fault-tolerant control method for an electric scooter system under actuator failure and input dead zone according to claim 3, characterized in that: The construction process of the nonlinear model is as follows: According to the input dead zone characteristics of the electric scooter system, the following electric scooter dead zone model is established: Where v is the dead zone input, u(v) is the dead zone output, β r (t), β l (t) is an unknown positive variable; the electric scooter actuator fault is modeled as: Among them, u p (t) is the nominal control input generated by the controller, is a multiplicative fault, β f (t) is an additive fault; Reconstruct the above relationship as: Where, The nonlinear model is constructed as follows:

5. The fault-tolerant control method for an electric scooter system under actuator failure and input dead zone according to claim 4, characterized in that: The specific process of establishing a sliding mode observer based on the state space model to reconstruct the actuator fault includes: Considering the actuator failure of the electric scooter, a new set of state space models is constructed: Where, f a (t) is the actuator failure; according to the state space model, a new state variable x3(t)=f a , thus rewriting the state space model of the electric scooter system as follows: Where, u f (t) is the fault-tolerant control law; Q is the matrix describing the nonlinear term; is a nonlinear term; x(x,t) is a lumped perturbation; σ(t) is a term used to represent f a (t) is an unknown function; Based on the above rewritten state space model, the extended sliding mode observer of the electric scooter system is obtained: Where, for estimated value of; is the estimated value of x(t); for estimated value of; is the estimated value of y(t); L is the linear gain matrix; v is the discontinuity, defined as: In the formula, κ is a positive constant, and ‖·‖ is the L2 norm; Use the continuous function v e To replace v to handle jitter, v e Defined as: Where δ is a positive constant less than 1.

6. The fault-tolerant control method for an electric scooter system under actuator failure and input dead zone according to claim 5, characterized in that: The specific process of introducing event trigger mechanism and fuzzy logic system when designing fault-tolerant control strategy is as follows: Definition of interval type-2 fuzzy system It is expressed as follows: Where x f ∈X, X is the main variable x f The number set of u is the second variable, is each x f ∈X’s principal membership, is the secondary membership function; The uncertainty trajectory FOU represents the union of all primary members as follows: Design a zero-order type-2 Takagi-SugenoKang fuzzy logic system, where the antecedent is IT 2FS, the consequent is a crisp number, and the jth IF-THEN rule R (j) Expressed as: Where x i ∈X i is the i-th input variable, the antecedent For IT2FS, post-processing For clear numbers; Consider the following state errors: In the formula, e1=y(t)-y d (t), α2 is the virtual control law, and the switching function k(t) is defined as follows: Where, t k For a positive number, the following event triggering mechanism is designed: u(t)=u b (t k ),t∈[t k ,t k +1) In the formula, inf represents the lower bound; ι is a constant greater than 0 and less than 1, c and n are positive constants; e t (t) is the event triggering error; t k is a positive constant; u n (t k ) is the control law at t k The value at the moment; at t1 = 0, e t (t) = u b (t)-u b (t k ).

7. The fault-tolerant control method for an electric scooter system under actuator failure and input dead zone according to claim 6, characterized in that: The specific process of introducing the barrier Lyapunov function in the process of deriving the control law according to the nonlinear model includes: Step 1: Design the virtual control law α2 as follows: Where, η1,∈,ρ are positive constants; is the estimated value of the unknown normal number b; η1 is a normal number; Design control law u b for: Where, H=[1,|u b1 |] T ; is the estimated result of the unknown parameter vector W; when hour, Among them, y d is the reference value, is the upper bound of the second-order reference value derivative; ω is the approximation error of the fuzzy logic system; Approximate the upper bound of the error for the fuzzy logic system; and They are The upper and lower bounds of for The lower bound of and They are The upper and lower bounds of and They are The upper and lower bounds of is the upper bound of β; β f The upper bound of β l The upper bound of β r The upper bound of Design b1 for: Where x and θ *T ξ(x) are the input and output of the fuzzy logic system; θ *T is the optimal parameter vector; η2>1 is a positive constant; The designed adaptive law is: Where, γ1, γ2, γ3, σ1, σ2, σ3 are all positive constants; θ is the fuzzy logic system parameter vector; for Adaptive law output; is the estimated value of b; the adaptive law ensures and is non-negative; Step 2: Consider the barrier Lyapunov function Where ρ is the predefined boundary of z1; Consider the following Lyapunov function V: Where, is the estimation error of θ; t c is a positive constant, k(t c ) is the switching function at t c The value of the moment; Step 3: Combining the adaptive law designed in step 1 and the Lyapunov function in step 2, when a judgment condition is met, verify that the electric scooter system is semi-globally asymptotically stable under the designed control law, that is, fault-tolerant control is achieved; the judgment condition is expressed as follows: In the formula, τ1=min[2η1,2η2,σ1,σ2,σ3], 8. The fault-tolerant control method for an electric scooter system under actuator failure and input dead zone according to claim 7, characterized in that: The specific process of designing a fault-tolerant control strategy based on the fault reconstruction results to achieve fault-tolerant control includes: Consider the case of an electric scooter actuator failure. When the actuator fails, the system input u(t) is expressed as: u(t)=u f (t)+f a (t) Where u f (t) is the fault-tolerant control law, which is designed as follows: Where u p (t) is the nominal control input generated by the controller, Reconstructed actuator fault signals for the extended sliding mode observer; This yields the following relationship: Where, is the actuator fault estimation error that converges to zero in finite time.

9. A computer terminal comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the computer program, the steps of the fault-tolerant control method of the electric scooter system under actuator failure and input dead band as claimed in any one of claims 1 to 8 are implemented.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the steps of the fault-tolerant control method of the electric scooter system under actuator failure and input dead band as claimed in any one of claims 1 to 8 are implemented.

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