Preset performance control method based on singular perturbation for multi-motor drive systems

Abstract

The application discloses a preset performance control method based on singular perturbation for a multi-motor driving system, realizes effective control of slow and fast states, and guarantees the performance and stability of the system in the presence of singular disturbance.The steps of the method are as follows: a dynamic model is established for the multi-motor driving system, the dynamic equation of the system is decomposed into two subsystems of fast and slow by using a singular perturbation system; the tracking error is converted by using a preset performance boundary, and a dynamic equation of the converted error is obtained; the original limited tracking error is converted into unlimited tracking error by error conversion, the originally limited tracking control problem is converted into unlimited tracking control problem, and the converted tracking error is guaranteed to be bounded, so that the original tracking error is kept within the preset performance boundary; a sliding surface and a disturbance observer are designed to estimate the external disturbance suffered by the system; and a sliding mode controller is designed to compensate the control by using the estimated external disturbance.

Description

Technical Field

[0001] This invention relates to the fields of control systems and motor drive technology, and more specifically to a preset performance control method based on singular perturbations for multi-motor drive systems. Background Technology

[0002] In existing technologies, several solutions exist for handling singular disturbances. One approach is a singular disturbance suppression method based on model predictive control. This method suppresses singular disturbances by establishing a singular disturbance model and performing predictive compensation. This method introduces a predictive mechanism into the control system, effectively reducing the impact of singular disturbances on system performance by predicting future disturbances and implementing corresponding control actions. Another method related to this invention is a singular disturbance suppression method based on adaptive control. This method improves system stability and performance by estimating and compensating for singular disturbances online. In this method, the controller can sense and adapt to changes in singular disturbances in real time and adjust the control strategy accordingly to maintain system stability and performance. Existing technologies have some drawbacks when dealing with kit drive systems with slow and fast states. Due to the presence of "parasitic" parameters in the system, such as small drag, small capacitance, moment of inertia, or time constant, the system exhibits "singular perturbation" phenomena. The presence of these parameters leads to problems such as increased system order, decreased performance, control difficulties, and instability.

[0003] Therefore, the existing technology faces the following technical problems: 1. The controller design for high-order multi-motor drive systems is complex and the parameter adjustment is difficult; 2. Under the presence of external disturbances, the performance and stability of the control system are affected, making it difficult to achieve the predetermined transient and steady-state performance indicators. Summary of the Invention

[0004] In view of this, the present invention provides a preset performance control method based on singular perturbation for multi-motor drive systems. By introducing singular perturbation technology, the system can be reduced in order, thereby achieving effective control of slow and fast states. At the same time, by designing a control strategy based on preset performance, the system's performance and stability can be guaranteed even in the presence of external disturbances.

[0005] To achieve the above objectives, the technical solution of the present invention—a preset performance control method based on singular perturbation for multi-motor drive systems—comprising the following steps:

[0006] S1: Dynamic modeling is performed on a multi-motor drive system, and the dynamic equations of the system are decomposed into two subsystems, fast and slow, using a singular perturbation system.

[0007] S2: The tracking error is transformed using a preset performance boundary, and the dynamic equation of the transformed error is obtained. Through error transformation, the original restricted tracking error is transformed into an unrestricted tracking error, and the original restricted tracking control problem is transformed into an unrestricted tracking control problem. The transformed tracking error is bounded, so the original tracking error remains within the preset performance boundary and meets the system's performance requirements.

[0008] S3: Design sliding surfaces and disturbance observers to estimate the external disturbances experienced by the system;

[0009] S4: Design a sliding mode controller and use the external disturbances estimated in S3 for compensation control.

[0010] Furthermore, in S1, dynamic modeling is performed on the multi-motor drive system. A singular perturbation system is used to decompose the system's dynamic equations into two subsystems: a fast subsystem and a slow subsystem. Specifically:

[0011]

[0012] Among them, J L b L D L These are the moment of inertia, damping coefficient, and static friction of the end link, respectively, and θ. L , These are the angle, angular velocity, and angular acceleration of the last motor, respectively, T. i J is the torque acting on the i-th motor; i b i D i These are the moment of inertia, damping coefficient, and static friction of the i-th motor, respectively; θ i , These are the angle, angular velocity, and angular acceleration of the i-th motor, respectively; u i It is the control input torque acting on the i-th motor;

[0013] Let x1 = θ L x3=θ i Equation (1) can be written as:

[0014]

[0015] Where z i =θ i -θ L =x 3i -x1、T di Let x be the total disturbance caused by the i-th motor at the load end, k be the elastic coefficient of the drive shaft, and x be the total disturbance caused by the i-th motor. 3i Let x be the angle of the i-th motor.4i Let be the angular velocity of the i-th motor;

[0016] definition b0 is a fixed parameter selected based on the system conditions, such that ε satisfies 0 < ε << 1, resulting in:

[0017]

[0018] For y 1i The first derivative, y 2i y is ε times 1i First derivative, T dj The total disturbance caused by the j-th motor;

[0019] If J i =J m i = 1, ..., 4, J m If is the moment of inertia of the motor rotor, then the last equation can be written as:

[0020]

[0021] Let ε→0, we get:

[0022]

[0023] u is This is the approximate control input for the system when ε = 0;

[0024] Solving equation (5) yields:

[0025]

[0026] in Substituting (6) into (3), we obtain the slow subsystem:

[0027]

[0028] The slow subsystem (7) simplifies to:

[0029]

[0030] in:

[0031]

[0032] definition:

[0033]

[0034] Define tracking error get:

[0035]

[0036] Define a new time variable τ = t / ε, let ε → 0, and then... Substituting (10) into (11), the fast subsystem is written as:

[0037]

[0038] in:

[0039]

[0040] Furthermore, in S2, the tracking error is transformed using a preset performance boundary, and the dynamic equation of the transformed error is obtained, specifically:

[0041] First consider the slow subsystem (8), let x r and Let the target position and target velocity be represented respectively, and the tracking error be defined as... The error dynamic equation of the slow subsystem (8) is:

[0042]

[0043] Consider the following error boundary:

[0044]

[0045] in The upper and lower bounds of the desired control error. The preset performance function has the following specific expression:

[0046]

[0047] in and κ represents the initial and steady-state values ​​of the preset performance function, respectively. x Let the convergence rate be denoted as ; the error is defined as follows:

[0048]

[0049] in:

[0050]

[0051] Error transformation is to transform the constrained original error e x1 Transform into an unrestricted error p1; this error transformation guarantees that as long as p1 is bounded, e x1 Always keep within the preset error boundary given in (15); using (18), the transformed error is obtained as:

[0052]

[0053] in

[0054] The derivative of p1 is:

[0055]

[0056] in

[0057] definition The derivative of p2 can be written as:

[0058]

[0059] in

[0060] From equation (19), it can be seen that when or When the tracking error approaches the given error boundary, p1(t) → +∞ or p1(t) → -∞; therefore, when p1(t) is bounded, e x1 (t) must also satisfy That is, the original tracking error e x1 (t) is constrained within the given error boundary; from this point on, the original control problem with limited tracking error becomes a control problem with unlimited tracking error.

[0061] Similarly, for fast subsystems, a predefined error after performance transformation is defined:

[0062]

[0063] in in The preset performance function has the following specific expression:

[0064]

[0065] in and κ represents the initial and steady-state values ​​of the preset performance function, respectively. y Let q be the convergence rate. 1i The derivative is:

[0066]

[0067] in:

[0068]

[0069] definition That q 2i The derivative of (τ) is:

[0070]

[0071] in:

[0072]

[0073] Furthermore, S3: By designing a sliding mode surface and a disturbance observer, the disturbances experienced by the system are estimated, specifically as follows:

[0074] For the slow subsystem, define the sliding surface s s :

[0075] s s =λ x p1+p2 (28)

[0076] Where λ x >0 is a proportionality coefficient, used to adjust the contribution of different state variables to the sliding surface, thereby adjusting the system's response rate;

[0077] Differentiating with respect to the sliding surface, we get:

[0078]

[0079] in:

[0080]

[0081] Note that equation (23) contains unknown interference. To estimate unknown interference Then, a corresponding compensation controller is designed. First, an interference observer is designed to estimate the interference signal present in the system by measuring the system's input and output. Here, the estimation error s s Design parameters are a key component of the observer; the interference observer is designed as follows:

[0082]

[0083] in It is s s The estimation error, ω x >0 is a design parameter that determines the bandwidth of the interference observer;

[0084] Similarly, for tachy subsystems, a sliding surface is defined:

[0085] s fi =λ y q 1i +q 2i (32)

[0086] Sliding surface s fiThe derivative with respect to the time variable τ is:

[0087]

[0088] in:

[0089] To estimate unknown interference The interference observer is designed as follows:

[0090]

[0091] in: ω y >0 is a design parameter that determines the bandwidth of the interference observer;

[0092] Using the designed interference observers (25) and (34), the unknown interference can be observed. and The estimate.

[0093] Furthermore, S4: Design a sliding mode controller and use the external disturbance estimated in S3 for compensation control, specifically:

[0094] For the slow subsystem, in order to ensure the sliding surface s s Convergence, sliding mode controller u is Designed as:

[0095]

[0096] Where k L1 >0,k L2 >0,k L3 >0, 0 < σ s1 <1,0<σ s2 <1, 0 < γs < 1 are design parameters; k L1 ,k L2 ,k L3 The convergence rate and steady-state error of the system are determined by σ. s1 ,σ s2 It determines the magnitude of chattering in the system output;

[0097] Similarly, for the fast subsystem, a sliding mode controller u is designed. if for:

[0098]

[0099] Where k f1 >0,k f2 >0,k f3 >0, 0 < σ f1 <1,0<σ f2 <1,0<γf <1 is a design parameter; k f1 ,k f2 ,k f3 The convergence rate and steady-state error of the system are determined by σ. f1 ,σ f2 It determines the magnitude of chattering in the system output;

[0100] Using sliding mode controllers (35) and (36), the final controller is obtained as u. i =u is +u if ; using controller u i To ensure the tracking errors p1, p2, q of the fast and slow subsystems 1i ,q 2i It converges to a neighborhood near 0, thus preserving the original tracking error e. x1 It also converges to a neighborhood near 0, and guarantees that... That is, the tracking error of the system meets the preset performance function index.

[0101] Beneficial effects:

[0102] 1. This invention provides a preset performance control method based on singular perturbations for multi-motor drive systems, applicable to modular drive systems. This method reduces the system's order by introducing a disturbance observer and a composite controller, thereby achieving effective control of both slow and fast states. Furthermore, by designing a suitable control strategy, it can ensure system performance and stability even in the presence of singular disturbances. In addition, the control method proposed in this invention simplifies the controller design process and provides convenience for parameter adjustment.

[0103] 2. This invention utilizes singular perturbation theory to address the fast and slow dynamics and singular perturbation phenomena present in multi-motor drive systems. By decomposing the system's dynamic equations into two subsystems, fast and slow, it is possible to better control system behavior and achieve a balance between rapid and slow changes. This separation and balancing control strategy improves the system's stability and performance.

[0104] 3. The present invention introduces a method of preset performance control and disturbance observer to ensure that the system meets the preset performance requirements during the control process, thereby improving the robustness and stability of the system. Attached Figure Description

[0105] Figure 1 A flowchart illustrating a multi-motor drive system with preset performance control based on singular perturbations;

[0106] Figure 2 This is a block diagram of a multi-motor drive system with preset performance control based on singular perturbations.

[0107] Figure 3 An angle tracking curve comparing the preset performance control method for singular perturbations in a multi-motor drive system with that of traditional sliding mode control;

[0108] Figure 4 An angle tracking error curve comparing the preset performance control method for singular perturbations in a multi-motor drive system with that of traditional sliding mode control;

[0109] Figure 5 Speed ​​tracking curves comparing the preset performance control method for singular perturbations in multi-motor drive systems with traditional sliding mode control;

[0110] Figure 6 The speed tracking error curves are shown in the figure, which compare the preset performance control method for singular perturbations of multi-motor drive systems with traditional sliding mode control. Detailed Implementation

[0111] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0112] like Figure 1 The flowchart shown is a step-by-step flowchart for a multi-motor drive system with preset performance control based on singular perturbations, specifically including:

[0113] S1: Dynamic modeling is performed on a multi-motor drive system. A singular perturbation system is used to decompose the dynamic equations of the system into two subsystems, fast and slow, as follows:

[0114]

[0115] Among them, J L b L D L These are the moment of inertia, damping coefficient, and static friction of the end link, respectively, and θ. L , These are the angle, angular velocity, and angular acceleration of the last motor, respectively, T. i J is the torque acting on the i-th motor. i b i D i θ represents the moment of inertia, damping coefficient, and static friction of the i-th motor, respectively. i , These are the angle, angular velocity, and angular acceleration of the i-th motor, respectively. i It is the control input torque acting on the i-th motor.

[0116] Let x1 = θ L x3=θ i Equation (1) can be written as:

[0117]

[0118] z i =θ i -θ L =x 3i -x1, We can obtain:

[0119] Where z i =θ i -θ L =x 3i -x1,T di Let x be the total disturbance caused by the i-th motor at the load end, k be the elastic coefficient of the drive shaft, and x be the total disturbance caused by the i-th motor. 3i Let x be the angle of the i-th motor. 4i Let be the angular velocity of the i-th motor.

[0120] definition b0 is a fixed parameter selected based on the system conditions, such that ε satisfies 0 < ε << 1, resulting in:

[0121]

[0122] in For y 1i The first derivative, y 2i y is ε times 1i First derivative, T dj The total disturbance caused by the j-th motor.

[0123] If J i =J m i = 1, ..., 4, J m Let be the moment of inertia of the motor rotor. Then the last equation can be written as:

[0124]

[0125] Let ε→0, we get:

[0126]

[0127] u is When ε = 0, it is the approximate control input of the system.

[0128] Solving equation (5) yields:

[0129]

[0130] in Substituting (6) into (3), we obtain the slow subsystem:

[0131]

[0132] The slow subsystem (7) simplifies to:

[0133]

[0134] in:

[0135]

[0136] definition:

[0137]

[0138] Define tracking error get:

[0139]

[0140] Define a new time variable τ = t / ε, let ε → 0, and then... Substituting (10) into (11), the fast subsystem is written as:

[0141]

[0142] in:

[0143]

[0144] S2: Design preset performance control, design appropriate control strategies and parameters to ensure that the system achieves the preset performance indicators and requirements during the control process, and ensures that the system can meet the expected performance standards under various operating conditions. Specifically:

[0145] First consider the slow subsystem (8), let x r and Let the target position and target velocity be represented respectively, and the tracking error be defined as... The error dynamic equation of the slow subsystem (8) is:

[0146]

[0147] Consider the following error boundary:

[0148]

[0149] in δ x , The upper and lower bounds of the desired control error. The preset performance function has the following specific expression:

[0150]

[0151] in and κ represents the initial and steady-state values ​​of the preset performance function, respectively. x Let this be the convergence rate. The error is defined as follows:

[0152]

[0153] in:

[0154]

[0155] The main purpose of error transformation is to transform the constrained original error e x1 This is converted to an unrestricted error p1. This error transformation guarantees that as long as p1 is bounded, e... x1 It always remains within the preset error boundary given in (15). Using (18), the transformed error can be obtained as:

[0156]

[0157] in

[0158] The derivative of p1 is:

[0159]

[0160] in

[0161] definition The derivative of p2 can be written as:

[0162]

[0163] in

[0164] From equation (19), it can be seen that when or When the tracking error approaches a given error boundary, p1(t) → +∞ or p1(t) → -∞. Therefore, when p1(t) is bounded, e x1 (t) must also satisfy That is, the original tracking error e x1 (t) is constrained within the given error boundary. From this point on, the original control problem with limited tracking error becomes a control problem with unlimited tracking error, which prepares the conditions for the subsequent controller design.

[0165] Similarly, for fast subsystems, a predefined error after performance transformation is defined:

[0166]

[0167] in in The preset performance function has the following specific expression:

[0168]

[0169] in and κ represents the initial and steady-state values ​​of the preset performance function, respectively. y Let q be the convergence rate. 1i The derivative is:

[0170]

[0171] in:

[0172]

[0173] definition That q 2i The derivative of (τ) is:

[0174]

[0175] in:

[0176]

[0177] S3: By designing a sliding mode surface and a disturbance observer, the disturbances experienced by the system are estimated, specifically as follows:

[0178] For the slow subsystem, define the sliding surface s s :

[0179] s s =λ x p1+p2 (28)

[0180] Where λ x A value greater than 0 represents the proportionality coefficient, used to adjust the contribution of different state variables to the sliding surface, thereby regulating the system's response rate. This sliding surface maps the system's high-dimensional state error to a low-dimensional space, thus simplifying the controller's design complexity.

[0181] Differentiating with respect to the sliding surface, we can obtain:

[0182]

[0183] in:

[0184]

[0185] Note that equation (23) contains unknown interference. To estimate unknown interference Then, a corresponding compensation controller is designed. First, an interference observer is designed to estimate the interference signal present in the system by measuring the system's input and output. Here, the estimation error s s The design parameters are key components of the observer. The interference observer is designed as follows:

[0186]

[0187] in It is s s The estimation error, ω x >0 is a design parameter that determines the bandwidth of the interference observer.

[0188] Similarly, for a fast subsystem, a sliding surface is defined:

[0189] s fi =λ y q 1i +q 2i (32)

[0190] Sliding surface s fi The derivative with respect to the time variable τ is:

[0191]

[0192] in:

[0193] To estimate unknown interference The interference observer is designed as follows:

[0194]

[0195] in: ω y >0 is a design parameter that determines the bandwidth of the interference observer.

[0196] Using the designed interference observers (25) and (34), the unknown interference can be observed. and The estimate.

[0197] S4: Design a sliding mode controller and use the external disturbance estimated in S3 for compensation control, specifically:

[0198] For the slow subsystem, in order to ensure the sliding surface s s Convergence, sliding mode controller u is Designed as:

[0199]

[0200] Where kL1 >0,k L2 >0,k L3 >0, 0 < σ s1 <1,0<σ s2 <1,0<γ s <1 is a design parameter. k L1 ,k L2 ,k L3 The σ value determines the system's convergence speed and steady-state error; a larger σ value results in faster convergence and smaller steady-state error. s1 ,σ s2 The magnitude of γ determines the amount of jitter in the system output. A larger γ results in less jitter, but increases tracking error; a smaller γ... s It can improve the convergence speed when the error is small.

[0201] Similarly, for fast subsystems, sliding mode controllers can be designed. if for:

[0202]

[0203] Where k f1 >0,k f2 >0,k f3 >0, 0 < σ f1 <1,0<σ f2 <1,0<γ f <1 is a design parameter. k f1 ,k f2 ,k f3 The σ value determines the system's convergence speed and steady-state error; a larger σ value results in faster convergence and smaller steady-state error. f1 ,σ f2 The magnitude of γ determines the amount of jitter in the system output. A larger γ results in less jitter, but increases tracking error; a smaller γ... s It can improve the convergence speed when the error is small.

[0204] Using sliding mode controllers (35) and (36), the final controller can be obtained as u. i =u is +u if Using controller u i This ensures that the tracking errors p1, p2, q of the fast and slow subsystems can be guaranteed. 1i ,q 2i It can converge to a neighborhood near 0, thus ensuring the original tracking error e is preserved. x1 It can also converge to a neighborhood near 0, and it is guaranteed that... That is, the tracking error of the system meets the preset performance function index.

[0205] Figure 2The block diagram illustrates the framework of a multi-motor drive system with preset performance control based on singular perturbations.

[0206] The technical solution disclosed in this invention was simulated and verified, as follows:

[0207] Step 1: Select the system parameters for the multi-motor drive and design the controller parameters. The system parameters are selected as follows: J L =1,b L =0.01,J m =0.1,b m =0.001.

[0208] The control parameters of the pre-defined performance control method based on singular perturbations are shown in Table 1:

[0209] Table 1 Control Parameter Table

[0210]

[0211] Step 2: Select a reference signal and design the sampling period and simulation duration.

[0212] The reference trajectory is chosen as sin(t+π / 2), the sampling period is set to dt=0.0001s, and the simulation duration is designed as t. stop =10s.

[0213] Step 3: Compare the proposed singular perturbation-based preset performance control method with the traditional sliding mode control method through simulation experiments.

[0214] The traditional sliding mode control method is as follows:

[0215]

[0216] The parameters therein are consistent with the parameters selected in this invention.

[0217] Experimental comparison results are as follows Figure 3 , Figure 4 , Figure 5 , Figure 6 As shown. Figure 3 An angle tracking curve comparing the preset performance control method for singular perturbations in a multi-motor drive system with that of traditional sliding mode control; Figure 4 An angle tracking error curve comparing the preset performance control method for singular perturbations in a multi-motor drive system with that of traditional sliding mode control; Figure 5 Speed ​​tracking curves comparing the preset performance control method for singular perturbations in multi-motor drive systems with traditional sliding mode control; Figure 6 The speed tracking error curves are shown in the figure, which compare the preset performance control method for singular perturbations of multi-motor drive systems with traditional sliding mode control.

[0218] As shown in the diagram, both controllers can drive the angle to the desired setpoint without violating predefined boundaries. Figure 3 It can be seen that the traditional sliding mode control method has a faster convergence speed than the method proposed in this invention, but the traditional sliding mode control method has a larger angle tracking error jitter and a larger absolute deviation from 0. According to Figure 4 and 6 It can be seen that both control methods have relatively small angular velocity tracking errors. According to... Figure 5 It can be seen that the preset performance control based on singular perturbations has a smaller gap with the preset trajectory compared to sliding mode control, and thus exhibits better tracking performance. This indicates that by introducing preset performance control and a disturbance observer, the angular velocity can be maintained within a small range, resulting in a smaller gap with the preset trajectory.

[0219] Based on the above technical content, this invention utilizes singular perturbation theory to address the fast and slow dynamics and singular perturbation phenomena existing in multi-motor drive systems. By decomposing the system's dynamic equations into two subsystems, fast and slow, the system's behavior can be better controlled, achieving a balance between rapid and slow changes. This separation and balancing control strategy improves the system's stability and performance. The introduction of preset performance control and disturbance observers ensures that the system meets pre-set performance requirements during control, thus improving the system's robustness and stability.

[0220] In summary, the above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A singular perturbation based preset performance control method for a multi-motor drive system, characterized by, Comprising the following steps: S1: dynamic modeling for multi-motor drive system, using singular perturbation system to decompose the dynamic equation of the system into fast and slow two subsystems; S2: using the preset performance boundary to convert the tracking error, and obtaining the dynamic equation of the converted error; Through error conversion, the original limited tracking error is converted into unlimited tracking error, and the originally limited tracking error is converted into unlimited tracking error. The originally limited tracking error is converted into unlimited tracking error, and the originally limited tracking error is converted into unlimited tracking error. The converted tracking error is bounded, and the original tracking error is kept within the preset performance boundary, which meets the performance index requirements of the system; S3: design of sliding mode surface and disturbance observer, estimation of external disturbance suffered by the system; S4: design of sliding mode controller, and compensation control by using the external disturbance estimated in S3; In the S1, dynamic modeling is performed for the multi-motor drive system, and the dynamic equation of the system is decomposed into fast and slow two subsystems by using singular perturbation system, specifically: （1） wherein, , , are respectively the moment of inertia, the damping coefficient, the static friction of the end link, , , are respectively the angle, the angular velocity, the angular acceleration of the last motor, is the torque acting on the first motor; , , are respectively the moment of inertia, the damping coefficient, the static friction of the first motor; , , are respectively the angle, the angular velocity, the angular acceleration of the first motor; is the control input torque acting on the first motor; Let , formula (1) is written as: （2） wherein , is the total disturbance from the i-th motor at the load end, is the spring constant of the transmission shaft, is the angle of the i-th motor, is the angular velocity of the i-th motor; Definition , b0 is a fixed parameter selected according to system conditions, so that satisfies , get: （3） is the first derivative of is the first derivative of is the first derivative of is the total disturbance brought by the jth motor;​​ Let , be the moment of inertia of the rotor of the electric machine, then the last equation is written as: （4） Let Obtained: （5） For approximate control input of the system; Solving equation (5) obtains: （6） wherein Substituting (6) into (3), we obtain the slow subsystem: （7） The slow subsystem (7) is simplified as: （8） Wherein: （9） Definition: （10） Defining a tracking error gives: （11） Define a new time variable , let , and substituting and (10) into (11), the fast subsystem writes as: （12） u if is the sliding mode controller function for the fast subsystem, where: （13）； In the S2, the tracking error is converted by using the preset performance boundary, and the dynamic equation of the converted error is obtained, specifically: Consider the slow subsystem (8) first, let and denote the target position and target velocity, respectively, define the tracking error as and the error dynamics of the slow subsystem (8) is （14） Considering the following error boundary: （15） wherein is an upper bound of the desired control error, is a preset performance function, whose specific expression is as follows: （16） wherein , and are the initial and steady state values of the predetermined performance function, respectively, is the convergence rate; the error conversion is defined as: （17） Wherein: （18） The error conversion is to convert the limited original error into an unlimited error ; the error conversion guarantees that as long as the error is bounded, then it will always remain within the preset error boundary given in (15); using (18), the transformed error is obtained as: （19） wherein ; The derivative is: （20） wherein , , ; Definitions Then The derivative of is written as: （21） wherein , , ; From (19), when or , i.e., the tracking error is close to the given error bound, or ; therefore, when is bounded, it is also necessary that , i.e., the original tracking error is constrained within the given error bound; from here, the originally tracking error constrained control problem becomes a tracking error unconstrained control problem; For the fast subsystem, define the error after performance transformation as: （22） wherein wherein is a preset performance function, wherein is the upper and lower bounds of the desired control error, which is expressed as follows: （23） wherein , and are the initial and steady state values of the predetermined performance function, respectively, is the convergence rate, then the derivative of （24） Wherein: （25） Definitions That is The derivative of that is: （26） Wherein: （27）。 2. The singular perturbation based pre-specified performance control method for a multi-motor drive system of claim 1, wherein, In the S3, the disturbance suffered by the system is estimated by designing the sliding mode surface and the disturbance observer, specifically: For the slow subsystem, a sliding surface is defined : （28） wherein is a proportionality factor used to adjust the contribution of the different state variables to the sliding surface, and thus to adjust the response rate of the system; Derivation of the sliding mode surface obtains: （29） Wherein: （30） The unknown disturbance is contained in equation (29) ; in order to estimate the unknown disturbance Further, a corresponding compensation controller is designed, first, a disturbance observer is designed to estimate the disturbance signal existing in the system by measuring the input and output of the system; the disturbance observer is designed as: （31） wherein is the estimation error of is a design parameter that determines the bandwidth of the disturbance observer; is the estimate of the unknown disturbance ; For the fast subsystem, define the sliding mode surface as: （32） λ y is a proportionality factor; Sliding surface With respect to the time variable The derivative with respect to the time variable is: （33） wherein: ; To estimate the unknown disturbance The disturbance observer is designed as follows: （34） in: yes The estimation error, The design parameters determine the bandwidth of the interference observer; for Estimated value; With the designed disturbance observers (31) and (34), the estimation of unknown disturbances and is achieved.

3. The singular perturbation based pre-specified performance control method for a multi-motor drive system of claim 2, wherein, In the S4, the sliding mode controller is designed, and the external disturbance estimated in S3 is compensated, specifically: For the slow subsystem, in order to guarantee the convergence of the sliding surface , the sliding mode controller is designed as: （35） wherein are design parameters; determine the convergence speed and steady-state error of the system; determine the chattering size in the system output; For the fast subsystem, a sliding mode controller is designed is: （36） wherein are design parameters; determine the convergence speed and steady-state error of the system; determine the chattering size in the system output; Using the sliding mode controllers (35) and (36), the final controller is ; Using a controller , the tracking error of the fast subsystem is guaranteed to converge to a neighborhood of 0 , and the tracking error of the slow subsystem is guaranteed to converge to a neighborhood of 0 , and the tracking error of the slow subsystem is guaranteed to satisfy , i.e., the tracking error of the system satisfies the pre-specified performance function index.

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