Singular perturbation-based preset performance control method for multi-motor driving system

Abstract

The invention discloses a singular perturbation-based preset performance control method for a multi-motor driving system, which realizes effective control on slow and fast states and ensures the performance and stability of the system in the presence of singular perturbation. The method comprises the following steps: carrying out dynamic modeling on a multi-motor driving system, and decomposing a dynamic equation of the system into a fast subsystem and a slow subsystem by adopting a singular perturbation system; converting the tracking error by using a preset performance boundary, and obtaining a dynamic equation of the conversion error; the method comprises the following steps: converting an original limited tracking error into an unlimited tracking error through error conversion, converting an original limited tracking control problem into an unlimited tracking control problem, and ensuring that the converted tracking error is bounded, so that the original tracking error is kept within a preset performance boundary; designing a sliding mode surface and a disturbance observer, and estimating external disturbance suffered by the system; and designing a sliding mode controller, and performing compensation control by using the estimated external disturbance.

Description

Technical Field

[0001] The present invention relates to the technical field of control systems and motor drive technologies, and in particular to a preset performance control method based on singular perturbations for a multi-motor drive system. Background Art

[0002] In the prior art, there are some solutions for dealing with the problem of singular disturbances. Among them, one method is a singular disturbance suppression method based on model predictive control. This method achieves the suppression of singular disturbances by establishing a singular disturbance model and performing predictive compensation. This method introduces a prediction mechanism in the control system, and effectively reduces the impact of singular disturbances on system performance by predicting future disturbances and performing corresponding control actions. Another method related to the present invention is a singular disturbance suppression method based on adaptive control. This method improves the stability and performance of the system by online estimation and compensation of singular disturbances. In this method, the controller can sense and adapt to the changes of singular disturbances in real time, and adjust the control strategy accordingly to maintain the stability and performance of the system. The prior art has some disadvantages when dealing with a set drive system with slow and fast states. Due to the presence of some "parasitic" parameters in the system, such as small resistance, small capacitance, moment of inertia or time constant, the system has a "singular perturbation" phenomenon. The presence of these parameters will lead to problems such as increased system order, reduced performance, difficult control 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 parameter adjustment is difficult; 2. In the presence of external disturbances, the performance and stability of the control system are affected, making it difficult to achieve 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 perturbations for a multi-motor drive system, which can reduce the order of the system by introducing singular perturbation technology, thereby achieving effective control of slow and fast states; at the same time, by designing a control strategy based on preset performance, it can ensure the performance and stability of the system in the presence of external disturbances.

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

[0006] S1: Dynamic modeling of the multi-motor drive system is carried out, 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 converted using the preset performance boundary, and the dynamic equation of the converted error is obtained; through error conversion, the original restricted tracking error is converted into an unrestricted tracking error, and the originally restricted tracking control problem is converted into an unrestricted tracking control problem, and the converted tracking error is guaranteed to be bounded, so that the original tracking error remains within the preset performance boundary and meets the performance index requirements of the system;

[0008] S3: Design sliding surface and disturbance observer to estimate the external disturbances to the system;

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

[0010] Furthermore, in S1, the dynamic modeling of the multi-motor drive system is carried out, and the dynamic equation of the system is decomposed into two subsystems, fast and slow, using a singular perturbation system, specifically:

[0011]

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

[0013] Let x 1 =θ L ,x 3 =θ i , formula (1) is written as:

[0014]

[0015] where z i =θ i -θ L =x 3i -x 1 、T diis the total disturbance caused by the i-th motor on the load end, k is the elastic coefficient of the transmission shaft, x 3i is the angle of the i-th motor, x 4i is the angular velocity of the i-th motor;

[0016] definition b 0 is a fixed parameter selected according to the system conditions, so that ε satisfies 0<ε<<1, and we get:

[0017]

[0018] for y 1i The first derivative of , y 2i ε times y 1i First-order derivative, T dj is the total disturbance brought by the jth motor;

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

[0020]

[0021] Let ε→0 to obtain:

[0022]

[0023] u is is the approximate control input of 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) is simplified to:

[0029]

[0030] in:

[0031]

[0032] definition:

[0033]

[0034] Defining Tracking Error get:

[0035]

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

[0037]

[0038] in:

[0039]

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

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

[0042]

[0043] Consider the following error bounds:

[0044]

[0045] in are the upper and lower bounds of the desired control error, is the preset performance function, and its specific expression is as follows:

[0046]

[0047] in and are the initial value and steady-state value of the preset performance function, κ x is the convergence rate; the error conversion is defined as:

[0048]

[0049] in:

[0050]

[0051] The error transformation is to convert the restricted original error e x1 Transformed into an unrestricted error p 1 ; This error conversion ensures that as long as p1 If e is bounded, x1 Always keep within the preset error boundary given by (15); using (18), the transformed error is:

[0052]

[0053] in

[0054] p 1 The derivative of is:

[0055]

[0056] in

[0057] definition Then p 2 The derivative of is written as:

[0058]

[0059] in

[0060] From formula (19), we can see that when or When the tracking error approaches the given error boundary, p 1 (t)→+∞or p 1 (t)→-∞; therefore, when p 1 When (t) is bounded, e x1 (t) must also satisfy That is, the original tracking error e x1 (t) is constrained within a given error boundary; hence, the original control problem with limited tracking error becomes a control problem with unrestricted tracking error;

[0061] Similarly, for the fast subsystem, define the error after the preset performance transformation:

[0062]

[0063] in in is the preset performance function, and its specific expression is as follows:

[0064]

[0065] in and are the initial value and steady-state value of the preset performance function, κ y is the convergence rate, then q 1i The derivative of is:

[0066]

[0067] in:

[0068]

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

[0070]

[0071] in:

[0072]

[0073] Furthermore, S3: by designing the sliding surface and the disturbance observer, the disturbance to the system is estimated, specifically:

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

[0075] s s =λ x p 1 +p 2 (28)

[0076] where λ x >0 is the proportional coefficient, which is used to adjust the contribution of different state variables to the sliding surface, thereby adjusting the response rate of the system;

[0077] Taking the derivative of the sliding surface, we get:

[0078]

[0079] in:

[0080]

[0081] Note that equation (23) contains unknown interference To estimate the unknown interference Then design the corresponding compensation controller. First, design the disturbance observer, which is used to estimate the disturbance signal in the system by measuring the input and output of the system. The estimation error s s and design parameters are the key components of the observer; the disturbance observer is designed as:

[0082]

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

[0084] Similarly, for the fast subsystem, the sliding surface is defined as:

[0085] s fi =λ y q 1i +q 2i (32)

[0086] Sliding surface fi The derivative with respect to the time variable τ is:

[0087]

[0088] in:

[0089] To estimate the unknown interference The disturbance 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 disturbance observers (25) and (34), we can achieve the unknown disturbance and Estimates.

[0093] Further, S4: design a sliding mode controller and use the external disturbance estimated in S3 to perform compensation control, specifically:

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

[0095]

[0096] where k L1 >0,k L2 >0,k L3 >0,0<σ s1 <1,0<σ s2 <1,0<γs<1 is a design parameter; k L1 ,k L2 ,k L3 Determines the convergence speed and steady-state error of the system; σ s1 ,σ s2 Determines the amount of jitter in the system output;

[0097] Similarly, for the fast subsystem, design the sliding mode controller u if for:

[0098]

[0099] 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 Determines the convergence speed and steady-state error of the system; σ f1 ,σ f2 Determines the amount of jitter in the system output;

[0100] Using the sliding mode controllers (35) and (36), the final controller is u i =u is +u if ; Using controller u i , to ensure the tracking error p of the fast and slow subsystems 1 ,p 2 ,q 1i ,q 2i Converges to a region near 0, thus ensuring the original tracking error e x1 It also converges to a neighborhood near 0 and is guaranteed to satisfy That is, the system's tracking error meets the preset performance function indicators.

[0101] Beneficial effects:

[0102] 1. The preset performance control method based on singular perturbation for a multi-motor drive system provided by the present invention is used for a suit drive system. The method reduces the order of the system by introducing a disturbance observer and a composite controller, thereby achieving effective control of slow and fast states. At the same time, by designing a suitable control strategy, the performance and stability of the system can be guaranteed in the presence of singular disturbances. In addition, the control method proposed by the present invention simplifies the controller design process and provides convenience for parameter adjustment.

[0103] 2. The present invention uses singular perturbation theory to deal with the fast and slow dynamics and singular perturbation phenomena in the multi-motor drive system. By decomposing the dynamic equations of the system into two subsystems, fast and slow, the behavior of the system can be better controlled and a balance can be achieved between fast changes and slow changes. This separation and balance control strategy improves the stability and performance of the system.

[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. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0106] Figure 2 A block diagram of a multi-motor drive system for controlling preset performance based on singular perturbations;

[0107] Figure 3 Angle tracking curve diagram comparing the preset performance control method with the traditional sliding mode control for the singular perturbation of the multi-motor drive system;

[0108] Figure 4 Angle tracking error curve graph comparing the preset performance control method with the traditional sliding mode control for the singular perturbation of the multi-motor drive system;

[0109] Figure 5 Speed ​​tracking curve diagram comparing the preset performance control method with the traditional sliding mode control for the singular perturbation of the multi-motor drive system;

[0110] Figure 6 Plot of velocity tracking error comparing the preset performance control method with traditional sliding mode control for singular perturbations of a multi-motor drive system. DETAILED DESCRIPTION

[0111] The present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0112] like Figure 1 The flowchart of a flowchart of a multi-motor drive system for preset performance control based on singular perturbations specifically includes:

[0113] S1: Dynamic modeling of the multi-motor drive system is carried out, and the dynamic equation of the system is decomposed into two subsystems, fast and slow, using a singular perturbation system, specifically;

[0114]

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

[0116] Let x 1 =θ L ,x 3 =θ i , formula (1) is written as:

[0117]

[0118] z i =θ i -θ L =x 3i -x 1 , You can get:

[0119] where z i =θ i -θ L =x 3i -x 1 , T di is the total disturbance caused by the i-th motor on the load end, k is the elastic coefficient of the transmission shaft, x 3i is the angle of the i-th motor, x 4i is the angular velocity of the i-th motor.

[0120] definition b 0 is a fixed parameter selected according to the system conditions, so that ε satisfies 0<ε<<1, and we get:

[0121]

[0122] in for y 1i The first derivative of , y 2i ε times y 1i First-order derivative, T dj is the total disturbance brought by the jth motor.

[0123] If J i =J m ,i=1,…,4,J m is the moment of inertia of the motor rotor, then the last equation is written as:

[0124]

[0125] Let ε→0 to obtain:

[0126]

[0127] u is When ε=0, 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) is simplified to:

[0133]

[0134] in:

[0135]

[0136] definition:

[0137]

[0138] Defining Tracking Error get:

[0139]

[0140] Define a new time variable τ = t / ε, set ε→0, and 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 meets the preset performance indicators and requirements during the control process, and ensure that the system can meet the expected performance standards under various working conditions, specifically:

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

[0146]

[0147] Consider the following error bounds:

[0148]

[0149] in δ x , are the upper and lower bounds of the desired control error, is the preset performance function, and its specific expression is as follows:

[0150]

[0151] in and are the initial value and steady-state value of the preset performance function, κ x is the convergence rate. The error conversion is defined as:

[0152]

[0153] in:

[0154]

[0155] The main purpose of error transformation is to convert the restricted original error e x1 Transformed into an unrestricted error p 1 This error conversion can ensure that as long as p 1 If e is bounded, x1 Always keep within the preset error boundary given by (15). Using (18), the transformed error can be obtained as:

[0156]

[0157] in

[0158] p 1 The derivative of is:

[0159]

[0160] in

[0161] definition Then p 2 The derivative of is written as:

[0162]

[0163] in

[0164] From formula (19), we can see that when or When the tracking error approaches the given error boundary, p 1 (t)→+∞or p 1 (t)→-∞. Therefore, when p 1 When (t) is bounded, e x1 (t) must also satisfy That is, the original tracking error e x1 (t) is constrained within a given error boundary. From then on, the original control problem with limited tracking error becomes a control problem with unrestricted tracking error, which prepares the conditions for the subsequent controller design.

[0165] Similarly, for the fast subsystem, define the error after the preset performance transformation:

[0166]

[0167] in in is the preset performance function, and its specific expression is as follows:

[0168]

[0169] in and are the initial value and steady-state value of the preset performance function, κ y is the convergence rate, then q 1i The derivative of is:

[0170]

[0171] in:

[0172]

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

[0174]

[0175] in:

[0176]

[0177] S3: By designing the sliding surface and disturbance observer, the disturbance to the system is estimated, specifically:

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

[0179] s s =λ x p 1 +p 2 (28)

[0180] where λ x >0 is the proportional coefficient, which is used to adjust the contribution of different state variables to the sliding surface, thereby adjusting the response rate of the system. The sliding surface maps the high-dimensional state error of the system to a low-dimensional space, thereby simplifying the design complexity of the controller.

[0181] Taking the derivative of the sliding surface, we can get:

[0182]

[0183] in:

[0184]

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

[0186]

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

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

[0189] s fi =λ y q 1i +q 2i (32)

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

[0191]

[0192] in:

[0193] To estimate the unknown interference The disturbance 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 disturbance observers (25) and (34), we can achieve the unknown disturbance and Estimates.

[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 The convergence of the sliding mode controller u is Designed to:

[0199]

[0200] where k L1 >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 Determines the convergence speed and steady-state error of the system. The larger the value, the faster the convergence speed and the smaller the steady-state error. s1 ,σ s2 Determines the magnitude of the jitter in the system output. The larger the value, the smaller the jitter, but the tracking error will increase; a smaller γ s It can improve the convergence speed when the error is small.

[0201] Similarly, for the fast subsystem, a sliding mode controller u 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 Determines the convergence speed and steady-state error of the system. The larger the value, the faster the convergence speed and the smaller the steady-state error. f1,σ f2 Determines the magnitude of the jitter in the system output. The larger the value, the smaller the jitter, but the tracking error will increase; a smaller γ s It can improve the convergence speed when the error is small.

[0204] Using the sliding mode controller (35) and (36), the final controller can be obtained as u i =u is +u if . Using controller u i , which can ensure the tracking error p of the fast and slow subsystems 1 ,p 2 ,q 1i ,q 2i It can converge to a region near 0, thus ensuring the original tracking error e x1 It can also converge to a local region near 0 and ensure that That is, the system's tracking error meets the preset performance function indicators.

[0205] Figure 2 A block diagram of a multi-motor drive system with preset performance control based on singular perturbations is presented, describing the framework of the entire control system.

[0206] The technical solution disclosed in the present invention is simulated and verified as follows:

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

[0208] The control parameters of the preset performance control method based on singular perturbation are shown in Table 1:

[0209] Table 1 Control parameters

[0210]

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

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

[0213] Step 3: Conduct simulation experiments to compare the preset performance control method based on singular perturbation proposed in the present invention with the traditional sliding mode control method.

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

[0215]

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

[0217] The experimental comparison results are as follows Figure 3 , Figure 4 , Figure 5 , Figure 6 shown. Figure 3 Angle tracking curve diagram comparing the preset performance control method with the traditional sliding mode control for the singular perturbation of the multi-motor drive system; Figure 4 Angle tracking error curve graph comparing the preset performance control method with the traditional sliding mode control for the singular perturbation of the multi-motor drive system; Figure 5 Speed ​​tracking curve diagram comparing the preset performance control method with the traditional sliding mode control for the singular perturbation of the multi-motor drive system; Figure 6 Plot of velocity tracking error comparing the preset performance control method with traditional sliding mode control for singular perturbations of a multi-motor drive system.

[0218] From the figure, it can be seen that both controllers can drive the angle to the desired set point without violating the 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 the present invention, but the angle tracking error jitter of the traditional sliding mode control method is larger and the absolute deviation from 0 is larger. Figure 4 and 6 It can be seen that both control methods have small angular velocity tracking errors. Figure 5 It can be seen that the preset performance control based on singular perturbation has a smaller gap with the preset trajectory than the sliding mode control, and has good tracking performance. This shows that by introducing the preset performance control and the disturbance observer, the angular velocity can be maintained within a smaller range, and the gap with the preset trajectory is smaller.

[0219] Based on the above technical content, the present invention uses singular perturbation theory to deal with the fast and slow dynamics and singular perturbation phenomena in multi-motor drive systems. By decomposing the dynamic equations of the system into two subsystems, fast and slow, the behavior of the system can be better controlled and a balance can be achieved between fast changes and slow changes. This separation and balance control strategy improves the stability and performance of the system. The method of preset performance control and disturbance observer is introduced to ensure that the system meets the preset performance requirements during the control process, thereby improving the robustness and stability of the system.

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

Claims

1. A preset performance control method based on singular perturbation for a multi-motor drive system, characterized in that: The steps include: S1: Dynamic modeling of the multi-motor drive system is carried out, and the dynamic equations of the system are decomposed into two subsystems, fast and slow, using a singular perturbation system; S2: Convert the tracking error using the preset performance boundary and obtain the dynamic equation of the converted error; Through error conversion, the original restricted tracking error is converted into an unrestricted tracking error, and the originally restricted tracking control problem is converted into an unrestricted tracking control problem. The converted tracking error is guaranteed to be bounded, so that the original tracking error remains within the preset performance boundary and meets the performance index requirements of the system. S3: Design sliding surface and disturbance observer to estimate the external disturbances to the system; S4: Design a sliding mode controller and use the external disturbance estimated in S3 for compensation control.

2. The preset performance control method based on singular perturbation for a multi-motor drive system according to claim 1, characterized in that: In S1, dynamic modeling is performed for the multi-motor drive system, and the dynamic equation of the system is decomposed into two subsystems, fast and slow, using a singular perturbation system, specifically: Among them, J L , b L , D L They are the moment of inertia, damping coefficient, and static friction of the end link, θ L , They are the angle, angular velocity, and angular acceleration of the last motor, T i is the torque acting on the i-th motor; J i , b i , D i are the moment of inertia, damping coefficient, and static friction of the i-th motor; θ i , are the angle, angular velocity, and angular acceleration of the i-th motor; u i is the control input torque acting on the i-th motor; Let x1 = θ L ,x3=θ i , formula (1) is written as: where z i =θ i -θ L =x 3i -x1, T di is the total disturbance caused by the i-th motor on the load end, k is the elastic coefficient of the transmission shaft, x 3i is the angle of the i-th motor, x 4i is the angular velocity of the i-th motor; definition b0 is a fixed parameter selected according to the system conditions, so that ε satisfies 0<ε<<1, and we get: for y 1i The first derivative of , y 2i ε times y 1i First-order derivative, T dj is the total disturbance brought by the jth motor; If J i =J m ,i=1,…,4,J m is the moment of inertia of the motor rotor, then the last equation is written as: Let ε→0 to obtain: u is is the approximate control input of the system when ε=0; Solving equation (5) yields: in Substituting (6) into (3), we obtain the slow subsystem: The slow subsystem (7) is simplified to: in: definition: Defining Tracking Error get: Define a new time variable τ = t / ε, set ε→0, and Substituting (10) into (11), the fast subsystem is written as: in:

3. The preset performance control method based on singular perturbation for a multi-motor drive system according to claim 1, characterized in that: In S2, the tracking error is converted using the preset performance boundary, and a dynamic equation of the conversion error is obtained, which is specifically: First consider the slow subsystem (8), let x r and They represent the target position and target velocity respectively, and the tracking error is defined as e x1 =x1-x r , The error dynamic equation of the slow subsystem (8) is: Consider the following error bounds: in are the upper and lower bounds of the desired control error, is the preset performance function, and its specific expression is as follows: in and are the initial value and steady-state value of the preset performance function, κ x is the convergence rate; the error conversion is defined as: in: The error transformation is to convert the restricted original error e x1 is converted to an unrestricted error p1; this error conversion ensures that as long as p1 is bounded, then e x1 Always keep within the preset error boundary given by (15); using (18), the error after transformation is: in The derivative of p1 is: in definition Then the derivative of p2 is written as: in From formula (19), we can see 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 a given error boundary; hence, the original control problem with limited tracking error becomes a control problem with unrestricted tracking error; Similarly, for the fast subsystem, define the error after the preset performance transformation: in in is the preset performance function, and its specific expression is as follows: in and are the initial value and steady-state value of the preset performance function, κ y is the convergence rate, then q 1i The derivative of is: in: definition That Q 2i The derivative of (τ) is: in:

4. The preset performance control method based on singular perturbation for a multi-motor drive system according to claim 3, characterized in that: S3: By designing the sliding surface and the disturbance observer, the disturbance to the system is estimated, specifically: For the slow subsystem, define the sliding surface s s : s s =λ x p1+p2 (28) where λ x >0 is the proportional coefficient, which is used to adjust the contribution of different state variables to the sliding surface, thereby adjusting the response rate of the system; Taking the derivative of the sliding surface, we get: in: Note that equation (23) contains unknown interference To estimate the unknown interference Then design the corresponding compensation controller. First, design the disturbance observer, which is used to estimate the disturbance signal in the system by measuring the input and output of the system. The estimation error s s and design parameters are the key components of the observer; the disturbance observer is designed as: in Yes s The estimation error, ω x >0 is a design parameter that determines the bandwidth of the interference observer; Similarly, for the fast subsystem, the sliding surface is defined as: s fi =λ y q 1i +q 2i (32) Sliding surface fi The derivative with respect to the time variable τ is: in: To estimate the unknown interference The disturbance observer is designed as follows: in: ω y >0 is a design parameter that determines the bandwidth of the interference observer; Using the designed disturbance observers (25) and (34), we can achieve the unknown disturbance and Estimates.

5. The preset performance control method based on singular perturbation for a multi-motor drive system according to claim 1, characterized in that: S4: Design a sliding mode controller and use the external disturbance estimated in S3 to perform compensation control, specifically: For the slow subsystem, in order to ensure the sliding surface s s The convergence of the sliding mode controller u is Designed to: where k L1 >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 Determines the convergence speed and steady-state error of the system; σ s1 ,σ s2 Determines the amount of jitter in the system output; Similarly, for the fast subsystem, design the sliding mode controller u if for: 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 Determines the convergence speed and steady-state error of the system; σ f1 ,σ f2 Determines the amount of jitter in the system output; Using the sliding mode controllers (35) and (36), the final controller is u i =u is +u if ; Using controller u i , to ensure the tracking error p1,p2,q of the fast and slow subsystems 1i ,q 2i Converges to a region near 0, thus ensuring the original tracking error e x1 It also converges to a neighborhood near 0 and is guaranteed to satisfy That is, the system's tracking error meets the preset performance function indicators.

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