A model-free anti-windup PD-SMC control method and system

Abstract

The application belongs to the technical field of automatic control, and particularly relates to a model-free anti-saturation PD-SMC control method and system, which is suitable for automatic control scenes with disturbance and actuator saturation risks. The application performs equivalent transformation on the controlled object model, establishes a unified lumped disturbance model, and then fuses proportional-differential (PD) control, sliding mode control (SMC) theory and hyperbolic tangent function to construct a model-free anti-saturation PD-SMC control law. Specifically, the application does not require an accurate mathematical model of the controlled object, and the control output is determined only by the error, showing a model-free control feature; the hyperbolic tangent function and the sign function are introduced in the control law, effectively suppressing the actuator saturation risk; in addition, the proportional-differential term guarantees accurate tracking of the target state, and the sliding mode robust control term is used to suppress system lumped disturbance, which can cooperatively improve the control accuracy and robustness on the premise of ensuring system stability.

Description

Technical Field

[0001] This invention belongs to the field of automatic control technology, specifically relating to a model-free anti-saturation PD-SMC control method and system for nonlinear systems, which is particularly suitable for automatic control scenarios with disturbances and actuator saturation risks. Background Technology

[0002] As modern industrial manufacturing and application systems continue to evolve towards higher precision, higher efficiency, and greater multifunctionality, the mechanical structures of advanced equipment are becoming increasingly complex, and their working scenarios are becoming more diverse. Consequently, the internal and external dynamic behaviors of these systems exhibit significant nonlinearity, strong coupling, and uncertainty. Faced with such complex systems, traditional modeling methods based on vector mechanics or analytical mechanics are no longer sufficient for accurate characterization. This leads to a dilemma for control strategies relying on precise models at both the theoretical analysis and engineering application levels: on the one hand, it is difficult to achieve efficient and high-precision control in real-world scenarios; on the other hand, it is difficult to provide rigorous guarantees for the stability of closed-loop systems in theory. The resulting decrease in robustness, control oscillations, and even the risk of instability become prominent challenges.

[0003] Meanwhile, commonly used actuators such as electric motors and hydraulic mechanisms generally have physical limits on the control parameters. Under dynamic conditions such as sudden load changes and high-speed start-stop, saturation can easily be triggered due to the limited capabilities of the actuators, resulting in a significant decline in control quality. This problem is widespread in typical application scenarios such as spacecraft attitude control, hydraulic servo systems, and autonomous underwater vehicles, and urgently requires sufficient attention.

[0004] To address the aforementioned problems, this invention proposes a model-free, anti-saturation PD-SMC control method and system based on proportional-derivative (PD) control and sliding mode control (SMC) theories. This scheme does not require a precise mathematical model of the controlled object during the control variable solution process, and simultaneously possesses anti-saturation characteristics, providing a practical and reliable solution path for the control of nonlinear systems. Summary of the Invention

[0005] In view of this, this invention proposes a model-free, anti-saturation PD-SMC control method and system for complex nonlinear control systems with model uncertainties, external disturbances, and actuator saturation. This technical solution combines multiple advantages such as model-free operation, anti-saturation, and anti-disturbance, providing a practical technical reference for solving real-world control problems. The specific technical solution is as follows:

[0006] Firstly, this invention provides a model-free anti-saturation PD-SMC control method. Within one control cycle, this method mainly performs the following key steps:

[0007] 1. Step 101: Obtain the controlled object at the current moment. Expected state The current actual state of the controlled object is collected through physical sensors or state observers. Further calculate the state error and its derivative. , ;in, , is the sampling period; Represents the state dimension.

[0008] 2. Step 102: Perform parameter initialization operation to obtain the preset parameters. , , , , and Control parameters; among which , , , , All are positive definite diagonal matrices; It is a positive real number.

[0009] 3. Step 103: Calculate the sliding mode variables based on the above control parameters and state error: ;in .

[0010] 4. Step 104: Substitute the above control parameters, state error, and sliding mode variable into the control law function to calculate the control output: ;in, In particular, the control law does not contain any system model parameters, and its control output is determined solely by the state error, thus exhibiting typical model-free control characteristics.

[0011] 5. Step 105: Based on the control output obtained in step 104, convert it into an actual control signal that drives the controlled object to change its state, so as to achieve precise closed-loop regulation of the state of the controlled object.

[0012] Preferably, to suppress the high-frequency chattering phenomenon caused by the sign function, the control law function described in step 104 can be adjusted to the following form in practical applications:

[0013] ;

[0014] in, , , ; This represents the boundary layer thickness constant, and its value is, in principle, set to the minimum value that can effectively suppress chattering.

[0015] Preferably, to meet the anti-saturation design requirements, the control parameters , , The following relationship must be satisfied:

[0016] ( );

[0017] in, Indicates control quantity The i-th component The upper bound of the absolute value.

[0018] Preferably, the control parameters , , , , and The following constraints can be referenced for setting:

[0019]

[0020] in, represent The i-th component The upper bound of the absolute value; Representative aggregate disturbance The i-th component The upper bound of the absolute value; the lumped disturbance is defined as... . Used to adjust the linear region range of the hyperbolic tangent function.

[0021] Secondly, the present invention also provides a model-free anti-saturation PD-SMC control system, which specifically includes the following modules: an error acquisition module 201, a control quantity inference module 202, and a drive execution module 203.

[0022] Furthermore, the present invention provides a computing device, including a memory and a processor; the memory is used to store a control program, and the processor is used to load the control program to execute the model-free anti-saturation PD-SMC control method.

[0023] In addition, the present invention provides a computer-readable storage medium storing a control program, which, when the control program is executed, enables the device containing the computer-readable storage medium to perform the model-free anti-saturation PD-SMC control method.

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

[0025] 1. Model-free characteristic: This method does not rely on any model parameters of the controlled object; the controller output is determined solely by the state error, exhibiting typical model-free control characteristics. This characteristic significantly simplifies the controller design process and effectively reduces the complexity and design difficulty of the controller.

[0026] 2. Strong robustness: This method does not require modeling and observation of disturbances, and the closed-loop system can still maintain stable and high-precision operation in the presence of disturbances.

[0027] 3. Anti-saturation characteristics: This method has a natural output amplitude limiting characteristic in its structure, and there is no need to design an additional anti-saturation compensation circuit. This method can effectively avoid the risk of system instability caused by actuator saturation and ensure that the amplitude of the control signal is always within a safe range.

[0028] 4. High versatility: This method is applicable to a variety of nonlinear systems (such as robotic arms, drones, spacecraft, etc.), without the need for complex model adaptation for specific objects. It only requires flexible adjustment of control parameters according to the actual application scenario, and has good versatility and adaptability.

[0029] In summary, the method disclosed in this invention has multiple superior performance characteristics, providing a reliable and easy-to-implement solution for the control of nonlinear systems.

[0030] The accompanying drawings and specific embodiments of the present invention will be further described below. Attached Figure Description

[0031] Figure 1 This is a flowchart illustrating the control principle of a model-free anti-saturation PD-SMC control method provided by the present invention.

[0032] Figure 2 This is a schematic diagram of a model-free anti-saturation PD-SMC control system provided by the present invention;

[0033] Figure 3 This is a comparison diagram of the angle response of the embodiment of the present invention under working condition 1;

[0034] Figure 4 This is a comparison diagram of the speed response of the embodiment of the present invention under operating condition 1;

[0035] Figure 5 This is a comparison chart of control quantities under operating condition 1 in the embodiment of the present invention;

[0036] Figure 6 This is a comparison diagram of the angle response of the embodiment of the present invention under working condition 2;

[0037] Figure 7 This is a comparison diagram of the speed response of the embodiment of the present invention under operating condition 2;

[0038] Figure 8 This is a comparison chart of control quantities under operating condition 2 in the embodiment of the present invention;

[0039] Figure 9 This is a comparison diagram of the angle response of the embodiment of the present invention under working condition 3;

[0040] Figure 10 This is a comparison diagram of the speed response of the embodiment of the present invention under operating condition 3;

[0041] Figure 11 This is a comparison chart of control quantities under operating condition 3 in the embodiment of the present invention. Detailed Implementation Plan

[0042] The present invention will be further described below with reference to the accompanying drawings:

[0043] Firstly, this invention provides a model-free anti-saturation PD-SMC control method, specifically employing the following technical solution:

[0044] Consider a typical Euler-Lagrange multibody system with uncertainties, whose dynamic model can be defined as a general second-order nonlinear form.

[0045] (1)

[0046] In equation (1), This is the system's generalized coordinate (state variable) vector; Let be the system inertia matrix, satisfying the symmetric positive definite property; Coriolis force-centrifugal force matrix; This is the term related to gravity. This is the disturbance vector, which encompasses external disturbances experienced by the system during operation, as well as unmodeled dynamic terms within the system. This is to control the input vector. In particular, the dynamic equations of a specific system may contain some or all of the above terms, which usually depends on the number of degrees of freedom or the structural complexity of the system.

[0047] Equation (1) establishes the relationship between the driving force / torque and the state variables (position), the first derivative of the state variables (velocity), and the second derivative of the state variables (acceleration). Furthermore, to mitigate the influence of system model uncertainties and internal / external disturbances, a diagonal parameter matrix is ​​introduced. The dynamic model is rewritten in the following form:

[0048] (2)

[0049] Furthermore, the tracking error of the system state variables is defined as follows: .in, Let be a constant vector representing the expected values ​​of the system state. Therefore, , Therefore, the error dynamics equation of the system can be expressed as:

[0050] (3)

[0051] In equation (3), , It encompasses all unmodeled dynamics, parameter uncertainties, external disturbances, and nonlinear terms in the system, and defines them as the lumped disturbance of the system.

[0052] In reality, due to the widespread uncertainties and disturbances both inside and outside the system, the established dynamic model can usually only obtain... The approximate value is difficult to know precisely. If the controller is designed directly based on this approximate model, it will inevitably lead to the degradation of control performance and make it difficult to achieve the expected control quality.

[0053] Furthermore, it introduces a system state-based approach. , and interference items Assumptions:

[0054] 1. Position variables and its derivative It is measurable and can be used to design controllers;

[0055] 2. Because the motion state of a real system is limited by physical constraints, and It is bounded;

[0056] 3. Distractor Items It is bounded.

[0057] Based on the above assumptions, the lumped disturbance vector can be further derived. Closed-loop system error With error change rate It is bounded:

[0058] , making The i-th component , , ;

[0059] , making The i-th component , , ;

[0060] , making The i-th component , , .

[0061] In fact, due to the finite energy of real physical systems and the saturation constraints of driving mechanisms, this boundedness condition is universally reasonable and is therefore widely recognized and adopted in the field of nonlinear control. Based on the above conditions, the subsequent controller design can be freed from dependence on an accurate dynamic model of the system, allowing the controller to be constructed only based on the upper bound information of errors and lumped disturbances, thus eliminating the need to identify complex internal / external characteristics of the system.

[0062] Preferably, the present invention is based on the sliding mode control principle and defines the following nonlinear sliding mode variables. :

[0063] (4)

[0064] In equation (4), The controller parameter matrix is ​​positive definite and is used to adjust the convergence characteristics and dynamic performance of the sliding mode variable. Its specific form is: ; It is a vector composed of hyperbolic tangent functions; Used to adjust the linear region range of the hyperbolic tangent function.

[0065] Furthermore, based on the nonlinear sliding mode variable, the PD control method is integrated to design the following model-free anti-saturation controller:

[0066] (5)

[0067] In equation (5), , and These are the positive definite proportional gain matrix, differential gain matrix, and sliding mode gain matrix, respectively, with the following specific forms: , , ;in addition, , is the symbolic function vector. Specifically, the designed controller does not contain any system model parameters; its control output is determined solely by the state error, thus exhibiting typical model-free control characteristics.

[0068] For the error dynamics system described by equation (3), the model-free anti-saturation controller proposed in this invention can guarantee that the system state error and its derivative asymptotically converge to... , The rigorous theoretical proof of this conclusion is given below.

[0069] First, the known theorems required for the proof are given:

[0070] Theorem 1: , ,when The equality sign holds true.

[0071] Theorem 2: , ,when The equality sign holds true.

[0072] Theorem 3: , and .

[0073] Theorem 4: If the function And its derivative ,in And the function Uniformly continuous (or its derivative) Then there is .

[0074] Preferably, the following method is used to provide a theoretical proof of its convergence.

[0075] First, construct the Lyapunov function as shown in the following equation:

[0076] (6)

[0077] in, , .

[0078] Obviously, Established. In addition... Preferably, according to Theorem 1, when the control parameters satisfy the constraint relationship shown in equation (7) Established.

[0079] , (7)

[0080] In summary, the Lyapunov function shown in equation (6) is positive semidefinite.

[0081] Preferably, when the value conditions shown in equation (7) are satisfied, according to Theorem 1, if and only if , hour .

[0082] Furthermore, find the derivative of the Lyapunov function with respect to time t:

[0083] (8)

[0084] in, , , , , .

[0085] Next, we will discuss them separately. The positive and negative aspects.

[0086] (9)

[0087] Preferably, when the constraint relationship shown in equation (10) holds, .

[0088] , (10)

[0089] Furthermore, according to Theorem 2, we can obtain:

[0090] (11)

[0091] Furthermore, the following inequality clearly holds:

[0092] (12)

[0093] (13)

[0094] (14)

[0095] In conclusion, we can conclude that:

[0096] (15)

[0097] Preferably, when the constraint relationship shown in equation (16) is valid, equation (17) can be derived from equation (15).

[0098] , (16)

[0099] (17)

[0100] Preferably, if the inequality shown in equation (18) holds, then it can be deduced that .

[0101] , (18)

[0102] This will be discussed in categories below. First, when At that time, the conclusion is obviously true. Furthermore, when... When, then equation (18) holds true, it is equivalent to equation (19) holding true.

[0103] , (19)

[0104] According to Theorem 3, equation (19) holds if equation (20) holds.

[0105] , (20)

[0106] Furthermore, based on the state boundedness assumption, if the control parameter values ​​satisfy the conditions shown in equation (21), then equation (20) holds.

[0107] , (twenty one)

[0108] Therefore, when the control parameters satisfy the constraint relationships shown in equations (7), (10), (16), and (21), and . Furthermore, by combining equations (15), (19), and (21), we can obtain:

[0109] (twenty two)

[0110] in, , .

[0111] Furthermore, define the following function:

[0112] (twenty three)

[0113] Obviously, the function and .

[0114] For functions Find the derivative with respect to time t:

[0115] (twenty four)

[0116] Based on the boundedness assumption, we can obtain Bounded, therefore It is consistent and continuous.

[0117] According to Theorem 4, we can obtain:

[0118] (25)

[0119] In summary, the control method disclosed in this invention can ensure the asymptotic stability of the closed-loop system.

[0120] Preferably, to suppress the high-frequency chattering phenomenon caused by the sign function, the control law function shown in equation (5) can be adjusted to the following form in practical applications:

[0121] (26)

[0122] in, , , ; This represents the boundary layer thickness constant, and its value is, in principle, set to the minimum value that can effectively suppress chattering.

[0123] Preferably, equation (5) can be further expanded into the following form:

[0124] (27)

[0125] Based on the properties of the hyperbolic tangent function and the sign function, both are bounded functions:

[0126] (28)

[0127] Therefore, the controller output satisfies the following boundedness constraint:

[0128] , (29)

[0129] Therefore, in order to meet the anti-saturation design requirements, control parameters , , The following relationship must be satisfied:

[0130] , (30)

[0131] in, Indicates control quantity The i-th component The upper bound of the absolute value.

[0132] Preferably, the control parameters are determined according to equations (7), (10), (16), and (21). , , , , and The following constraints can be referenced for setting:

[0133] (31)

[0134] Preferred, Used to adjust the linear region range of the hyperbolic tangent function. Theoretically, A larger value results in a narrower linear region, which is beneficial for improving the controller's response performance; however, Excessively high values ​​can cause chattering. Therefore, in practical applications, the value must be adjusted based on specific control requirements and the actual response of the system. The values ​​are optimized and configured.

[0135] Preferably, the upper bounds of the state variables, their derivatives, and the lumped disturbance can be estimated using the following method: Based on prior information such as the mechanical structure, motion range, and actuator capability of the controlled object, the possible ranges of values ​​for the state variables and their derivatives are determined in advance. According to the definition of lumped disturbance given in equation (3), appropriate parameters are selected... It can reasonably match the order of magnitude between the control input and the second derivative of the error, thus allowing for the utilization of... Effective adjustment or constraint of disturbance amplitude is necessary. Based on this, the maximum possible intensity of external disturbances to the system can be considered first, and the lumped disturbance can be adjusted by referring to engineering experience or offline experimental data. The upper bound is conservatively estimated.

[0136] Furthermore, based on conservative estimates of the upper bounds of the state and disturbance, and combined with the inequality constraints between the control parameters shown in Equation (31), initial values ​​of each control parameter are initially selected to obtain a complete controller expression. Subsequently, the controller is applied to a closed-loop control system built on a physical platform or a virtual prototype platform. By fine-tuning the initial parameters, the closed-loop system achieves stable operation. On this basis, the upper bounds of the state and disturbance are accurately estimated using measured data or simulation results.

[0137] Furthermore, based on the above accurate estimates, the control parameters are precisely tuned, and the control parameters can be optimized according to specific control performance indicators, implementation costs, and other factors, combined with the actual response characteristics of the closed-loop system, such as overshoot, settling time, and steady-state error.

[0138] Secondly, the present invention also provides a model-free anti-saturation PD-SMC control system, such as... Figure 2 As shown, the system specifically includes the following modules:

[0139] 1. Error acquisition module 201: used to acquire the actual state and desired state of the controlled object in real time, and further generate error and error derivative signals;

[0140] 2. Control quantity inference module 202: connected to the error acquisition module 201, used to receive the error and its error derivative signal generated by the error acquisition module 201, and generate control quantity according to the preset control law; the control law includes a proportional-differential term based on the hyperbolic tangent function and a robust compensation term based on the nonlinear sliding surface, so as to achieve accurate tracking of the target value and adaptive compensation for internal / external disturbances of the system, while ensuring that the control output amplitude is bounded and has anti-saturation characteristics;

[0141] 3. Drive execution module 203: connected to the control quantity inference module 202, used to receive the control quantity generated by the control quantity inference module 202, and convert it into an actual control signal that drives the controlled object to produce a state change, thereby realizing closed-loop control of the controlled object.

[0142] Preferably, the present invention will be further illustrated with reference to a specific embodiment. This embodiment takes a typical dynamic system as the controlled object, mainly illustrating the implementation process of the method described in the present invention, and provides corresponding simulation results to help those skilled in the art better understand the technical solution, implementation method, and beneficial effects of the present invention.

[0143] In this embodiment, the nonlinear dynamic equation shown in equation (32) is selected as the mathematical model of the controlled object. In order to link the abstract mathematical expression with the specific physical entity, it is corresponding to the classical single-degree-of-freedom inverted pendulum system.

[0144] (32)

[0145] in, The joint rotation angle is expressed in rad. To account for the moment of inertia on the joint motor shaft, The coefficient of viscous friction is... The gravitational torque constant, The control torque output by the joint motor (unit: N·m). This refers to the external disturbance torque (in N·m). Additionally, in this embodiment, the upper limit of the joint motor's output is set to... The actual control torque meets the amplitude constraint. .

[0146] Preferably, in this embodiment, the error acquisition module 201 is implemented as a software program within the computing device, which can acquire the joint motor rotation angle in real time and calculate and generate an error signal. , .

[0147] Preferably, in this embodiment, the control parameter is set to the following values: , , , , , , .

[0148] Furthermore, the two widely used classical control methods shown in equations (33) and (34) are compared with the method disclosed in this invention. In particular, for the two comparison methods, the controller parameters are tuned based on simulation results, with the optimal combination of parameters selected based on the goals of system stability, fast response, chatter suppression capability, and no overshoot characteristics.

[0149] Comparison Method 1: This comparison method uses proportional-derivative (PD) control, as shown in Equation (33). Obviously, this control method has typical model-free characteristics.

[0150] (33)

[0151] The values ​​of the control parameters are as follows: , .

[0152] Comparison Method 2: This comparison method uses sliding mode control (SMC) based on exponential reaching rate, as shown in Equation (34). The control law of this method contains specific model parameters, so it is a model-based control method and requires the controller to be constructed based on an accurate model of the controlled object.

[0153] (34)

[0154] in, The control parameter values ​​are: , , , In particular, to suppress the high-frequency chattering phenomenon caused by the sign function, the control law function shown in equation (34) is adjusted to the following form in practical applications:

[0155] (35)

[0156] Among them, the function Same as the definition in equation (26).

[0157] Preferably, this embodiment sets three operating conditions:

[0158] Operating Condition 1 (Impact Disturbance): This condition aims to test the stability and robustness of the system under impact disturbances. The desired state of the controlled object is set as follows: and within the time interval An amplitude of 2 is applied to the controlled object from the inside. External disturbances, namely:

[0159] (36)

[0160] Operating Condition 2 (Step Tracking): This operating condition aims to test the stability and dynamic response performance of the system when a step change occurs in the desired state. The external disturbance torque is set to 0 in this operating condition. The desired state of the controlled object undergoes a step change in 5s, as shown in equation (37).

[0161] (37)

[0162] Operating Case 3 (Continuous Disturbance): This operating case aims to test the stability and robustness of the system under continuous disturbances. The desired state of the controlled object is set as follows: And continuously apply the disturbance torque defined by equation (38) to the controlled object.

[0163] (38)

[0164] like Figures 3 to 5 The figures show the angle, angular velocity, and control response curves under operating condition 1 in this embodiment. Comparing this method with comparative methods 1 and 2, the results show that all three methods can achieve accurate tracking of the desired value by the controlled object under pulse disturbance. However, the settling time of the two comparative methods is longer than that of this method; furthermore, at the instant the disturbance is applied, the control quantity of both comparative methods quickly reaches the upper limit of the actuator output and operates in the saturation region for a long time. In contrast, when using this method, thanks to its inherent anti-saturation characteristics, the control quantity does not exhibit saturation.

[0165] like Figures 6 to 8 The figures show the angle, angular velocity, and control response curves under operating condition 2 in this embodiment. Comparing this method with comparative methods 1 and 2, the results show that all three methods can achieve tracking of the desired value by the controlled object when the desired value changes abruptly. However, the settling time of the two comparative methods is significantly longer than that of this method, and comparative method 1 has a steady-state error, failing to achieve precise tracking. Furthermore, at the instant of the desired value step change, the control quantity of both comparative methods rapidly reaches the upper limit of the actuator output and operates in the saturation region for a long time. In contrast, when using this method, thanks to its inherent anti-saturation characteristics, the control quantity does not exhibit saturation, and the amplitude of the control quantity is significantly lower than that of the two comparative methods.

[0166] like Figures 9 to 11The figures show the angle, angular velocity, and control response curves under operating condition 3 in this embodiment. Comparing this method with comparative methods 1 and 2, the results show that all three methods can achieve tracking of the desired value by the controlled object under continuous disturbance, and the steady-state error amplitude is less than [value missing]. However, due to continuous external disturbances, all three methods exhibit steady-state errors. In comparison, our method demonstrates the highest tracking accuracy, with its steady-state error amplitude reduced by approximately 70% compared to Comparison Method 1 and by approximately 35% compared to Comparison Method 2. Furthermore, none of the three control methods exhibited control saturation.

[0167] In summary, this method effectively improves control accuracy and disturbance suppression capability while ensuring system stability. It also features model-free control, robustness, and anti-saturation characteristics, resulting in better overall control performance compared to traditional control schemes.

[0168] Furthermore, in one embodiment of the present invention, a computing device is provided, including a memory and a processor; the memory is used to store a control program, and the processor is used to load the control program to execute the model-free anti-saturation PD-SMC control method. Additionally, the present invention provides a computer-readable storage medium storing a control program, which, when the control program is executed, enables the device containing the computer-readable storage medium to execute the model-free anti-saturation PD-SMC control method.

[0169] Those skilled in the art will recognize that, for the sake of convenience and brevity, the details of the above embodiments can be found in the detailed description of the methods, steps, principles and systems disclosed in the invention content and specific implementation schemes, and will not be repeated here.

[0170] Those skilled in the art will recognize that the functions, methods, or modules described in the methods, systems, and embodiments disclosed in this invention can be implemented using electronic hardware, computer software, or a combination of both. Whether hardware or software is used depends on the specific application and design constraints of the technical solution. The computer software can be stored in a non-volatile computer-readable storage medium and, when executed, can implement the method steps and embodiment flows disclosed in the above-described description and specific implementation sections. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this invention.

[0171] Finally, it should be particularly noted that the embodiments provided above are only used to explain the technical solutions of the present invention, and their descriptions are relatively specific and detailed, but they do not constitute a limitation on the application scope, protection scope, or other forms of the present invention. For those skilled in the art, several modifications and improvements can be made without departing from the concept of this application. These modifications or improvements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions disclosed in this invention, and should all be covered within the scope of the claims and specification of this invention. It should be understood that the process steps described in this invention are not limited to the specific order disclosed; where feasible, rearranging or parallel execution of these steps may also be feasible or advantageous.

Claims

1. A model-free anti-saturation PD-SMC control method, characterized in that, The following steps are mainly performed within a control cycle: (1) Obtain the controlled object at the current moment Expected state The current actual state of the controlled object is collected through physical sensors or state observers. Further calculate the state error and its derivative. , ;in, , is the sampling period; For the state dimension; (2) Perform parameter initialization operation to obtain preset control parameters. , , , , and etc.; among them , , , , All are positive definite diagonal matrices; It is a positive real number; (3) Calculate the sliding mode variables based on the above control parameters and state errors: ;in ; (4) Substitute the above control parameters, state error, and sliding mode variable into the control law function to calculate the control output: ;in, , ; (5) Based on the control output obtained in step (4), convert it into an actual control signal that drives the controlled object to change its state, so as to achieve precise closed-loop regulation of the state of the controlled object.

2. The method according to claim 1, characterized in that, To suppress the high-frequency chattering phenomenon caused by the sign function, in practical applications, the control law function described in step (4) can be adjusted to the following form: ;in, , , ; is the boundary layer thickness constant.

3. A model-free anti-saturation PD-SMC control system, characterized in that, The system, applied to the method of claim 1, comprises: Error acquisition module: used to acquire the actual and desired state of the controlled object in real time, and further generate error and error derivative signals; Control quantity inference module: connected to the error acquisition module, used to receive the error and its error derivative signal generated by the error acquisition module, and generate control quantity according to the preset control law; the control law includes a proportional-differential term based on the hyperbolic tangent function and a robust compensation term based on the nonlinear sliding surface, so as to achieve accurate tracking of the target value and adaptive compensation for internal / external disturbances of the system, while ensuring that the control output amplitude is bounded and has anti-saturation characteristics; Drive execution module: connected to the control quantity inference module, used to receive the control quantity generated by the control quantity inference module and convert it into an actual control signal that drives the controlled object to change its state, thereby realizing closed-loop control of the controlled object.

4. A computing device, characterized in that, include: Memory, used to store control programs; A processor for loading the control program to execute the method of claim 1.

5. A computer-readable storage medium, characterized in that, The computer-readable storage medium includes a stored program, wherein, when the program is executed, it controls the device on which the computer-readable storage medium is located to perform the method of claim 1.

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