A sliding mode control method and system for a clamping positioning system

Abstract

The application discloses a sliding mode control method and system of a clamping positioning system, and comprises the following steps: acquiring a target position, an actual position and a speed of an output end, and determining a position error and an error change rate; determining a time-varying control input gain varying with the actual position based on a nonlinear kinematic mapping relationship between an input end and the output end; constructing a terminal sliding mode surface based on the position error and the error change rate, and acquiring a lumped disturbance estimation value through a nonlinear disturbance observer; and generating an enhanced control amount based on the time-varying control input gain, the terminal sliding mode surface and the lumped disturbance estimation value, and outputting the enhanced control amount to the input end. The application effectively corrects model mismatch, and improves tracking accuracy, dynamic response speed and anti-disturbance ability of the system.

Description

Technical Field

[0001] This invention relates to the fields of electromechanical servo control and nonlinear robust control technology, and particularly to a sliding mode control method and system for a clamping and positioning system. Background Technology

[0002] In the field of industrial automation, clamping and positioning systems such as multi-link clamping mechanisms, variable transmission ratio tensioning devices, and clamping and positioning systems are widely used. A significant characteristic of these systems is that the displacement mapping between their input end (e.g., the motor drive side) and output end (e.g., the actuator end) is not constant and linear, but rather exhibits a significant nonlinear change with the position of the output end. Traditional control strategies often simplify this complex nonlinear kinematic relationship to a fixed average transmission ratio or nominal model. However, when the system operates over a large range or has high dynamic performance requirements, this simplification leads to severe model mismatch, causing controllers based on fixed-gain designs to generate large tracking errors in actual operation.

[0003] Furthermore, sliding mode control is widely used due to its strong robustness to address uncertainties such as friction, load variations, and unmodeled dynamics. Although global fast terminal sliding mode control can guarantee system convergence within a finite time, when dealing with clamping and positioning systems with time-varying input gain characteristics, relying solely on a nominal model without accurate compensation for real-time gain changes and online estimation of lumped disturbances often results in the control variable failing to precisely match the system's instantaneous dynamic requirements. This leads to problems such as limited response speed, insufficient steady-state accuracy, and excessively long recovery time under disturbances. Therefore, a control scheme that can effectively integrate nonlinear kinematic characteristics and disturbance suppression capabilities is urgently needed. Summary of the Invention

[0004] The purpose of this invention is to provide a sliding mode control method and system for a clamping and positioning system. This invention effectively corrects model mismatch and improves the system's tracking accuracy, dynamic response speed, and anti-disturbance capability.

[0005] The technical solution of this invention: A sliding mode control method for a clamping and positioning system, applied to a clamping and positioning system including an input end and an output end, comprising:

[0006] Step 1: Obtain the target position, actual position, and output velocity at the output end, and determine the position error and the rate of change of error;

[0007] Step 2: Based on the preset nonlinear kinematic mapping relationship between the input and output terminals, determine the time-varying control input gain that varies with the actual position;

[0008] Step 3: Construct the terminal sliding surface based on the position error and the rate of change of error, and obtain the lumped disturbance estimate of the clamping and positioning system through a nonlinear disturbance observer;

[0009] Step 4: Generate an enhanced control quantity based on the time-varying control input gain, terminal sliding surface, and lumped disturbance estimate, and output the enhanced control quantity to the input terminal.

[0010] In the above method, the nonlinear kinematic mapping relationship characterizes the nonlinear correspondence between the displacement at the input end and the displacement at the output end;

[0011] Based on the aforementioned nonlinear kinematic mapping relationship, the nonlinear transmission ratio that varies with the actual position is determined;

[0012] The time-varying control input gain is determined based on the nonlinear transmission ratio.

[0013] The aforementioned method, wherein the nonlinear transmission ratio is obtained by polynomial fitting of corresponding data of multiple sets of input and output displacements, is expressed as:

[0014] ;

[0015] in, For nonlinear transmission ratios, The displacement at the output terminal. , , and These are the fitting coefficients;

[0016] The time-varying control input gain satisfies:

[0017] ;

[0018] in, For time-varying control input gain, For actual location, and The transmission ratio of the clamping and positioning system. For the lead screw, It is the equivalent moment of inertia.

[0019] In the aforementioned method, the terminal sliding surface is a global fast terminal sliding surface, and the structure of the global fast terminal sliding surface includes the position error, the error change rate, and a fractional power term that guarantees finite-time convergence.

[0020] The global fast terminal sliding surface is represented as follows:

[0021] ;

[0022] in, For global fast terminal sliding surface, For positional error, The rate of change of error, and The default parameter is greater than zero. and It is a positive odd number and , It is a symbolic function.

[0023] In the aforementioned method, the nonlinear perturbation observer satisfies the following state differential equation:

[0024] ;

[0025] ;

[0026] in, and For observer state variables, This is the estimated value of the lumped disturbance. For speed estimation error, For the output speed, For nominal system dynamic items, For nominal input gain, The control quantity applied to the input terminal. and For observer gain, and Preset observer parameters;

[0027] The It is a nonlinear function that satisfies:

[0028] when hour, ;when hour, .

[0029] The aforementioned method employs the following second-order state-space dynamics model for the clamping and positioning system:

[0030] ;

[0031] ;

[0032] in, For actual location, For the output speed, and Their derivatives are respectively. It is the ratio of the equivalent stiffness coefficient to the equivalent moment of inertia. It is the ratio of the equivalent viscous damping coefficient to the equivalent moment of inertia. For aggregated disturbances, For time-varying control input gain, This refers to the control quantity applied to the input terminal.

[0033] The aforementioned method, which outputs the enhanced control quantity to the input terminal, includes:

[0034] Before the enhanced control quantity is output to the input terminal, at least one of amplitude limiting and rate of change limiting is performed on the enhanced control quantity to obtain the limited enhanced control quantity;

[0035] The enhanced control quantity after the amplitude limiting is output to the input terminal.

[0036] The aforementioned method for obtaining the target position, actual position, and output speed of the output terminal includes:

[0037] The actual position is obtained through a position sensor, and the output speed is obtained through a speed sensor; or...

[0038] The actual position is obtained by a position sensor, and at least one of differential, low-pass filtering, or state observation is performed on the output signal of the position sensor to obtain the output speed.

[0039] A nonlinear transmission control system, comprising:

[0040] A nonlinear transmission actuator, comprising an input end and an output end;

[0041] The sensor assembly is configured to detect the actual position of the output terminal;

[0042] Processor; and

[0043] The memory stores a computer program that, when executed by the processor, causes the processor to implement the sliding mode control method of the clamping and positioning system as described above.

[0044] A computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to implement the sliding mode control method of the clamping and positioning system as described above.

[0045] Compared with existing technologies, this invention determines the time-varying control input gain that changes with the actual position of the output end in real time based on a preset nonlinear kinematic mapping relationship, thus correcting the model mismatch problem caused by treating the nonlinear transmission ratio as a constant in traditional control methods. This time-varying gain can accurately reflect the true dynamic transmission characteristics of the system at different operating points, making the calculation of the reference control quantity more in line with physical reality, thereby significantly improving the tracking accuracy and dynamic response consistency of the system throughout the entire stroke range.

[0046] Furthermore, this invention combines terminal sliding mode control with a nonlinear disturbance observer. It utilizes the terminal sliding surface to ensure the system's rapid convergence within a finite time, while simultaneously using the disturbance observer to perform online estimation and feedforward compensation of lumped disturbances, including friction, load fluctuations, and parameter perturbations. This enhanced control architecture not only overcomes the limitations of single sliding mode control in complex time-varying gain systems but also effectively suppresses the impact of external disturbances on system performance, significantly shortens the disturbance recovery time, and enhances the system's robustness and engineering practicality. (See attached figures.)

[0047] Figure 1 This is a schematic diagram of the clamping mechanism and partial components according to an embodiment of the present invention;

[0048] Figure 2 This is a schematic diagram of the kinematic analysis of a single rocker arm according to an embodiment of the present invention;

[0049] Figure 3 This is a schematic diagram of the closed-loop control (a) and motor drive transmission structure (b) of the clamping and positioning system according to an embodiment of the present invention;

[0050] Figure 4 This is a block diagram of the enhanced global fast terminal sliding mode controller according to an embodiment of the present invention.

[0051] Among them, 1-clamping end, 2-clamping rod, 3-support seat, 4-worktable, 5-top block, 6-connecting rod, 7-rocker arm, 8-drive rod. Detailed Implementation

[0052] The present invention will be further described below with reference to the accompanying drawings and embodiments, but this should not be construed as limiting the present invention.

[0053] Example 1: This example provides a sliding mode control method for a clamping and positioning system. This method is applied to a clamping and positioning system including input and output ends. This example aims to establish the upper-level execution logic of the control method and solve the model mismatch problem caused by nonlinear transmission characteristics through a closed-loop process of sensing, modeling, control, and compensation. Specifically, the control method includes the following steps:

[0054] Step 1: Obtain the target position, actual position, and output velocity at the output end, and determine the position error and the rate of change of error.

[0055] In this step, the target position is typically given by the upper-level planning module or user instructions, representing the desired endpoint or trajectory point of the system. The actual position is acquired in real time by a position sensor, such as a linear encoder, magnetic encoder, or potentiometer. For acquiring the output speed, this invention provides several optional implementation paths to adapt to different hardware configurations and accuracy requirements. As a preferred approach, the output speed can be directly acquired using a speed sensor, such as a tachogenerator or photoelectric encoder. Alternatively, the actual position can be acquired using a position sensor, and at least one of differential, low-pass filtering, or state observation can be performed on the output signal of the position sensor to obtain the output speed. Specifically, when the system is not equipped with a dedicated speed sensor or to reduce hardware costs, a differential algorithm with low-pass filtering can extract smoother speed information from the position signal, effectively suppressing the amplification effect of high-frequency noise on differential operations; or a state observer (such as a Luneburg observer) can be used to reconstruct the speed state from the position signal. This method often has a better signal-to-noise ratio than pure differential under low-speed conditions. Subsequently, the controller calculates the difference between the target position and the actual position to obtain the position error, and obtains the error change rate by differentiating the position error or by using the aforementioned velocity information, providing the basic state variables for the subsequent calculation of the control law.

[0056] Step 2: Based on the preset nonlinear kinematic mapping relationship between the input and output terminals, determine the time-varying control input gain that varies with the actual position.

[0057] In this step, the nonlinear kinematic mapping relationship characterizes the inherent geometric coupling between the input displacement (such as motor rotation angle or lead screw stroke) and the output displacement (such as the linear displacement of the actuator end). This characteristic is typically nonlinear and varies with the operating point. In this embodiment, this mapping relationship is pre-calibrated and stored in the controller's memory. Within each control cycle, the controller queries or calculates the corresponding mapping value in real time based on the currently sampled actual position, thereby deriving the current time-varying control input gain. It should be understood that "time-varying" here does not refer to a function of time itself, but rather to the dynamic change of the gain as the actual position of the output changes, thus accurately reflecting the system's true force transmission capability at different strokes. This mechanism corrects the model error caused by simplifying nonlinear transmission to a constant transmission ratio, enabling the calculation of the control quantity to closely match the instantaneous physical characteristics of the system.

[0058] Step 3: Construct the terminal sliding surface based on the position error and the rate of change of error, and obtain the lumped disturbance estimate of the clamping positioning system through a nonlinear disturbance observer.

[0059] To achieve precise control over the system's dynamic performance, this invention employs a second-order state-space dynamics model as the benchmark for the nominal model. Specifically, the clamping and positioning system adopts the following second-order state-space dynamics model:

[0060] ;

[0061] ;

[0062] in, For actual location, For the output speed, and Their derivatives are respectively. It is the ratio of the equivalent stiffness coefficient to the equivalent moment of inertia. It is the ratio of the equivalent viscous damping coefficient to the equivalent moment of inertia. For aggregated disturbances, For time-varying control input gain, This refers to the control quantity applied to the input. The model unifies friction, load fluctuations, parameter perturbations, and unmodeled dynamics into a lumped disturbance term. and the time-varying gain determined in step 2 An explicit input channel is introduced. Based on this, the controller constructs a terminal sliding surface using position error and the rate of change of error to ensure system convergence within a finite time. Simultaneously, a nonlinear disturbance observer operates in parallel, using measured states and control inputs to estimate the lumped disturbance, including external loads and internal uncertainties, online. This design allows the control system to improve robustness through a unified compensation mechanism without precisely identifying the physical source of each disturbance.

[0063] Step 4: Generate enhanced control quantities based on time-varying control input gain, terminal sliding surface, and lumped disturbance estimates.

[0064] In this step, the generation of enhanced control variables integrates three mechanisms: model feedforward, sliding mode feedback, and disturbance compensation. The time-varying control input gain is used to offset the system's own nonlinear transfer characteristics, making the equivalent object approximately linear. The control component generated by the terminal sliding surface drives the system state to rapidly approach and remain on the sliding surface, ensuring dynamic response speed and steady-state accuracy. The lumped disturbance estimate is directly superimposed as a feedforward compensation term or integrated into the control law, actively offsetting the effects of external disturbances and model biases. Through the synergistic effect of these three mechanisms, the generated enhanced control variable not only theoretically satisfies the finite-time convergence condition but also possesses adaptability to complex operating conditions in engineering.

[0065] Step 5: Output the enhanced control quantity to the input terminal.

[0066] Before applying the enhanced control quantity to the actuator, the safety constraints and performance boundaries of the physical actuator must be considered. Therefore, before outputting the enhanced control quantity to the input, at least one of amplitude limiting and rate-of-change limiting is applied to the enhanced control quantity to obtain a limited enhanced control quantity; then, the limited enhanced control quantity is output to the input. Specifically, amplitude limiting is used to prevent the control command from exceeding the rated voltage, current, or torque limits of the motor driver or power amplifier, avoiding equipment overload damage; rate-of-change limiting (i.e., slope limiting) is used to smooth abrupt changes in the control signal, reduce mechanical shock and vibration, and extend the life of transmission components. It should be understood that although limiting operations may temporarily sacrifice some theoretical control performance under extreme conditions, it is a necessary engineering measure to ensure the long-term reliable operation of the system. The limited enhanced control quantity is finally sent to the servo driver or power stage circuit to drive the input to move, thereby causing the output to track the target position and complete a complete control cycle.

[0067] By iteratively executing steps 1 to 5 above, this embodiment establishes a complete execution logic. This logic not only covers the core nonlinear gain compensation and sliding mode control algorithms, but also ensures the integrity and robustness of the technical solution in practical engineering applications by incorporating alternative solutions for speed acquisition and output limiting protection mechanisms.

[0068] Preferably, the nonlinear kinematic mapping relationship characterizes the nonlinear correspondence between the displacement at the input end and the displacement at the output end; based on the nonlinear kinematic mapping relationship, the nonlinear transmission ratio that varies with the actual position is determined; based on the nonlinear transmission ratio, the time-varying control input gain is determined. Specifically, this nonlinear correspondence is not an artificially introduced mathematical abstraction, but rather originates from the inherent geometric characteristics of the actuator. Figure 2 Taking the single rocker arm kinematics analysis as an example, the input end displacement (such as the drive rod displacement) ) and output end displacement (such as clamping end displacement) The mechanism forms a closed-loop vector chain through components such as linkages and rocker arms. In this mechanism, as the drive rod moves, the angle between the rocker arm and the linkage changes continuously, causing the instantaneous transmission ratio (i.e., the derivative of the output displacement with respect to the input displacement) to no longer be constant, but rather exhibits significant nonlinear fluctuations with position. For example, at the beginning of the stroke, the mechanism may be near its dead center, with a small transmission ratio and slow output movement; while in the middle of the stroke, the transmission ratio increases, and the output movement accelerates. If this geometric nonlinearity is ignored and a fixed transmission ratio is used for control, model mismatch will inevitably occur in different stroke segments, thus affecting tracking accuracy. Therefore, this invention establishes a precise nonlinear kinematic mapping relationship, explicitly incorporating this geometric characteristic into the control model, providing a physical basis for subsequent high-precision control.

[0069] Combination Figure 2 The geometric relationship can be represented by the lengths of each rod as... to The displacement of the drive rod is denoted as The displacement of the clamping end is denoted as The installation angle of the mechanism is denoted as Based on the law of cosines and closed-loop vector relationships, the following kinematic formulas can be derived. Intermediate variables satisfy:

[0070] ;

[0071] The angle cosine relationship is:

[0072] ;

[0073] Clamping end displacement satisfy:

[0074] ;

[0075] The above formula establishes the displacement from the drive rod. Displacement at the clamping end The complete nonlinear mapping relationship is shown. The nonlinear displacement data obtained from the above geometric relationship indicates that the displacement of the clamping end increases relatively slowly within the range of approximately 0 to 3.44 cm of drive rod feed; beyond this range, the displacement growth rate increases, therefore the stroke ratio is considered as a function of the position variable rather than a constant.

[0076] To facilitate real-time control, the nonlinear transmission ratio is obtained by polynomial fitting of corresponding data from multiple sets of input and output displacements, expressed as:

[0077] ;

[0078] in, For nonlinear transmission ratios, The displacement at the output terminal. , , and The fitting coefficients are denoted as .

[0079] In practical implementation, the corresponding data can be obtained through calculations using theoretical geometric models or through actual calibration tests after system assembly. Considering the potential for machining and assembly errors in theoretical models, actual calibration data is preferred to improve model accuracy. Regarding the selection of the polynomial fitting order, a balance needs to be struck between fitting accuracy and computational efficiency. An order that is too low (e.g., first or second order) may not adequately capture the nonlinear characteristics of the mechanism, resulting in large residuals; an order that is too high (e.g., fifth order or higher), while theoretically improving fitting accuracy, will significantly increase the real-time computational burden on the processor and is prone to overfitting due to sensitivity to noise in the calibration data. For most multi-link clamping or tensioning mechanisms, cubic polynomials can typically meet the real-time requirements of embedded controllers while ensuring sufficient fitting accuracy (residuals within acceptable limits). Of course, in other embodiments, depending on the complexity of the mechanism and the processor performance, quadratic, fourth, or other order polynomials can be used, or even alternative solutions such as spline interpolation or neural network fitting can be employed, as long as the nonlinear relationship between input and output can be accurately represented.

[0080] As a concrete example, when the length unit is centimeters, the coefficients obtained by fitting the calibration data for a certain type of three-jaw gripper mechanism are: , , , This set of coefficients reflects the nonlinear transmission characteristics of the specific mechanism within its operating range. It should be understood that these values ​​are merely illustrative examples and do not constitute a limitation on the scope of protection of this invention. In practical applications, the values ​​should be determined based on the calibration results of the specific mechanism.

[0081] As a specific prototype example, the length of the lever of the aforementioned three-jaw clamping mechanism is... to The displacements are 8.00cm, 5.04cm, 4.78cm, 10.49cm, 26.60cm, and 36.00cm, respectively. The drive rod displacement is selected. Calculate the corresponding clamping end displacements for 0.02, 0.50, 1.00, 1.50, 2.00, 2.50, 3.00, 3.50, 4.00, and 4.50 cm. Then, a cubic polynomial fitting is performed to obtain the aforementioned fitting coefficients. In practical applications, the fitting order can be adjusted based on the residuals, computational resources, and working interval.

[0082] Furthermore, the time-varying control input gain satisfies the following relationship:

[0083]

[0084] in, For time-varying control input gain, For actual location, and The transmission ratio (such as gear reduction ratio) of the clamping and positioning system. For the lead screw, It is the equivalent moment of inertia. This represents the linear transmission section from the motor side to the output end, while This represents the nonlinear transmission component that varies with position. Multiplying the two and dividing by the equivalent moment of inertia... This yields the time-varying gain that reflects the system's instantaneous force transmission capability. It should be noted that here... It is based on the actual location The controller uses dynamic variables that change in real time, rather than fixed values ​​calculated offline or simple lookup table results. Within each control cycle, the controller recalculates based on the currently sampled actual location. And then update This real-time update mechanism ensures that the control law always matches the current actual dynamic state of the system, effectively overcoming the parameter drift problem caused by changes in operating conditions or wear, thereby maintaining consistent high-performance control effects throughout the entire stroke range.

[0085] In engineering implementation, to prevent calibration errors or numerical anomalies from causing... Approaching zero and triggering a division-by-zero error, the controller calculates... Then, restrict it to a preset positive range. This limiting operation ensures the numerical stability of the control law throughout its entire stroke range, and is a necessary measure to guarantee the reliable operation of the system.

[0086] Furthermore, the above dynamic model can be obtained through the conversion of a multi-layered transmission system. For example... Figure 3 As shown, the transmission system can be divided into three layers: the first layer is the motor shaft layer, and its parameters are... , , The second layer is via gears. , The parameters of the connected intermediate shaft layer are as follows: , , The third layer is via gears. , The parameters of the connected lead screw layer are as follows: , , The adjusted torque balance relationship is as follows:

[0087] ;

[0088] in Input the rotation angle for the motor. This is the equivalent motor rotation angle converted to load displacement. This is the equivalent load torque. Let the transmission ratio be... , Then the conversion relationship between the equivalent rotation angle of the motor and the position of the clamping end is as follows: Substituting this relationship into the torque balance equation yields a nonlinear dynamic model that varies with the position of the clamping end.

[0089] As a specific example of the parameters, the values ​​of each dynamic parameter are shown in Table 1 below:

[0090] Table 1

[0091]

[0092] Under the above parameters, , .

[0093] Preferably, the terminal sliding surface is a globally fast terminal sliding surface. The structure of the globally fast terminal sliding surface includes position error, error change rate, and fractional power terms that guarantee finite-time convergence. This globally fast terminal sliding surface is represented as:

[0094] ;

[0095] in, For global fast terminal sliding surface, For positional error, The rate of change of error, and The default parameter is greater than zero. and It is a positive odd number and , It is a symbolic function.

[0096] In this sliding surface structure, fractional power terms This is the key mechanism for achieving finite-time convergence. Because... ,index The value is between 0 and 1. When the system is far from equilibrium (i.e., position error), the value is between 0 and 1. When larger), linear terms Numerical dominance gives the system a fast response characteristic similar to traditional linear sliding mode, ensuring that the state rapidly approaches the sliding surface; while when the system enters the region close to the equilibrium point (i.e., position error) When the value is relatively small, due to the amplification effect of exponentiation less than 1, the value of the fractional power term will be significantly larger than that of the linear term, thus generating a large equivalent control gain on the sliding surface. This nonlinear gain characteristic can overcome the defect of traditional asymptotic convergent control laws where the convergence rate tends to zero near the origin, forcing the system state to converge precisely to zero in a finite time. Regarding the parameters... and The choice constraint, limiting it to positive odd numbers, is to ensure that the fractional power function is defined throughout the entire real domain and maintains odd symmetry, avoiding complex solutions or sign ambiguity when the error crosses zero, while also satisfying... This is the mathematical prerequisite for ensuring that the term possesses the aforementioned "small error, large gain" characteristic. In practical engineering applications, and The value of needs to be comprehensively tuned based on the system's inertia, actuator bandwidth, and allowable overshoot. For example, in the debugging of a clamping and positioning system, a value of can be taken as follows: , , , To balance dynamic response speed and steady-state accuracy. Furthermore, to avoid fractional power terms... In position error Numerical singularities arise when the value approaches zero, which can be used to... Set a small positive lower limit (e.g.) Alternatively, a continuous approximation function can be used to replace the symbolic function, in order to eliminate the singularity problem in numerical computation while ensuring finite-time convergence.

[0097] To further enhance the system's robustness under complex operating conditions, this invention introduces a nonlinear disturbance observer to estimate and compensate for lumped disturbances in real time. The nonlinear disturbance observer satisfies the following state differential equation:

[0098] ;

[0099] ;

[0100] in, and For observer state variables, This is the estimated value of the lumped disturbance. For speed estimation error, For the output speed, For nominal system dynamic items, For nominal input gain, The control quantity applied to the input terminal. and For observer gain, and These are the preset observer parameters.

[0101] In this observer design, As a nonlinear function, its piecewise characteristics are crucial for the accuracy of balance estimation and chatter suppression. This function satisfies: when hour, ;when hour, Specifically, when the speed estimation error... When the value is large, use the power function form and utilize... The nonlinear characteristics accelerate the convergence speed of the observer, enabling it to quickly track changes in disturbances; while when the estimation error enters a state where... When the boundary is within a small neighborhood, it automatically switches to a linear function form. This linearization effectively avoids the chattering phenomenon caused by high-frequency switching near the origin in traditional sliding mode observers, and also prevents sensor measurement noise from being nonlinearly amplified, thus ensuring the perturbation estimation signal. Smoothness and usability. Parameters This is the switching threshold between the linear and nonlinear regions, and its value is usually slightly larger than the standard deviation of the sensor noise; observer gain. and The tuning must ensure that the observer poles are located in the left half-plane and that the bandwidth is higher than the highest frequency of the system disturbance variation to ensure real-time tracking capability of time-varying disturbances. As a specific parameter example, a suitable parameter could be... , And tuned according to the sampling period and noise level. and .

[0102] Obtaining the lumped disturbance estimate Subsequently, this invention incorporates it directly into the control law as a feedforward compensation term. Specifically, the reference control quantity... It is synthesized from the nominal model compensation term, the error dynamic term, and the arrival law term, wherein the structure of the arrival law term is as follows: , and The arrival law gain parameter is greater than zero. and It is a positive odd number and This arrival law term provides a large approach velocity when the system state is far from the sliding surface, and a smooth transition when approaching the sliding surface, effectively balancing speed and chatter suppression. From the baseline control quantity Subtract from the middle (or add with a negative sign) to obtain the final enhanced control quantity. This synthesis approach allows the enhanced control quantity to include not only the feedback stabilizing term provided by the global fast terminal sliding surface, but also the active cancellation term for unknown disturbances provided by the observer. In this way, even if the system has unmodeled dynamics or sudden external load changes, the controller can... Real-time compensation maintains the nominal characteristics of the equivalent object, thereby significantly reducing the demand for sliding mode switching gain, which in turn reduces the chattering amplitude of the control input and achieves a balance between high precision and stability.

[0103] In engineering implementation, the control cycle is preferably between 0.1 ms and 10 ms, with the specific value determined based on the mechanism bandwidth, sensor noise, and processor performance. A shorter control cycle is beneficial for improving the real-time performance and control accuracy of disturbance estimation, but it increases the computational burden on the processor; a longer control cycle may reduce the ability to track rapidly changing disturbances.

[0104] Furthermore, it should be understood that the aforementioned nonlinear disturbance observer based on the fal function is only a preferred embodiment of the present invention. In other embodiments, the disturbance observer can also be replaced by an extended state observer (ESO), a sliding mode disturbance observer, an unknown input observer, or a neural network estimator, as long as its output is used to compensate for the lumped disturbance of the clamping positioning system. All of these can be combined with the control framework of the present invention to achieve similar disturbance suppression effects.

[0105] Example 2: This example provides a nonlinear transmission control system, such as... Figure 3 and Figure 1 As shown, the nonlinear transmission control system includes a nonlinear transmission actuator, sensor components, a processor, and a memory.

[0106] The nonlinear transmission actuator includes an input end and an output end, constituting the physical carrier of the control method of this invention. Specifically, as... Figure 3 As shown, the input end typically consists of a servo motor and its drive unit, responsible for receiving control commands and generating rotational motion; the output end is the actuator that directly acts on the workpiece or load, for example... Figure 1 The clamping end 1 shown is provided between the input and output ends. A transmission chain including gear pairs, a lead screw and nut pair, and a multi-link mechanism is provided. For example, the output shaft of the servo motor is connected to the lead screw via a reduction mechanism composed of gears Z1, Z2, Z3, and Z4. The lead screw and nut drive the drive rod 8 to move linearly, which in turn drives the clamping end 1 to generate displacement through components such as the rocker arm 7 and the connecting rod 6. It should be understood that although... Figure 1The specific form of the three-jaw gripping mechanism is shown, but in other embodiments of the present invention, the nonlinear transmission actuator can also be a two-jaw gripper, a four-jaw chuck, a variable transmission ratio tensioning device, a clamping mechanism, or an expansion positioning mechanism, etc., as long as there is a nonlinear mapping relationship between its input end displacement and output end displacement that varies with position, it falls within the protection scope of the present invention. This nonlinear geometric structure is the physical root cause of the time-varying input gain of the system, and it is also the core object that the control system of the present invention needs to adapt to.

[0107] Specifically, such as Figure 1 As shown, the aforementioned three-jaw clamping mechanism includes a worktable 4, a support base 3, a top block 5, a drive rod 8, and three sets of clamping branches arranged at intervals along the circumference of the circular workpiece to be clamped. Each clamping branch includes a clamping end 1, a clamping rod 2, a connecting rod 6, and a rocker arm 7. The rocker arm 7 is hinged to the support base 3 and the connecting rod 6, and the drive rod 8 drives the three sets of clamping branches to move synchronously through a sliding joint. During operation, the drive rod 8 moves along the central axis, and through the linkage of the rocker arm 7 and the connecting rod 6, the three sets of clamping ends 1 synchronously retract or open radially, thereby achieving centering clamping or release of the circular workpiece. This circumferentially uniformly arranged three-branch structure ensures the symmetry of the clamping force and the centering accuracy of the workpiece.

[0108] The sensor assembly is configured to detect the actual position at the output, providing real-time feedback information for closed-loop control. Combined with... Figure 3 Sensor components are typically mounted near the output end or at critical nodes in the drivetrain. For example, an optical or magnetic scale can be placed next to the moving guide rail at clamping end 1 to directly measure the linear displacement of the output end; or a high-precision photoelectric encoder can be installed at the tail of the motor to indirectly calculate the output end position by detecting the motor rotation angle and combining it with a preset nonlinear kinematic mapping relationship. Furthermore, to support the speed acquisition alternatives mentioned in the preceding embodiments, the sensor components can also include a separate speed sensor (such as a tachogenerator), or rely solely on a position sensor in conjunction with a differential filtering algorithm within the processor to reconstruct the speed signal. This flexible sensor configuration allows the system to optimize hardware selection based on cost budget and installation space while ensuring control accuracy.

[0109] The processor and memory together constitute the control core of the system. The memory stores the computer program, which, when executed by the processor, enables the processor to implement the control method of the clamping and positioning system described in the previous embodiments. Specifically, the processor can be a computing unit with real-time computing capabilities, such as a microcontroller (MCU), digital signal processor (DSP), field-programmable gate array (FPGA), or industrial control computer. The memory includes read-only memory (ROM, Flash) for storing program code and random access memory (RAM) for storing runtime data (such as target position, state variables, observer states, etc.). In terms of physical connection, the processor is connected to the sensor components and servo drivers through a communication bus or dedicated interface, forming a complete information interaction loop. During operation, the processor periodically reads the actual position signals collected by the sensor components, executes algorithmic steps such as nonlinear gain calculation, sliding mode surface construction, disturbance observation, and enhanced control quantity synthesis, and sends the finally generated amplitude-limited control command to the servo driver, thereby driving the nonlinear transmission actuator to accurately track the target trajectory.

[0110] Example 3: This example provides a computer-readable storage medium. The computer-readable storage medium stores a computer program, which, when executed by a processor, causes the processor to implement the control method for the clamping and positioning system as described in the foregoing examples.

[0111] Specifically, the computer-readable storage medium referred to in this invention means any tangible medium that contains or stores programs for or relating to an instruction execution system, apparatus, or device; its essence is a carrier for transforming a technical solution from abstract logic to a physical entity. In practical applications, the specific form of this medium is highly diverse. For example, it can be an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any suitable combination of the above. More specific examples include, but are not limited to: portable computer disks, hard disk drives, solid-state drives (SSDs), random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fibers, portable compact disc read-only memory (CD-ROM), digital multifunction discs (DVDs), Blu-ray discs, magnetic tapes, floppy disks, and mechanical encoding devices (such as punched cards or paper tapes with instructions recorded in grooves). Furthermore, it should be understood that with the development of information storage technology, media based on new storage principles (such as phase-change memory, resistive switching memory, DNA storage media, etc.) should also be included within the scope of protection of this invention. In some implementations, when a computer program is transmitted over a network or other communication link, the transmission medium carrying the program signal or the buffer area of ​​the receiving end used to temporarily store the program can also be regarded as a computer-readable storage medium in a broad sense.

[0112] The computer program stored in the medium consists of a series of machine-readable instructions. These instructions logically correspond strictly to the steps described in the aforementioned method embodiments, including core algorithm flows such as acquiring the output state, calculating the time-varying input gain based on nonlinear mapping, constructing a global fast terminal sliding surface, running a nonlinear disturbance observer, and synthesizing and outputting enhanced control quantities. When a processor (such as an MCU, DSP, FPGA, or general-purpose CPU) loads and executes this program, it invokes underlying hardware resources to achieve high-precision and robust control of the clamping and positioning system.

[0113] Example 4: In order to verify the effectiveness of the clamping and positioning system control method provided in the previous examples in actual engineering applications, this example takes a precision clamping and positioning system for circular workpieces as a specific application scenario and conducts performance verification and comparative testing.

[0114] In the test scenario of this embodiment, specific experimental conditions were set to simulate real working conditions. The initial state of the system was set to a position of 5cm and a speed of 0cm / s, and the target trajectory was set to a precision positioning process starting from 1cm from the working starting point. Choosing 1cm as the working starting point was to avoid the large fitting error area caused by mechanical clearance or assembly tolerances in the extremely low displacement region of the prototype, ensuring the validity of the test data. To evaluate the system's anti-disturbance capability, an equivalent step load disturbance was artificially applied at the 6th second of system operation to simulate sudden changes in workpiece contact resistance or external cutting force interference during clamping. During the controller testing or parameter tuning phase, the lumped disturbance can also be set to the sum of at least one Gaussian function, i.e. ,in , and These represent the magnitude, center, and width of the Gaussian function, respectively. This disturbance modeling method based on the Gaussian function can approximate various complex disturbance patterns, providing a flexible testing method for controller parameter tuning and performance verification.

[0115] To intuitively demonstrate the advantages of the technical solution of this invention, three control strategies are set up for horizontal comparison: the first is traditional sliding mode control (SMC), which adopts a fixed transmission ratio model and does not include disturbance observation compensation; the second is ordinary global fast terminal sliding mode control (GFTSMC), which introduces a fractional power sliding surface to ensure finite-time convergence, but is still based on a fixed transmission ratio model and has no disturbance compensation; the third is the enhanced global fast terminal sliding mode control (EGFTSMC) proposed in this invention, which integrates time-varying control input gain based on nonlinear kinematic mapping and nonlinear disturbance observer compensation mechanism.

[0116] After multiple rounds of simulation and prototype testing, the key performance indicators of the three control strategies are compared as shown in Table 2 below:

[0117] Table 2

[0118]

[0119] Analysis of the data in the table above and the dynamic response curves during the testing process shows that the technical solution of this invention exhibits significant advantages in all indicators. Specifically, compared with traditional sliding mode control, ordinary global fast terminal sliding mode control effectively improves the convergence speed of the system near the equilibrium point by introducing fractional power terms, shortening the settling time by about 35% and significantly reducing overshoot, which verifies the superiority of the terminal sliding surface structure itself. However, since neither of them considers the nonlinear change of the transmission ratio, there is still a steady-state error caused by model mismatch in the middle of the stroke, and when facing step disturbances, it relies solely on feedback gain for suppression, resulting in a long disturbance recovery time and a large peak deviation.

[0120] In contrast, the enhanced control strategy of this invention achieves a further leap in performance. Its advantages stem primarily from the synergistic effect of two levels: First, by calculating the time-varying control input gain that changes with the actual position in real time, the controller can accurately match the true mechanical transmission characteristics of the clamping mechanism at different strokes, eliminating model mismatch errors caused by the fixed transmission ratio assumption. This improves steady-state accuracy from the micrometer level to the sub-micrometer level. Second, the nonlinear disturbance observer can accurately estimate the lumped disturbance, including friction, sudden load changes, and unmodeled dynamics, within milliseconds and actively cancel it as a feedforward term, rather than passively waiting for the error to occur before eliminating it through feedback. This dual enhancement mechanism reduces the disturbance recovery time by more than 50% compared to ordinary global fast terminal sliding mode control when the system encounters a step disturbance at the 6th second, and almost no obvious dynamic drop is observed. This fully demonstrates the substantial technical contribution of this invention in solving the model mismatch and disturbance suppression problems of clamping and positioning systems.

[0121] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art, within the technical scope disclosed in this invention and based on the core concept revealed, can easily conceive of variations or substitutions, such as using fitting models of other orders, different types of finite-time convergent sliding surfaces, alternative nonlinear feedback functions, or applications to other transmission mechanisms with similar nonlinear geometric characteristics, etc., all of which should be covered within the scope of protection of this invention. Therefore, the scope of protection of this invention should be determined by the scope of the claims.

Claims

1. A sliding mode control method for a clamping and positioning system, applied to a clamping and positioning system including an input end and an output end, characterized in that, include: Step 1: Obtain the target position, actual position, and output velocity at the output end, and determine the position error and the rate of change of error; Step 2: Based on the preset nonlinear kinematic mapping relationship between the input and output terminals, determine the time-varying control input gain that varies with the actual position; Step 3: Construct the terminal sliding surface based on the position error and the rate of change of error, and obtain the lumped disturbance estimate of the clamping and positioning system through a nonlinear disturbance observer; Step 4: Generate an enhanced control quantity based on the time-varying control input gain, terminal sliding surface, and lumped disturbance estimate, and output the enhanced control quantity to the input terminal.

2. The method according to claim 1, characterized in that, The nonlinear kinematic mapping relationship characterizes the nonlinear correspondence between the displacement at the input end and the displacement at the output end; Based on the aforementioned nonlinear kinematic mapping relationship, the nonlinear transmission ratio that varies with the actual position is determined; The time-varying control input gain is determined based on the nonlinear transmission ratio.

3. The method according to claim 2, characterized in that, The nonlinear transmission ratio is obtained by polynomial fitting of corresponding data of multiple sets of input and output displacements, and is expressed as: ； in, For nonlinear transmission ratios, The displacement at the output terminal. , , and These are the fitting coefficients; The time-varying control input gain satisfies: ； in, For time-varying control input gain, For actual location, and The transmission ratio of the clamping and positioning system. For the lead screw, It is the equivalent moment of inertia.

4. The method according to claim 1, characterized in that, The terminal sliding surface is a global fast terminal sliding surface, and the structure of the global fast terminal sliding surface includes the position error, the error change rate, and a fractional power term that guarantees finite-time convergence. The global fast terminal sliding surface is represented as follows: ； in, For global fast terminal sliding surface, For positional error, The rate of change of error, and The default parameter is greater than zero. and It is a positive odd number and , It is a symbolic function.

5. The method according to claim 4, characterized in that, The nonlinear perturbation observer satisfies the following state differential equation: ； ； in, and For observer state variables, This is the estimated value of the lumped disturbance. For speed estimation error, For the output speed, For nominal system dynamic items, For nominal input gain, The control quantity applied to the input terminal. and For observer gain, and Preset observer parameters; The It is a nonlinear function that satisfies: when hour, ;when hour, .

6. The method according to claim 1, characterized in that, The clamping and positioning system adopts the following second-order state-space dynamics model: ； ； in, For actual location, For the output speed, and Their derivatives are respectively. It is the ratio of the equivalent stiffness coefficient to the equivalent moment of inertia. It is the ratio of the equivalent viscous damping coefficient to the equivalent moment of inertia. For aggregated disturbances, For time-varying control input gain, This refers to the control quantity applied to the input terminal.

7. The method according to claim 1, characterized in that, Outputting the enhanced control quantity to the input terminal includes: Before the enhanced control quantity is output to the input terminal, at least one of amplitude limiting and rate of change limiting is performed on the enhanced control quantity to obtain the limited enhanced control quantity; The enhanced control quantity after the amplitude limiting is output to the input terminal.

8. The method according to claim 1, characterized in that, Obtaining the target position, actual position, and output speed of the output terminal includes: The actual position is obtained through a position sensor, and the output speed is obtained through a speed sensor; or... The actual position is obtained by a position sensor, and at least one of differential, low-pass filtering, or state observation is performed on the output signal of the position sensor to obtain the output speed.

9. A nonlinear transmission control system, characterized in that, include: A nonlinear transmission actuator, comprising an input end and an output end; The sensor assembly is configured to detect the actual position of the output terminal; processor; as well as The memory stores a computer program, which, when executed by the processor, causes the processor to implement the sliding mode control method of the clamping and positioning system as described in any one of claims 1 to 8.

10. A computer-readable storage medium, characterized in that, The system contains a computer program that, when executed by a processor, causes the processor to implement the sliding mode control method of the clamping and positioning system as described in any one of claims 1 to 8.

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