Nonlinear PID (Proportion Integration Differentiation) control method for displacement adjustment of electric cylinder

Abstract

The invention discloses a nonlinear PID control method for displacement adjustment of an electric cylinder. The nonlinear PID control method comprises the following steps: S1, constructing a mathematical model of the electric cylinder; s2, constructing an electric cylinder position control system model in combination with the electric cylinder mathematical model and a nonlinear PID control algorithm; and S3, adjusting the displacement of the electric cylinder by using the electric cylinder position control system model. Accurate control over the displacement of the electric cylinder is achieved, the problem that parameter setting is difficult in a traditional method is solved, and the anti-interference capacity and the dynamic response characteristic of the system are improved. When external disturbance exists, steady-state errors can be rapidly eliminated in the nonlinear integration link, and the overshoot trend is inhibited in advance through the dynamic differential effect. The method is particularly suitable for industrial scenes needing high-precision positioning and frequent load change, and the robustness of an electric cylinder control system is remarkably improved.

Description

Technical Field

[0001] The present invention relates to the technical field of electric cylinder control, and in particular to a nonlinear PID control method for adjusting the displacement of an electric cylinder. Background Art

[0002] As a precision actuator that converts rotary motion into linear motion, electric cylinders are widely used in fields such as industrial automation and aerospace. Their core components include a drive motor, a reduction gear, a lead screw, and a piston rod. During operation, the drive motor rotates the lead screw shaft through the reduction gear, converting the rotary motion into linear motion of the lead screw nut, which in turn pushes the piston rod to achieve telescopic motion. This motion conversion mechanism gives electric cylinders unique advantages in displacement control.

[0003] In the field of electric cylinder displacement control, the traditional PID control algorithm is widely adopted due to its simple structure and ease of implementation. This algorithm achieves system control through the combined action of proportional, integral, and differential components. However, in practical applications, traditional PID control has many limitations: First, its parameter tuning process is complex, often requiring repeated debugging based on manual experience, which is particularly prominent when dealing with complex systems; second, the fixed-parameter PID controller has difficulty adapting to dynamic changes during system operation, resulting in reduced control performance; third, traditional PID control has limited ability to suppress disturbances, and is prone to overshoot or oscillation in the presence of external interference.

[0004] Specifically, the proportional phase of traditional PID control can only generate control output based on the current error, and its control effect is limited when the error is small. While the integral phase can eliminate steady-state errors, it can easily cause integral saturation, resulting in slow system response or overshoot. While the differential phase can predict error trends, it is sensitive to noise and difficult to optimize parameters. These problems are particularly evident in systems with nonlinear characteristics such as electric cylinders, seriously affecting the system's control accuracy and dynamic performance. Summary of the Invention

[0005] In view of this, the present invention provides a nonlinear PID control method for electric cylinder displacement regulation, which has the advantages of improving control accuracy, suppressing overshoot oscillation, and enhancing dynamic performance.

[0006] To achieve the above object, the present invention provides the following technical solutions: A nonlinear PID control method for adjusting the displacement of an electric cylinder comprises: S1, constructing a mathematical model of the electric cylinder; S2, combining the mathematical model of the electric cylinder with a nonlinear PID control algorithm to construct a position control system model of the electric cylinder; S3, adjusting the displacement of the electric cylinder using the electric cylinder position control system model.

[0007] Preferably, step S1 includes: using the armature circuit voltage balance equation, the back electromotive force equation, the electromagnetic torque equation and the torque balance equation, and combining the electric cylinder transmission mechanism to construct a mathematical model of the electric cylinder; the armature circuit voltage balance equation is: Where, is the armature voltage; and are the resistance and inductance of the armature winding respectively; is the armature current; the back electromotive force equation is: Where, represents back electromotive force; is the back electromotive force constant; is the motor speed; the electromagnetic torque equation is: Where, is the electromagnetic torque produced by the armature current; is the torque coefficient of the motor; the torque balance equation is: Where, is the load torque converted to the motor shaft; is the total moment of inertia converted to the motor shaft; is the equivalent viscous friction coefficient of the system.

[0008] Preferably, step S2 includes: S21, based on the mathematical model of the electric cylinder, adopting a position single closed-loop control mode; S22, writing a nonlinear PID control algorithm into the position regulator, and constructing an electric cylinder position control system model with a nonlinear PID algorithm as the control strategy.

[0009] Preferably, the result of the nonlinear PID control algorithm is a control output that varies with the response time. The nonlinear PID control algorithm equation is: Where, is the control output; is the response time; It is a nonlinear proportional link; It is a nonlinear integral link; It is a nonlinear differential link.

[0010] Preferably, the calculation formula of the nonlinear proportional link is: Where, and are coefficients, , ; is the instantaneous error; is the response time; is the nonlinear proportional link coefficient.

[0011] Preferably, when the instantaneous error hour, , The bigger, The bigger, The smaller, The smaller the error, the faster the action is. At the beginning of the response, the faster the action is. At the end of the response, when the absolute value of the error is relatively small, overshoot can be avoided. When the instantaneous error is When , it means that overshoot occurs. , , the larger the overshoot, The larger the value is, the more the control output is reduced, thus suppressing overshoot; when the overshoot amplitude is small, Small enough to avoid oscillation.

[0012] Preferably, the calculation formula of the nonlinear integral link is: , ;in, Where, is the instantaneous error; is the response time; is the coefficient of the nonlinear integral link; and is the instantaneous error Two thresholds of the absolute value of .

[0013] Preferably, when the instantaneous error The absolute value of is greater than or equal to hour, is a constant not less than 1; when the instantaneous error The absolute value of Internal time, Is a positive number greater than 0 and less than 1; when the instantaneous error The absolute value of is not greater than hour, Approaching 0.

[0014] Preferably, the calculation formula of the nonlinear differential link is: Where, and are coefficients, , ; is the instantaneous error, is the response time, is the coefficient of the nonlinear differential link.

[0015] Preferably, when the instantaneous error When it is greater than 0, it is reflected in the rising stage of the response, as the instantaneous error The decrease of the nonlinear differential link coefficient increases, and the instantaneous error The rate of change is less than 0, and the nonlinear differential link is negative, which plays a role in suppressing overshoot in advance; when the instantaneous error When it is less than 0, it indicates that overshoot occurs at this time; as the instantaneous error As the absolute value increases, the coefficient of the nonlinear differential link increases, and the instantaneous error The rate of change is less than 0. At this time, the nonlinear differential link is negative, which suppresses the increase of the overshoot amplitude.

[0016] The beneficial effects of this invention are as follows: Compared with existing technologies, this application achieves precise control of electric cylinder displacement, solves the difficulty of parameter tuning in traditional methods, and improves the system's anti-interference ability and dynamic response characteristics. In the presence of external disturbances, the nonlinear integral link can quickly eliminate steady-state errors, and the dynamic differential action can proactively suppress overshoot trends. This method is particularly suitable for industrial scenarios requiring high-precision positioning and frequently changing loads, significantly improving the robustness of electric cylinder control systems.

[0017] Additional aspects and advantages of the present invention will be set forth in part in the description which follows and, in part, will be obvious from the description which follows, or may be learned by practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 is a schematic diagram of the mathematical model of the electric cylinder of the present invention; Figure 2 is a schematic diagram of the electric cylinder position control system model of the present invention; Figure 3 It is a schematic diagram of simulation results of the nonlinear PID control method of the present invention and the traditional PID control method. DETAILED DESCRIPTION

[0019] The following describes embodiments of the present invention in detail, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to be used to explain the present invention, and are not to be construed as limiting the present invention.

[0020] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of the technical features being referred to. Thus, a feature identified as "first" or "second" may explicitly or implicitly include one or more of the features. In the description of the present invention, "plurality" means two or more, unless otherwise specifically defined.

[0021] Reference below Figures 1 to 3 A nonlinear PID control method for adjusting the displacement of an electric cylinder in an embodiment of the present invention is described.

[0022] In an embodiment of the present application, a nonlinear PID control method for adjusting the displacement of an electric cylinder is disclosed, including: S1, constructing a mathematical model of the electric cylinder; S2, combining the mathematical model of the electric cylinder and a nonlinear PID control algorithm to construct a position control system model of the electric cylinder; S3, using the electric cylinder position control system model to adjust the displacement of the electric cylinder.

[0023] Constructing a mathematical model for the electric cylinder involves describing the system's dynamic characteristics through electrical and mechanical motion equations. This can be achieved using the armature circuit voltage balance equation, back-electromotive force equation, electromagnetic torque equation, and torque balance equation. This mathematical model provides an accurate description of the physical system for control algorithm design. A nonlinear PID control algorithm involves proportional, integral, and differential control steps with variable gain. This can be achieved by dynamically adjusting the coefficients of each step using an error-related function. This algorithm can adjust control intensity based on real-time error, resolving response lag issues caused by fixed parameters. The electric cylinder position control system model involves embedding a nonlinear PID algorithm into the control loop. This can be achieved using a single closed-loop position architecture. This architecture simplifies the system structure, reduces computational latency, and improves response speed.

[0024] Specifically, the dynamic model of the drive motor is first established using the armature voltage equation and the torque balance equation, and the piston rod displacement is calculated in combination with the screw transmission ratio. Subsequently, a nonlinear PID algorithm is embedded in the position regulator. The proportional link coefficient varies with the square of the error, enhancing the control output when the error is large and automatically reducing the gain to prevent overshoot when the error decreases. A piecewise function is introduced into the integral link to adjust the accumulation speed, accelerating integration when the error is large and suppressing integral saturation when approaching the target. An exponential function is used in the differential link to adjust the damping effect, enhancing the suppression effect when the error change rate is large. Finally, by solving the mathematical model in real time, the control quantity output by the nonlinear PID is converted into an armature voltage signal, and the drive motor achieves precise displacement regulation.

[0025] Compared to existing technologies, traditional PID control relies on manual trial and error to determine fixed parameters, making it difficult to adapt to load changes and external disturbances. This method uses a mathematical model to accurately describe the system's dynamic characteristics, incorporates nonlinear functions to achieve adaptive parameter adjustment, and automatically optimizes the control output at different error levels. Compared to linear PID, this method can rapidly adjust the control variable when a sudden load is applied, effectively suppressing position fluctuations and automatically reducing control intensity near the target position to avoid overshoot and oscillation.

[0026] Through the above-mentioned technical solution, this application achieves precise control of electric cylinder displacement, solves the difficulty of parameter tuning in traditional methods, and improves the system's anti-interference ability and dynamic response characteristics. In the presence of external disturbances, the nonlinear integral link can quickly eliminate steady-state errors, and the dynamic differential action can proactively suppress overshoot trends. This method is particularly suitable for industrial scenarios requiring high-precision positioning and frequently changing loads, significantly improving the robustness of electric cylinder control systems.

[0027] In some embodiments, step S1 includes: constructing a mathematical model of the electric cylinder using an armature circuit voltage balance equation, a back electromotive force equation, an electromagnetic torque equation, and a torque balance equation in combination with the electric cylinder transmission mechanism; The voltage balance equation of the armature circuit is: Where, is the armature voltage; and are the resistance and inductance of the armature winding respectively; is the armature current; The back EMF equation is: Where, represents back electromotive force; is the back electromotive force constant; is the motor speed; The electromagnetic torque equation is: Where, is the electromagnetic torque produced by the armature current; is the torque coefficient of the motor; The torque balance equation is: Where, is the load torque converted to the motor shaft; is the total moment of inertia converted to the motor shaft; is the equivalent viscous friction coefficient of the system.

[0028] Among them, the armature circuit voltage balance equation refers to the decomposition of the armature voltage into three parts: resistance voltage drop, inductance voltage drop, and back electromotive force, which is used to characterize the electrical dynamic characteristics of the armature winding. The back electromotive force equation refers to the linear correlation between the motor speed and the back electromotive force, which reflects the energy conversion characteristics during the motor rotation process. The electromagnetic torque equation refers to establishing a direct relationship between the armature current and the output torque, which reveals the dynamic demand of the load torque for current. The torque balance equation refers to the comprehensive electromagnetic torque, load torque, moment of inertia and viscous friction effects, which describes the mechanical motion characteristics on the motor shaft.

[0029] Specifically, the armature circuit voltage balance equation decomposes the armature voltage into three components: resistance voltage drop, inductance voltage drop, and back EMF, fully characterizing the electrical dynamic characteristics of the armature winding. The back EMF equation linearly relates the motor speed to the back EMF, reflecting the energy conversion characteristics during motor rotation. The electromagnetic torque equation establishes a direct relationship between the armature current and output torque, revealing the dynamic current demand of the load torque. The torque balance equation combines the electromagnetic torque, load torque, moment of inertia, and viscous friction effects to describe the mechanical motion characteristics of the motor shaft. In conjunction with the electric cylinder transmission mechanism, the above equations are coupled with the physical processes of screw-nut transmission and rotational-linear motion conversion to form a complete mathematical model that includes electrical, mechanical, and transmission links. This model is derived through mechanism rather than empirical fitting, ensuring that the physical meaning of the parameters is clear, providing an accurate description of the dynamic characteristics of the controlled object for the nonlinear PID control algorithm.

[0030] Compared to existing technologies, traditional methods often rely on empirical models or simplified assumptions to construct mathematical models of electric cylinders, resulting in unclear physical meanings of parameters and incomplete descriptions of dynamic characteristics. This solution establishes a set of equations based on strict adherence to electromagnetic and mechanical principles, fully covering the armature circuit, mechanical transmission, and energy conversion processes. This allows the model to accurately reflect the voltage-current-torque-speed coupling relationship in actual electric cylinder operation.

[0031] Through the above technical solution, this application solves the problems of difficult parameter tuning and insufficient disturbance suppression capability caused by inaccurate models in traditional PID control. The mechanism modeling method ensures that the model parameters have clear physical meaning, provides an accurate basis for the dynamic characteristics of the controlled object for the nonlinear PID controller, and enables the control strategy to dynamically compensate for the inherent characteristics of the system, thereby effectively improving parameter tuning efficiency and anti-interference ability.

[0032] In some embodiments, step S2 includes: S21, employing a single closed-loop position control mode based on the mathematical model of the electric cylinder; S22, implementing a nonlinear PID control algorithm into the position regulator to construct an electric cylinder position control system model using the nonlinear PID algorithm as the control strategy. The single closed-loop position control mode refers to a control structure that uses only displacement error as a feedback signal to form a closed loop. This mode simplifies the control loop hierarchy, reduces parameter coupling issues associated with multiple closed-loop structures, and thus shortens program solution time.

[0033] Specifically, the position single closed-loop control mode directly uses the displacement error as the input signal, and generates a control quantity through the position regulator to drive the electric cylinder to move. In the position regulator, the nonlinear proportional link dynamically adjusts the gain coefficient based on the square of the error. For example, when the absolute value of the error is large, the proportional action is increased to speed up the response speed, and when the absolute value of the error is small, the proportional action is reduced to suppress overshoot. The nonlinear integral link adjusts the integral weight through a piecewise function. For example, when the absolute value of the error exceeds the threshold, the integral accumulation speed is accelerated to improve the anti-interference ability, and when the error approaches the target value, the integral action is suppressed to avoid integral saturation. The nonlinear differential link adjusts the differential coefficient based on the change of the error exponent. For example, when the error decreases rapidly, the differential action is enhanced to suppress the overshoot trend in advance.

[0034] Compared with existing technologies, traditional PID control uses fixed-parameter proportional, integral, and differential components, making it impossible to dynamically adjust control intensity based on error. This can easily lead to a conflict between response speed and overshoot suppression. While multi-closed-loop control structures can improve control accuracy, they also suffer from complex parameter tuning and delayed system response. This solution simplifies the control hierarchy through a single closed-loop structure and incorporates a nonlinear parameter adjustment mechanism to achieve rapid response while maintaining control accuracy.

[0035] Through the above technical solution, the present application can effectively reduce the difficulty of control parameter adjustment, quickly eliminate large-scale errors during the startup phase of the electric cylinder, automatically reduce the control intensity when approaching the target position to avoid overshoot, and maintain position stability by strengthening the integral action when the external load suddenly changes, thereby improving the system's dynamic tracking performance and anti-interference ability.

[0036] In some embodiments, the result of the nonlinear PID control algorithm is a control output that varies with response time. The nonlinear PID control algorithm equation is: Where, is the control output; is the response time; It is a nonlinear proportional link; It is a nonlinear integral link; It is a nonlinear differential link.

[0037] The nonlinear proportional link is a control unit that dynamically adjusts the proportional coefficient using a quadratic function. It automatically strengthens the proportional effect as the absolute value of the error increases and reduces the gain as the error approaches zero. The nonlinear integral link is a unit that adjusts the integral strength based on the absolute value of the error. It strengthens integral accumulation when the error is large, weakens it when the error is moderate, and suppresses it when the error is small. The nonlinear differential link is an adaptive differential coefficient unit that combines an exponential function. It enhances lead suppression during the positive phase of the error and strengthens negative regulation during the overshoot phase.

[0038] Specifically, when the system error is in the rising stage, the nonlinear proportional link uses a quadratic function to increase the proportional coefficient with the square of the error. For example, when the error reaches 10mm, the proportional gain may increase to 3 times the initial value, thereby quickly generating a control amount to drive the actuator to move. When the error enters the convergence stage, the proportional coefficient automatically decreases as the error decreases. For example, when the error is reduced to 2mm, the gain returns to the basic level, effectively avoiding terminal overshoot. For the integral link, the enhanced integral mode is activated when the error exceeds the threshold. For example, when the error exceeds 5mm, the integral strength is increased to 1.5 times the normal value to accelerate the reduction of the error; when the error enters the 1-5mm range, a linearly attenuated integral weight is used to maintain the adjustment strength and prevent integral saturation; when the error is less than 1mm, the integral effect is basically turned off to completely eliminate small oscillations. In the positive error stage, the differential link achieves gain increase through an exponential attenuation function. For example, when the error decreases from 10mm to 5mm, the differential gain gradually increases by 50%, strengthening the predictive suppression of overshoot. When a negative error occurs, the gain increases exponentially with the increase in overshoot. For example, when the overshoot reaches -3mm, the differential gain increases to twice the normal value, forming a strong curb on the expansion of overshoot.

[0039] Compared with existing technologies, traditional PID control uses fixed linear combinations for the proportional, integral, and differential components, which creates a conflict between response speed and overshoot suppression when dealing with large-scale error variations. This solution constructs a nonlinear functional relationship to enable dynamic adjustment of the parameters of each component based on the real-time error. For example, it simultaneously increases the proportional and integral effects when the error is large, automatically reduces the gain when the error approaches zero, and enhances differential suppression when overshoot occurs, forming a multi-dimensional coordinated adjustment mechanism. Compared to the fixed-parameter PID algorithm, this solution achieves adaptive optimization of control parameters while maintaining structural simplicity.

[0040] Through the above technical solution, this application effectively solves the contradiction between response speed and overshoot suppression caused by the fixed parameters of traditional PID, achieves a balance between rapid response to large errors and fine adjustment of small errors through a nonlinear proportional link, eliminates oscillations caused by integral saturation with the help of a segmented integral mechanism, and uses adaptive differential gain to enhance the ability to suppress dynamic error changes, thereby significantly improving the system robustness and control accuracy.

[0041] In some embodiments, the calculation formula of the nonlinear proportional link is: Where, and are coefficients, , ; is the instantaneous error; is the response time; is the nonlinear proportional link coefficient. When the instantaneous error hour, , The bigger, The bigger, The smaller, The smaller the error, the faster the action is. At the beginning of the response, the faster the action is. At the end of the response, when the absolute value of the error is relatively small, overshoot can be avoided. When the instantaneous error is When , it means that overshoot occurs. , , the larger the overshoot, The larger the value is, the more the control output is reduced, thus suppressing overshoot; when the overshoot amplitude is small, Small enough to avoid oscillation.

[0042] Among them, the coefficient Used to adjust the influence of the squared error on the gain, the coefficient Used to set the basic gain value. It refers to the difference between the target displacement and the actual displacement at the current moment, which can be measured in real time by the displacement sensor. With the absolute value of the error The square change can be adjusted by and The numerical relationship of realizes the gain characteristics of different error ranges.

[0043] Specifically, when the instantaneous error When the nonlinear proportional link coefficient With the absolute value of the error increases with the square of Take 0.5 and When the value is 1, the gain when the error is 2mm is 0.5×2²+1=3, and the gain when the error is 1mm is 0.5×1²+1=1.5. This nonlinear relationship significantly improves the control output in the initial stage of response when the error is large, speeding up the displacement of the piston rod. When the error approaches zero, the effect of the square term weakens. For example, when the error is 0.2mm, the gain drops to 0.5×0.2²+1=1.02, avoiding overshoot caused by excessive proportional gain. When the instantaneous error When the nonlinear proportional link coefficient Still maintain a positive value, for example, when the error is -1mm, the gain is 0.5×(-1)²+1=1.5. At this time, the control output is a negative value. The larger the overshoot amplitude, the greater the gain. For example, when the error is -3mm, the gain rises to 0.5×9+1=5.5, forming a restraining force proportional to the overshoot. At the same time, through Maintain basic regulatory capabilities.

[0044] Through the above technical solution, the present application can improve the control output of the proportional link when the displacement deviation is large and shorten the response time during the displacement adjustment process of the electric cylinder; automatically reduce the proportional gain when the displacement is close to the target value to avoid overshoot caused by overshoot; when overshoot occurs, the reverse correction force is automatically enhanced according to the overshoot amplitude to effectively suppress the expansion of the overshoot amount, and at the same time, through the constant value Maintain stability control under small error conditions to prevent system oscillation.

[0045] In some embodiments, the calculation formula of the nonlinear integral link is: , ;in, Where, is the instantaneous error; is the response time; is the coefficient of the nonlinear integral link; and is the instantaneous error Two thresholds of the absolute value of When the instantaneous error The absolute value of is greater than or equal to hour, is a constant not less than 1; when the instantaneous error The absolute value of Internal time, Is a positive number greater than 0 and less than 1; when the instantaneous error The absolute value of is not greater than hour, Approaching 0.

[0046] in, and The absolute value of the error The two thresholds are used to divide the different areas of integration action. Refers to a positive number approaching zero, which is used to calculate the absolute value of the error When it is smaller, the integral effect is weakened. Refers to a constant not less than 1, which is used to enhance the integral effect when the absolute value of the error is large.

[0047] Specifically, when the absolute value of the error Exceeding the threshold When , the weight coefficient of the integral term is activated, and the integral effect is amplified. For example, in the early stage of the rising phase, the error accumulation can be accelerated to improve the response speed. In the overshoot phase, the control output is quickly reduced through the integral effect of the negative error. In the middle range, the weight coefficient changes linearly with the error. For example, in the middle of the rising stage, the integral accumulation speed can be moderately slowed down to avoid integral saturation; in the overshoot stage, the integral effect is weakened to prevent oscillation caused by a sudden decrease in the control amount. Below threshold When the weight coefficient Approaching zero, for example, almost eliminating the integral effect at the end of the rising phase, avoiding the continuous accumulation of small errors and causing overshoot.

[0048] Through the above technical solution, the present application realizes the dynamic adjustment of the integral action strength according to the error size, accelerates the response speed in the early stage of the rising phase, avoids integral saturation in the middle stage, and eliminates the overshoot risk in the final stage; in the overshoot stage, the overshoot amplitude is suppressed by the integral action of the negative error, and at the same time prevents oscillation caused by excessive adjustment of the control quantity, thereby improving the system robustness and control accuracy.

[0049] In some embodiments, the calculation formula of the nonlinear differential link is: Where, and are coefficients, , ; is the instantaneous error, is the response time, is the coefficient of the nonlinear differential link. When the instantaneous error When it is greater than 0, it is reflected in the rising stage of the response, as the instantaneous error The decrease of the nonlinear differential link coefficient increases, and the instantaneous error The rate of change is less than 0, and the nonlinear differential link is negative, which plays a role in suppressing overshoot in advance; when the instantaneous error When it is less than 0, it indicates that overshoot occurs at this time; as the instantaneous error As the absolute value increases, the coefficient of the nonlinear differential link increases, and the instantaneous error The rate of change is less than 0. At this time, the nonlinear differential link is negative, which suppresses the increase of the overshoot amplitude.

[0050] in, Refers to the differential gain adjustment coefficient, which is used to control the adjustment amplitude of the differential gain by the error; Refers to the basic differential gain coefficient, which is used to ensure the minimum intensity of the differential link; exponential function For instantaneous error The absolute value of the error dynamically adjusts the differential gain. When the error increases, the exponential function value decreases, thereby reducing the increase in the differential gain; when the absolute value of the error When decreases, the exponential function value increases, thereby increasing the increase in the differential gain.

[0051] Specifically, during the rising phase of the system response, the instantaneous error is positive and gradually decreases. At this time, the error change rate is negative, and the differential link output is a negative adjustment amount. As the error decreases, the exponential function The output of gradually increases, making the nonlinear differential link coefficient Depend on and When the system overshoots, the instantaneous error It turns to negative and the absolute value increases. At this time, the error change rate is still negative, and the output of the differential link further increases the negative adjustment amount. As the absolute value of the error increases, it decays, making the nonlinear differential link coefficient The increase in the gain is limited to avoid sudden changes in the adjustment amount due to excessive gain. The existence of the error ensures that the absolute value When it is at its maximum, the basic differential effect is still maintained to prevent the system from becoming unstable.

[0052] Through the above technical solution, the present application can adaptively adjust the strength of the differential action according to the error size and change trend during the electric cylinder displacement adjustment process: when the error is large in the initial rising phase, it avoids sudden changes in the control amount due to excessive differential gain; when the error approaches the target position, the differential action is enhanced to suppress overshoot; after overshoot occurs, the overshoot amplitude is quickly converged through the inverse correlation between the absolute value of the error and the differential gain. This solution resolves the trade-off between dynamic response and steady-state accuracy in traditional PID control and improves the system's anti-interference ability.

[0053] Through simulation analysis, we can more intuitively observe the superiority of the nonlinear PID control method of the present application compared with the traditional PID control method. Figure 3 As shown in the figure, a model of electric cylinder position servo control system is built based on the simulation software platform. Under load operation, the position loop PID control and position loop nonlinear PID control are simulated respectively. Among them, the given position signal is a step signal with an amplitude of 100, and a torque interference signal is applied when the response time reaches 10s. The total response time is set to 20s. Figure 3 As can be seen from the figure, for a given position signal of 100 mm, the system under nonlinear PID control responds faster, reaches steady state in less time, and has a smaller steady-state error than PID control. The system under PID control experiences significant position output fluctuations and a long adjustment time under external disturbances, while the system under nonlinear PID control exhibits virtually no position output fluctuations and exhibits greater robustness.

[0054] Other structures and operations of the nonlinear PID control method for electric cylinder displacement regulation according to the embodiment of the present invention are well known to those skilled in the art and will not be described in detail here.

[0055] In the description of this specification, the reference terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" mean that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art can combine and combine different embodiments or examples described in this specification and features of different embodiments or examples without contradiction.

[0056] While embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions, and variations may be made to the embodiments without departing from the principles and spirit of the invention, and that the scope of the invention is defined by the claims and their equivalents.

Claims

1. A nonlinear PID control method for electric cylinder displacement regulation, characterized in that: include: S1. Constructing a mathematical model of the electric cylinder; S2. Construct an electric cylinder position control system model by combining the electric cylinder mathematical model and nonlinear PID control algorithm; S3. Use the electric cylinder position control system model to adjust the electric cylinder displacement.

2. The nonlinear PID control method for electric cylinder displacement regulation according to claim 1, characterized in that: Step S1 includes: using the armature circuit voltage balance equation, back electromotive force equation, electromagnetic torque equation and torque balance equation, and combining the electric cylinder transmission mechanism to construct an electric cylinder mathematical model; The voltage balance equation of the armature circuit is: Where, is the armature voltage; and are the resistance and inductance of the armature winding respectively; is the armature current; The back EMF equation is: Where, represents back electromotive force; is the back electromotive force constant; is the motor speed; The electromagnetic torque equation is: Where, is the electromagnetic torque produced by the armature current; is the torque coefficient of the motor; The torque balance equation is: Where, is the load torque converted to the motor shaft; is the total moment of inertia converted to the motor shaft; is the equivalent viscous friction coefficient of the system.

3. The nonlinear PID control method for electric cylinder displacement regulation according to claim 1, characterized in that: Step S2 includes: S21. Based on the mathematical model of the electric cylinder, a position single closed-loop control mode is adopted; S22. Write the nonlinear PID control algorithm into the position regulator and construct an electric cylinder position control system model using the nonlinear PID algorithm as the control strategy.

4. The nonlinear PID control method for electric cylinder displacement regulation according to claim 3, characterized in that: The result of the nonlinear PID control algorithm is a control output that changes with response time. The nonlinear PID control algorithm equation is: Where, is the control output; is the response time; It is a nonlinear proportional link; It is a nonlinear integral link; It is a nonlinear differential link.

5. The nonlinear PID control method for electric cylinder displacement regulation according to claim 4, characterized in that: The calculation formula of the nonlinear proportional link is: Where, and are coefficients, , ; is the instantaneous error; is the response time; is the nonlinear proportional link coefficient.

6. The nonlinear PID control method for electric cylinder displacement regulation according to claim 5, characterized in that: When the instantaneous error hour, , The bigger, The bigger, The smaller, The smaller the error, the faster the action is. At the beginning of the response, the faster the action is. At the end of the response, when the absolute value of the error is relatively small, overshoot can be avoided. When the instantaneous error When , it means that overshoot occurs. , , the larger the overshoot, The larger the value is, the more the control output is reduced, thus suppressing overshoot; when the overshoot amplitude is small, Small enough to avoid oscillation.

7. The nonlinear PID control method for electric cylinder displacement regulation according to claim 4, characterized in that: The calculation formula of the nonlinear integral link is: , ; in, Where, is the instantaneous error; is the response time; is the coefficient of the nonlinear integral link; and is the instantaneous error Two thresholds of the absolute value of .

8. The nonlinear PID control method for electric cylinder displacement regulation according to claim 7, characterized in that: When the instantaneous error The absolute value of is greater than or equal to hour, is a constant not less than 1; When the instantaneous error The absolute value of Internal time, is a positive number greater than 0 and less than 1; When the instantaneous error The absolute value of is not greater than hour, Approaching 0.

9. The nonlinear PID control method for electric cylinder displacement regulation according to claim 4, characterized in that: The calculation formula of the nonlinear differential link is: Where, and are coefficients, , ; is the instantaneous error, is the response time, is the coefficient of the nonlinear differential link.

10. The nonlinear PID control method for electric cylinder displacement regulation according to claim 9, characterized in that: When the instantaneous error When it is greater than 0, it is reflected in the rising stage of the response, as the instantaneous error The decrease of the nonlinear differential link coefficient increases, and the instantaneous error The rate of change is less than 0, and the nonlinear differential link is negative, which plays a role in suppressing overshoot in advance; when the instantaneous error When it is less than 0, it indicates that overshoot occurs at this time; With the instantaneous error As the absolute value increases, the coefficient of the nonlinear differential link increases, and the instantaneous error The rate of change is less than 0. At this time, the nonlinear differential link is negative, which suppresses the increase of the overshoot amplitude.

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