Anti-saturation PI control method based on integral steady-state prediction

Abstract

The invention discloses an anti-saturation PI control method based on integral steady-state prediction, and aims to solve a saturation phenomenon caused by output amplitude limiting of each stage in a position servo system. The method comprises the following specific steps: firstly, constructing a position servo system three-loop control structure based on PI control, secondly, designing a speed loop anti-saturation PI controller based on integral steady-state prediction, and finally, designing a position loop anti-saturation PI controller based on integral steady-state prediction. The anti-saturation PI control method provided by the invention is simple, high in response speed and free of overshoot.

Description

Technical Field

[0001] The invention relates to the field of anti-saturation PI control methods, in particular to an anti-saturation PI control method based on integral steady-state prediction. Background Art

[0002] The electric servo drive control system usually consists of three control loops: current loop, speed loop and position loop. Among them, due to the limitations of factors such as the maximum current and output torque of the motor, the current loop setting, that is, the speed controller output, needs to be limited. In addition, in systems with large load inertia such as turntables and radar antenna bases, in order to ensure system safety, the speed loop speed setting, that is, the position controller output, is usually limited. In this way, nonlinear links of output limiting appear in both the speed and position loops. When the loop setting value exceeds the limit value, the output of the upper controller is not equal to the actual input of the controlled object, thereby affecting the closed-loop performance of the entire system. This phenomenon of poor system response due to input limitation is called the Wind-up phenomenon. For the PI controller, which is the most widely used in current servo systems, the integral saturation phenomenon is a typical representative of the Wind-up phenomenon. The integral saturation phenomenon will cause the servo system to have phenomena such as increased overshoot, prolonged adjustment time, increased number of oscillations, etc. under the condition of a given large-scale mutation, and even cause system instability.

[0003] Patent No. CN201610830333.6 discloses an adaptive passive PI control method for a grid-connected inverter system based on MMC. This patent proposes a passive PI control method for the PI control problem in the grid-connected control of modular multilevel inverters (MMC). By establishing a bilinear Lagrangian model and adding adaptive gain adjustment to the control method, the robustness of the control system under different load conditions is enhanced. Its advantages are simple structure and wide stability domain, and it is particularly suitable for complex working condition control of high-power grid-connected inverters. This method is based on a specific MMC structure, relies on a bilinear Lagrangian model and passive design, and is suitable for high-power grid-connected inverter systems, but lacks in the wide applicability of the control system and is difficult to be extended to other types of control systems. Patent No. CN202210487026.8 discloses an intelligent PI control method for a dual-active full-bridge converter. This patent combines a deep reinforcement learning algorithm and proposes an intelligent PI control method. The parameters of the PI controller are dynamically adjusted through the TD3 algorithm, so that it can adapt to complex operating environments and improve dynamic performance. This method overcomes the limitation of fixed parameters of traditional PI control and greatly improves the dynamic response speed and steady-state performance of the system. This method introduces deep reinforcement learning to achieve intelligent parameter adjustment, but because it relies on complex TD3 algorithms and a large amount of training data, it increases the complexity of system implementation and has application bottlenecks for systems with high real-time requirements.

[0004] At present, the control methods to overcome the integral saturation phenomenon are mainly divided into two categories: conditional integration method and tracking back calculation method. The conditional integration method stops or limits the integration according to the pre-set conditions. The main disadvantage of this method is the lack of robustness. The switching conditions are often for a fixed object. Once the object or other system parameters change, this method not only cannot suppress the integral saturation phenomenon, but also causes the system to lose control. The tracking back calculation method is to use the difference between the controller output and the input of the controlled object as a feedback signal to form a feedback branch to eliminate it. The system dynamic performance of this method depends not only on the PI control parameters, but also on the tracking back calculation parameters. However, since the changes in instructions and loads are not considered when designing the regulator parameters, fixed back calculation parameters are generally difficult to ensure the consistency of system response in a large range. When the back calculation parameters are selected too small, the integral saturation phenomenon is not suppressed. When the parameters are selected too large, the system response speed slows down. Summary of the invention

[0005] In view of the defects of the prior art, the present invention proposes an anti-saturation PI control method based on integral steady-state prediction, which introduces anti-saturation modules in the speed loop and the position loop respectively, dynamically detects the saturation state of the controller, and adjusts the integral term in real time through the integral steady-state prediction formula to avoid excessive accumulation of the integral term in the saturation state. Combined with the design of the first-order filter, the noise interference introduced by the differential operation in the prediction process is reduced, thereby achieving comprehensive optimization of the dynamic response speed, steady-state performance and robustness. The method described in the present invention specifically includes the following steps:

[0006] S1: Build an anti-saturation PI control system, which includes a speed controller and a position controller; the speed controller includes a PI controller A and a speed loop anti-saturation module, and the position controller includes a PI controller B and a position loop anti-saturation module;

[0007] S2: Perform speed loop closed-loop control, which specifically includes the following steps:

[0008] S2-1: The input of PI controller A is the speed error signal e , the output is given by the ideal current u , and its calculation formula is:

[0009] u=K PS e+K IS α (1)

[0010] Where u is the ideal current given; K PS , K IS are the proportional coefficient and integral coefficient of PI controller A respectively; α is the integral term value of PI controller A; e is the input error of PI controller A, e=ω * -ω;ω * is the given speed; ω is the actual speed;

[0011] S2-2: Establish a speed loop dynamic model. The model regards the current loop as a dynamic link that responds faster than the speed loop. Its dynamic equation is described as:

[0012]

[0013] in, is the current given; k T is the motor torque coefficient; J is the load moment of inertia; B is the viscous friction coefficient; T L is the load torque; where, The relationship with u is:

[0014]

[0015] Among them, u MIN The speed loop output limit minimum value; uMAX It is the maximum value of speed loop output limit;

[0016] S2-3: When the speed loop is in steady state, ω * =ω, the dynamic equation of the speed loop dynamic model is described as:

[0017]

[0018] Among them, α S is the final value of the integral of PI controller A in steady state, and the integral steady-state condition is The calculation formula of the final value of the integral is:

[0019]

[0020] S2-4: Update the motion equation when the PI controller A is saturated. The calculation formula is:

[0021]

[0022] in, is the PI controller A error differential;

[0023] S2-5: When the speed loop is saturated, the integral prediction value is calculated using the error dynamic equation and the integral prediction formula. The calculation formula is:

[0024]

[0025] in, is the differential term of the speed error;

[0026] S2-6: Perform a first-order filter on the steady-state prediction value of the integral term of the PI controller A to eliminate noise interference and obtain the speed loop anti-saturation integral term α1. The calculation formula of α1 is:

[0027]

[0028] Among them, τ S is the time constant of the speed controller integral filter;

[0029] S2-7: The current setting corrected by the speed controller output is finally The calculation formula is:

[0030]

[0031] S3: Perform position loop closed-loop control, which specifically includes the following steps:

[0032] S3-1: The input of PI controller B is the position error signal E, and the output is the ideal speed reference v. The calculation formula is:

[0033] v=K PP E+K IP β (11)

[0034] Where, v is the ideal speed given; K PP , K IP are the proportional coefficient and integral coefficient of PI controller B respectively; β is the integral term of PI controller B; E is the input error of PI controller B, E=θ * -θ; θ * is the given position; θ is the actual position;

[0035] S3-2: Since the dynamic response speed of the speed loop is faster than that of the position loop, the speed loop is approximated as a link with a proportional coefficient of 1, and then the dynamic relationship of the position loop is established. Its mathematical expression is:

[0036]

[0037] in, is the actual position differential; ω is the actual speed, ω * is the speed given; ω * The relationship with v is the limiting rule, and the specific calculation formula is as follows:

[0038]

[0039] Among them, v MIN is the minimum value of the position loop output limit; v MAX It is the maximum value of the position loop output limit;

[0040] S3-3: When the position loop reaches a steady state, θ * =θ, the final value of the integral is β P It is derived through the integral steady-state condition, and the specific calculation formula is:

[0041]

[0042] in, The differential is given for the position;

[0043] S3-4: When the position loop is in saturation, the integral steady-state value is predicted by the error dynamic model The calculation formula is:

[0044]

[0045] in, is the differential of the input error of PI controller B;

[0046] S3-5: In order to suppress the noise interference caused by the error differential in the integral prediction process, a first-order filter is used to correct the integral term value, and finally the anti-saturation integral term value β1 is obtained, and its calculation formula is:

[0047]

[0048] Among them, τ P is the time constant of the integral filter of the position controller;

[0049] S3-6: Finally, the position controller outputs a speed reference ω * , and its calculation formula is:

[0050]

[0051] Through the above steps, the anti-saturation PI control based on integral steady-state prediction is completed.

[0052] As a technical preferred solution of the present invention, the anti-saturation PI control system in step S1 specifically includes:

[0053] Speed ​​controller: The speed controller consists of a PI controller A and a speed loop anti-saturation module. The PI controller A is used to generate an ideal current setting based on a speed error signal; the speed loop anti-saturation module is used to detect the output saturation state of the PI controller A in the speed loop, and adjust the integral term of the PI controller A through an integral steady-state prediction formula in the saturated state to make it approach the steady-state integral value, thereby realizing speed loop integral anti-saturation control.

[0054] Position controller: The position controller consists of a PI controller B and a position loop anti-saturation module. The PI controller B is used to generate an ideal speed setting based on a position error signal. The position loop anti-saturation module is used to detect the output saturation state of the PI controller B in the position loop, and adjust the integral term of the PI controller B through the integral steady-state prediction formula in the saturated state to make it approach the steady-state integral value, thereby realizing the position loop integral anti-saturation control.

[0055] As a technical preferred solution of the present invention, when the PI controller A in step S2 is in different working states, the control method of the speed loop anti-saturation module includes:

[0056] When the PI controller A is in the linear segment, that is, u MIN <u<u MAX When , the integral action works normally, and the integral term value α is obtained by accumulating the error signal.

[0057] When the PI controller A is in saturation, that is, u>u MAX or u<u MINWhen the speed loop anti-saturation module stops the integral action, the integral steady-state prediction formula is used to calculate the steady-state value of the integral term. And the accumulated value of the integral term is adjusted to the steady-state integral prediction value, thereby realizing dynamic adjustment of the integral action.

[0058] As a technical preferred solution of the present invention, when the PI controller B in step S3 is in different working states, the control method of the position loop anti-saturation module includes:

[0059] When PI controller B is in the linear segment, that is, v MIN <v<v MAX When , the integral action works normally, and the anti-saturation integral term value β1 is obtained by accumulating the position error signal;

[0060] When PI controller B is in saturation state, that is, v>v MAX or v<v MIN When the position loop anti-saturation module stops the integral action, the integral steady-state prediction formula is used to calculate the steady-state value of the integral term. This enables dynamic adjustment of the integral action.

[0061] As a technical preferred solution of the present invention, the speed loop anti-saturation module in step S2 corrects the integral prediction value through a first-order filter, and its working mechanism includes:

[0062] When the output of PI controller A satisfies u MIN <u<u MAX When , the filter keeps the integral term accumulated normally, and its output integral value is α1 = ∫e; where e = ω * -ω is the speed error;

[0063] When the output of PI controller A satisfies u>u MAX or u<u MI When N, the filter calculates the corrected anti-saturation integral term through the integral steady-state prediction formula in, is the predicted value of the steady-state integral of the speed loop, τ S is the filter time constant, which is used to suppress noise interference in the integral prediction process.

[0064] As a technical preferred solution of the present invention, the position loop anti-saturation module in step S3 corrects the integral prediction value through a first-order filter, and its working mechanism includes:

[0065] When the output of PI controller B satisfies v MIN <v<v MAX When , the filter keeps the integral term accumulated normally, and its output integral value β1=∫E; where E=θ*-θ is the position error;

[0066] When the output of PI controller B satisfies v>v MAX or v<v MIN When the filter calculates the corrected anti-saturation integral term through the integral steady-state prediction formula in, is the steady-state integral prediction value of the position loop, τ P is the filter time constant, which is used to reduce noise interference in the integral prediction process.

[0067] Compared with the prior art, the present invention has the following beneficial effects:

[0068] To solve the problem of performance degradation caused by integral saturation, the present invention calculates the system steady-state prediction value of the integral term when the regulator is saturated, and uses it as the initial value of the integral when the controller restores the linear segment, thereby effectively suppressing the cumulative effect caused by integral saturation, thereby significantly improving the dynamic response and steady-state performance of the system.

[0069] Optimize the response characteristics of the control system. Under the condition that the system parameters are accurate, the method of the present invention adjusts the initial value of the integral to make the response curve of the system close to the optimal characteristics, thereby achieving rapid convergence and precise adjustment of the control system under complex operating conditions, and greatly improving the overall performance of the control system.

[0070] To maintain the original stability of the system, this method only adjusts the initial value of the integral when the controller switches from a nonlinear state to a linear state, without changing the dynamic characteristics and design framework of the original controller. Therefore, it will not have a negative impact on the original stability of the system, ensuring the safe and reliable operation of the control system.

[0071] The method is simple and has low calculation complexity. The method of the invention only needs to introduce an integral steady-state prediction formula and a simple first-order filter to calculate and correct the integral value. The algorithm is simple to implement and has low calculation complexity, and is suitable for control systems with high real-time requirements. BRIEF DESCRIPTION OF THE DRAWINGS

[0072] Figure 1 The present invention provides a flow chart of an anti-saturation PI control method based on integral steady-state prediction. DETAILED DESCRIPTION

[0073] The present invention is further described below in conjunction with the examples. However, the present invention can be implemented in many different ways and should not be construed as being limited to the examples shown; on the contrary, these examples provide those skilled in the art with implementation methods that meet applicable legal requirements.

[0074] Example 1: Figure 1 As shown, the present invention proposes an anti-saturation PI control method based on integral steady-state prediction, which specifically includes the following steps:

[0075] Step S1: Building an anti-saturation PI control system.

[0076] The anti-saturation PI control system includes: a speed controller and a position controller. The speed controller includes: a PI controller A and a speed loop anti-saturation module. The position controller includes: a PI controller B and a position loop anti-saturation module.

[0077] The function of the speed loop anti-saturation module is to realize the speed loop integral anti-saturation closed-loop control.

[0078] The function of the position loop anti-saturation module is to realize the position loop integral anti-saturation closed-loop control.

[0079] Step S2: Perform speed loop closed-loop control.

[0080] The ideal current given by PI controller A is:

[0081] u=K PS e+K IS α (1)

[0082] In formula (1), u is the ideal current given; K PS , K IS are the proportional coefficient and integral coefficient of PI controller A respectively; α is the integral term of PI controller A; e is the input error of PI controller A, e=ω * -ω;ω * is the given speed; ω is the actual speed.

[0083] Since the bandwidth of the current loop is much larger than that of the speed loop and the position loop, the current loop is equivalent to a link with a proportional coefficient of 1, and the motion equation is obtained as follows:

[0084]

[0085] In formula (2), is the current given; k T is the motor torque coefficient; J is the load moment of inertia; B is the viscous friction coefficient; T L is the load torque.

[0086] The relationship with u is:

[0087]

[0088] In formula (3), u MIN The speed loop output limit minimum value; u MAX It is the maximum value of speed loop output limit.

[0089] When the speed loop is in steady state, e=0 and ω* =ω, we get:

[0090]

[0091] In formula (5), α S It is the final value of the integral of PI controller A in steady state.

[0092] From formula (4) and formula (5), we can get:

[0093]

[0094] From ω=ω * -e and formula (2) to obtain the motion equation when the PI controller A is saturated:

[0095]

[0096] In formula (5), is the PI controller A error differential.

[0097] The steady-state prediction value of the integral term of PI controller A is obtained from formula (6) and formula (7):

[0098]

[0099] When the PI controller A is in the linear segment, that is, u MIN <u<u MAX When u>u, the integral action works normally; when the PI controller A is in saturation, that is, u>u MAX or u<u MIN When , the integral action is stopped, the speed loop anti-saturation module predicts the steady-state value of the integral term, and adjusts the accumulated value of the integral term to the integral prediction value when the speed loop is in steady state.

[0100] Since formula (8) contains a differential term, a first-order filter is added to reduce noise interference, and the speed loop anti-saturation integral term α1 is obtained:

[0101]

[0102] In formula (9), τ S is the speed controller integral filter time constant.

[0103] The final speed controller is:

[0104]

[0105] Step S3: Perform position loop closed-loop control.

[0106] The ideal speed given by PI controller B is:

[0107] v=K PP E+K IP β (11)

[0108] In formula (11), v is the ideal speed given; K PP , K IP are the proportional coefficient and integral coefficient of PI controller B respectively; β is the integral term of PI controller B; E is the input error of PI controller B, E=θ * -θ; θ * is the given position; θ is the actual position.

[0109] Since the bandwidth of the speed loop is much larger than that of the position loop, the speed loop is equivalent to a link with a proportional coefficient of 1, and the following is obtained:

[0110]

[0111] In formula (12), is the actual position differential.

[0112] ω * The relationship with v is:

[0113]

[0114] In formula (13), v MIN is the minimum value of the position loop output limit; v MAX It is the maximum value of position loop output limit.

[0115] When the position loop is in steady state, E = 0 and θ * =θ, the final value of the integral is:

[0116]

[0117] In formula (14), Give the differential for the position.

[0118] From θ = θ * -E and formula (12) and formula (14) to obtain the predicted value of the integral term of PI controller B in steady state:

[0119]

[0120] In formula (15), is the derivative of the input error of PI controller B.

[0121] When PI controller B is in the linear segment, that is, v MIN <v<v MAX When PI controller B is in saturation state, that is, v>v MAX or v<vMIN When , the integral action is stopped, the position loop anti-saturation module predicts the steady-state value of the integral term, and adjusts the accumulated value of the integral term to the integral prediction value when the position loop is in steady state.

[0122] Since formula (15) contains a differential term, a first-order filter is added to reduce noise interference, and the anti-saturation integral term β1 of the position loop is obtained:

[0123]

[0124] In formula (16), τ P is the time constant of the position controller integral filter.

[0125] The final position controller is:

[0126]

[0127] Based on the above steps, the anti-saturation PI control based on integral steady-state prediction is realized.

[0128] Example 2: This example aims to verify the actual effect of an anti-saturation PI control method based on integral steady-state prediction proposed in the present invention in a motor drive system. By comparing the control performance of the traditional PI control method with that of the present method, the degree of improvement in dynamic response, steady-state error and robustness under saturation conditions is analyzed.

[0129] The experimental platform uses a three-phase asynchronous motor with a rated power of 2.2kW to build a closed-loop control system including a speed control loop and a position control loop. The controller is implemented using DSP (model TMS320F28335) with a sampling period of 1ms. A load simulation device is added to the system to test the response performance of the control system by setting different load torques and dynamic commands. The key control parameters set in the experiment are shown in Table 1:

[0130] Table 1: Key control parameters

[0131] Control parameters symbol value unit Proportional coefficient of PI controller A <![CDATA[K PS ]]> 5 - Integral coefficient of PI controller A <![CDATA[K IS ]]> 0.1 - Proportional coefficient of PI controller B <![CDATA[K PP ]]> 8 - Integral coefficient of PI controller B <![CDATA[K IP ]]> 0.2 - Speed ​​loop output limit range <![CDATA[[u MIN ,in MAX ]]> [-10,10] A Position loop output limit range <![CDATA[[v MIN ,in MAX ]]> [-5,5] rad / s Filter time constant <![CDATA[τ S ,t P ]]> 0.05 s

[0132] The experiment uses the traditional PI control method and the method of the present invention to test. In the test, two different working conditions are set:

[0133] Working condition 1: Steady-state command response test, set the speed command to 1500rpm and the position command to 30rad, observe the dynamic response process of the system from the initial static state to the steady state, and the steady-state error performance of the system under load disturbance.

[0134] Working condition 2: Dynamic command response test, set the speed command from 1500rpm to 1800rpm, and the position command from 30rad to 50rad, to test the dynamic tracking performance of the system, including response time, overshoot and stabilization time.

[0135] The experimental steps include:

[0136] 1. Initialize system parameters, start the experimental platform, and set the initial values ​​of speed and position to 0 respectively;

[0137] 2. Using the traditional PI control method and the method of the present invention respectively, run the experiment under working condition 1 and working condition 2, and record the dynamic response curve and steady-state data;

[0138] 3. Compare the performance of different methods in terms of dynamic response and steady-state error, organize the experimental data and generate a comparison table.

[0139] Working condition 1: Steady-state command response test

[0140] The speed and position response curves of the system from the initial static state to the steady state are recorded in the experiment. The performance comparison between the traditional PI control method and the method of the present invention is shown in the following table:

[0141] Table 2: Experimental comparison results 1

[0142] Test indicators Traditional PI control method Method of the present invention Improvement rate Speed ​​steady state error (rpm) 10 0.5 95％ Position steady-state error (rad) 0.5 0.02 96％ Dynamic response time(s) 2.5 1.8 28％ Overshoot (%) 15％ 5％ 67％

[0143] As can be seen from the table, the method of the present invention is significantly superior to the traditional PI control method in terms of steady-state error and dynamic response. In the speed control loop, the traditional PI control method accumulates a large integral value in the saturated state, resulting in an obvious steady-state deviation after the system recovers the linear segment. The method of the present invention adjusts the initial value of the integral through the integral steady-state prediction formula, allowing the system to quickly enter the steady state, and the steady-state error is reduced by 95%.

[0144] Similarly, in the position control loop, the method of the present invention performs well in suppressing the integral accumulation effect of the saturation state, reducing the position steady-state error from 0.5rad to 0.02rad, and improving the accuracy by 96%. In addition, due to the dynamic adjustment of the initial value of the integral, the overshoot is reduced by 67% and the dynamic response time is shortened by 28%.

[0145] Working condition 2: Dynamic command response test

[0146] When the speed and position instructions suddenly change, the dynamic tracking curve of the system is recorded, and the response time, overshoot and final error are counted. The experimental data are shown in the following table:

[0147] Table 3: Experimental comparison results 2

[0148] Test indicators Traditional PI control method Method of the present invention Improvement rate Speed ​​overshoot (%) 20％ 8％ 60％ Speed ​​stabilization time(s) 3 2 33％ Position overshoot (%) 25％ 10％ 60％ Position stabilization time (s) 4 2.5 38％

[0149] It can be seen from the data that when the traditional PI control method processes dynamic command mutations, it is easy to cause a large integral accumulation due to the saturation state, resulting in obvious overshoot and a long stabilization time. The method of the present invention avoids excessive integral accumulation effects under saturation conditions by adjusting the initial value of the integral, significantly reduces the overshoot, and shortens the stabilization time. In the speed control loop, the overshoot is reduced from 20% to 8%, and the stabilization time is reduced from 3.0 seconds to 2.0 seconds. In the position control loop, the overshoot is reduced by 60% and the stabilization time is shortened by 38%.

[0150] The experiment further added noise interference to observe the control effects of the two methods in a noisy environment. The results show that the method of the present invention corrects the integral prediction value through a first-order filter, effectively suppresses the influence of noise on the system, and the system output is smoother and the robustness is significantly improved. Through the experimental verification of this embodiment, the anti-saturation PI control method based on integral steady-state prediction proposed by the present invention is significantly superior to the traditional PI control method in dynamic response and steady-state performance, which is specifically manifested in: reducing the integral accumulation effect under saturation state and reducing steady-state error; improving dynamic command tracking performance and shortening response time; enhancing the robustness of the system and performing stably in a noise interference environment.

[0151] The above embodiments only express the implementation methods of the present invention, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the invention. It should be pointed out that, for those of ordinary skill in the art, several variations and improvements can be made without departing from the concept of the present invention, and these all belong to the protection scope of the present invention.

Claims

1. An anti-saturation PI control method based on integral steady-state prediction, characterized in that: The following steps are involved: S1: Build an anti-saturation PI control system, which includes a speed controller and a position controller; the speed controller includes a PI controller A and a speed loop anti-saturation module, and the position controller includes a PI controller B and a position loop anti-saturation module; S2: Perform speed loop closed-loop control, which specifically includes the following steps: S2-1: The input of PI controller A is the speed error signal e, and the output is the ideal current given u. The calculation formula is: u=K PS e+K IS α (1) Where u is the ideal current given; K PS , K IS are the proportional coefficient and integral coefficient of PI controller A respectively; α is the integral term value of PI controller A; e is the input error of PI controller A, e=ω * -ω;ω * is the given speed; ω is the actual speed; S2-2: Establish a speed loop dynamic model. The model regards the current loop as a dynamic link that responds faster than the speed loop. Its dynamic equation is described as: in, is the current given; k T is the motor torque coefficient; J is the load moment of inertia; B is the viscous friction coefficient; T L is the load torque; where, The relationship with u is: Among them, u MIN The speed loop output limit minimum value; u MAX It is the maximum value of speed loop output limit; S2-3: When the speed loop is in steady state, ω * =ω, the dynamic equation of the speed loop dynamic model is described as: Among them, α S is the final value of the integral of PI controller A in steady state; the integral steady-state condition is The calculation formula of the final value of the integral is: S2-4: Update the motion equation when the PI controller A is saturated. The calculation formula is: in, is the PI controller A error differential; S2-5: When the speed loop is saturated, the integral prediction value is calculated using the error dynamic equation and the integral prediction formula. The calculation formula is: in, is the differential term of the speed error; S2-6: Perform a first-order filter on the steady-state prediction value of the integral term of the PI controller A to eliminate noise interference and obtain the speed loop anti-saturation integral term α1. The calculation formula of α1 is: Among them, τ S is the time constant of the speed controller integral filter; S2-7: The current setting corrected by the speed controller output is finally The calculation formula is: S3: Perform position loop closed-loop control, which specifically includes the following steps: S3-1: The input of PI controller B is the position error signal E, and the output is the ideal speed reference v. The calculation formula is: v=K PP E+K IP β (11) Where, v is the ideal speed given; K PP , K IP are the proportional coefficient and integral coefficient of PI controller B respectively; β is the integral term of PI controller B; E is the input error of PI controller B, E=θ * -θ; θ * is the given position; θ is the actual position; S3-2: Since the dynamic response speed of the speed loop is faster than that of the position loop, the speed loop is approximated as a link with a proportional coefficient of 1, and then the dynamic relationship of the position loop is established. Its mathematical expression is: in, is the actual position differential; ω is the actual speed; ω * is the speed given; ω * The relationship with v is the limiting rule, and the specific calculation formula is as follows: Among them, v MIN is the minimum value of the position loop output limit; v MAX It is the maximum value of the position loop output limit; S3-3: When the position loop reaches a steady state, θ * =θ, the final value of the integral is β P It is derived through the integral steady-state condition, and the specific calculation formula is: in, The differential is given for the position; S3-4: When the position loop is in saturation, the integral steady-state value is predicted by the error dynamic model The calculation formula is: in, is the differential of the input error of PI controller B; S3-5: In order to suppress the noise interference caused by the error differential in the integral prediction process, a first-order filter is used to correct the integral term value, and finally the anti-saturation integral term value β1 is obtained, and its calculation formula is: Among them, τ P is the time constant of the integral filter of the position controller; S3-6: Finally, the position controller outputs a speed reference ω * , and its calculation formula is: Through the above steps, the anti-saturation PI control based on integral steady-state prediction is completed.

2. The anti-saturation PI control method based on integral steady-state prediction according to claim 1, characterized in that: The anti-saturation PI control system in step S1 specifically includes: Speed ​​controller: The speed controller is composed of a PI controller A and a speed loop anti-saturation module. The PI controller A is used to generate an ideal current setting according to a speed error signal; the speed loop anti-saturation module is used to detect the output saturation state of the PI controller A in the speed loop, and adjust the integral term of the PI controller A through an integral steady-state prediction formula under the saturation state to make it approach the steady-state integral value, thereby realizing speed loop integral anti-saturation control; Position controller: The position controller consists of a PI controller B and a position loop anti-saturation module. The PI controller B is used to generate an ideal speed setting based on a position error signal. The position loop anti-saturation module is used to detect the output saturation state of the PI controller B in the position loop, and adjust the integral term of the PI controller B through the integral steady-state prediction formula in the saturated state to make it approach the steady-state integral value, thereby realizing the position loop integral anti-saturation control.

3. The anti-saturation PI control method based on integral steady-state prediction according to claim 1, characterized in that: When the PI controller A in step S2 is in different working states, the control method of the speed loop anti-saturation module includes: When the PI controller A is in the linear segment, that is, u MIN <u<u MAX When , the integral action works normally, and the integral term value α is obtained by accumulating the error signal; When the PI controller A is in saturation, that is, u>u MAX or u<u MIN When the speed loop anti-saturation module stops the integral action, the integral steady-state prediction formula is used to calculate the steady-state value of the integral term. And the accumulated value of the integral term is adjusted to the steady-state integral prediction value, thereby realizing dynamic adjustment of the integral action.

4. The anti-saturation PI control method based on integral steady-state prediction according to claim 1, characterized in that: When the PI controller B is in different working states in step S3, the control method of the position loop anti-saturation module includes: When PI controller B is in the linear segment, that is, v MIN <v<v MAX When , the integral action works normally, and the anti-saturation integral term value β1 is obtained by accumulating the position error signal; When PI controller B is in saturation state, that is, v>v MAX or v<v MIN When the position loop anti-saturation module stops the integral action, the integral steady-state prediction formula is used to calculate the steady-state value of the integral term. This enables dynamic adjustment of the integral action.

5. The anti-saturation PI control method based on integral steady-state prediction according to claim 1, characterized in that: In step S2, the speed loop anti-saturation module corrects the integral prediction value through a first-order filter, and its working mechanism includes: When the output of PI controller A satisfies u MIN <u<u MAX When , the filter keeps the integral term accumulated normally, and its output integral value is α1 = ∫e; where e = ω * -ω is the speed error; When the output of PI controller A satisfies u>u MAX or u<u MIN When the filter calculates the corrected anti-saturation integral term through the integral steady-state prediction formula in, is the predicted value of the steady-state integral of the speed loop; τ S is the filter time constant, which is used to suppress noise interference in the integral prediction process.

6. The anti-saturation PI control method based on integral steady-state prediction according to claim 1, characterized in that: In step S3, the position loop anti-saturation module corrects the integral prediction value through a first-order filter, and its working mechanism includes: When the output of PI controller B satisfies v MIN <v<v MAX When , the filter keeps the integral term accumulated normally, and its output integral value β1=∫E; where E=θ*-θ is the position error; When the output of PI controller B satisfies v>v MAX or v<v MIN When the filter calculates the corrected anti-saturation integral term through the integral steady-state prediction formula in, is the predicted value of the steady-state integral of the position loop; τ P is the filter time constant, which is used to reduce noise interference in the integral prediction process.

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