Servo system resonance suppression method based on rotating speed loop PIPD feedback control

Abstract

The invention relates to the technical field of servo system control, and discloses a servo system resonance suppression method based on rotating speed loop PIPD feedback control, and the method employs a double-inertia system state variable observer to observe the load end variable of a servo system. On the basis of traditional P I control, the rotating speed difference between a motor end and a load end is additionally introduced to serve as a feedback signal, a PD controller is used for regulating and controlling the feedback signal, a full-closed-loop control system of rotating speed loop P IPD feedback control is constructed, all adjustable parameters are set through a pole assignment method, and the system response performance is improved while resonance suppression is achieved.

Description

Technical Field

[0001] The invention relates to the technical field of servo system control, and in particular to a servo system resonance suppression method based on speed loop PI_PD feedback control. Background Art

[0002] The servo system mainly consists of a controller, a power drive device, a feedback device, a transmission device, a motor, and a load group. It is widely used in various industrial fields, especially industrial robots, precision machine tools, and rail transportation. Ideally, the transmission device is regarded as a rigid body, that is, an object whose shape and size remain unchanged, and the relative position of each point inside remains unchanged during movement or after being subjected to force. However, an absolute rigid body does not exist. As the requirements for control performance become higher and higher, the elastic characteristics of the actual transmission device can no longer be ignored. When the moment of inertia of the load is relatively large and the elasticity of the transmission device is relatively large, the system is prone to mechanical resonance, which seriously affects the control performance of the servo system. Summary of the invention

[0003] The purpose of the present invention is to solve the above problems. A servo system resonance suppression method based on speed loop PI_PD feedback control is designed. The method is mainly used to solve the technical problem that the servo system is prone to mechanical resonance, thereby improving the control performance of the servo system.

[0004] To achieve the above-mentioned purpose, the technical solution of the present invention is a servo system resonance suppression method based on speed loop PI_PD feedback control, the method comprising the following steps:

[0005] Step 1: construct a dual-inertia system Lumberg-sliding mode state variable observer to observe the load-end variables of the servo system;

[0006] Step 2: Based on the traditional PI control, the speed difference between the motor end and the load end is additionally introduced as a feedback signal, and the PD controller is used to regulate it, so as to construct a full closed-loop control system of the speed loop PI_PD feedback control;

[0007] Step three, use the pole configuration method to adjust the adjustable parameters in the full closed-loop control system of the speed loop PI_PD feedback control, so as to improve the system response performance while achieving resonance suppression.

[0008] The construction process of the Lumberg-sliding mode state variable observer in step 1 is:

[0009] Assume that the dynamic equation of the dual inertia system is:

[0010]

[0011] Where t represents continuous time, ω m ,ω LRefers to the electrical and load angular velocity, T e is the electromagnetic torque output by the motor, T L is the load torque, T s is the torque transmitted on the transmission device, K s is the stiffness coefficient of the connection device, J m , J L They refer to the motor rotor moment of inertia and the equivalent moment of inertia on the load side respectively;

[0012] Therefore, the state equation of the dual-inertia system is:

[0013]

[0014] Where x(t) = [ω m ω L T s T L ] T is the system state variable, u(t)=[T e ] is the system input, y(t)=[ω m ] is the system output, F, G, H are the system matrix, input matrix and output matrix respectively, and their respective expressions are:

[0015]

[0016] Based on formula (2), the Lumberg-sliding mode observer of the dual-inertia system is obtained as follows:

[0017]

[0018] in, and are the observed estimated values ​​of the system state variables and output quantities, L and M are the Romberg gain matrix and the sliding mode gain matrix, respectively;

[0019] In actual control systems, the continuous state equation needs to be discretized to ensure digital control. The forward Euler method is used to discretize the observer with T as the sampling period:

[0020]

[0021] in," d " indicates discretization, k and k+1 represent the system at time k and time k+1 respectively, and I is the unit matrix. The discretization expressions of each matrix are:

[0022]

[0023] For the Romberg gain matrix L d, first ignore the sliding mode part, adjust the parameters of the gain matrix L based on the observation characteristic equation under the continuous state, and then obtain L through the mapping relationship between the continuous system and the discrete system d The setting formula of the parameters in ;

[0024] The observation characteristic equation under continuous state is:

[0025]

[0026] Where s is the Laplace operator and λ is the target pole. According to the design concept of the closed-loop pole of the traditional Lumberg observer, for a 4th-order system, its 4 closed-loop poles are set to be quadruple fixed poles λ and less than zero, then the state equation of the system is:

[0027] f(s)=(s-λ) 4 =s 4 -4λs 3 +6λ 2 s 2 -4λ 3 s+λ 4 =0 (9)

[0028] The parameters in L are solved as follows:

[0029]

[0030] In order to ensure good convergence of the observer, it is necessary to configure the observer poles to be larger than the poles of the observed system. Then, from the corresponding relationship of the discretized matrix in equation (7), we can get L d Medium parameters;

[0031] For the sliding mode gain matrix M d , expanding the observation error equation of the observation system, we can get:

[0032]

[0033] in, are the observation errors of each state variable;

[0034] First, the sliding mode gain m is determined by Lyapunov stability analysis d1 and m d2 ,definition:

[0035]

[0036] By taking the derivative of formula (12), we can get:

[0037]

[0038] In order to make the observation stable, the derivative must be less than zero. At this time, m d1and m d2 Need to meet:

[0039]

[0040] Using equivalent control to describe the SMO dynamics, when the system is stable, the speed error between the motor and the load remains on the sliding film plane. At this time, equation (11) can be simplified as:

[0041]

[0042] definition:

[0043]

[0044] By making its derivative less than zero, we can get the sliding mode gain m d3 and m d4 Need to meet:

[0045]

[0046] By d and M d With reasonable settings, the load-side state variables can be observed.

[0047] The construction process of the full closed-loop control system of the speed loop PI_PD feedback control in step 2 is:

[0048] On the basis of the traditional speed loop PI control, the speed difference between the motor end and the load end is additionally introduced as the feedback signal, and the PD controller is used to regulate it, forming a full closed-loop control structure of the speed loop PI_PD feedback control. Based on this structure, the transfer function from the load end speed to the given speed is written using the Mersenne gain formula

[0049]

[0050] Among them, G speed is a traditional PI controller, G p-d For PD controller, G te-m , G m-ts , G ts-l They are respectively expressed as the transfer functions from the motor electromagnetic torque to the motor speed, from the motor speed to the shaft torque, and from the shaft torque to the load speed. Expanding equation (18) yields:

[0051]

[0052] In the formula, K ps With K is PI controller G speed The proportional coefficient and integral coefficient, K pe With Kde PD controller G p-d The proportionality coefficient and differential coefficient of K s is the stiffness coefficient of the connection device, J m , J L They refer to the motor rotor moment of inertia and the equivalent moment of inertia on the load side respectively.

[0053] The adjustable parameters of the speed loop PI_PD feedback control in step 3 are set to K pe , K pd , K ps and K is Four adjustable parameters are set:

[0054] From formula (19), we can see that the characteristic equation of the system is:

[0055]

[0056] Transform formula (20) to get:

[0057]

[0058] For a 4th-order system, the system is usually configured to have two pairs of identical conjugate poles, and its characteristic equation is as follows:

[0059] s 4 +4ξωs 3 +(2ω 2 +4ξ 2 ω 2 )s 2 +4ξω 3 s+ω 4 =0 (22)

[0060] Among them, ω and ξ are the corner frequency and damping ratio of the system;

[0061] Based on equation (21) and equation (22), the coefficients are equivalently arranged to obtain:

[0062]

[0063] Introduce two variables x1 and y1, let K de +J m =x1J L , let K ps +K pe =y1K ps , substituting it into formula (23), we can get:

[0064]

[0065] make Inertia ratio R = JL / J m , the expressions of the adjustable parameters are solved as follows:

[0066]

[0067] At this time, the expressions of system corner frequency and damping ratio are:

[0068]

[0069] In order to improve the response performance of the system while achieving resonance suppression, it is necessary to ensure that the system has a good damping ratio while maximizing the turning frequency. It can be found that y1 is directly related to the turning frequency, and after y1 is determined, the damping ratio can be adjusted to a better value by adjusting x1.

[0070] Further solve the expression of the intermediate variable y1:

[0071]

[0072] In order to meet the requirement of increasing the turning frequency, y1 should be less than 1 and have a solution, which requires x1 to satisfy:

[0073]

[0074] In the step three, based on the adjustable parameter setting formula shown in formula (25), the adjustable parameter values ​​are determined for different systems, so as to improve the system response performance while achieving resonance suppression. It is determined that this method will not have obvious oscillation links in systems with relatively small inertia (inertia ratio of 0.224) compared with traditional speed loop PI control, and the response performance is significantly improved in systems with relatively large inertia (inertia ratio of 5.89).

[0075] Compared with the prior art, the technical solution proposed in this application has the following advantages:

[0076] 1. The present invention realizes the acquisition of load speed signal by designing a Lumberg-sliding mode variable observer;

[0077] 2. Based on the traditional speed loop PI control, the present invention additionally introduces the speed difference between the motor end and the load end as a feedback signal, and designs a speed loop PI_PD feedback control;

[0078] 3. The present invention adjusts the adjustable parameters in the speed loop PI_PD feedback control and configures the system turning frequency and damping ratio to a more optimal value, so that the system has a better control effect than the traditional speed loop PI control. Under the premise of ensuring resonance suppression, the system has better response performance and a wider range of applications.

[0079] 4. Compared with the traditional speed loop PI control, the present invention will not have obvious oscillation links in the system with relatively small inertia, and the response performance is significantly improved in the system with relatively large inertia, thereby achieving resonance suppression and improving the system response performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0080] Figure 1 It is a flow chart of a servo system resonance suppression method based on speed loop PI_PD feedback control according to the present invention;

[0081] Figure 2 is a structural block diagram of the Lumberg-sliding mode observer of the present invention;

[0082] Figure 3 It is a block diagram of a dual-inertia system of the speed loop PI_PD feedback control of the present invention;

[0083] Figure 4 is a pole distribution diagram under different control modes of the present invention;

[0084] Figure 5 It is a structural block diagram of the speed loop PI_PD feedback control of the present invention;

[0085] Figure 6 This is a diagram of the experimental platform of the dual-inertia permanent magnet servo system of the present invention;

[0086] Figure 7 This is the load speed observation effect diagram of the present invention;

[0087] Figure 8 This is a control effect diagram of the system with an inertia ratio of 0.224 according to the present invention;

[0088] Fig. 9 This is a control effect diagram of the system with an inertia ratio of 2.68 according to the present invention;

[0089] Fig.10 This is a system control effect diagram of the inertia ratio of 5.89 described in the present invention. DETAILED DESCRIPTION

[0090] The present invention will be described in detail below in conjunction with the accompanying drawings. Figure 1-4 As shown;

[0091] The structural diagram of the Lumberg-sliding mode observer is as follows: Figure 2 As shown in the figure, by constructing an observer estimation model with the same structure as the actual system, the error between the actual output of the system and the observer output is fed back to the observer for continuous correction, so that the observed output value is constantly close to the actual output value. For the dual-inertia servo system, the Lumberg-sliding mode observer is;

[0092]

[0093] Where x(t) = [ω m ω L T s T L ] T is the system state variable, u(t)=[T e ] is the system input, y(t)=[ω m ] is the system output. F, G, H are the system matrix, input matrix and output matrix respectively, L and M are the Romberg gain matrix and sliding mode gain matrix respectively, and the matrix expression is:

[0094]

[0095] The observation error is fed back to the observer through proportional adjustment (Lomborg gain) and sign function adjustment (sliding mode gain), and the observed value is continuously corrected so that the observed load-end variables are constantly close to the actual load-end variables, thereby realizing the acquisition of various load-end variables.

[0096] In actual control systems, the continuous state equation needs to be discretized to ensure digital control. Using the forward Euler method, the observer is discretized with T as the sampling period to obtain:

[0097]

[0098] in," d ” denotes discretization, k and k+1 denote the system at time k and time k+1 respectively, and I is the unit matrix.

[0099] At the same time, in order to ensure that the observer has a good observation effect, the Lumberg gain matrix and the sliding mode gain matrix need to be reasonably configured.

[0100] For the Romberg gain matrix L d , first ignore the sliding mode part, and adjust the parameters of the gain matrix L based on the observation characteristic equation under the continuous state, and get:

[0101]

[0102] Through the mapping relationship between the continuous system and the discrete system, L d Parameter setting formula:

[0103]

[0104] The observer pole λ must be greater than the pole of the observed system to achieve a better observation effect.

[0105] For the sliding mode gain matrix M d Based on the system observation error equation, the sliding mode gain m is first determined by Lyapunov stability analysis.d1 and m d2 ,definition:

[0106]

[0107] In order to make the observation stable, the derivative must be less than zero. At this time, m d1 and m d2 Need to meet:

[0108]

[0109] Use equivalent control to describe the SMO dynamics. When the system is stable, the speed error between the motor and the load remains on the sliding membrane plane and is defined as:

[0110]

[0111] So that the derivative is less than zero, we can get m d3 and m d4 Need to meet:

[0112]

[0113] By d and M d With reasonable settings, the load-side state variables can be observed.

[0114] The block diagram of the dual-inertia system of the speed loop PI_PD feedback control is as follows: Figure 3 As shown in the figure, on the basis of the traditional speed loop PI control, the speed difference between the motor end and the load end is used as an additional feedback signal, which is regulated by the PD controller and then fed back to the speed loop output, forming a full closed-loop control structure of the speed loop PI_PD feedback control.

[0115] Among them, G speed is a traditional PI controller, G p-d For PD controller, G te-m , G m-ts , G ts-l They are respectively expressed as the transfer functions from the motor electromagnetic torque to the motor speed, from the motor speed to the shaft torque, and from the shaft torque to the load speed, which are:

[0116]

[0117] In the formula, K ps With K is PI controller G speed The proportional coefficient and integral coefficient, K pe With K de PD controller G p-d The proportionality and differential coefficients.

[0118] based on Figure 3 , use the Mason gain formula to write the transfer function G from the load end speed to the given speed Lω*2 (s):

[0119]

[0120] Expanding formula (18) yields:

[0121]

[0122] The adjustable parameters of the speed loop PI_PD feedback control refer to the K pe , K pd , K ps and K is Four adjustable parameters, tuned using pole placement method:

[0123] From formula (19), we can see that the characteristic equation of the system can be transformed into:

[0124]

[0125] For a 4th-order system, the system is usually configured to have two pairs of identical conjugate poles, and its characteristic equation is as follows:

[0126] s 4 +4ξωs 3 +(2ω 2 +4ξ 2 ω 2 )s 2 +4ξω 3 s+ω 4 =0 (22)

[0127] Where ω and ξ are the corner frequency and damping ratio of the system.

[0128] Based on formula (22) and formula (23), the coefficients are equivalently arranged to obtain:

[0129]

[0130] Introduce two variables x1 and y1, let K de +J m =x1J L , let K ps +K pe =y1K ps , substitute it into formula (23), and let Inertia ratio R = J L / J m , the expressions of the adjustable parameters can be solved as follows:

[0131]

[0132] At this time, the expressions of system corner frequency and damping ratio are:

[0133]

[0134] In order to improve the response performance of the system while achieving resonance suppression, it is necessary to ensure that the system has a good damping ratio while keeping the turning frequency as large as possible. It can be found that y1 is directly related to the turning frequency, and after y1 is determined, the damping ratio can be adjusted to a better value by adjusting x1.

[0135] Further solve the expression of the intermediate variable y1:

[0136]

[0137] In order to meet the requirement of increasing the turning frequency, y1 should be less than 1 and have a solution, which requires x1 to satisfy:

[0138]

[0139] Figure 4 After the adjustable parameters are set, the pole distribution diagrams of different inertia ratio systems under traditional speed loop PI control and speed loop PI_PD feedback control are shown. For the damping ratio of the system, its value between (0.7, 1) has a good control effect. It is usually configured to 0.707 in engineering. Therefore, for the speed loop PI_PD feedback control, the system damping ratio can be configured to 0.707 in any inertia ratio system. For PI control, in a system with a small inertia ratio (inertia ratio of 0.224), the configured system damping ratio is too small, the system damping effect is insufficient, and oscillation is easy to occur; in a system with a moderate inertia ratio (inertia ratio of 2.68), the damping ratio can be configured between (0.7, 1); in a system with a large inertia ratio (inertia ratio of 5.89), the damping ratio will be greater than 1, which is in an over-damped state, and the system responds slowly. The system transition frequency is closely related to the system bandwidth. It is generally believed that the system bandwidth is approximately equal to its transition frequency. In any inertia ratio system, the turning frequency of the system under the speed loop PI_PD feedback control is greater than the turning frequency of the system under PI control, so the response speed of the system under the speed loop PI_PD feedback control is faster.

[0140] In summary, compared with the traditional speed loop PI control, this method can configure the system's damping ratio and corner frequency to a more optimal value, so that the system has a better control effect and has better response performance while satisfying resonance suppression.

[0141] In addition, the technical solution of the present application can be verified by experimental comparison, proving that the proposed speed loop PI_PD feedback control method can effectively suppress resonance and make regulation more flexible. By reasonably configuring its adjustable parameters, the system can respond faster, have smaller overshoot, and have better control effect. The control structure diagram is shown in FIG. Figure 5 shown.

[0142] Embodiment 1;

[0143] In order to verify the correctness of the servo system resonance suppression method based on the speed loop PI_PD feedback control in this application, this application built a dual-inertia permanent magnet servo system experimental platform based on the dSPACE control system. The entire experimental platform is divided into: power unit, control unit, sampling unit and controlled unit according to its function. Its structural diagram is shown in the figure. Figure 6 As shown. The controlled unit includes a drive motor and a load part, which are connected by a groove-type elastic coupling with low stiffness to form a dual-inertia system structure. The load part consists of an inertia disk and a magnetic powder brake, which are connected by a rigid coupling to form a whole. By replacing inertia disks of different sizes to adjust the rotational inertia of the load end, the system inertia ratio R can be configured to 0.224, 2.68, and 5.89 respectively. The magnetic powder brake control provides load torque to the system through the tension controller.

[0144] First, the load speed observation effect is verified. The control method adopts the speed loop PI control and the parameters are not adjusted. The speed setting is set to 300r / min. Figure 7 As shown, it can be found that the designed Lumberg-sliding mode state variable observer can realize the estimation of load speed, which lays the foundation for the application of the designed speed loop PI_PD feedback control method in practical engineering. In addition, it can be found that when the PI controller parameters are not processed, the motor load speed response is poor, there is a large overshoot in the startup phase, and there is obvious oscillation.

[0145] Then, the proposed speed loop PI_PD feedback control method and the traditional speed loop PI control method are compared in different inertia ratio systems after adjusting their respective adjustable parameters. The experimental conditions are: the motor operation conditions are: no-load start, the initial speed is set to 600r / min, and a 5N·m load torque is suddenly added at 0.5s. In the systems with inertia ratios of 0.224, 2.68, and 5.89, the load speed and electromagnetic torque waveforms of the system under the two control methods are shown in the figure below: Figure 8 , 9 , as shown in 10.

[0146] Figure 8It can be found that for a system with a relatively small inertia ratio (inertia ratio of 0.224), the traditional speed loop PI control is used. After the adjustable parameters are adjusted, although the control effect is improved, the adjustment time is 89ms and 62ms respectively, and the overshoot is 86.2r / min and -37.2r / min respectively in the startup stage and the load mutation stage, and there is still obvious oscillation. However, by using the speed loop PI_PD feedback control, after adjusting the adjustable parameters, the system has no obvious oscillation phenomenon in the startup stage and the load mutation stage, and the adjustment time is 47ms and 34ms respectively, and the overshoot is 43.7r / min and -32.9r / min respectively, and the overshoot and adjustment time are lower. Experimental results and Figure 4 The pole distribution diagram analysis is consistent.

[0147] Fig. 9 It can be found that for the system with moderate inertia ratio (inertia ratio of 2.68), the traditional speed loop PI control can also make the system have better control effect. In the startup stage and the load mutation stage, the system can have no obvious oscillation phenomenon. The adjustment time is 74ms and 47ms respectively, and the overshoot is 51.4r / min and -21.3r / min respectively. However, the use of speed loop PI_PD feedback control can make the system control effect better. In the startup stage and the load mutation stage, the adjustment time is 53ms and 28ms respectively, and the overshoot is 30.1r / min and -13.5r / min respectively, and the overshoot and adjustment time are lower. Experimental results and Figure 4 The pole distribution diagram analysis is consistent.

[0148] Fig.10 It can be found that for systems with relatively large inertia (inertia ratio of 5.89), the traditional speed loop PI control is used. Although the system has no obvious oscillation phenomenon, the adjustment time is too long. In the startup stage and the load mutation stage, the adjustment time is 242ms and 104ms respectively, and the overshoot is 46.4r / min and -16.2r / min respectively. The speed loop PI_PD feedback control can significantly shorten the system adjustment time. In the startup stage and the load mutation stage, the adjustment time is 92ms and 48ms respectively, and the overshoot is 33.7r / min and -12.8r / min respectively. Experimental results and Figure 4 The pole distribution diagram analysis is consistent.

[0149] In summary, the speed loop PI_PD feedback control proposed in this application, based on the traditional speed loop PI control, further adjusts the system turning frequency and damping ratio by introducing the speed difference proportional coefficient and the speed difference differential coefficient, respectively, to make them a more optimal value, so that the system can have a better control effect. In addition, the adjustable parameter setting formula obtained based on the pole configuration method in this way has a corresponding feasible solution for any inertia ratio system, and the scope of application is also wider.

[0150] The above technical solutions only reflect the preferred technical solutions of the technical solutions of the present invention. Some changes that may be made to certain parts thereof by technicians in this technical field all reflect the principles of the present invention and fall within the protection scope of the present invention.

Claims

1. A servo system resonance suppression method based on speed loop PI_PD feedback control, characterized in that: The method comprises the following steps: Step 1: construct a dual-inertia system Lumberg-sliding mode state variable observer to observe the load-end variables of the servo system; Step 2: Based on the traditional PI control, the speed difference between the motor end and the load end is additionally introduced as a feedback signal, and the PD controller is used to regulate it, so as to construct a full closed-loop control system of the speed loop PI_PD feedback control; Step three, use the pole configuration method to adjust the adjustable parameters in the full closed-loop control system of the speed loop PI_PD feedback control.

2. The method for suppressing resonance of a servo system based on the speed loop PI_PD feedback control according to claim 1, characterized in that: The construction process of the Lumberg-sliding mode state variable observer in step 1 is: Assume that the dynamic equation of the dual inertia system is: Where t represents continuous time, ω m ,ω L Refers to the electrical and load angular velocity, T e is the electromagnetic torque output by the motor, T L is the load torque, T s is the torque transmitted on the transmission device, K s is the stiffness coefficient of the connection device, J m , J L They refer to the motor rotor moment of inertia and the equivalent moment of inertia on the load side respectively; Therefore, the state equation of the dual-inertia system is: Where x(t) = [ω m ω L T s T L ] T is the system state variable, u(t)=[T e ] is the system input, y(t)=[ω m ] is the system output, F, G, H are the system matrix, input matrix and output matrix respectively, and their respective expressions are: Based on formula (2), the Lumberg-sliding mode observer of the dual-inertia system is obtained as follows: in, and are the observed estimated values ​​of the system state variables and output quantities, L and M are the Romberg gain matrix and the sliding mode gain matrix, respectively; The forward Euler method is used to discretize the observer with T as the sampling period: in," d " represents discretization, k and k+1 represent the system at time k and time k+1 respectively, and I is the unit matrix; the discretization expressions of each matrix are: For the Romberg gain matrix L d , first ignore the sliding mode part, adjust the parameters of the gain matrix L based on the observation characteristic equation under the continuous state, and then obtain L through the mapping relationship between the continuous system and the discrete system d The setting formula of the parameters in ; The observation characteristic equation under continuous state is: Where s is the Laplace operator and λ is the target pole. For a 4th-order system, its 4 closed-loop poles are set to quadruple fixed poles λ and are less than zero. Then the state equation of the system is: f(s)=(s-λ) 4 =s 4 -4λs 3 +6min 2 s 2 -4m 3 s+λ 4 =0 (9) The parameters in L are solved as follows: In order to ensure good convergence of the observer, it is necessary to configure the observer poles to be larger than the poles of the observed system. Then, from the corresponding relationship of the discretized matrix in equation (7), we can get L d Medium parameters; For the sliding mode gain matrix M d , expanding the observation error equation of the observation system, we can get: in, are the observation errors of each state variable; First, the sliding mode gain m is determined by Lyapunov stability analysis d1 and m d2 ,definition: By taking the derivative of formula (12), we can get: In order to make the observation stable, the derivative must be less than zero. At this time, m d1 and m d2 Need to meet: Simplifying formula (11) yields: definition: By making its derivative less than zero, we can get the sliding mode gain m d3 and m d4 Need to meet: By d and M d With reasonable settings, the load-side state variables can be observed.

3. The method for suppressing resonance of a servo system based on speed loop PI_PD feedback control according to claim 1, characterized in that: The construction process of the full closed-loop control system of the speed loop PI_PD feedback control in step 2 is: Use the Mason gain formula to write the transfer function G from the load end speed to the given speed Lω*2 (s): Among them, G speed is a traditional PI controller, G p-d For PD controller, G te-m , G m-ts , G ts-l They are respectively expressed as transfer functions from motor electromagnetic torque to motor speed, motor speed to shaft torque, and shaft torque to load speed; Expanding formula (18) yields: In the formula, K ps With K is PI controller G speed The proportional coefficient and integral coefficient, K pe With K de PD controller G p-d The proportionality and differential coefficients of .

4. The method for suppressing resonance of a servo system based on the speed loop PI_PD feedback control according to claim 3 is characterized in that: The step 3 of adjusting the adjustable parameters refers to adjusting K pe , K pd , K ps and K is Four adjustable parameters are set: From formula (19), we can see that the characteristic equation of the system is: Transform formula (20) to get: For a 4th-order system, the system is usually configured to have two pairs of identical conjugate poles, and its characteristic equation is as follows: s 4 +4 odd 3 +(2h 2 +4x 2 oh 2 )s 2 +45h 3 s+ω 4 =0 (22) Among them, ω and ξ are the corner frequency and damping ratio of the system; Based on equation (21) and equation (22), the coefficients are equivalently arranged to obtain: Introduce two variables x1 and y1, let K de +J m =x1J L , let K ps +K pe =y1K ps , substituting it into formula (23), we can get: make Inertia ratio R = J L / J m , the expressions of the adjustable parameters are solved as follows: Then the expressions of system corner frequency and damping ratio are: Further solve the expression of the intermediate variable y1: In order to meet the requirement of increasing the turning frequency, y1 should be less than 1 and have a solution, which requires x1 to satisfy:

5. The method for suppressing resonance of a servo system based on the speed loop PI_PD feedback control according to claim 4, characterized in that: The setting of the adjustable parameters in step three is achieved based on the formula shown in equation (25).

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