阅读说明：本技术 一种低压伺服离散线性自抗扰控制方法 (Low-voltage servo discrete linear active disturbance rejection control method ) 是由 邢科新 权欣文 林叶贵 吴昊 于 2021-06-16 设计创作，主要内容包括：一种低压伺服离散线性自抗扰控制方法,根据伺服电机的电流微分方程和运动方程确定低压伺服驱动器速度环和电流环被控对象阶数,根据被控对象阶数确定线性自抗扰控制器的阶数,先对于速度环和电流环设计连续线性自抗扰控制器,再通过欧拉离散法将连续的控制器离散化,确定连续控制器和离散控制器各个矩阵的对应关系；利用参数辨识的方法对电机的转动惯量和电感参数进行辨识,用于设计线性自抗扰控制器的补偿因子,将电流环的数字控制器延时考虑在参数整定中,整定出相应的参数。本发明使线性自抗扰控制器的离散模式运用在低压伺服驱动器中,借助于离散线性自抗扰控制算法可以提高永磁同步电机控制系统的稳定性、抗干扰性、快速性、鲁棒性等。(A low-voltage servo discrete linear active disturbance rejection control method comprises the steps of determining the order of a controlled object of a speed ring and a current ring of a low-voltage servo driver according to a current differential equation and a motion equation of a servo motor, determining the order of a linear active disturbance rejection controller according to the order of the controlled object, designing a continuous linear active disturbance rejection controller for the speed ring and the current ring, discretizing the continuous controller by an Euler discretization method, and determining the corresponding relation of each matrix of the continuous controller and the discrete controller; the method for identifying the parameters of the rotary inertia and the inductance of the motor is used for designing a compensation factor of the linear active disturbance rejection controller, and a digital controller of a current loop is subjected to time delay consideration in parameter setting to set corresponding parameters. The discrete mode of the linear active disturbance rejection controller is applied to the low-voltage servo driver, and the stability, the disturbance rejection, the rapidity, the robustness and the like of the permanent magnet synchronous motor control system can be improved by means of a discrete linear active disturbance rejection control algorithm.)

1. A low-voltage servo discrete linear active disturbance rejection control method, comprising the steps of:

step 1) determining the order of a controlled object of a current loop and a speed loop, wherein the determined order is determined by a differential equation of current and a motion equation, and the differential equation of quadrature-direct axis current is as follows:

in the above formula i_d、i_qIs a quadrature-direct axis current value, R_sIs the motor resistance value, L_d、L_qIs a quadrature-direct axis inductance value, omega_eFor motor speed value, #_fIs the flux linkage value of the permanent magnet;

the equation of motion is:

in the above formula n_pIs the number of pole pairs, T, of the motor_eIs the electromagnetic torque of the machine, T_LIs the load torque of the motor, J is the moment of inertia of the motor, L_md、L_mqThe armature reaction inductor is a quadrature-direct axis armature reaction inductor;

as can be seen from (1.1) to (1.3), the order of the passive object of the current loop and the speed loop is 1, and according to the design rule of the active disturbance rejection controller, the order of the extended observer needs to be increased by 1 on the basis of the order of the controlled object, so the order of the extended observer is 2 orders;

step 2) the differential equation of the current loop and the motion equation of the motor are rewritten into a form of input plus disturbance, because the adopted form is i_dThe control strategy is 0, so that only the quadrature axis current is analyzed when the current loop is analyzed, the direct axis current is not analyzed any more, and the differential equation of the quadrature axis current is rewritten as follows:

in the above formulaThe total disturbance of the quadrature axis current loop can be regarded as the total disturbance, and the total disturbance comprises resistance, inductance, permanent magnet flux linkage change and external disturbance;

the equation of motion is rewritten as:

in the above formula f_ωIs the total disturbance of the speed loop, caused by internal parameter changes and external load torque changes;

step 3) designing a current loop continuous linear active disturbance rejection controller, firstly analyzing the current loop, inputting the current loop as a cross-axis current reference value, outputting as a cross-axis voltage control value, and recording a state variableThen equation (1.4) is expressed in the form of the following equation of state:

a linear state observer is designed by utilizing the design principle of Luenberger to observe disturbance quantity and state variables, and the equation of the state observer is as follows:

in the above formula Respectively represent state variables Which represents the value of the gain of the observer,in order to be able to observe the error of the observer,the current loop linear expansion observer is written as:

the upper typeIn

Step 4) designing a continuous linear active disturbance rejection controller of a speed loop, wherein a linear extended observer of the speed loop is expressed as:

the state variable matrix z in the above equation_ω＝[z_{1_ω},z_{2_ω}]^TMatrix of statesObserver gain matrix L_ω＝[l_{1_ω},l_{2_ω}]^TOutput matrix C_ω＝[1,0]Input matrix B_ω＝[b_ω',0]^T，u_{c_ω}＝[u_{o_ω},y_ω]^T；

Step 5) designing a tracking differentiator of the speed loop, wherein the current loop does not need to track the differentiator because the expected current value of the current loop is changed rapidly along with the reference value of the current; because of the inertia effect of the speed ring, if the arrangement of the transition process is carried out without using a tracking differentiator, the speed ring system can generate bad dynamic processes such as overshoot, and the arrangement of the transition process adopts a first-order inertia link, and the expression of the first-order inertia link is as follows:

meanwhile, the relation between the output and the input through an inertia link is obtained as follows:

step 6) designing a gain matrix of the linear extended observer, connecting the gain of the observer with the bandwidth commonly used in the actual control, and writing a characteristic equation of the system in the formula (1.8) as follows:

expanding the characteristic expression, placing the poles of the characteristic expression at the same position, wherein the position is the bandwidth value of the observer, and obtaining a gain matrix of the observer as follows:

and 7) designing control laws of the speed loop and the current loop continuous linear active disturbance rejection controller, and adopting single P control for a first-order controlled object, wherein the control laws of the current loop and the speed loop are as follows:

u_ω＝K_ω(r_ω-y_ω) (0.15)

in the above formulaK_ωIn order to control the gain of the laws,r_ωreference signals for the speed loop and the current loop;

step 8) discretizing the continuous linear active disturbance rejection controller, wherein a control law part in the continuous linear active disturbance rejection controller only amplifies an output signal of the linear extended observer, so that the control law part does not need to carry outDiscretization only needs to be carried out on a continuous linear expansion observer part, the continuous linear expansion observer part is discretized by adopting an Euler discretization method, the discretization mode of a speed loop is similar to that of a current loop, only the discretization process of the current loop is deduced, and state variables are subjected to state variable discretizationDifferentiation is performed using the following equation:

in the above formulaFor the delay time caused by the current loop digital controller, the above equation is rewritten as the change of the current time compared to the previous time:

substituting the above equation into the state equation of the continuous system to obtain:

in the above formulaCorresponding to the state matrixThe expression is as follows:

wherein I is a unit momentThe number of the arrays is determined,corresponding to the input matrixThe expression is as follows:

equaling the output matrix in a continuous controllerIs a zero matrix, and simultaneously obtains an expression equation of the discrete linear extended observer as follows:

in the above formulaThe expression of (a) is:

whereinThe characteristic equation is written for a discrete linear extended observer gain matrix similar to a continuous system as follows:

the characteristic roots are placed at the same polar point, and a gain matrix is obtained after expansionComprises the following steps:

simultaneously obtaining:

the corresponding input matrix is:

the corresponding output matrix is:

corresponding toThe matrix expression of (a) is:

the conversion expressions of the bandwidth of the continuous linear expansion observer and the bandwidth of the discrete linear expansion observer are as follows:

step 9) discretization of a velocity loop tracking differentiator, wherein a forward Euler method is adopted for discretization of a first-order inertia link, and a reverse Laler identification is carried out on the inertia link to obtain:

obtained by a forward Euler method:

the simultaneous expression is as follows:

step 10) identifying the rotational inertia and the inductance value of the low-voltage servo motor as a determination reference of a compensation factor, and obtaining the rotational inertia value and the inductance value through an identification algorithm according to a formula:

the base numbers of the compensation factors of the current loop and the speed loop are determined, because the anti-interference performance and the dynamic performance of the system can be improved by properly increasing the value of the compensation factor in the linear active-disturbance-rejection controller, the compensation factor is multiplied by a gain factor a to obtain the compensation factor in the actual controller as follows:

b_{0_ω}'＝a_ω*b_{0_ω} (0.36)

step 11) using a steady state diagram mode to control the control law bandwidth omega of the current loop and the speed loop_cAnd observer bandwidth ω_oAnd setting, and reserving enough amplitude margin and phase margin for the two systems.

Technical Field

The invention relates to the field of low-voltage servo motor control, in particular to a discrete linear active disturbance rejection control method for a low-voltage servo driver.

Background

The low-voltage servo motor has the remarkable advantages of no need of brush phase change, simple structure, high operation precision, low power supply voltage, small volume, light weight, high working efficiency, flexible modification of design appearance and size under the basic design condition and the like. In the coming of the 4.0 times of industry, power devices and permanent magnet materials are developed vigorously, the control precision of a low-voltage servo motor is improved to a great extent, the low-voltage servo motor is slowly and widely applied to the fields of robot control, hydraulic devices, aerospace, medical equipment, ship and naval vessel equipment and the like, and the cost of replacing an electric brush at the later stage is saved because the electric brush is not required to be used for phase change, so that the occupation ratio of the low-voltage brush motor is replaced in a certain field. However, because there is no brush, the controller is required to perform electronic phase change on the motor, the low-voltage servo motor is a complex controlled object with multivariable, strong coupling, nonlinearity and variable parameters, and in order to make the low-voltage servo motor have high working accuracy, strong external interference resistance and better dynamic performance, some specific algorithms must be adopted to control the low-voltage servo motor.

The control strategy of the low-voltage servo motor mainly comprises square wave control and vector control, and the square wave control has the influences of large torque fluctuation, low control precision and the like due to the control scheme of the square wave control. Therefore, vector control is generally used under the high-precision control working condition. The control scheme of the low-voltage servo motor mainly comprises the following steps: current loop (torque control), speed loop control and position loop. Wherein a current loop is generally nested in the speed loop and the position loop for control. Control algorithms for three loops have been extensively studied. The control algorithms that are currently in common use: traditional PID control, sliding mode variable structure control, model-based adaptive control, model predictive control, fuzzy control, active disturbance rejection control and the like. In the industrial field, the PID control is widely used by application engineers because the content of the information amount required by the model is small. The active disturbance rejection control is control which is not based on a model and is proposed by a research staff in Konjin and Qing of Chinese academy of sciences, can be regarded as continuation and development of traditional PID control, regards internal parameter disturbance and external environment disturbance of a system as the concept of total disturbance together through the concept of an observer, and observes and compensates the total disturbance through the observer. But since the proposed active disturbance rejection controller is a non-linear controller, the tuning of the non-linear function and the tuning of the controller parameters is not understood by most application engineers. In 2003, the senior has proposed to convert the nonlinear active disturbance rejection controller into a linear active disturbance rejection controller through the concept of bandwidth, the tuning parameters of the controller are reduced to 4 parameters by combining the concept of bandwidth with the tuning parameters of the controller, and the bandwidth of the controller and the bandwidth of the observer are connected in a proportional manner. This method can be understood by application engineers and achieves better control than PID.

Disclosure of Invention

In order to overcome the defects of the prior art, the invention provides a low-voltage servo discrete linear active-disturbance-rejection control method, a discrete linear active-disturbance-rejection controller is designed on a current loop and a speed loop to replace the traditional PID control to control a motor, the parameters of the speed loop and the controller of the current loop are adjusted, the parameters obtained by parameter identification are fused into the parameters of the controller to determine the approximate range of a compensation factor, and therefore, the control precision of the discrete linear active-disturbance-rejection controller is improved.

In order to solve the above technical problem, the present invention is implemented as follows:

a low-voltage servo discrete linear active-disturbance-rejection control method, the method comprising the steps of:

step 1) determining the order of a controlled object of a current loop and a speed loop, wherein the determined order is determined by a differential equation of current and a motion equation, and the differential equation of quadrature-direct axis current is as follows:

in the above formula i_d、i_qIs a quadrature-direct axis current value, R_sIs the motor resistance value, L_d、L_qIs a quadrature-direct axis inductance value, omega_eFor motor speed value, #_fIs the flux linkage value of the permanent magnet;

the equation of motion is:

in the above formula n_pIs the number of pole pairs, T, of the motor_eIs the electromagnetic torque of the machine, T_LIs the load torque of the motor, J is the moment of inertia of the motor, L_md、L_mqThe armature reaction inductor is a quadrature-direct axis armature reaction inductor;

as can be seen from (1.1) to (1.3), the order of the passive object of the current loop and the speed loop is 1, and according to the design rule of the active disturbance rejection controller, the order of the extended observer needs to be increased by 1 on the basis of the order of the controlled object, so the order of the extended observer is 2 orders;

step 2) the differential equation of the current loop and the motion equation of the motor are rewritten into a form of input plus disturbance, because the adopted form is i_dThe control strategy is 0, so that only the quadrature axis current is analyzed when the current loop is analyzed, the direct axis current is not analyzed any more, and the differential equation of the quadrature axis current is rewritten as follows:

in the above formulaCan be regarded as the total disturbance of quadrature axis current loop, which is composed of resistance, inductance, and permanent magnetFlux linkage change and external disturbance;

the equation of motion is rewritten as:

in the above formula f_ωTotal disturbance of the speed loop, caused by internal parameter changes and external load torque changes;

step 3) designing a current loop continuous linear active disturbance rejection controller, firstly analyzing the current loop, inputting the current loop as a cross-axis current reference value, outputting as a cross-axis voltage control value, and recording a state variableThen equation (1.4) is expressed in the form of the following equation of state:

a linear state observer is designed by utilizing the design principle of Luenberger to observe disturbance quantity and state variables, and the equation of the state observer is as follows:

in the above formula Respectively represent state variables Which represents the value of the gain of the observer,in order to be able to observe the error of the observer,the current loop linear expansion observer is written as:

in the above formula

Step 4) designing a continuous linear active disturbance rejection controller of a speed loop, wherein a linear extended observer of the speed loop is expressed as:

the state variable matrix z in the above equation_ω＝[z_{1_ω},z_{2_ω}]^TMatrix of statesObserver gain matrix L_ω＝[l_{1_ω},l_{2_ω}]^TOutput matrix C_ω＝[1,0]Input matrix B_ω＝[b_ω',0]^T，u_{c_ω}＝[u_{o_ω},y_ω]^T

Step 5) designing a tracking differentiator of the speed loop, wherein the current loop does not need to track the differentiator because the expected current value of the current loop is changed rapidly along with the reference value of the current; because of the inertia effect of the speed ring, if the arrangement of the transition process is carried out without using a tracking differentiator, the speed ring system can generate bad dynamic processes such as overshoot, and the arrangement of the transition process adopts a first-order inertia link, and the expression of the first-order inertia link is as follows:

meanwhile, the relation between the output and the input through an inertia link is obtained as follows:

step 6) designing a gain matrix of the linear extended observer, connecting the gain of the observer with the bandwidth commonly used in the actual control, and writing a characteristic equation of the system in the formula (1.8) as follows:

expanding the characteristic expression, placing the poles of the characteristic expression at the same position, wherein the position is the bandwidth value of the observer, and obtaining a gain matrix of the observer as follows:

and 7) designing control laws of the speed loop and the current loop continuous linear active disturbance rejection controller, and adopting single P control for a first-order controlled object, wherein the control laws of the current loop and the speed loop are as follows:

u_ω＝K_ω(r_ω-y_ω) (1.15)

in the above formulaK_ωIn order to control the gain of the laws,r_ωreference signals for the speed loop and the current loop;

step 8) discretizing the continuous linear active disturbance rejection controller, wherein the control law part in the continuous linear active disturbance rejection controller only amplifies the output signal of the linear extended observer, so the control law part does not need to carry out discretization treatment, only the continuous linear extended observer part needs to be discretized, an Euler discretization method is adopted for discretization, the discretization mode of a speed ring is similar to that of a current ring, only the discretization process of the current ring is deduced, and a state variable is subjected to state variable derivationDifferentiation is performed using the following equation:

in the above formulaFor the delay time caused by the current loop digital controller, the above equation is rewritten as the change of the current time compared to the previous time:

substituting the above equation into the state equation of the continuous system to obtain:

in the above formulaCorresponding to the state matrixThe expression is as follows:

wherein I is an identity matrix, and I is an identity matrix,corresponding to the input matrixThe expression is as follows:

equaling the output matrix in a continuous controllerIs a zero matrix, and simultaneously obtains an expression equation of the discrete linear extended observer as follows:

in the above formulaThe expression of (a) is:

whereinThe characteristic equation is written for a discrete linear extended observer gain matrix similar to a continuous system as follows:

the characteristic roots are placed at the same polar point, and a gain matrix is obtained after expansionComprises the following steps:

simultaneously obtaining:

the corresponding input matrix is:

the corresponding output matrix is:

corresponding toThe matrix expression of (a) is:

the conversion expressions of the bandwidth of the continuous linear expansion observer and the bandwidth of the discrete linear expansion observer are as follows:

step 9) discretization of a velocity loop tracking differentiator, wherein a forward Euler method is adopted for discretization of a first-order inertia link, and a reverse Laler identification is carried out on the inertia link to obtain:

obtained by a forward Euler method:

the simultaneous expression is as follows:

step 10) identifying the rotational inertia and the inductance value of the low-voltage servo motor as a determination reference of a compensation factor, and obtaining the rotational inertia value and the inductance value through an identification algorithm according to a formula:

the base numbers of the compensation factors of the current loop and the speed loop are determined, because the anti-interference performance and the dynamic performance of the system can be improved by properly increasing the value of the compensation factor in the linear active-disturbance-rejection controller, the compensation factor is multiplied by a gain factor a to obtain the compensation factor in the actual controller as follows:

b_{0_ω}'＝a_ω*b_{0_ω} (1.36)

step 11) using a steady state diagram mode to control the control law bandwidth omega of the current loop and the speed loop_cAnd observer bandwidth ω_oAnd setting, and reserving enough amplitude margin and phase margin for the two systems.

The invention has the beneficial effects that: the discrete linear active-disturbance-rejection controller is designed on the current ring and the speed ring to replace the traditional PID control to control the motor, the controller parameters of the speed ring and the current ring are subjected to parameter setting, and the parameters obtained through parameter identification are fused into the parameters of the controller to be used for determining the approximate range of the compensation factor, so that the control precision of the discrete linear active-disturbance-rejection controller is improved.

Drawings

Fig. 1 is a control block diagram of a low-voltage servo controller.

Fig. 2 is a control block diagram of a current loop linear active disturbance rejection controller.

Fig. 3 is a controller block diagram of a speed loop linear active disturbance rejection controller.

FIG. 4 is a flow chart of a low-voltage servo discrete linear active disturbance rejection control method.

Detailed Description

The present invention will be described in further detail with reference to the accompanying drawings.

Referring to fig. 1-4, a low-voltage servo discrete linear active-disturbance-rejection control method includes the steps of:

step 1) determining the order of a controlled object of a current loop and a speed loop, wherein the determined order is determined by a differential equation of current and a motion equation, and the differential equation of quadrature-direct axis current is as follows:

in the above formula i_d、i_qIs a quadrature-direct axis current value, R_sIs the motor resistance value, L_d、L_qIs a quadrature-direct axis inductance value, omega_eFor motor speed value, #_fIs the flux linkage value of the permanent magnet;

the equation of motion is:

in the above formula n_pIs the number of pole pairs, T, of the motor_eIs the electromagnetic torque of the machine, T_LIs the load torque of the motor, J is the moment of inertia of the motor, L_md、L_mqThe armature reaction inductor is a quadrature-direct axis armature reaction inductor;

as can be seen from (1.1) to (1.3), the order of the passive object of the current loop and the speed loop is 1, and according to the design rule of the active disturbance rejection controller, the order of the extended observer needs to be increased by 1 on the basis of the order of the controlled object, so the order of the extended observer is 2 orders;

step 2) the differential equation of the current loop and the motion equation of the motor are rewritten into a form of input plus disturbance, because the adopted form is i_dThe control strategy is 0, so that only the quadrature axis current is analyzed when the current loop is analyzed, the direct axis current is not analyzed any more, and the differential equation of the quadrature axis current is rewritten as follows:

in the above formulaThe total disturbance of the quadrature axis current loop can be regarded as the total disturbance, and the total disturbance comprises resistance, inductance, permanent magnet flux linkage change and external disturbance;

the equation of motion is rewritten as:

in the above formula f_ωTotal disturbance of the speed loop, caused by internal parameter changes and external load torque changes;

step 3) designing a current loop continuous linear active disturbance rejection controller, firstly analyzing the current loop, inputting the current loop as a cross-axis current reference value, outputting as a cross-axis voltage control value, and recording a state variableThen equation (1.4) is expressed in the form of the following equation of state:

a linear state observer is designed by utilizing the design principle of Luenberger to observe disturbance quantity and state variables, and the equation of the state observer is as follows:

in the above formula Respectively represent state variables Which represents the value of the gain of the observer,in order to be able to observe the error of the observer,the current loop linear expansion observer is written as:

in the above formula

Step 4) designing a continuous linear active disturbance rejection controller of a speed loop, wherein a linear extended observer of the speed loop is expressed as:

the state variable matrix z in the above equation_ω＝[z_{1_ω},z_{2_ω}]^TMatrix of statesObserver gain matrix L_ω＝[l_{1_ω},l_{2_ω}]^TOutput matrix C_ω＝[1,0]Input matrix B_ω＝[b_ω',0]^T，u_{c_ω}＝[u_{o_ω},y_ω]^T

Step 5) designing a tracking differentiator of the speed loop, wherein the current loop does not need to track the differentiator because the expected current value of the current loop is changed rapidly along with the reference value of the current; because of the inertia effect of the speed ring, if the arrangement of the transition process is carried out without using a tracking differentiator, the speed ring system can generate bad dynamic processes such as overshoot, and the arrangement of the transition process adopts a first-order inertia link, and the expression of the first-order inertia link is as follows:

meanwhile, the relation between the output and the input through an inertia link is obtained as follows:

step 6) designing a gain matrix of the linear extended observer, connecting the gain of the observer with the bandwidth commonly used in the actual control, and writing a characteristic equation of the system in the formula (1.8) as follows:

expanding the characteristic expression, placing the poles of the characteristic expression at the same position, wherein the position is the bandwidth value of the observer, and obtaining a gain matrix of the observer as follows:

and 7) designing control laws of the speed loop and the current loop continuous linear active disturbance rejection controller, and adopting single P control for a first-order controlled object, wherein the control laws of the current loop and the speed loop are as follows:

u_ω＝K_ω(r_ω-y_ω)(1.51)

in the above formulaK_ωIn order to control the gain of the laws,r_ωreference signals for the speed loop and the current loop;

step 8) discretizing the continuous linear active disturbance rejection controller, wherein the control law part in the continuous linear active disturbance rejection controller only carries out input on the output signal of the linear extended observerThe control law part does not need discretization processing, only needs to discretize the continuous linear extended observer part and adopt an Euler discretization method to discretize the control law part, the discretization mode of the speed loop is similar to that of the current loop, only the discretization process of the current loop is deduced, and the state variable is subjected to state variable processingDifferentiation is performed using the following equation:

in the above formulaFor the delay time caused by the current loop digital controller, the above equation is rewritten as the change of the current time compared to the previous time:

substituting the above equation into the state equation of the continuous system to obtain:

in the above formulaCorresponding to the state matrixThe expression is as follows:

wherein I is an identity matrix, and I is an identity matrix,corresponding to the input matrixThe expression is as follows:

equaling the output matrix in a continuous controllerIs a zero matrix, and simultaneously obtains an expression equation of the discrete linear extended observer as follows:

in the above formulaThe expression of (a) is:

whereinThe characteristic equation is written for a discrete linear extended observer gain matrix similar to a continuous system as follows:

the characteristic roots are placed at the same polar point, and a gain matrix is obtained after expansionComprises the following steps:

simultaneously obtaining:

the corresponding input matrix is:

the corresponding output matrix is:

corresponding toThe matrix expression of (a) is:

the conversion expressions of the bandwidth of the continuous linear expansion observer and the bandwidth of the discrete linear expansion observer are as follows:

step 9) discretization of a velocity loop tracking differentiator, wherein a forward Euler method is adopted for discretization of a first-order inertia link, and a reverse Laler identification is carried out on the inertia link to obtain:

obtained by a forward Euler method:

the simultaneous expression is as follows:

step 10) identifying the rotational inertia and the inductance value of the low-voltage servo motor as a determination reference of a compensation factor, and obtaining the rotational inertia value and the inductance value through an identification algorithm according to a formula:

the base numbers of the compensation factors of the current loop and the speed loop are determined, because the anti-interference performance and the dynamic performance of the system can be improved by properly increasing the value of the compensation factor in the linear active-disturbance-rejection controller, the compensation factor is multiplied by a gain factor a to obtain the compensation factor in the actual controller as follows:

b_{0_ω}'＝a_ω*b_{0_ω} (1.72)

step 11) using a steady state diagram mode to control the control law bandwidth omega of the current loop and the speed loop_cAnd observer bandwidth ω_oAnd setting, and reserving enough amplitude margin and phase margin for the two systems.

The true bookIn the embodiment, the reference input of the speed loop is given through the software of the upper computer, the given input is introduced into a discrete first-order inertia link, the time constant tau in the inertia link is adjusted, and the sampling time is the control period of the speed loop, namely t_s0.001, wherein the larger the value of the time constant, the stronger the suppression of overshoot, but at the same time the longer the adjustment time required by the system.

Firstly, a PID controller is used for enabling a low-voltage servo motor to work under the condition of constant speed, at the moment, inductance parameters and rotational inertia parameters of the motor are identified, cardinalities of compensation factors of a speed loop and a current loop are determined according to the identified parameters, and meanwhile, the cardinalities are multiplied by a scale factor to obtain the compensation factors of the controller.

The output value of the operational amplifier circuit is used for sampling the direct-quadrature axis current value of the motor and is used as the input of a discrete linear extension observer, and the output of the observer from a control law is input into a control quantity obtained by a limiting function.

And designing parameters of the discrete linear active disturbance rejection controller. Firstly, considering the transfer function of a linear active disturbance rejection device, converting the linear active disturbance rejection controller into the form of the transfer function through a state equation, simultaneously considering the time delay generated by the time delay caused by a digital controller, converting the time delay into the form of the transfer function, and simultaneously writing the transfer function of a controlled object. And writing a closed-loop transfer function of the whole system, independently writing a closed-loop characteristic equation of the system, writing an iterative program, combining different control law bandwidths and proportional factors between the control laws and the observer bandwidths, substituting the combined values into the characteristic equation, and judging whether a characteristic root of the characteristic equation is positioned on a left half plane or not.

Drawing the obtained control law bandwidth and a scale factor between the control law and the observer bandwidth into a graph, determining a stable region, and obtaining controller parameters meeting requirements in the stable region through a performance evaluation function, wherein the maximum value of the scale factor cannot exceed 10.

The bandwidth of the current loop discrete linear expansion observer is obtained through a formula (1.29), and the bandwidth is substituted into a current loop controller to look up actual working conditions and find an optimal solution.

The low-voltage servo controller generally receives output values from an incremental encoder, a rotary encoder, and an absolute value encoder, and processes the signals by the controller to determine the real-time speed of the low-voltage servo motor. The linear expansion observer is used as the input of the discrete linear expansion observer of the speed loop, and the input and the current loop adopt the control quantity after amplitude limiting as the input.

The speed ring is set by adopting a setting method, so that the low-voltage servo motor can stably run under the speed ring.

The above examples merely represent one embodiment of the present invention and are not to be construed as limiting the scope of the invention. It should be noted that a person skilled in the art could make several alternative designs without departing from the inventive concept, which falls within the scope of the invention.