Optimal servo control method based on RST controller

Abstract

The invention discloses an optimal servo control method based on an RST controller, which belongs to the technical field of servo control, and comprises a target model construction module, a transfer function construction setting module, an interference suppression optimization amplitude limiting robust module and a simulation module. In order to solve the technical problems of setting the time domain performance and stability of the system and optimizing controller parameters to improve the robustness, interference suppression capability, vibration suppression capability and control quantity limitation of the system, through detailed modeling and discretization processing, an accurate servo control system model is established, the effectiveness of a control algorithm is ensured, and the control precision is improved. A Q parameterization method is used for optimizing controller parameters, and the purposes of parameter robustness, vibration suppression, controlled quantity limitation and energy saving are achieved, and both optimization and robust design do not sacrifice designed time domain performance and stability. And the formed optimization problem is guaranteed to be a convex problem and is very easy to solve, and global optimum is guaranteed.

Description

Technical Field

[0001] The invention belongs to the technical field of servo control, and in particular relates to an optimized servo control method based on a RST controller. Background Art

[0002] In traditional servo control systems, after the controller is designed, some performance indicators of the system, such as interference suppression, should be optimized. Traditional optimization methods include optimization methods based on linear fractional transformation and linear matrix inequality, etc. However, all these methods require a trade-off between the designed time domain performance and the desired interference suppression and other indicators.

[0003] The optimization algorithm based on linear matrix inequality needs to complete the design of the control system in the state space form. The designed controller cannot be implemented directly because such a controller needs to know all the intermediate states to generate the control quantity. However, in many working conditions, not all intermediate states can be obtained from sensors. It is necessary to use a state observer (which requires convergence time, observability issues and stability issues), and it is also necessary to use many filters. This increases the complexity of implementation and affects the performance of the control system. Although the robust and optimal control instructions based on linear fractional transformation that come with Matlab do not require a state observer. However, the optimal controller designed for a simple second-order controlled system (DC motor) model has an order of up to 13, which is difficult to implement (and the optimization of the controller output has not been considered).

[0004] Most servo controllers use PI controllers. I With only two parameters, proportional gain and integral gain, it is difficult to stabilize high-order controlled systems and system dynamics, and it is even more difficult to make more requirements on this basis. The industry mainly uses TI's P I The controller design method is to use the crossover frequency of the open-loop transfer function of the speed loop on the servo side to approximate the bandwidth of the closed-loop transfer function (to design the entire speed loop controller), and use the distance between the zero and pole of the open-loop transfer function in the figure below to infer the stability margin of the closed-loop control system. But in fact, in collaborative robots or any non-direct-drive loads with harmonic reducers, the harmonics themselves also have damping and spring stiffness, and their actual open-loop transfer function is far from the figure below. Not to mention whether the bandwidth can be guaranteed, the stability margin is most likely unknown. Summary of the invention

[0005] The purpose of the present invention is to provide an optimal servo control method based on a RST controller, which solves the technical problems of setting the time domain performance of the system by tracking the design of the transfer function and adjusting the transfer function, and optimizing the controller parameters to improve the robustness and interference suppression capability of the system.

[0006] To achieve the above object, the present invention adopts the following technical solution:

[0007] An optimal servo control method based on a RST controller comprises the following steps:

[0008] Step 1: Establish a servo control system. The servo control system includes a target model building module, a transfer function building setting module, a disturbance suppression optimization limiting robust module and a simulation module. The target model is established for the controlled target, and the controlled target model is discretized;

[0009] Step 2: Transfer function construction setting module determines the tracking transfer function and the regulation transfer function, forces the tracking and regulation dynamics to have the same characteristic polynomial, and calculates the three polynomials S(q -1 )R(q -1 )T(q -1 ), when designing the tracking transfer function and the regulating transfer function, the damping coefficient ξ and the natural angular frequency ω are used n Set system time domain performance;

[0010] By using the pole placement method, S(q -1 ) and R(q -1 ) satisfies the following relationship:

[0011] A(q -1 )H S (q -1 )S(q -1 )+q -d B(q -1 )H R (q -1 )R(q -1 )=P(q -1 );

[0012] Among them, S(q -1 )=H S (q -1 )S'(q -1 ), R(q -1 )=H R (q -1 )R'(q -1 );

[0013] Step 3: The interference suppression optimization limit robust module uses the Q parameterization method to increase S(q -1 ) and R(q -1 ) parameter number, optimize S(q -1 ) and R(q -1 ), thereby improving the robustness and disturbance rejection capability of the servo control system;

[0014] Step 4: The simulation module outputs the control algorithm, according to the calculated T(q -1 )、S(q -1 ) and R(q -1 ) Generate a simulation control process and perform simulation, implement the simulation control process in the controlled target, adjust the damping coefficient and natural angular frequency, so that the response of the controlled target meets expectations.

[0015] Preferably, when executing step 1, the servo control system also includes a reference signal module, a speed controller module, a current loop module, a motor module and a feedback mechanism module, the reference signal module is used to generate a target signal r(t), the speed controller module is used to construct a speed controller and calculate controller parameters, the current loop module is used to implement current loop control and provide a current loop transfer function, the motor module is used to provide the mechanical parameters of the motor, including the moment of inertia J and the number of poles P, the reducer module is used to convert the load inertia to the motor side, and the feedback mechanism module is used to provide output signal y(t) feedback.

[0016] 1. The RST controller-based optimization servo control method according to claim 2, characterized in that: when executing step 1, the method specifically comprises the following steps:

[0017] Step 1-1: Use the parameters provided by the motor module to establish the transfer function G(s) of the controlled target:

[0018]

[0019] Among them, current_closed_loop is the current loop transfer function, P is the number of poles of the motor, J is the total moment of inertia of the motor, which is the moment of inertia of the motor rotor plus the moment of inertia of the load converted to the motor rotor side through the reducer, ψ f is the rotor flux of the PMSM motor, s is the Laplace operator;

[0020] Step 1-2: Use MATLAB to discretize the transfer function G(s) into a discrete transfer function And use MATLAB to find the delayed instruction pair to find the delay d of the transfer function, and get the discretized result G(q -1 ):

[0021]

[0022] Preferably, when executing step 2, the following steps are specifically included:

[0023] Step 2-1: Determine the characteristic polynomials of the tracking transfer function T and the regulation transfer function S:

[0024]

[0025] Step 2-2: Set the damping coefficient ξ and natural angular frequency ω n Set the system time domain performance and calculate two terms of the RST controller: S(q -1 ) and R(q -1 ):

[0026]

[0027] And discretize H(s) to obtain the denominator P(q -1 ), P(q -1 ) is equal to the characteristic polynomial of the tracking transfer function T, that is, A(q -1 )S(q -1 )+q -d B(q -1 )R(q -1 );

[0028] Step 2-3: Use the pole placement method to add an integrator to eliminate static errors and open the loop above the Nyquist frequency point, and let S(q -1 )=H S (q -1 )S′(q -1 ), R(q -1 )=H R (q -1 )R′(q -1 )get:

[0029] A(q -1 )H S (q -1 )S′(q -1 )+q -d B(q -1 )H R (q -1 )R′(q -1 )=P(q -1 );

[0030] Among them, H R (q -1 ) opens the loop above the Nyquist frequency, so that the disturbance v(t) cannot enter the controller output u(t);

[0031] Step 2-4: Set tracking and regulation to have the same characteristic polynomial, and then obtain T(q -1 ):

[0032]

[0033] Preferably, when executing step 3, the following steps are specifically included:

[0034] Step 3-1: R(q -1 ) and S(q -1 ) was renamed R0(q -1 ) and S0(q -1 ), using the Q parameterization method, increasing the number of parameters and optimizing R(q -1 ) and S(q -1 ), improving the system's robustness and interference suppression capabilities:

[0035] R(q -1 )=R0(q -1 )+A(q -1 )H R (q -1 )H S (q -1 )Q(q -1 )

[0036] S(q -1 )=S0(q -1 )-q -d B(q -1 )H S (q -1 )H R (q -1 )Q(q -1 );

[0037] in,

[0038] Step 3-2: Set the optimization goal and constraints, and solve the controller parameter Q:

[0039]

[0040] subject to:||M m S(Q)|| ∞ <1

[0041] ||U(Q)|| ∞ <U max

[0042] ||W2T(Q)|| ∞ <1;

[0043] in, It represents minimizing the 2-norm of disturbance to controller output and reference input to controller output to save energy and suppress the influence of disturbance vibration on the control quantity;

[0044] ||M m S(Q)|| ∞ <1By converting M mSet to 0.5 to ensure that the closed-loop control loop has a 30-degree stability phase margin and that the interference sensitivity transfer function amplitude-frequency response is less than 6 dB at mid- and high-frequency levels to suppress interference;

[0045] ||U(Q)|| ∞ <U max Make the infinite norm of the reference input to the controller output and the disturbance to the controller output less than a constant, so as to prevent saturation from occurring by considering the ability of the controller output, and also suppress the absolute size of the disturbance to the control quantity output;

[0046] ||W2T(Q)|| ∞ <1 means that the controlled system still has robust stability after the controlled system parameters change within a certain range, and the uncertainty weight filter W2 is calculated using the ucover command of MATLAB according to the multiplicative uncertainty principle.

[0047] The present invention discloses an optimized servo control method based on an RST controller, which solves the technical problems of setting the time domain performance of the system by tracking the design of the transfer function and adjusting the transfer function, and optimizing the controller parameters to improve the robustness and interference suppression capability of the system. The present invention establishes an accurate servo control system model through detailed modeling and discretization processing to ensure the effectiveness of the control algorithm, and uses the Q parameterization method to optimize the controller parameters to achieve the purpose of interference suppression and energy saving. The optimized controller parameters improve the robustness of the system, can effectively suppress interference, and adapt to the uncertainty in the actual environment. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 It is the main flow chart of the present invention;

[0049] Figure 2 is a control structure diagram of the RST controller of the present invention;

[0050] Figure 3 It is a schematic diagram of the present invention after the loop is opened. DETAILED DESCRIPTION

[0051] Depend on Figure 1-Figure 3 An optimized servo control method based on a RST controller is shown, comprising the following steps:

[0052] Step 1: Establish a servo control system. The servo control system includes a target model building module, a transfer function building setting module, an interference suppression optimization limiting robust module and a simulation module. The target model builds a controlled target model for the controlled target and discretizes the controlled target model. The servo control system also includes a reference signal module, a speed controller module, a current loop module, a motor module and a feedback mechanism module. The reference signal module is used to generate a target signal r(t). The speed controller module is used to build a speed controller and calculate controller parameters. The current loop module is used to realize current control and provide a current loop transfer function. The motor module is used to provide the mechanical parameters of the motor, including the moment of inertia J and the number of poles P. The reducer module is used to convert the load inertia to the motor side. The feedback mechanism module is used to provide output signal y(t) feedback.

[0053] When executing step 1, the specific steps include:

[0054] Step 1-1: Use the parameters provided by the motor module to establish the transfer function G(s) of the controlled target:

[0055]

[0056] Among them, current_closed_loop is the current loop transfer function, P is the number of poles of the motor, J is the total moment of inertia of the motor, which is the moment of inertia of the motor rotor plus the moment of inertia of the load converted to the motor rotor side through the reducer, ψ f is the rotor flux of the PMSM motor, s is the Laplace operator;

[0057] Step 1-2: Use MATLAB to discretize the transfer function G(s) into a discrete transfer function And use MATLAB to find the delayed instruction pair to find the delay d of the transfer function, and get the discretized result G(q -1 ):

[0058]

[0059] Step 2: Transfer function construction setting module determines the tracking transfer function and the regulation transfer function, forces the tracking and regulation dynamics to have the same characteristic polynomial, and calculates the three polynomials S(q -1 )R(q -1 )T(q -1 ) ; When designing the tracking transfer function and the regulating transfer function, the damping coefficient ξ and the natural angular frequency ω are used n Set system time domain performance;

[0060] In this embodiment, T(q -1 )、S(q -1 ) and R(q-1 ) are three polynomials controlled by RST, specifically:

[0061]

[0062]

[0063]

[0064] S(q -1 ): A tuning polynomial used to adjust the interference suppression performance of the system. It is usually related to the suppression of interference signals and affects the system's response to external interference.

[0065] R(q -1 ): Tracking polynomial, used to define the tracking performance of the system. It helps the system track the reference input signal (such as speed setpoint) to ensure that the output can follow the changes of the reference signal.

[0066] T(q -1 ): Control polynomial, used to define the control action of the system. It is a polynomial used to generate the control quantity, based on the dynamics of the system and the desired performance.

[0067] By using the pole placement method, S(q -1 ) and R(q -1 ) satisfies the following relationship. In this process, two fixed terms are added so that the controller can eliminate static errors and open the loop above the Nyquist frequency so that noise cannot affect the system. After P is obtained, T(q -1 ):

[0068] A(q -1 )H S (q -1 )S(q -1 )+q -d B(q -1 )H R (q -1 )R′(q -1 )=P(q -1 );

[0069] Among them, S(q -1 )=H S (q -1 )S′(q -1 ), R(q -1 )=H R (q -1 )R′(q -1 );

[0070] When executing step 2, the specific steps include:

[0071] Step 2-1: Determine the characteristic polynomials of the tracking transfer function T and the regulation transfer function S:

[0072]

[0073] In this embodiment, the transfer function from r(t) to output y(t) is called the tracking transfer function T, which determines the time domain performance of the control loop, such as bandwidth, overshoot, and settling time. The disturbance v(t) to output y(t) is called the regulation transfer function S, and the output u(t) from v(t) to controller K is the regulation transfer function S multiplied by controller K. This transfer function is represented by capital U (the reference input r(t) to controller output is also the transfer function, but with an opposite sign).

[0074] Step 2-2: Set the damping coefficient ξ and natural angular frequency ω n Set the system time domain performance and calculate two terms of the RST controller: S(q -1 ) and R(q -1 ):

[0075]

[0076] And discretize H(s) to obtain the denominator P(q -1 ), P(q -1 ) is equal to the characteristic polynomial of the tracking transfer function T, that is, A(q -1 )S(q -1 )+q -d B(q -1 )R(q -1 ); the numerator of H(s) is a constant, and its amplitude-frequency response is 1 in the steady state, that is, when s tends to zero.

[0077] The numerator of T is composed of the delay d(q -1 ) and T(q -1 )B(q -1 ), T(q -1 ) is selected as the characteristic polynomial A(q -1 )S(q -1 )+q - d B(q -1 )R(q -1 ) and B(q -1 ) value at steady state q=1 (T(q -1 ) is a constant and has no dynamics), T is also 1 in the steady-state amplitude-frequency response, ignoring the numerator polynomial B(q -1)'s dynamics are in transient state (not reaching steady state), which is a reasonable assumption, because the current loop bandwidth is first-order dynamics, so the numerator of the entire speed loop controlled target (as shown below) is a constant, and there is no dynamics at all.

[0078] In this embodiment, the characteristic polynomial is determined by first focusing on the time domain indicators of the system, the damping coefficient (vibration suppression, overshoot), and the natural angular frequency (bandwidth, stabilization time, and rise speed).

[0079] In this implementation, the current loop bandwidth is given, and the speed loop bandwidth is generally set to one fifth to one tenth of it. n It is determined that we set the damping coefficient ξ to 1 to avoid both vibration overshoot and excessive impact on the bandwidth.

[0080] Step 2-3: Use the pole placement method to add an integrator to eliminate static errors and open the loop above the Nyquist frequency point, and let S(q -1 )=H S (q -1 )S′(q -1 ), R(q -1 )=H R (q -1 )R′(q -1 )get:

[0081] A(q -1 )H S (q -1 )S′(q -1 )+q -d B(q -1 )H R (q -1 )R′(q -1 )=P(q -1 );

[0082] Among them, H R (q -1 ) opens the loop above the Nyquist frequency, so that the disturbance v(t) cannot enter the controller output u(t); the effect is as follows Figure 3 shown.

[0083] Step 2-4: Set tracking and regulation to have the same characteristic polynomial, and then obtain T(q- 1 ):

[0084]

[0085] In this embodiment, the optimization will be in S(q -1 ) and R(q -1 ) and no matter S(q-1 ) and R(q -1 ) No matter how the order of the parameter changes, it will not affect T(q -1 ).

[0086] If you select The gain of the tracking transfer function T in the steady state is 1, and the tracking and regulation have exactly the same characteristic polynomial.

[0087] Step 3: Interference suppression optimization limit robust module uses Q parameterization method to increase S(q -1 ) and R(q -1 ) parameter number, optimize S(q -1 ) and R(q -1 ), thereby improving the robustness and disturbance rejection capability of the servo control system;

[0088] When executing step 3, the specific steps include:

[0089] Step 3-1: R(q -1 ) and S(q -1 ) was renamed R0(q -1 ) and S0(q -1 ), using the Q parameterization method, increasing the number of parameters and optimizing R(q -1 ) and S(q -1 ), improving the system's robustness and interference suppression capabilities:

[0090] R(q -1 )=R0(q -1 )+A(q -1 )H R (q -1 )H S (q -1 )Q(q -1 )

[0091] S(q -1 )=S0(q -1 )-q -d B(q -1 )H S (q -1 )H R (q -1 )Q(q -1 );

[0092] in,

[0093] Step 3-2: Set the optimization goal and constraints, and solve the controller parameter Q:

[0094]

[0095] subject to:||M m S(Q)|| ∞ <1

[0096] ||U(Q)|| ∞ <U max

[0097] ||W2T(Q)|| ∞ <1;

[0098] in, It represents minimizing the 2-norm of disturbance to controller output and reference input to controller output to save energy and suppress the influence of disturbance vibration on the control quantity;

[0099] ||M m S(Q)|| ∞ <1By converting M m Set to 0.5 to ensure that the closed-loop control loop has a 30-degree stability phase margin and that the interference sensitivity transfer function amplitude-frequency response is less than 6 dB at mid- and high-frequency levels to suppress interference;

[0100] ||U(Q)|| ∞ <U max Make the infinite norm of the reference input to the controller output and the disturbance to the controller output less than a constant, so as to prevent saturation from occurring by considering the ability of the controller output, and also suppress the absolute size of the disturbance to the control quantity output;

[0101] ||W2T(Q)|| ∞ <1 means that the controlled system still has robust stability after the controlled system parameters change within a certain range, and the uncertainty weight filter W2 is calculated using the ucover command of MATLAB according to the multiplicative uncertainty principle.

[0102] In this embodiment, ||U(Q)||2 is a convex function, and the solution set is convex, so it is a convex optimization problem, which means that even if the parameter order is extremely high, the optimal solution can be obtained instantly, and it is the global optimal solution, and the objective function and constraints can handle mixed infinite norms and 2 norms.

[0103] Compared with MATLAB's own method of mixing multiple objective functions together, this embodiment has great advantages (MATLAB's optimization problem is not convex, cannot guarantee global optimality, and cannot mix infinite norm and two norms. The calculated order is extremely high, and cannot retain the originally calculated time domain indicators). The present invention can maximize the performance limits of system equipment.

[0104] Step 4: The simulation module outputs the control algorithm, according to the calculated T(q -1 )、S(q -1 ) and R(q -1 ) Generate a simulation control process and perform simulation, implement the simulation control process in the controlled target, adjust the damping coefficient and natural angular frequency, so that the response of the controlled target meets expectations.

[0105] In this embodiment, by focusing on the time domain indicators of the system first, determining the overshoot, damping coefficient (vibration suppression), natural angular frequency (bandwidth), and stabilization time, it is possible to immediately determine the characteristic polynomials for tracking and adjusting the two transfer functions T [r (t) to output y (t)] and S [v (t) to output y (t)], and the characteristic polynomials will not change due to subsequent optimization behavior (optimization is done on the added parameters). This embodiment can not sacrifice the already designed system time domain performance such as bandwidth, pole position, overshoot, stabilization time, step time, etc.

[0106] Optimization behaviors include:

[0107] ① Minimize the 2-norm of the disturbance to the controller output and the reference input to the controller output to reduce vibration, the impact of disturbance on the control quantity, and also save energy (because the 2-norm of the control quantity is the area under the line of the control signal in the time domain).

[0108] ② Further limiting the amplitude-frequency response of the transfer function from the reference input to the controller output limits the control amount to within the range we allow.

[0109] ③Through||M m S(Q)|| ∞ <1Limit the impact of disturbance on the closed-loop system output, M m The size of the phase margin for stability can be guaranteed.

[0110] ④Supplementary robust constraint ||W2T(Q)|| ∞ <1, ensuring that the system remains stable after the system parameters change (within the range we know), fully considering the robust performance of inaccurate system modeling and parameter changes, and the performance is guaranteed, where W2 is the uncertainty weight filter

[0111] When this embodiment is designed in the discrete domain and used directly in the discrete domain, there is no conversion process between the continuous domain and the accuracy is very high. Unlike the integral part of the PID controller, it does not need to accumulate signals of all past moments, nor does it need future signals like the differential part of the PID controller. It also does not need a state observer. The bandwidth of the entire speed loop is accurately specified in the closed loop rather than approximated by the open loop. The stability margin is accurately calculated after considering inaccurate system modeling and parameter changes, rather than approximating with a simple open-loop cross-frequency without considering key factors. Very high-order controlled targets can be taken into account.

[0112] The present invention discloses an optimized servo control method based on an RST controller, which solves the technical problems of setting the time domain performance of the system by tracking the design of the transfer function and adjusting the transfer function, and optimizing the controller parameters to improve the robustness and interference suppression capability of the system. The present invention establishes an accurate servo control system model through detailed modeling and discretization processing to ensure the effectiveness of the control algorithm, and uses the Q parameterization method to optimize the controller parameters to achieve the purpose of interference suppression and energy saving. The optimized controller parameters improve the robustness of the system, can effectively suppress interference, and adapt to the uncertainty in the actual environment.

Claims

1. An optimized servo control method based on a RST controller, characterized in that: The steps include: Step 1: Establish a servo control system. The servo control system includes a target model building module, a transfer function building setting module, a disturbance suppression optimization limiting robust module and a simulation module. The target model is established for the controlled target, and the controlled target model is discretized; Step 2: Transfer function construction setting module determines the tracking transfer function and the regulation transfer function, forces the tracking and regulation dynamics to have the same characteristic polynomial, and calculates the three polynomials S(q -1 )R(q -1 )T(q -1 ), when designing the tracking transfer function and the regulating transfer function, the damping coefficient ξ and the natural angular frequency ω are used n Set system time domain performance; By using the pole placement method, S(q -1 ) and R(q -1 ) satisfies the following relationship: A(q -1 )H S (q -1 )S′(q -1 )+q -d B(q -1 )H R (q -1 )R′(q -1 )=P(q -1 ); where S(q -1 ) = H S (q -1 )S′(q -1 ) and R(q -1 ) = H R (q -1 )R′(q -1 ) Step 3: The interference suppression optimization limit robust module uses the Q parameterization method to increase S(q -1 ) and R(q -1 ) parameter number, optimize S(q -1 ) and R(q -1 ), thereby improving the robustness and disturbance rejection capability of the servo control system; Step 4: The simulation module outputs the control algorithm, according to the calculated T(q -1 )、S(q -1 ) and R(q -1 ) Generate a simulation control process and perform simulation, implement the simulation control process in the controlled target, adjust the damping coefficient and natural angular frequency, so that the response of the controlled target meets expectations.

2. The optimized servo control method based on the RST controller as claimed in claim 1, characterized in that: When executing step 1, the servo control system also includes a reference signal module, a speed controller module, a current loop module, a motor module and a feedback mechanism module. The reference signal module is used to generate a target signal r(t). The speed controller module is used to build a speed controller and calculate controller parameters. The current loop module is used to implement current loop control and provide a current loop transfer function. The motor module is used to provide the mechanical parameters of the motor, including the moment of inertia J and the number of poles P. The reducer module is used to convert the load inertia to the motor side. The feedback mechanism module is used to provide output signal y(t) feedback.

3. The optimized servo control method based on the RST controller as claimed in claim 2, characterized in that: When executing step 1, the specific steps include: Step 1-1: Use the parameters provided by the motor module to establish the transfer function G(s) of the controlled target: Among them, current_closed_loop is the current loop transfer function, P is the number of poles of the motor, J is the total moment of inertia of the motor, which is the moment of inertia of the motor rotor plus the moment of inertia of the load converted to the motor rotor side through the reducer, ψ f is the rotor flux of the PMSM motor, s is the Laplace operator; Step 1-2: Use MATLAB to discretize the transfer function G(s) into a discrete transfer function And use MATLAB to find the delayed instruction pair to find the delay d of the transfer function, and get the discretized result G(q -1 ):

4. The optimized servo control method based on the RST controller as claimed in claim 3, characterized in that: When executing step 2, the specific steps include: Step 2-1: Determine the characteristic polynomials of the tracking transfer function T and the regulation transfer function S: Step 2-2: Set the damping coefficient ξ and natural angular frequency ω n Set the system time domain performance and calculate two terms of the RST controller: S(q -1 ) and R(q -1 ): And discretize H(s) to obtain the denominator P(q -1 ), P(q -1 ) is equal to the characteristic polynomial of the tracking transfer function T, that is, A(q -1 )S(q -1 )+q -d B(q -1 )R(q -1 ); Step 2-3: Use the pole placement method to add an integrator to eliminate static errors and open the loop above the Nyquist frequency point, and let S(q -1 )=H S (q -1 )S′(q -1 ), R(q -1 )=H R (q -1 )R′(q -1 ),get: A(q -1 )H S (q -1 )S′(q -1 )+q -d B(q -1 )H R (q -1 )R′(q -1 )=P(q -1 ): Among them, H R (q -1 ) opens the loop above the Nyquist frequency, so that the disturbance v(t) cannot enter the controller output u(t); Step 2-4: Set tracking and regulation to have the same characteristic polynomial, and then obtain T(q -1 ):

5. The optimized servo control method based on the RST controller as claimed in claim 4, characterized in that: When executing step 3, the specific steps include: Step 3-1: R(q- 1 ) and S(q- 1 ) was renamed R0(q- 1 ) and S0(q- 1 ), using the Q parameterization method to increase the number of parameters and optimize R(q- 1 ) and S(q- 1 ), improving the robustness and interference suppression capabilities of the system: R(q -1 )=R 0 (q -1 )+A(q -1 )H R (q -1 )H S (q -1 )Q(q -1 ) S(q -1 )=S0(q -1 )-q -d B(q -1 )H S (q -1 )H R (q -1 )Q(q -1 ); in, Step 3-2: Set the optimization goal and constraints, and solve the controller parameter Q: in, Indicates minimizing the 2-norm of disturbance to controller output and reference input to controller output to save energy and suppress the influence of disturbance vibration on the control quantity; ||M m S(Q)|| ∞ <1By converting M m Set to 0.5 to ensure that the closed-loop control loop has a 30-degree stability phase margin and that the interference sensitivity transfer function amplitude-frequency response is less than 6 dB at mid- and high-frequency levels to suppress interference; ||U(Q)|| ∞ <U max Make the infinite norm of the reference input to the controller output and the disturbance to the controller output less than a constant, thereby considering the ability of the controller output to prevent saturation and also suppress the absolute size of the disturbance to the control quantity output; ||W2T(Q)|| ∞ <1 means that the controlled system still has robust stability after the controlled system parameters change within a certain range, and the uncertainty weight filter W2 is calculated using the ucover command of MATLAB according to the multiplicative uncertainty principle.

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