Network construction type converter power oscillation suppression strategy based on variable quadrature axis power feedback

Abstract

The network construction type converter based on virtual synchronous generator (VSG) control can effectively support the frequency and voltage of a large power grid, and is considered as an optimal control strategy widely applied to a novel power system. However, a traditional active power control link is a second-order oscillation system, when a fixed virtual damping coefficient deals with disturbance such as active power reference value step change and power grid strength change, the phenomenon of low-frequency oscillation of output active power may be caused, and system instability is caused in serious cases. Meanwhile, the primary frequency modulation coefficient and the virtual damping coefficient are mutually coupled, so that respective control targets cannot be realized. Therefore, the invention discloses a network construction type converter power oscillation suppression strategy based on variable quadrature axis power feedback. When the frequency step of the power grid changes, the strategy adjusts the steady-state output active power of the converter according to the primary frequency modulation coefficient, and decoupling between control parameters is achieved. When the active power reference value changes in a step or the power grid intensity changes, the dynamic response performance of the output active power is good, and the control performance of the converter is effectively improved.

Description

Technical Field

[0001] The invention relates to a power oscillation suppression strategy for a grid-type converter based on variable quadrature-axis power feedback, and belongs to the technical field of power electronic converter control. Background Art

[0002] Under the background of "dual carbon", the proportion of traditional synchronous generators continues to decrease, the penetration rate of new energy power generation continues to increase, and the large-scale access of power electronic equipment is an inevitable evolution trend of modern power systems. Since there are no actual rotor components in the converter, it presents the characteristics of weak damping and weak support, which introduces new stability problems to the robust operation of the power system. Compared with the grid-following converter whose external characteristics are current sources, the grid-forming converter has external characteristics as voltage sources, which can provide the system with necessary frequency support and voltage support and enhance the anti-interference characteristics of the system. Therefore, the grid-forming control technology has attracted great attention and is considered to be widely used in new power systems. There are many grid-forming control strategies, among which virtual synchronous generator (VSG) control is one of the commonly used strategies, which can provide virtual inertia and damping for the system and effectively support the frequency and voltage of the large power grid.

[0003] Traditional active power control simulates the rotor motion equation of the synchronous generator and replaces the phase-locked loop with power synchronization to obtain phase information. However, the rotor motion equation is a second-order oscillation system, and the output active power may have low-frequency oscillations. Traditional active power control inherits this feature. When the active power reference value changes in steps and the grid strength changes, if a fixed virtual damping coefficient is used, the output active power may produce low-frequency oscillations, which may cause system instability in severe cases. At the same time, there is a coupling effect between the primary frequency modulation coefficient and the virtual damping coefficient, which blurs the effects of primary frequency modulation and damping when the grid frequency is disturbed, and their respective control targets cannot be achieved. In order to improve the control performance of grid-connected converters under the background of new power systems, it is necessary to propose a power oscillation suppression strategy, which is crucial to ensure the stable operation of the power system. Summary of the invention

[0004] In view of the problems existing in the traditional active power control strategy, the present invention provides a power oscillation suppression strategy for a grid-type converter based on variable quadrature-axis power feedback. This control strategy abandons the virtual damping term in the traditional active power control strategy, constructs a variable quadrature-axis power for suppressing low-frequency oscillations using the q-axis component of the grid-connected point voltage, and provides a control parameter expression that is suitable for a wide grid impedance range from the perspective of configuring the zero-pole position of the system. The present invention not only achieves decoupling between control parameters, but also improves the dynamic response performance of the grid-type converter output active power.

[0005] The power oscillation suppression strategy of grid-connected converter based on variable quadrature-axis power feedback includes the following six parts:

[0006] Part I: Coordinate transformation, power calculation and positive and negative sequence separation.

[0007] The specific steps include:

[0008] Step (1): Sample the three-phase AC voltage and current at the inverter grid connection point to obtain the three-phase voltage u pcca 、u pccb 、u pccc and current i pcca 、i pccb 、i pccc , the subscripts “a”, “b”, and “c” represent the A-phase, B-phase, and C-phase of the voltage and current, respectively;

[0009] Step (2): Perform a 3s / 2s transformation on the sampled three-phase voltage and current to obtain the αβ axis components of the voltage and current: u pccα 、u pccβ and i pccα 、i pccβ . Calculate the active power P according to the αβ axis components of voltage and current e and reactive power Q e ;

[0010] Step (3): Separate the positive and negative sequence of the αβ axis components of the voltage and current to obtain u αp 、u βp 、u αn 、u βn and i αp 、i βp 、i αn 、i βn , the subscripts "p" and "n" represent the positive and negative sequence components of voltage and current, respectively, the same below. Then, the positive and negative sequence αβ axis components of voltage and current are transformed into positive and negative sequence 2s / 2r to obtain the positive sequence dq axis components of voltage and current u dp 、u qp 、i dp 、i qp and the negative sequence dq axis component u dn 、u qn 、i dn 、i qn ; Phase θ GMF Generated by the active power control loop.

[0011] Part II: Power control outer loop.

[0012] The power control outer loop includes a reactive power control loop and an active power control loop. Specifically, it includes the following steps:

[0013] Step (1): According to the active power target value P refAnd the calculated active power value P e , simulate the rotor motion equation to perform closed-loop control on the converter output active power and generate θ GMF ;

[0014] Step (2): According to the reactive power target value Q ref And reactive power calculation value Q e , a low-pass filter and a PI controller are used to control the reactive power transmitted between the converter and the grid to generate a virtual internal potential E emf ;

[0015] Step (3): Based on the phase θ generated by the active power control loop GMF and the virtual internal potential E generated by the reactive power control loop emf , the combined reference internal potential e emfa , e emfb , e emfc .

[0016] Part 3: Constructing the quadrature axis power P q .

[0017] Using the q-axis component of the grid-connected voltage Construct quadrature axis power P q .

[0018] Part 4: Solve the control parameter expressions that adapt to a wide grid impedance range.

[0019] A small signal model of the active power control loop is established, and the characteristic equation of the system is obtained. The characteristic equation of the system is written as a combination of two first-order systems and a standard system, and the two poles are set as known quantities. According to the relationship between the coefficients of the original characteristic equation of the system and the coefficients of the deformed characteristic equation, the control parameter expression is solved.

[0020] Part V: Virtual impedance control and current control inner loop.

[0021] The specific steps include:

[0022] Step (1): The inner potential e generated by the power control outer loop emf With the grid voltage u pcc The voltage difference between them passes through the virtual impedance link to generate a current reference value i aref ,i bref ,i cref ;

[0023] Step (2): Perform a 3s / 2r transformation on the current reference value to obtain the positive and negative sequence dq axis components of the current reference value: i dpref 、i qpref and i dnref 、i qnrefPI controller is generally used to control the grid-connected current i pcc To follow the reference value i ref The output of the PI controller is I dpPI ,I qpPI and I dnPI ,I qnPI .

[0024] Part 6: trigger pulse generation link.

[0025] The specific steps include:

[0026] Step (1): Calculate the positive and negative sequence dq axis components u of the modulation voltage command dpref 、u qpref 、u dnref 、u qnref ;

[0027] Step (2): Modulate the voltage command u dpref 、u qpref 、u dnref 、u qnref Perform 2r / 3s transformation to obtain the abc axis component u of the modulation voltage command apref 、u bpref 、u cpref and u anref 、u bnref 、u cnref The final modulation voltage command u is obtained by adding them in phase. oaref 、u obref 、u ocref ;

[0028] Step (3): Three-phase modulation voltage command u oaref ,u obref ,u ocref After the duty cycle calculation, the three-phase duty cycle signal g is obtained a , g b and g c , g a , g b and g c Modulation is performed to obtain the trigger pulses of each switching tube.

[0029] The beneficial effects of the present invention are:

[0030] 1. The control strategy disclosed in the present invention utilizes the q-axis component of the grid-connected point voltage to construct a virtual damping power, thereby achieving decoupling between control parameters while suppressing power oscillation.

[0031] 2. From the perspective of freely configuring the zero-pole positions of the system, the present invention combines the order reduction process to provide a control parameter expression that is adaptable to a wide grid impedance range, thereby improving the dynamic response performance of the output active power.

[0032] 3. The control strategy algorithm disclosed in the present invention is simple and easy to implement digitally, and is suitable for power electronic converters in various scenarios such as energy storage, wind power, and photovoltaics. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 Schematic diagram of power oscillation suppression strategy for grid-connected converter based on variable cross-axis power feedback.

[0034] Figure 2 To improve the active power control block diagram. DETAILED DESCRIPTION

[0035] The present invention will be further described below in conjunction with the accompanying drawings.

[0036] like Figure 1 The power oscillation suppression strategy of grid-connected converter based on variable quadrature-axis power feedback includes the following six parts:

[0037] Part I: Coordinate transformation, power calculation and positive and negative sequence separation.

[0038] like Figure 1 , specifically including the following steps:

[0039] Step (1): Sample the three-phase AC voltage and current at the inverter grid connection point to obtain the three-phase voltage u pcca 、u pccb 、u pccc and current i pcca 、i pccb 、i pccc , the subscripts “a”, “b”, and “c” represent the A-phase, B-phase, and C-phase of the voltage and current, respectively;

[0040] Step (2): Perform a 3s / 2s transformation on the sampled three-phase voltage and current. The 3s / 2s transformation formula is shown in formula (1) to obtain the αβ axis components of the voltage and current: pccα 、u pccβ and i pccα 、i pccβ . Calculate the active power P according to the αβ axis components of voltage and current e and reactive power Q e , the calculation expression is shown in formula (2);

[0041]

[0042] Where: F represents voltage or current signal.

[0043]

[0044] Step (3): Separate the positive and negative sequence of the αβ axis components of the voltage and current. The separation formulas are shown in equations (3) and (4), and u is obtained. αp 、u βp 、u αn 、u βn and i αp 、i βp 、i αn 、i βn , the subscripts "p" and "n" represent the positive and negative sequence components of voltage and current, respectively, the same below. Then, the positive and negative sequence αβ axis components of voltage and current are transformed into positive and negative sequence 2s / 2r. The transformation formulas are shown in equations (5) and (6), and the positive sequence dq axis components of voltage and current are obtained. dp 、u qp 、i dp 、i qp and the negative sequence dq axis component u dn 、u qn 、i dn 、i qn ; Phase θ GMF Generated by the active power control loop.

[0045]

[0046]

[0047] Where: F p ' ccα 、F p ' ccβ F pccα 、F pccβ An electrical quantity obtained by delaying 1 / 4 of the power frequency cycle.

[0048]

[0049] Part II: Power control outer loop.

[0050] The power control outer loop includes the reactive power control loop and the active power control loop. The reactive power control block diagram is shown in Figure 1 As shown, the active power control block diagram is as follows Figure 2 As shown. Specifically including the following steps:

[0051] Step (1): According to the active power target value P ref And the calculated active power value P e , simulate the rotor motion equation to perform closed-loop control on the converter output active power and generate θ GMF , as shown in formula (7);

[0052]

[0053] Where: H is the inertia constant, k ω is the primary frequency modulation coefficient. Δ is the virtual angular frequency error signal, ω N is the angular frequency rating. q is the variable quadrature axis power introduced to suppress output power oscillation. The above powers and angular frequencies are all per-unit values.

[0054] Step (2): According to the reactive power target value Q ref And reactive power calculation value Q e , a low-pass filter and a PI controller are used to control the reactive power transmitted between the converter and the grid to generate a virtual internal potential E emf , as shown in formula (8);

[0055]

[0056] Where: k Qp , k Qi are the proportional coefficient and integral coefficient of the PI controller, ω cq is the cut-off frequency of the low-pass filter, E0 is the rated voltage. The above voltages are per-unit values.

[0057] Step (3): Based on the phase θ generated by the active power control loop GMF and the virtual internal potential E generated by the reactive power control loop emf , the combined reference internal potential e emfa , e emfb , e emfc , as shown in formula (9).

[0058]

[0059] Where: E emf is the virtual internal potential E emf The named value of .

[0060] Part 3: Constructing the quadrature axis power P q .

[0061] like Figure 1 and Figure 2 , specifically including the following steps:

[0062] Step (1): Substitute the αβ axis component u of the grid connection point voltage pccα 、u pccβ Perform 2s / 2r transformation to obtain the q-axis component of the grid connection point voltage The specific expression is shown in formula (10);

[0063]

[0064] Step (2): Using the q-axis component of the grid-connected point voltage Construction power P q0 , its specific expression is shown in formula (11);

[0065]

[0066] Where: K A0 is the gain in amperes (A).

[0067] Step (3): introduce a second-order filter to filter out high-frequency components, and its specific expression is shown in formula (12);

[0068]

[0069] Where: c is the bandwidth, ω n is the center angular frequency.

[0070] Step (4): Combine equations (11) and (12) to obtain the variable quadrature axis power P q The expression of is shown in formula (13).

[0071]

[0072] Where: K A is the gain after standardization, K A and K A0 The relationship between them satisfies K A =K A0 / S n , S n is the rated power.

[0073] Part 4: Solve the control parameter expressions that adapt to a wide grid impedance range.

[0074] like Figure 2 , specifically including the following steps:

[0075] Step (1): Establish a small signal model of the active power control loop and obtain the characteristic equation of the system, as shown in formula (14); the specific expressions of the coefficients a1 to a5 of the characteristic equation are shown in formula (15);

[0076] G c (s)=a1s 4 +a2s 3 +a3s 2 +a4s+a5 (14)

[0077]

[0078] Where: E s , U g are the converter output voltage and grid voltage amplitude respectively, X m +X g is the equivalent impedance between the converter and the grid. The above voltages are per unit values.

[0079] Step (2): Write the characteristic equation of the system as a combination of two first-order systems and a standard system, as shown in equation (16);

[0080]

[0081] Where: -p1, -p2 are the two poles of the system, ξ, ω n0 are the damping ratio and natural oscillation frequency of the standard second-order system respectively.

[0082] Step (3): Compare equation (14) and equation (16) to obtain the relationship between the coefficients of the original characteristic equation of the system and the coefficients of the characteristic equation after deformation, as shown in equation (17);

[0083]

[0084] Step (4): Set the two poles of the system to -p1 = -p2 = -4ξω n0 The expression of ξ is obtained from the first equation of equation (17), as shown in equation (18); ξ and ω are obtained from the fourth equation of equation (17): n and ω n0 The first relationship between is shown in equation (19); combining equations (18) and (19), eliminating the intermediate quantity ξ, we get ω n0 The expression of is shown in formula (20);

[0085]

[0086] Step (5): From the second equation of equation (17), we can obtain ξ and ω n and ω n0 The first relationship between is shown in equation (21); by combining equations (18), (20) and (21), we can solve ω n The expression of is shown in formula (22);

[0087]

[0088] Step (6): Let Get ω c The expression of is shown in formula (23);

[0089]

[0090] Step (7): Substitute the variable a, equation (20) and equation (22) into equation (18) to obtain another expression for ξ, as shown in equation (24); ignore the terms related to the first power of a, simplify equation (24), and the simplified equation is shown in equation (25). The transformed characteristic equation is reduced to a second-order system. According to the response characteristics of the system after the reduction, a suitable ξ value is selected and substituted into equation (25) to obtain the value of a. Substitute the solved a into equation (23) to obtain ω c The value of; using the solved ω c Substitute into equation (22) and solve for ω n The value of ω c and ω n Substitute into equation (20) and solve to obtain ω n0 The value of ω c and ω n0 Substituting into equation (18) we can get the actual ξ value;

[0091]

[0092] Step (8): From the three equations in formula (17), we can get K A The expression of is shown in formula (26); the ω calculated above is c ,ω n ,ω n0 And the actual ξ value is substituted into formula (26) to obtain K A The value of .

[0093]

[0094] Part V: Virtual impedance control and current control inner loop.

[0095] like Figure 1 , specifically including the following steps:

[0096] Step (1): The inner potential e generated by the power control outer loop emf With the grid voltage u pcc The voltage difference between them passes through the virtual impedance link to generate a current reference value i aref ,i bref ,i cref , as shown in formula (27);

[0097]

[0098] Where: R v and L V They are virtual resistance and virtual inductance respectively.

[0099] Step (2): Perform a 3s / 2r transformation on the current reference value to obtain the positive and negative sequence dq axis components of the current reference value: i dpref 、i qpref and i dnref 、i qnref PI controller is generally used to control the grid-connected current i pcc To follow the reference value i ref The output of the PI controller is I dpPI ,I qpPI and I dnPI ,I qnPI , the specific expression is shown in formula (28).

[0100]

[0101] Where: k pi , k ii They are the proportional coefficient and integral coefficient of the inner loop of current control respectively.

[0102] Part 6: trigger pulse generation link.

[0103] like Figure 1 , specifically including the following steps:

[0104] Step (1): Calculate the positive and negative sequence dq axis components u of the modulation voltage command dpref 、u qpref 、u dnref 、u qnref , as shown in formula (29);

[0105]

[0106] Where: L m is the filter inductance of the LC filter.

[0107] Step (2): Modulate the voltage command u dpref 、u qpref 、u dnref 、u qnref Perform 2r / 3s transformation to obtain the abc axis component u of the modulation voltage command apref 、u bpref 、u cpref and u anref 、u bnref 、u cnref The final modulation voltage command u is obtained by adding them in phase. oaref 、u obref 、u ocref , as shown in formula (30);

[0108]

[0109] Step (3): Three-phase modulation voltage command u oaref ,u obref ,u ocref After the duty cycle calculation, the three-phase duty cycle signal g is obtained a , g b and g c , the specific calculation formula is shown in (31); g a , g b and g c Modulation is performed to obtain the trigger pulses of each switching tube.

[0110]

[0111] Where: U dc is the measured value of the DC side voltage of the grid-connected converter.

[0112] The applicant of the present invention has made a detailed explanation and description of the implementation examples of the present invention in conjunction with the drawings in the specification. However, those skilled in the art should understand that the above implementation examples are only preferred implementation schemes of the present invention, and the detailed description is only to help readers better understand the spirit of the present invention, but not to limit the scope of protection of the present invention. On the contrary, any improvements or modifications based on the inventive spirit of the present invention should fall within the scope of protection of the present invention.

[0113] The contents not described in detail in this specification belong to the prior art known to professional and technical personnel in this field.

Claims

1. A power oscillation suppression strategy for a grid-connected converter based on variable quadrature-axis power feedback, characterized in that: It includes the following six parts: Part I: Coordinate transformation, power calculation and positive and negative sequence separation. The specific steps include: Step (1): Sample the three-phase AC voltage and current at the inverter grid connection point to obtain the three-phase voltage u pcca 、u pccb 、u pccc and current i pcca 、i pccb 、i pccc , the subscripts "a", "b", and "c" represent the A phase, B phase, and C phase of the voltage and current, respectively; Step (2): Perform a 3s / 2s transformation on the sampled three-phase voltage and current to obtain the αβ axis components of the voltage and current: u pccα 、u pccβ and i pccα 、i pccβ . Calculate the active power P according to the αβ axis components of voltage and current e and reactive power Q e ; Step (3): Separate the positive and negative sequence of the αβ axis components of the voltage and current to obtain u αp 、u βp 、u αn 、u βn and i αp 、i βp 、i αn 、i βn , the subscripts "p" and "n" represent the positive and negative sequence components of voltage and current, respectively. Then, the positive and negative sequence αβ axis components of voltage and current are transformed into positive and negative sequence 2s / 2r to obtain the positive sequence dq axis components of voltage and current u dp 、u qp 、i dp 、i qp and the negative sequence dq axis component u dn 、u qn 、i dn 、i qn ; Phase θ GMF Generated by the active power control loop. Part II: Power control outer loop. The power control outer loop includes a reactive power control loop and an active power control loop. Specifically, it includes the following steps: Step (1): According to the active power target value P ref And the active power calculation value P e , simulate the rotor motion equation to perform closed-loop control on the converter output active power and generate θ GMF ; Step (2): According to the reactive power target value Q ref And reactive power calculation value Q e , a low-pass filter and a PI controller are used to control the reactive power transmitted between the converter and the grid to generate a virtual internal potential E emf ; Step (3): Based on the phase θ generated by the active power control loop GMF and the virtual internal potential E generated by the reactive power control loop emf , the combined reference internal potential e emfa , e emfb , e emfc . Part 3: Constructing the quadrature axis power P q . Using the q-axis component of the grid voltage Construct quadrature axis power P q . Part 4: Solve the control parameter expressions that adapt to a wide grid impedance range. A small signal model of the active power control loop is established, and the characteristic equation of the system is obtained. The characteristic equation of the system is written as a combination of two first-order systems and a standard system, and the two poles are set as known quantities. According to the relationship between the coefficients of the original characteristic equation of the system and the coefficients of the deformed characteristic equation, the control parameter expression is solved. Part V: Virtual impedance control and current control inner loop. The specific steps include: Step (1): The inner potential e generated by the power control outer loop emf With the grid voltage u pcc The voltage difference between them passes through the virtual impedance link to generate a current reference value i aref ,i bref ,i cref ; Step (2): Perform a 3s / 2r transformation on the current reference value to obtain the positive and negative sequence dq axis components of the current reference value: i dpref 、i qpref and i dnref 、i qnref PI controller is generally used to control the grid-connected current i pcc To follow the reference value i ref The output of the PI controller is I dpPI ,I qpPI and I dnPI ,I qnPI . Part 6: trigger pulse generation link. The specific steps include: Step (1): Calculate the positive and negative sequence dq axis components u of the modulation voltage command dpref 、u qpref 、u dnref 、u qnref ; Step (2): Modulate the voltage command u dpref 、u qpref 、u dnref 、u qnref Perform 2r / 3s transformation to obtain the abc axis component u of the modulation voltage command apref 、u bpref 、u cpref and u anref 、u bnref 、u cnref The final modulation voltage command u is obtained by adding them in phase. oaref 、u obref 、u ocref ; Step (3): Three-phase modulation voltage command u oaref ,u obref ,u ocref After the duty cycle calculation, the three-phase duty cycle signal g is obtained a , g b and g c , g a , g b and g c Modulation is performed to obtain the trigger pulses of each switching tube.

2. The power oscillation suppression strategy of a grid-connected converter based on variable quadrature-axis power feedback according to claim 1 is characterized in that: The third part describes the construction of the quadrature axis power P q , specifically including the following steps: Step (1): Substitute the αβ axis component u of the grid connection point voltage pccα 、u pccβ Perform 2s / 2r transformation to obtain the q-axis component of the grid connection point voltage The specific expression is shown in formula (1); Step (2): Using the q-axis component of the grid-connected voltage Construction power P q0 , its specific expression is shown in formula (2); Where: K A0 is the gain in amperes (A). Step (3): introduce a second-order filter to filter out high-frequency components, and its specific expression is shown in formula (3); Where: c is the bandwidth, ω n is the center angular frequency. Step (4): Combine equations (2) and (3) to obtain the variable quadrature axis power P q The expression of is shown in formula (4). Where: K A is the gain after standardization, K A and K A0 The relationship between them satisfies K A =K A0 / S n , S n is the rated power.

3. The power oscillation suppression strategy of a grid-connected converter based on variable quadrature-axis power feedback according to claim 1 is characterized in that: The fourth part describes solving the control parameter expression adapted to the wide grid impedance range, specifically including the following steps: Step (1): Establish a small signal model of the active power control loop to obtain the characteristic equation of the system, as shown in formula (5); the specific expressions of the coefficients a1 to a5 of the characteristic equation are shown in formula (6); <h2 style=";text-align:left;direction:ltr">G<h2 style=";text-align:left;direction:ltr"> c <h2 style=";text-align:left;direction:ltr"> (s)=a1s<h2 style=";text-align:left;direction:ltr"> 4 <h2 style=";text-align:left;direction:ltr"> +a2s<h2 style=";text-align:left;direction:ltr"> 3 <h2 style=";text-align:left;direction:ltr"> +a3s<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> +a4s+a5 (5) Where: E s , U g are the converter output voltage and grid voltage amplitude respectively, X m +X g is the equivalent impedance between the converter and the grid. The above voltages are per unit values. Step (2): Write the characteristic equation of the system as a combination of two first-order systems and a standard system, as shown in equation (7); Where: -p1, -p2 are the two poles of the system, ξ, ω n0 are the damping ratio and natural oscillation frequency of the standard second-order system respectively. Step (3): Compare equation (5) and equation (7) to obtain the relationship between the coefficients of the original characteristic equation of the system and the coefficients of the characteristic equation after deformation, as shown in equation (8); Step (4): Set the two poles of the system to -p1 = -p2 = -4ξω n0 The expression of ξ is obtained from the first equation of equation (8), as shown in equation (9); ξ and ω are obtained from the fourth equation of equation (8): n and ω n0 The first relationship between is shown in equation (10); combining equations (9) and (10), eliminating the intermediate quantity ξ, we get ω n0 The expression of is shown in formula (11); Step (5): From the second equation of equation (8), we can obtain ξ and ω n and ω n0 The first relationship between is shown in equation (12); by combining equations (9), (11) and (12), we can solve ω n The expression of is shown in formula (13); Step (6): Let Get ω c The expression of is shown in formula (14); Step (7): Substitute the variable a, equation (11) and equation (13) into equation (9) to obtain another expression for ξ, as shown in equation (15); ignore the terms related to the first power of a, simplify equation (15), and the simplified equation is shown in equation (16). The transformed characteristic equation is reduced to a second-order system. According to the response characteristics of the system after the reduction, a suitable ξ value is selected and substituted into equation (16) to obtain the value of a. Substitute the solved a into equation (14) to obtain ω c The value of; using the solved ω c Substituting into equation (13), we can obtain ω n The value of ω c and ω n Substitute into equation (11) and solve for ω n0 The value of ω c and ω n0 Substitute into formula (9) to obtain the actual ξ value; Step (8): From the three equations in formula (17), we can get K A The expression of is shown in formula (17); the ω calculated above is c ,ω n ,ω n0 And the actual ξ value is substituted into formula (17) to obtain K A The value of .

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