CN114114913B - Secondary passage modeling method of vibration active control system - Google Patents
Secondary passage modeling method of vibration active control system Download PDFInfo
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Abstract
The application provides a modeling method for a secondary channel of a vibration active control system, which comprises the following steps: determining output force F of an actuator in the vibration active control system; determining an output force frequency domain cosine component Fc and a frequency domain sine component Fs according to the output force F; according to control sensor acceleration response Z 0 Determining an initial value T of the secondary path transfer function 0 (ii) a The initial value matrix T 0 Substituting an iteration formula, and performing iterative computation; according to the output force F and the cosine component Zc of the acceleration response 0 Acceleration response sinusoidal component Zs 0 Tc (n), ts (n), calculating an acceleration response residual cosine component ec (n) and an acceleration response residual sine component es (n); calculating a convergence residual err (n) according to the acceleration response residual cosine component ec (n) and the acceleration response residual sine component es (n); calculating an updated convergence coefficient u (n) according to the convergence residual err (n); when iterative calculation is carried out, and the convergence residual error (n) is smaller than a preset value, acquiring current Tc (n) and Ts (n); and obtaining a transfer function T between the output force of the actuator in the vibration active control system and the acceleration response of the control sensor according to the current Tc (n) and Ts (n).
Description
Technical Field
The application relates to the field of helicopter vibration active control, in particular to a secondary passage modeling method of a vibration active control system.
Background
The helicopter vibration active control system is used for reducing the body vibration level of a helicopter, the identification accuracy of a secondary passage model in the vibration active control system directly influences the vibration reduction effect of the system, if the identification deviation is large, the vibration of the system can be dispersed and even changed into a vibration exciter, and the vibration reduction effect cannot be achieved.
A transfer function from the excitation force of the helicopter rotor to the acceleration response of the control sensor is generally defined as a primary path; the transfer function between the output force of the actuator in the vibrating active control system and the acceleration response of the control sensor is defined as a secondary path. The identification of the secondary path is generally divided into two ways: a) Online identification; b) And (5) offline identification. The online identification method requires higher calculation speed and higher response precision of the actuator, and is difficult to realize in engineering, so that the offline identification method is adopted more. The offline identification mode, which is mostly a single identification or multiple averaging method at present, is limited by actuator response and sensor acquisition deviation, and results have certain dispersibility and larger errors.
Disclosure of Invention
The application provides a modeling method for a secondary channel of a vibration active control system, which can quickly and accurately identify a secondary channel transfer function model of the vibration active control system.
The technical scheme is as follows: the application provides a vibration active control system secondary channel modeling method, which comprises the following steps:
determining output force F of an actuator in the vibration active control system;
determining an output force frequency domain cosine component Fc and a frequency domain sine component Fs according to the output force F;
according to control sensor acceleration response Z 0 Determining an initial value T of the secondary path transfer function 0 ；
The initial value matrix T is divided into 0 Carry over into the following iterative formula, carry over intoAnd (4) performing iterative calculation to determine a secondary path model of each step:
Tc(n)＝Tc(n-1)-μ(n-1)·ec(n-1)
Ts(n)＝Ts(n-1)-μ(n-1)·es(n-1)
wherein n is the nth step iteration, mu is a convergence coefficient, es is an acceleration response residual sine component, ec is an acceleration response residual cosine component, tc (n) is a secondary channel transfer function cosine component, and Ts (n) is a secondary channel transfer function cosine component;
according to the output force F and the cosine component zc of the acceleration response 0 Acceleration response sinusoidal component zs 0 Tc (n), ts (n), calculating an acceleration response residual cosine component ec (n) and an acceleration response residual sine component es (n);
calculating a convergence residual error (err (n) according to the acceleration response residual cosine component ec (n) and the acceleration response residual sine component es (n);
calculating an updated convergence coefficient u (n) according to the convergence residual err (n);
substituting the updated convergence coefficient u (n) into the iterative formula again for iterative calculation;
when iterative calculation is carried out, and the convergence residual error (n) is smaller than a preset value, considering that the convergence of the secondary path model is completed until the response residual error is obtained, and obtaining the current Tc (n) and Ts (n);
and obtaining a transfer function T between the output force of the actuator in the vibration active control system and the acceleration response of the control sensor according to the current Tc (n) and Ts (n).
Specifically, determining a frequency domain cosine component Fc and a frequency domain sine component Fs of the output force according to the output force F specifically includes:
calculating the cosine component Fc of the output force frequency domain according to the formula Fc = F · cos (2 π F);
according to F s = F · sin (2 π F), calculating the output force frequency domain sinusoidal component Fs;
wherein f is the output force frequency of the actuator in the vibration active control system.
In particular, the acceleration response Z is based on the control sensor 0 Determining an initial value T of the secondary path transfer function 0 The method specifically comprises the following steps:
collecting acceleration response Z at control sensor 0 Calculating the cosine component Zc of the acceleration response by frequency domain analysis 0 Acceleration response sinusoidal component Zs 0 ；
Responding to cosine component Zc according to output force F and acceleration of actuator 0 Acceleration response sinusoidal component Zs 0 Using the formula:
T 0 ＝[Tc 0 Ts 0 ]
calculating to obtain an initial value matrix T 0 。
Specifically, calculating a convergence residual err (n) according to an acceleration response residual cosine component ec (n) and an acceleration response residual sine component es (n), specifically includes:
according to the acceleration response residual cosine component ec (n) and the acceleration response residual sine component es (n), using a formula
The convergence residual err (n) is calculated.
Specifically, the cosine component Zc is responded according to the output force F and the acceleration 0 Acceleration response sinusoidal component Zs 0 Tc (n), ts (n), calculating an acceleration response residual cosine component ec (n) and an acceleration response residual sine component es (n), specifically comprising:
according to the output force F and the cosine component Zc of the acceleration response 0 Acceleration response sinusoidal component Zs 0 Tc (n), ts (n), using the following formula:
ec(n)＝Zc(n)-F·Tc(n)
es(n)＝Zs(n)-F·Ts(n)
an acceleration response residual cosine component ec (n) and an acceleration response residual sine component es (n) are calculated.
Specifically, when the number of sensors for vibration control is N, a formula is used
The convergence residual err (n) is calculated.
Specifically, calculating an updated convergence coefficient u (n) according to the convergence residuals err (n), α and β specifically includes:
calculating an updated convergence coefficient u (n) according to the convergence residuals err (n), alpha and beta by using the following formula;
where α is an adjustment coefficient used for calculating the convergence coefficient, and β is an adjustment coefficient used for calculating the convergence coefficient.
Specifically, obtaining a transfer function T between an output force of an actuator in the active vibration control system and an acceleration response of a control sensor according to the current Tc (n) and Ts (n), specifically includes:
and obtaining a transfer function T between the output force of the actuator in the vibration active control system and the acceleration response of the control sensor by using a formula T (0) = [ Tc (0) Ts (0) ] according to the current Tc (n) and Ts (n).
In summary, the secondary path transfer function model of the vibration active control system can be identified more quickly and accurately by using the secondary path modeling method of the vibration active control system, and in the actual engineering, the calculation amount is small, the occupied resource is small, and the method is easy to implement.
Drawings
Fig. 1 is a flowchart of a secondary path model identification method provided in the present application.
Detailed Description
The application provides a method for modeling a secondary path of a vibration active control system, wherein the secondary path modeling is a transfer function for identifying the output force of an actuator in the vibration active control system to the acceleration response of a control sensor, and as shown in fig. 1, the implementation process is as follows:
step 101: determining output force F of an actuator in the vibration active control system;
in practical application, the amplitude of the output force is adjusted, so that the response magnitude of a sensor in the vibration active control system is about 0.2g.
Step 102: determining an output force frequency domain cosine component Fc and a frequency domain sine component Fs according to the output force F;
specifically, according to a formula Fc = F · cos (2 π F), calculating an output force frequency domain cosine component Fc;
calculating an output force frequency domain sinusoidal component Fs according to Fs = F · sin (2 pi F);
wherein f is the output force frequency of the actuator in the vibration active control system.
Step 103: according to control sensor acceleration response Z 0 Determining an initial value T of the secondary path transfer function 0 ；
Specifically, step 103 includes:
step 1031: collecting acceleration response Z at control sensor 0 Calculating the cosine component Zc of the acceleration response by frequency domain analysis 0 Acceleration response sinusoidal component Zs 0 ；
Step 1032: responding to cosine component Zc according to output force F and acceleration of actuator 0 Acceleration response sinusoidal component Zs 0 Using the formula of passage
T 0 ＝[Tc 0 Ts 0 ]
Calculating to obtain an initial value matrix T 0 。
It should be noted that the initial value matrix T 0 Is not a requirement for the initial value, but the moment is usedThe convergence rate of the secondary path identification can be increased.
Step 104: the initial value matrix T is divided into o Introducing an iterative formula, performing iterative calculation, and determining a secondary path model of each step;
Tc(n)＝Tc(n-1)-μ(n-1)·ec(n-1)
Ts(n)＝Ts(n-1)-μ(n-1)·es(n-1)
wherein n is the nth step iteration, mu is a convergence coefficient, es is an acceleration response residual sine component, ec is an acceleration response residual cosine component, tc (n) is a secondary channel transfer function cosine component, and Ts (n) is a secondary channel transfer function cosine component;
step 105: according to the output force F and the cosine component Zc of the acceleration response 0 Acceleration response sinusoidal component Zs 0 Tc (n), ts (n), calculating an acceleration response residual cosine component ec (n) and an acceleration response residual sine component es (n) using the following formulas;
ec(n)＝Zc(n)-F·Tc(n)
es(n)＝Zs(n)-F·Ts(n)。
step 106: according to the acceleration response residual cosine component ec (n) and the acceleration response residual sine component es (n), using a formula
The convergence residual err (n) is calculated.
Specifically, when the number of sensors for vibration control is N, a formula is used
The convergence residual err (n) is calculated.
Step 107: from the convergence residual err (n), the following formula is used:
and calculating an updated convergence coefficient u (n), wherein alpha is an adjusting coefficient used for calculating the convergence coefficient, and beta is an adjusting coefficient used for calculating the convergence coefficient.
In practical application, α and β need to be determined according to the requirements of residual error and convergence rate.
It is added that the convergence coefficient u (n) is calculated based on the variable step LMS algorithm.
Step 108: substituting the updated convergence coefficient u (n) into the following iterative formula again for iterative calculation;
Tc(n)＝Tc(n-1)-μ(n-1)·ec(n-1)
Ts(n)＝Ts(n-1)-μ(n-1)·es(n-1)。
it should be noted that the iterative calculation is realized by repeating step 105 to step 108.
Step 109: when the convergence residual error (n) is smaller than a preset value in iterative calculation, the secondary path model is considered to be converged completely until the response residual error is obtained, and the current Tc (n) and Ts (n) are obtained;
step 110: and obtaining a transfer function T between the output force of the actuator in the vibration active control system and the acceleration response of the control sensor by using a formula T (0) = [ Tc (0) Ts (0) ] according to the current Tc (n) and Ts (n).
In summary, the secondary path transfer function model of the vibration active control system can be identified more quickly and accurately by using the secondary path modeling method of the vibration active control system, and in the actual engineering, the calculation amount is small, the occupied resource is small, and the method is easy to implement.
Claims (8)
1. A method of modeling a secondary path of a vibratory active control system, the method comprising:
determining output force F of an actuator in the vibration active control system;
determining an output force frequency domain cosine component Fc and a frequency domain sine component Fs according to the output force F;
according to control sensor acceleration response Z 0 Determining an initial value T of the secondary path transfer function 0 ；
The initial value matrix T 0 And substituting the following iterative formula, performing iterative calculation, and determining a secondary path model of each step:
Tc(n)＝Tc(n-1)-μ(n-1)·ec(n-1)
Ts(n)＝Ts(n-1)-μ(n-1)·es(n-1)
wherein n is the nth step iteration, mu is a convergence coefficient, es is an acceleration response residual sine component, ec is an acceleration response residual cosine component, tc (n) is a secondary channel transfer function cosine component, and Ts (n) is a secondary channel transfer function cosine component;
according to the output force F and the cosine component Zc of the acceleration response 0 Acceleration response sinusoidal component Zs 0 Tc (n), ts (n), calculating an acceleration response residual cosine component ec (n) and an acceleration response residual sine component es (n);
calculating a convergence residual err (n) according to the acceleration response residual cosine component ec (n) and the acceleration response residual sine component es (n);
calculating an updated convergence coefficient u (n) according to the convergence residual err (n);
substituting the updated convergence coefficient u (n) into the iterative formula again for iterative calculation;
when iterative calculation is carried out, and the convergence residual error (n) is smaller than a preset value, the secondary path model is considered to be converged completely until response residual error is obtained, and current Tc (n) and Ts (n) are obtained;
and obtaining a transfer function T between the output force of the actuator in the vibration active control system and the acceleration response of the control sensor according to the current Tc (n) and Ts (n).
2. The method of claim 1, wherein determining the frequency domain cosine component Fc and the frequency domain sine component Fs of the output force based on the output force F comprises:
calculating the cosine component Fc of the output force frequency domain according to the formula Fc = F · cos (2 π F);
calculating an output force frequency domain sinusoidal component Fs according to Fs = F · sin (2 pi F);
wherein f is the output force frequency of the actuator in the vibration active control system.
3. The method of claim 1, wherein acceleration is based on a control sensorResponse Z 0 Determining an initial value T of the secondary path transfer function 0 The method specifically comprises the following steps:
collecting acceleration response Z at control sensor 0 Calculating the cosine component Zc of the acceleration response by frequency domain analysis 0 Acceleration response sinusoidal component Zs 0 ；
According to the output force F of the actuator and the cosine component Zc of the acceleration response 0 Acceleration response sinusoidal component Zs 0 Using the formula:
T 0 ＝[Tc 0 Ts 0 ]
calculating to obtain an initial value matrix T 0 。
4. The method of claim 1, wherein computing a convergence residual err (n) from the acceleration response residual cosine component ec (n) and the acceleration response residual sine component es (n) comprises:
according to the acceleration response residual cosine component ec (n) and the acceleration response residual sine component es (n), using a formula
The convergence residual err (n) is calculated.
5. A method according to claim 1, characterized in that the cosine component Zc of the acceleration response is determined from the output force F 0 Acceleration response sinusoidal component Zs 0 Tc (n), ts (n), calculating an acceleration response residual cosine component ec (n) and an acceleration response residual sine component es (n), and specifically comprising:
according to the output force F and the cosine component Zc of the acceleration response 0 Acceleration soundShould be sinusoidal with the component Zs 0 Tc (n), ts (n), using the following formula:
ec(n)＝Zc(n)-F·Tc(n)
es(n)＝Zs(n)-F·Ts(n)
an acceleration response residual cosine component ec (n) and an acceleration response residual sine component es (n) are calculated.
6. Method according to claim 1, characterized in that when the number of sensors for vibration control is N, a formula is used
The convergence residual err (n) is calculated.
7. The method according to claim 1, wherein calculating an updated convergence coefficient u (n) from the convergence residuals err (n), α, and β comprises:
calculating an updated convergence coefficient u (n) according to the convergence residuals err (n), alpha and beta by using the following formula;
where α is an adjustment coefficient used for calculating the convergence coefficient, and β is an adjustment coefficient used for calculating the convergence coefficient.
8. The method of claim 1, wherein obtaining a transfer function T between actuator output force in the active vibration control system and acceleration response of the control sensor based on the current Tc (n) and Ts (n), comprises:
and obtaining a transfer function T between the output force of the actuator in the vibration active control system and the acceleration response of the control sensor by using a formula T (0) = [ Tc (0) Ts (0) ] according to the current Tc (n) and Ts (n).
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