CN-121995747-A - LQG control method and system for integral configuration link

CN121995747ACN 121995747 ACN121995747 ACN 121995747ACN-121995747-A

Abstract

The invention relates to the technical field of load control, and discloses an LQG control method and system of an integral configuration link, which are used for obtaining an actually measured output vector, an expected output vector and a system state observation vector of a load control system in a current control period and constructing an integral performance index functional; the method comprises the steps of obtaining an augmented state space model and an augmented state estimation vector according to an original state space equation, a process noise covariance matrix, a measurement noise covariance matrix and a system state observation vector of a loading control system, establishing an extended Li Kadi differential equation based on the augmented state space model and an integral performance index functional to obtain an optimal feedback gain matrix, performing linear feedback operation on the augmented state estimation vector based on the optimal feedback gain matrix, generating a control instruction of the loading control system, and realizing static-difference-free optimal tracking, independent accurate setting of multi-channel integral intensity, adaptive optimization of controller parameters and robust stable operation under uncertainty.

Inventors

TANG DAOYU
WANG XIAODONG
LI ZHUFENG

Assignees

北京品创联拓科技有限公司

Dates

Publication Date: 20260508
Application Date: 20251226

Claims (10)

1. The LQG control method of the integral configuration link is characterized by comprising the following steps: Acquiring an actual measurement output vector, an expected output vector and a system state observation vector of a loading control system in a current control period, and constructing an integral performance index functional according to a deviation vector between the expected output vector and the actual measurement output vector, wherein the integral performance index functional comprises a state quadratic penalty term, a control energy penalty term and an output deviation integral penalty term; Obtaining an augmented state space model and an augmented state estimation vector of the load control system according to an original state space equation, a process noise covariance matrix, a measurement noise covariance matrix and the system state observation vector of the load control system; Based on the augmented state space model and the integral performance index functional, an extended Li Kadi differential equation is established, and an optimal feedback gain matrix is obtained by solving; And performing linear feedback operation on the augmented state estimation vector based on the optimal feedback gain matrix to generate a control instruction of the loading control system.
2. The LQG control method of an integral configuration link according to claim 1, wherein when constructing an integral performance index functional from a deviation vector between the expected output vector and the actually measured output vector, it includes: Determining the dimension of the expected output vector and the dimension of the actually measured output vector, and calculating real-time deviation components of the two dimensions on each output channel; Performing time integral operation on the real-time deviation component of each output channel to obtain an integral deviation state quantity of each channel; weighting the integral deviation state quantity based on a preset integral weight matrix to obtain the output deviation integral penalty term, wherein the integral weight matrix is a half positive diagonal matrix, and the dimension of the integral weight matrix is equal to the number of output channels; and carrying out time domain integration and summation on the state quadratic penalty term, the control energy penalty term and the output deviation integral penalty term to construct the integral performance index functional, wherein the integral time domain of the integral performance index functional is a continuous interval from zero time to terminal time.
3. The LQG control method of an integral configuration link according to claim 1, wherein when obtaining an augmented state space model and an augmented state estimation vector of the load control system according to an original state space equation, a process noise covariance matrix, a measurement noise covariance matrix, and the system state observation vector of the load control system, the LQG control method comprises: Introducing the deviation vector as an integral state variable, and establishing an augmented state space model, wherein the augmented state space model comprises an original state dynamic equation and an integral state dynamic equation; and constructing a Kalman filter based on the process noise covariance matrix, the measurement noise covariance matrix and the augmented state space model, and obtaining an augmented state estimation vector according to the Kalman filter and the system state observation vector.
4. The LQG control method of an integral configuration link according to claim 3, wherein when introducing the bias vector as an integral state variable, establishing an augmented state space model includes: Extracting a system matrix, an input matrix, an output matrix and a direct transmission matrix in the original state space equation, and determining the dimension of an original state vector; Taking the deviation vector as a newly added integral state vector, defining the derivative of the integral state vector as the deviation vector, and constructing an integral state dynamic equation; vertically splicing the original state vector and the integral state vector to obtain the augmented state vector, wherein the dimension of the augmented state vector is the sum of the original state dimension and the output dimension; and constructing the augmented state space model based on the system matrix, the input matrix and the output matrix, wherein the augmented state space model comprises an augmented system matrix, an augmented input matrix and an augmented output matrix.
5. The LQG control method of an integral configuration link according to claim 4, wherein when constructing a kalman filter based on the process noise covariance matrix, the measurement noise covariance matrix, and the augmented state space model, obtaining an augmented state estimation vector from the kalman filter and the system state observation vector comprises: Acquiring sensing measurement data of the loading control system in an off-line calibration stage, and estimating and obtaining initial values of the process noise covariance matrix and the measurement noise covariance matrix based on a statistical analysis method; expanding the process noise covariance matrix into an augmented process noise covariance matrix in the same dimension as the augmented state vector, and retaining the original dimension of the measurement noise covariance matrix; Constructing a Kalman filter based on the augmentation system matrix, the augmentation input matrix and the augmentation process noise covariance matrix; And constructing a measurement update equation of a Kalman filter based on the augmentation output matrix and the measurement noise covariance matrix to obtain an augmentation state estimation vector.
6. The LQG control method of an integral configuration link according to claim 1, wherein when establishing an extended Li Kadi differential equation based on an augmented state space model and the integral performance index functional, solving to obtain an optimal feedback gain matrix, the method comprises: Extracting a state weight matrix corresponding to the state quadratic penalty term, a control weight matrix corresponding to the control energy penalty term and an integral state weight submatrix corresponding to the output deviation integral penalty term from the integral performance index functional; constructing a combination weight matrix matched with the dimension of the augmented state space model, wherein the combination weight matrix consists of the state weight matrix, the integral state weight submatrix and a cross coupling term, and the cross coupling term is used for representing performance association between an original state and an integral state; Aiming at a continuous time system, establishing an extended Li Kadi differential equation corresponding to the augmentation system matrix, the combination weight matrix and the control weight matrix, and solving by using a reverse time integration method to obtain a symmetric positive solution matrix; Aiming at a discrete time system, establishing a corresponding expansion algebra Li-Ka-One equation, and solving by using an iterative numerical algorithm to obtain the solution matrix; And calculating the optimal feedback gain matrix based on the solution matrix, the augmented input matrix and the control weight matrix, wherein the optimal feedback gain matrix comprises an original state feedback sub-matrix and an integral state feedback sub-matrix.
7. The LQG control method of an integral configuration link according to claim 1, wherein when performing a linear feedback operation on the augmented state estimation vector based on the optimal feedback gain matrix, generating a control instruction of the load control system includes: Splitting the optimal feedback gain matrix into an original state feedback gain sub-matrix and an integral state feedback gain sub-matrix according to the block structures of the original state vector and the integral state vector; Performing matrix multiplication operation on the original state feedback gain submatrices and original state estimation components in the augmented state estimation vectors to obtain original state feedback components; Performing matrix multiplication operation on the integral state feedback gain submatrix and an integral state estimation component in the augmented state estimation vector to obtain an integral state feedback component; Vector superposition is carried out on the original state feedback component and the integral state feedback component, and a preset feedforward compensation term is added to generate the optimal control instruction; and converting the optimal control instruction into an actual control signal conforming to the object to be controlled through amplitude limiting processing and rate constraint processing, and taking the actual control signal as a control instruction of the loading control system, wherein the amplitude limiting processing comprises a dynamic adjustment mechanism of an upper amplitude limiting value and a lower amplitude limiting value.
8. The LQG control method of an integral configuration link according to claim 1, wherein after performing a linear feedback operation on the augmented state estimation vector based on the optimal feedback gain matrix, generating a control instruction of the load control system, further comprising: monitoring real-time tracking errors between the actual measurement output vector and the expected output vector of the loading control system, and calculating an absolute average value of the real-time tracking errors as a steady-state error index; And when the steady-state error index exceeds a preset error threshold value and the duration exceeds a preset time window, triggering an integral action intensity self-adaptive adjustment flow.
9. An LQG control system of an integral configuration link, applied to an LQG control method of an integral configuration link as set forth in any one of claims 1 to 8, comprising: The system comprises a first analysis module, a second analysis module and a third analysis module, wherein the first analysis module is used for acquiring an actual measurement output vector, an expected output vector and a system state observation vector of a loading control system in a current control period, and constructing an integral performance index functional according to a deviation vector between the expected output vector and the actual measurement output vector, and the integral performance index functional comprises a state quadratic penalty term, a control energy penalty term and an output deviation integral penalty term; the second analysis module is used for obtaining an augmented state space model and an augmented state estimation vector of the load control system according to the original state space equation, the process noise covariance matrix, the measurement noise covariance matrix and the system state observation vector of the load control system; The matrix solving module is used for establishing an extended Li Kadi differential equation based on the augmented state space model and the integral performance index functional, and solving to obtain an optimal feedback gain matrix; And the loading control module is used for carrying out linear feedback operation on the augmented state estimation vector based on the optimal feedback gain matrix and generating a control instruction of the loading control system.
10. The LQG control system of an integration configuration procedure according to claim 9, further comprising: the error adjustment module is used for: monitoring real-time tracking errors between the actual measurement output vector and the expected output vector of the loading control system, and calculating an absolute average value of the real-time tracking errors as a steady-state error index; And when the steady-state error index exceeds a preset error threshold value and the duration exceeds a preset time window, triggering an integral action intensity self-adaptive adjustment flow.

Description

LQG control method and system for integral configuration link Technical Field The invention relates to the technical field of loading control, in particular to an LQG control method and system of an integral configuration link. Background Linear quadratic gaussian control (LQG) is taken as a typical representative of a modern control theory, is widely applied to the fields of aerospace, precision manufacturing, electromechanical servo, chemical engineering process and the like through a separation design principle of optimal state estimation and optimal state feedback, and shows effective inhibition capability on random noise and good dynamic response characteristic. The existing LQG technology is mainly based on a cascade architecture of a linear quadratic regulator and a Kalman filter, and optimal gain is obtained by solving a Li-Kalman equation, so that recursive optimal control of a loading control system in a noise environment is realized. However, the traditional LQG control framework is inherently sensitive to constant disturbance and model parameter mismatch, and is difficult to thoroughly eliminate steady-state tracking errors, so that the performance of the traditional LQG control framework in a high-precision positioning and constant-value control scene is restricted. The existing improvement scheme generally adopts a mode of controlling an outer ring at LQG to independently connect in series with an integrator, but the structure fails to bring an integration link into a unified optimal performance index to carry out collaborative design, so that adjustment conflict is easy to generate between a dynamic response speed and steady-state precision due to state feedback gain and integration effect. In addition, in the multiple input multiple output system, the strong coupling characteristic among the control channels makes the integration effect difficult to be configured differently and accurately, partial channels are easy to generate excessive integration to cause continuous oscillation, partial channels are still poor due to insufficient integration, and meanwhile, the dynamic interaction of the system measurement noise and the integration state lacks a systematic inhibition mechanism, so that the overall control quality is further improved. Disclosure of Invention The embodiment of the invention provides an LQG control method and an LQG control system for an integral configuration link, which are used for solving the problems that the traditional LQG control has steady-state errors under constant disturbance, the outer loop integral and an optimal frame lack of collaborative design, the multi-variable system coupling channel integral effect is difficult to differentially configure and the robustness is insufficient when a model is in mismatch, and realizing the optimal tracking without static difference, independent accurate setting of multi-channel integral intensity, adaptive optimization of controller parameters and the robust stable operation of the system under the uncertainty of the model in a random noise environment. In order to achieve the above object, the present invention provides an LQG control method for an integral configuration link, including: Acquiring an actual measurement output vector, an expected output vector and a system state observation vector of a loading control system in a current control period, and constructing an integral performance index functional according to a deviation vector between the expected output vector and the actual measurement output vector, wherein the integral performance index functional comprises a state quadratic penalty term, a control energy penalty term and an output deviation integral penalty term; Obtaining an augmented state space model and an augmented state estimation vector of the load control system according to an original state space equation, a process noise covariance matrix, a measurement noise covariance matrix and the system state observation vector of the load control system; Based on the augmented state space model and the integral performance index functional, an extended Li Kadi differential equation is established, and an optimal feedback gain matrix is obtained by solving; And performing linear feedback operation on the augmented state estimation vector based on the optimal feedback gain matrix to generate a control instruction of the loading control system. Further, when constructing an integral performance index functional according to a deviation vector between the expected output vector and the actually measured output vector, the method includes: Determining the dimension of the expected output vector and the dimension of the actually measured output vector, and calculating real-time deviation components of the two dimensions on each output channel; Performing time integral operation on the real-time deviation component of each output channel to obtain an integral deviation state quantity of each channel; weighting