LQG control method and system of integral configuration link

Abstract

The invention relates to the technical field of loading control, and discloses an LQG control method and system for an integral configuration link, and the method comprises the steps: obtaining 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 type performance index functional; 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 the loading control system; based on the augmented state space model and the integral type performance index functional, establishing an extended Riccati differential equation to obtain an optimal feedback gain matrix; and performing linear feedback operation on the augmented state estimation vector based on the optimal feedback gain matrix, generating a control instruction of a loading control system, and realizing zero-static-error optimal tracking, independent and accurate setting of multi-channel integral intensity, adaptive optimization of controller parameters and robust stable operation under uncertainty.

Description

Technical Field

[0001] This invention relates to the field of loading control technology, and more specifically, to an LQG control method and system for an integral configuration stage. Background Technology

[0002] Linear quadratic Gaussian control (LQG), as a typical representative of modern control theory, has been widely used in aerospace, precision manufacturing, electromechanical servo and chemical processes through the design principle of separating optimal state estimation and optimal state feedback. It has shown effective suppression of random noise and good dynamic response characteristics.

[0003] Existing LQG technology is mainly based on a cascaded architecture of a linear quadratic regulator and a Kalman filter. It obtains the optimal gain by solving the Riccati equation, achieving recursive optimal control of the loaded control system in noisy environments. However, the traditional LQG control framework is inherently sensitive to constant disturbances and model parameter mismatches, making it difficult to completely eliminate steady-state tracking errors, thus limiting its performance in high-precision positioning and setpoint control scenarios. Existing improvement schemes typically employ an independent series integrator in the outer loop of the LQG control. However, this structure fails to incorporate the integral element into a unified optimal performance index for collaborative design, leading to adjustment conflicts between state feedback gain and integral action in terms of dynamic response speed and steady-state accuracy. Furthermore, in multi-input multi-output systems, the strong coupling characteristics between control channels make it difficult to precisely configure the integral action. Some channels are prone to over-integration leading to continuous oscillations, while others suffer from residual steady-state error due to under-integration. Simultaneously, the lack of a systematic suppression mechanism for the dynamic interaction between system measurement noise and integral state hinders further improvement in overall control quality. Summary of the Invention

[0004] This invention provides an LQG control method and system for integral configuration, which solves the problems of steady-state error under constant disturbance, lack of coordinated design between outer loop integral and optimal framework, difficulty in differentiated configuration of integral action of coupled channels in multivariable systems, and insufficient robustness under model mismatch in traditional LQG control. It achieves zero steady-state error optimal tracking under random noise environment, independent and accurate tuning of multi-channel integral intensity, adaptive optimization of controller parameters, and robust and stable operation of the system under model uncertainty.

[0005] To achieve the above objectives, the present invention provides an LQG control method for an integral configuration stage, comprising: The measured output vector, desired output vector, and system state observation vector of the loading control system in the current control cycle are obtained. Based on the deviation vector between the desired output vector and the measured output vector, an integral performance index functional is constructed. The integral performance index functional includes a state quadratic penalty term, a control energy penalty term, and an output deviation integral penalty term. Based on the original state-space equations, process noise covariance matrix, measurement noise covariance matrix, and system state observation vector of the loading control system, the augmented state-space model and augmented state estimation vector of the loading control system are obtained. Based on the augmented state-space model and the integral performance index functional, an extended Riccati differential equation is established, and the optimal feedback gain matrix is ​​obtained by solving it. Based on the optimal feedback gain matrix, a linear feedback operation is performed on the augmented state estimation vector to generate the control command of the loading control system.

[0006] Furthermore, when constructing the integral performance index functional based on the deviation vector between the expected output vector and the measured output vector, the following steps are included: Determine the dimension of the desired output vector and the dimension of the measured output vector, and calculate the real-time deviation components of the two dimensions on each output channel; Perform time integration on the real-time deviation component of each output channel to obtain the integral deviation state quantity of each channel; The integral deviation state quantity is weighted based on a preset integral weight matrix to obtain the output deviation integral penalty term. The integral weight matrix is ​​a positive semi-definite diagonal matrix and its dimension is equal to the number of output channels. The state quadratic penalty term, the control energy penalty term, and the output deviation integral penalty term are integrated in the time domain and summed to construct the integral performance index functional, wherein the integration time domain of the integral performance index functional is a continuous interval from time zero to the terminal time.

[0007] Further, when obtaining the augmented state-space model and augmented state estimation vector of the loading control system based on the original state-space equations, process noise covariance matrix, measurement noise covariance matrix, and system state observation vector of the loading control system, the process includes: The deviation vector is introduced as an integral state variable to establish an augmented state space model, which includes the original state dynamic equation and the integral state dynamic equation. A Kalman filter is constructed based on the process noise covariance matrix, the measurement noise covariance matrix, and the augmented state space model. An augmented state estimation vector is obtained based on the Kalman filter and the system state observation vector.

[0008] Furthermore, when introducing the deviation vector as an integral state variable to establish an augmented state-space model, the following steps are included: Extract the system matrix, input matrix, output matrix, and direct transfer matrix from the original state-space equations to determine the dimension of the original state vector; The deviation vector is used as a new integral state vector, and the derivative of the integral state vector is defined as the deviation vector itself, to construct the integral state dynamic equation. The original state vector and the integral state vector are vertically concatenated to obtain the augmented state vector, the dimension of which is the sum of the original state dimension and the output dimension. Based on the system matrix, the input matrix, and the output matrix, the augmented state space model is constructed, wherein the augmented state space model includes an augmented system matrix, an augmented input matrix, and an augmented output matrix.

[0009] Further, when constructing a Kalman filter based on the process noise covariance matrix, the measurement noise covariance matrix, and the augmented state-space model, and obtaining the augmented state estimation vector based on the Kalman filter and the system state observation vector, the process includes: The sensor measurement data of the loading control system during the offline calibration phase are collected, and the initial values ​​of the process noise covariance matrix and the measurement noise covariance matrix are estimated based on statistical analysis methods. The process noise covariance matrix is ​​expanded into an augmented process noise covariance matrix with the same dimension as the augmented state vector, while retaining the original dimension of the measurement noise covariance matrix; A Kalman filter is constructed based on the augmented system matrix, the augmented input matrix, and the augmented process noise covariance matrix. Based on the augmented output matrix and the measurement noise covariance matrix, the measurement update equation of the Kalman filter is constructed to obtain the augmented state estimation vector.

[0010] Furthermore, when establishing the extended Riccati differential equation based on the augmented state-space model and the integral performance index functional, and solving for the optimal feedback gain matrix, the following steps are included: Extract the state weight matrix corresponding to the state quadratic penalty term, the control weight matrix corresponding to the control energy penalty term, and the integral state weight submatrix corresponding to the output deviation integral penalty term from the integral performance index functional. Construct a combined weight matrix that matches the dimension of the augmented state space model. The combined weight matrix consists of the state weight matrix, the integral state weight submatrix, and a cross-coupling term. The cross-coupling term is used to characterize the performance correlation between the original state and the integral state. For a continuous-time system, an extended Riccati differential equation corresponding to the augmented system matrix, the combined weight matrix, and the control weight matrix is ​​established, and a symmetric positive definite solution matrix is ​​obtained by using the inverse time integration method. For discrete-time systems, the corresponding extended algebraic Riccati equation is established, and the solution matrix is ​​obtained by using an iterative numerical algorithm. Based on the solution matrix, the augmented input matrix, and the control weight matrix, the optimal feedback gain matrix is ​​calculated, which includes the original state feedback submatrix and the integral state feedback submatrix.

[0011] Further, when performing linear feedback operation on the augmented state estimation vector based on the optimal feedback gain matrix to generate the control command for the loading control system, the following steps are included: The optimal feedback gain matrix is ​​split into an original state feedback gain submatrix and an integral state feedback gain submatrix according to the block structure of the original state vector and the integral state vector. The original state feedback gain submatrix is ​​multiplied with the original state estimation component in the augmented state estimation vector to obtain the original state feedback component. The integral state feedback gain submatrix is ​​multiplied with the integral state estimation component in the augmented state estimation vector to obtain the integral state feedback component. The original state feedback component and the integral state feedback component are vector-superimposed, and a preset feedforward compensation term is added to generate the optimal control command. Through amplitude limiting and rate constraint processing, the optimal control command is converted into an actual control signal that conforms to the controlled object and serves as the control command of the loading control system. The amplitude limiting process includes a dynamic adjustment mechanism for the upper and lower amplitude values.

[0012] Furthermore, after performing linear feedback operation on the augmented state estimation vector based on the optimal feedback gain matrix to generate the control command for the loading control system, the method further includes: The real-time tracking error between the measured output vector and the desired output vector of the loading control system is monitored, and the absolute mean of the real-time tracking error is calculated as a steady-state error index. When the steady-state error index exceeds the preset error threshold and the duration exceeds the preset time window, the adaptive adjustment process of the integral action intensity is triggered.

[0013] To achieve the above objectives, the present invention also provides an LQG control system for an integral configuration stage, comprising: The first analysis module is used to obtain the measured output vector, the expected output vector, and the system state observation vector of the loading control system in the current control cycle, and to construct an integral performance index functional based on the deviation vector between the expected output vector and the measured output vector. The integral performance index functional includes a state quadratic penalty term, a control energy penalty term, and an output deviation integral penalty term. The second analysis module is used to obtain the augmented state space model and the augmented state estimation vector of the loading control system based on the original state space equation, process noise covariance matrix, measurement noise covariance matrix and system state observation vector of the loading control system. The matrix solving module is used to establish the extended Riccati differential equation based on the augmented state-space model and the integral performance index functional, and solve for the optimal feedback gain matrix. The loading control module is used to perform linear feedback calculation on the augmented state estimation vector based on the optimal feedback gain matrix, and generate control commands for the loading control system.

[0014] Furthermore, it also includes: Error adjustment module, used for: The real-time tracking error between the measured output vector and the desired output vector of the loading control system is monitored, and the absolute mean of the real-time tracking error is calculated as a steady-state error index. When the steady-state error index exceeds the preset error threshold and the duration exceeds the preset time window, the adaptive adjustment process of the integral action intensity is triggered.

[0015] Compared with the prior art, the beneficial effects of the present invention are as follows: This invention discloses an LQG control method and system for an integral configuration stage. It obtains the measured output vector, desired output vector, and system state observation vector of the loaded control system within the current control cycle, and constructs an integral performance index functional. Based on the original state-space equations, process noise covariance matrix, measurement noise covariance matrix, and system state observation vector of the loaded control system, an augmented state-space model and an augmented state estimation vector are obtained. Based on the augmented state-space model and the integral performance index functional, an extended Riccati differential equation is established, and the optimal feedback gain matrix is ​​obtained by solving it. Based on the optimal feedback gain matrix, a linear feedback operation is performed on the augmented state estimation vector to generate control commands for the loaded control system, achieving zero steady-state error optimal tracking, independent and accurate tuning of multi-channel integral strengths, adaptive optimization of controller parameters, and robust stable operation under uncertainty. Attached Figure Description

[0016] Various other advantages and benefits will become apparent to those skilled in the art upon reading the following detailed description of preferred embodiments. The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Furthermore, the same reference numerals denote the same parts throughout the drawings. In the drawings: Figure 1 A flowchart illustrating an LQG control method for an integral configuration stage according to an embodiment of the present invention is shown. Figure 2 A schematic diagram of the structure of an LQG control system for an integral configuration stage is shown in an embodiment of the present invention. Detailed Implementation

[0017] The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples. The following examples are for illustrative purposes only and are not intended to limit the scope of the invention.

[0018] In the description of this application, it should be understood that the terms "center", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this application and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this application.

[0019] The terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Therefore, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this application, unless otherwise stated, "a plurality of" means two or more.

[0020] In the description of this application, it should be noted that, unless otherwise expressly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection between two components. Those skilled in the art can understand the specific meaning of the above terms in this application based on the specific circumstances.

[0021] The following is a description of preferred embodiments of the present invention in conjunction with the accompanying drawings.

[0022] like Figure 1 As shown, an embodiment of the present invention discloses an LQG control method for an integral configuration stage, comprising: S110: Obtain the measured output vector, the desired output vector, and the system state observation vector of the loading control system in the current control cycle, and construct an integral performance index functional based on the deviation vector between the desired output vector and the measured output vector. The integral performance index functional includes a state quadratic penalty term, a control energy penalty term, and an output deviation integral penalty term. S120: Based on the original state-space equations, process noise covariance matrix, measurement noise covariance matrix, and system state observation vector of the loading control system, obtain the augmented state-space model and augmented state estimation vector of the loading control system. S130: Based on the augmented state-space model and the integral performance index functional, an extended Riccati differential equation is established, and the optimal feedback gain matrix is ​​obtained by solving it. S140: Perform linear feedback operation on the augmented state estimation vector based on the optimal feedback gain matrix to generate control commands for the loading control system.

[0023] In this embodiment, the measured output vector refers to the system response data actually collected by sensors, such as the position signal fed back by the motor encoder or the current signal collected by the current sensor. The desired output vector refers to the target trajectory or setpoint that the control system hopes to achieve. The system state observation vector refers to the estimated internal state of the system obtained by the state observer or sensor fusion algorithm. The deviation vector is obtained by vector subtraction and reflects the gap between the actual system performance and the desired target. The integral performance index functional is a mathematical framework for evaluating control quality. Its characteristic is that it introduces a penalty for the cumulative deviation, which can effectively eliminate steady-state error. The augmented state-space model is achieved by extending the dimension of the original state vector, incorporating the deviation integral as a new state variable into the system dynamic description, forming a unified model that includes the original dynamics and integral dynamics. The Kalman filter performs optimal estimation of the system state based on the noise statistics, effectively suppressing the influence of measurement noise and process disturbances. The extended Riccati equation is the core tool for solving the optimal control law, and its solution matrix contains state feedback weight information. The optimal feedback gain matrix is ​​obtained through matrix operations, and its dimension matches the augmented state vector, realizing joint feedback regulation of the original state and integral state. The optimal control command provides the actuator with physical control quantities such as voltage, torque or flow.

[0024] The beneficial effects of the above technical solution are as follows: By constructing a performance index that includes deviation integral penalty, the steady-state error defect of traditional LQG control is fundamentally solved. The introduction of an augmented state-space model achieves systematic fusion of the integral element, rather than simple outer-loop superposition. The coordinated design of the Kalman filter and the optimal control law ensures optimality and robustness under random noise environments.

[0025] In some embodiments of this application, when constructing an integral performance index functional based on the deviation vector between the expected output vector and the measured output vector, the following steps are included: Determine the dimension of the desired output vector and the dimension of the measured output vector, and calculate the real-time deviation components of the two dimensions on each output channel; Perform time integration on the real-time deviation component of each output channel to obtain the integral deviation state quantity of each channel; The integral deviation state quantity is weighted based on a preset integral weight matrix to obtain the output deviation integral penalty term. The integral weight matrix is ​​a positive semi-definite diagonal matrix and its dimension is equal to the number of output channels. The state quadratic penalty term, the control energy penalty term, and the output deviation integral penalty term are integrated in the time domain and summed to construct the integral performance index functional, wherein the integral time domain of the integral performance index functional is a continuous interval or a discrete sampling point sequence from time zero to the terminal time.

[0026] In this embodiment, the number of output channels is determined by the number of controlled variables in the controlled system. For example, a two-axis motion platform includes two channels: X-axis position and Y-axis position. Real-time deviation components are obtained through period-by-per-sampling calculations, and integration can be performed using numerical integration methods, such as trapezoidal integration or rectangular integration. The diagonal elements of the integral weight matrix reflect the steady-state accuracy requirements of different output channels, assigning greater weights to channels with higher accuracy requirements. The state quadratic form penalty term is used to limit overshoot and oscillation of the state variables; its weight matrix is ​​typically a diagonal matrix. The control energy penalty term is used to limit the amplitude of the control variable to avoid actuator saturation. The selection of the integral time domain depends on the characteristics of the control task; a finite time domain is used during the adjustment process, while an infinite time domain or a rolling time domain is used for steady-state operation.

[0027] The beneficial effects of the above technical solution are as follows: By separating the integral deviation state variables of each output channel, the steady-state accuracy of the multivariable system is decoupled and configured. The design of the semi-definite diagonal weight matrix allows for independent adjustment of the integral action intensity of each channel according to process requirements. Integrating the integral penalty term along with the state and control penalty terms into the performance index ensures the globality of the optimal solution and avoids stability conflicts that may be caused by hierarchical design.

[0028] In some embodiments of this application, when obtaining the augmented state-space model and augmented state estimation vector of the loading control system based on the original state-space equations of the loading control system, the process noise covariance matrix, the measurement noise covariance matrix, and the system state observation vector, the process includes: The deviation vector is introduced as an integral state variable to establish an augmented state space model, which includes the original state dynamic equation and the integral state dynamic equation. A Kalman filter is constructed based on the process noise covariance matrix, the measurement noise covariance matrix, and the augmented state space model. An augmented state estimation vector is obtained based on the Kalman filter and the system state observation vector.

[0029] In some embodiments of this application, when introducing the deviation vector as an integral state variable to establish an augmented state-space model, the following is included: Extract the system matrix, input matrix, output matrix, and direct transfer matrix from the original state-space equations to determine the dimension of the original state vector; The deviation vector is used as a new integral state vector, and the derivative of the integral state vector is defined as the deviation vector itself, to construct the integral state dynamic equation. The original state vector and the integral state vector are vertically concatenated to obtain the augmented state vector, the dimension of which is the sum of the original state dimension and the output dimension. Based on the system matrix, the input matrix, and the output matrix, the augmented state space model is constructed, wherein the augmented state space model includes an augmented system matrix, an augmented input matrix, and an augmented output matrix.

[0030] In this embodiment, the upper right sub-block of the augmented system matrix is ​​set to a negative identity matrix to achieve dynamic coupling of the deviation integral feedback channel. The original state-space equations are obtained through mechanistic modeling or system identification; for example, a motor system contains a dynamic chain of voltage-current-torque-motion. The system matrix describes the interaction between state variables, the input matrix describes the influence of control quantities on the state, the output matrix describes the mapping relationship from state to output, and the direct transmission matrix describes the direct effect of control quantities on the output. The derivative definition of the integral state vector reflects the basic properties of the integrator. The vertical splicing operation is mathematically represented by the stacking of block matrices. The upper left sub-block of the augmented system matrix is ​​the original system matrix, the lower left is the zero matrix, the upper right is the negative identity matrix, and the lower right is the zero matrix. This structure ensures that the integral state is dynamically and correctly coupled to the original state deviation. The upper part of the augmented input matrix is ​​the original input matrix, and the lower part is the zero matrix. The augmented output matrix includes the original output part and the integral state feedback part.

[0031] The beneficial effects of the above technical solution are as follows: The method for constructing the augmented state-space model achieves standardized embedding of the integral state, making the integral element an intrinsic dynamic of the system rather than an external addition. The ingenious configuration of the negative identity matrix establishes a direct path from the initial state deviation to the growth of the integral state, which conforms to the error accumulation mechanism of the integrator in traditional control. The structured design of the block matrix facilitates implementation in engineering software and can be quickly constructed through matrix concatenation functions. This modeling method preserves all dynamic information of the original system while expanding the state dimension, providing a complete system description for unified optimal control design.

[0032] In some embodiments of this application, when constructing a Kalman filter based on the process noise covariance matrix, the measurement noise covariance matrix, and the augmented state-space model, and obtaining the augmented state estimation vector based on the Kalman filter and the system state observation vector, the process includes: The sensor measurement data of the loading control system during the offline calibration phase are collected, and the initial values ​​of the process noise covariance matrix and the measurement noise covariance matrix are estimated based on statistical analysis methods. The process noise covariance matrix is ​​expanded into an augmented process noise covariance matrix with the same dimension as the augmented state vector, while retaining the original dimension of the measurement noise covariance matrix; A Kalman filter is constructed based on the augmented system matrix, the augmented input matrix, and the augmented process noise covariance matrix. Based on the augmented output matrix and the measurement noise covariance matrix, the measurement update equation of the Kalman filter is constructed to obtain the augmented state estimation vector.

[0033] In this embodiment, offline calibration is performed during the system debugging phase, calculating the mean, variance, and covariance by recording sensor data sequences. During the online steady-state operation phase, data statistical characteristics within a sliding time window are used for real-time updates. The diagonal elements of the process noise covariance matrix reflect the disturbance intensity of each state channel, while the off-diagonal elements reflect the coupling disturbance between channels. The measurement noise covariance matrix describes the sensor's own measurement uncertainty. The lower half of the augmented process noise covariance matrix is ​​a zero block because the integral state dynamics are deterministic differential equations, unaffected by random noise. The time update equation includes two stages: state prediction and covariance prediction, achieved through the state transition effect of the augmented system matrix. The measurement update equation uses the residual between the actual and predicted measurements, weighted by Kalman gain, to correct the state estimate. The calculation of the Kalman gain matrix involves a trade-off between the relative magnitudes of the estimation error covariance matrix and the measurement noise covariance matrix.

[0034] The beneficial effects of the above technical solution are as follows: The strategy of combining offline calibration with online updates ensures the accuracy of noise statistical characteristics and avoids the degradation of filtering performance caused by model mismatch. The reasonable expansion of the augmented noise covariance matrix maintains consistency with the augmented state model, enabling the filter to correctly estimate the integral state. The two-stage structure of time update and measurement update achieves recursive optimal estimation of the stochastic process, significantly reducing the impact of measurement noise on state feedback. Real-time calculation of the Kalman gain enables the filter to have adaptive capabilities, maintaining high estimation accuracy even when noise characteristics change, providing reliable augmented state information for subsequent optimal control.

[0035] In some embodiments of this application, when establishing the extended Riccati differential equation based on the augmented state-space model and the integral performance index functional, and solving for the optimal feedback gain matrix, the following steps are included: Extract the state weight matrix corresponding to the state quadratic penalty term, the control weight matrix corresponding to the control energy penalty term, and the integral state weight submatrix corresponding to the output deviation integral penalty term from the integral performance index functional. Construct a combined weight matrix that matches the dimension of the augmented state space model. The combined weight matrix consists of the state weight matrix, the integral state weight submatrix, and a cross-coupling term. The cross-coupling term is used to characterize the performance correlation between the original state and the integral state. For a continuous-time system, an extended Riccati differential equation corresponding to the augmented system matrix, the combined weight matrix, and the control weight matrix is ​​established, and a symmetric positive definite solution matrix is ​​obtained by using the inverse time integration method. For discrete-time systems, the corresponding extended algebraic Riccati equation is established, and the solution matrix is ​​obtained by using an iterative numerical algorithm. Based on the solution matrix, the augmented input matrix, and the control weight matrix, the optimal feedback gain matrix is ​​calculated, which includes the original state feedback submatrix and the integral state feedback submatrix.

[0036] In this embodiment, the state weight matrix is ​​typically a diagonal matrix, with the size of its diagonal elements reflecting the degree of importance given to each state component. The control weight matrix determines the penalty strength of the control energy; a larger value results in a more conservative control action. The integral state weight submatrix directly affects the rate of steady-state error elimination; a larger weight results in a stronger integral effect. Cross-coupling terms can be set as a zero matrix in most cases to simplify the design process, but under specific performance requirements, they can be used to adjust the mutual influence between the original state and the integral state. The extended Riccati differential equation of a continuous-time system is solved by inverse-time numerical integration, degenerating into an algebraic equation in steady state. The extended algebraic Riccati equation of a discrete-time system is solved by iterative iteration until the solution matrix converges, or by using matrix eigenvalue decomposition to obtain an analytical solution. The symmetric positive definiteness of the solution matrix ensures the stability of the closed-loop system. The left half of the optimal feedback gain matrix acts on the original state estimation to achieve dynamic compensation; the right half acts on the integral state estimation to achieve zero steady-state error tracking.

[0037] The beneficial effects of the above technical solution are as follows: The structured design of the combined weight matrix ensures that the performance index perfectly matches the augmented state model, guaranteeing the accuracy of the optimal solution. The establishment of the extended Riccati equation extends the traditional LQG method to a generalized performance index framework that includes integral penalties, expanding the theoretical applicability. The selection of numerical solution methods balances computational efficiency and solution accuracy; inverse time integration is suitable for finite-time domain regulation problems, while iterative algorithms are suitable for infinite-time domain steady-state problems. The block structure of the optimal feedback gain matrix has clear physical meaning, facilitating engineers' understanding of the different roles of original state feedback and integral state feedback, and also allowing for the recalculation of only a portion of the gain when adjusting the integral weights online, reducing the computational burden.

[0038] In some embodiments of this application, when performing linear feedback operation on the augmented state estimation vector based on the optimal feedback gain matrix to generate control commands for the loading control system, the following steps are included: The optimal feedback gain matrix is ​​split into an original state feedback gain submatrix and an integral state feedback gain submatrix according to the block structure of the original state vector and the integral state vector. The original state feedback gain submatrix is ​​multiplied with the original state estimation component in the augmented state estimation vector to obtain the original state feedback component. The integral state feedback gain submatrix is ​​multiplied with the integral state estimation component in the augmented state estimation vector to obtain the integral state feedback component. The original state feedback component and the integral state feedback component are vector-superimposed, and a preset feedforward compensation term or disturbance suppression term is added to generate the optimal control command. Through amplitude limiting and rate constraint processing, the optimal control command is converted into an actual control signal that conforms to the controlled object and serves as the control command of the loading control system. The amplitude limiting process includes a dynamic adjustment mechanism for the upper and lower amplitude values.

[0039] In this embodiment, the feedforward compensation term can be pre-calculated based on the known dynamic characteristics of the desired trajectory to improve the tracking response speed. The disturbance suppression term is constructed based on the system disturbance estimated by the observer to counteract the influence of external disturbances. The amplitude range of the limiting process is set according to the rated operating range of the actuator, such as the voltage output range of a motor driver. The rate constraint process limits the rate of change of the control command to prevent mechanical shock to the actuator. The dynamic adjustment mechanism allows the limiting boundary to change smoothly according to the system operating state, for example, relaxing the limit during the startup phase to speed up the response and tightening the limit during the steady-state phase to enhance safety. Matrix multiplication is performed once in each control cycle, and the computational load is proportional to the square of the state dimension.

[0040] The beneficial effects of the above technical solution are as follows: Block feedback computation achieves decoupled calculation between the original state and the integral state, facilitating modular software implementation. The addition of feedforward and disturbance suppression terms combines the passive adjustment characteristics of optimal feedback with active compensation capabilities, significantly improving the dynamic tracking accuracy and anti-interference ability of the system. Amplitude limiting and rate constraint processing ensure that the theoretically optimal control command can be safely applied to the physical system, avoiding mechanical damage.

[0041] In some embodiments of this application, after performing linear feedback operation on the augmented state estimation vector based on the optimal feedback gain matrix to generate the control command of the loading control system, the method further includes: The real-time tracking error between the measured output vector and the desired output vector of the loading control system is monitored, and the absolute mean of the real-time tracking error is calculated as a steady-state error index. When the steady-state error index exceeds the preset error threshold and the duration exceeds the preset time window, the adaptive adjustment process of the integral action intensity is triggered.

[0042] In this embodiment, the absolute mean is calculated by averaging the absolute value of the tracking error over a time window, and the root mean square is calculated by averaging the squared errors and then taking the square root. A preset error threshold is set according to process requirements; for example, if the positioning accuracy requirement is 0.01mm, the threshold can be set to 0.005mm. A preset time window is used to prevent misjudgments triggered by instantaneous disturbances, typically ranging from 10 to 50 control cycles. The rate of change is obtained through differential or derivative calculations, and the direction of change is determined by the error sign sequence. The monotonic mapping relationship can be achieved through a lookup table or linear interpolation; for example, if the error increases by 10%, the integral weight increases by 5%. The parameter adaptive optimization process can be executed in a background thread to avoid interrupting real-time control. The updated optimal feedback gain matrix is ​​put into use using a smooth switching strategy to prevent sudden changes in control input.

[0043] The beneficial effects of the above technical solution are as follows: Online monitoring of steady-state error indicators enables real-time quantitative evaluation of control performance, providing a trigger basis for adaptive adjustment. Analysis of error change trends allows the integral action strength to dynamically match the actual system requirements, avoiding the inadequacy of fixed integral weights under changing operating conditions. The monotonic mapping adjustment strategy is simple, reliable, easy to implement in engineering, and conforms to control intuition. The entire adaptive process forms a closed loop of performance monitoring, parameter adjustment, and control law update, enabling the LQG controller to possess self-optimization capabilities. It can maintain high performance even when system parameters drift or load changes, extending the controller's uninterrupted operating time and reducing maintenance costs.

[0044] To further illustrate the technical concept of this invention, the technical solution of this invention will now be described in conjunction with specific application scenarios.

[0045] Correspondingly, such as Figure 2 As shown, this application also provides an LQG control system for an integral configuration stage, including: The first analysis module is used to obtain the measured output vector, the expected output vector, and the system state observation vector of the loading control system in the current control cycle, and to construct an integral performance index functional based on the deviation vector between the expected output vector and the measured output vector. The integral performance index functional includes a state quadratic penalty term, a control energy penalty term, and an output deviation integral penalty term. The second analysis module is used to obtain the augmented state space model and the augmented state estimation vector of the loading control system based on the original state space equation, process noise covariance matrix, measurement noise covariance matrix and system state observation vector of the loading control system. The matrix solving module is used to establish the extended Riccati differential equation based on the augmented state-space model and the integral performance index functional, and solve for the optimal feedback gain matrix. The loading control module is used to perform linear feedback calculation on the augmented state estimation vector based on the optimal feedback gain matrix, and generate control commands for the loading control system.

[0046] In some embodiments of this application, it also includes: Error adjustment module, used for: The real-time tracking error between the measured output vector and the desired output vector of the loading control system is monitored, and the absolute mean of the real-time tracking error is calculated as a steady-state error index. When the steady-state error index exceeds the preset error threshold and the duration exceeds the preset time window, the adaptive adjustment process of the integral action intensity is triggered.

[0047] In the description of the above embodiments, specific features, structures, materials, or characteristics may be combined in any suitable manner in one or more embodiments or examples.

[0048] Although the invention has been described above with reference to embodiments, various modifications can be made and components can be replaced with equivalents without departing from the scope of the invention. In particular, as long as there is no structural conflict, the features in the embodiments disclosed in this invention can be combined with each other in any way. The fact that not all of these combinations are described in this specification is merely for the sake of brevity and resource conservation.

[0049] It will be understood by those skilled in the art that the above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. An LQG control method for an integral configuration stage, characterized in that, include: The measured output vector, desired output vector, and system state observation vector of the loading control system in the current control cycle are obtained. Based on the deviation vector between the desired output vector and the measured output vector, an integral performance index functional is constructed. The integral performance index functional includes a state quadratic penalty term, a control energy penalty term, and an output deviation integral penalty term. Based on the original state-space equations, process noise covariance matrix, measurement noise covariance matrix, and system state observation vector of the loading control system, the augmented state-space model and augmented state estimation vector of the loading control system are obtained. Based on the augmented state-space model and the integral performance index functional, an extended Riccati differential equation is established, and the optimal feedback gain matrix is ​​obtained by solving it. Based on the optimal feedback gain matrix, a linear feedback operation is performed on the augmented state estimation vector to generate the control command of the loading control system.

2. The LQG control method for the integral configuration stage according to claim 1, characterized in that, When constructing an integral performance index functional based on the deviation vector between the expected output vector and the measured output vector, the following steps are included: Determine the dimension of the desired output vector and the dimension of the measured output vector, and calculate the real-time deviation components of the two dimensions on each output channel; Perform time integration on the real-time deviation component of each output channel to obtain the integral deviation state quantity of each channel; The integral deviation state quantity is weighted based on a preset integral weight matrix to obtain the output deviation integral penalty term. The integral weight matrix is ​​a positive semi-definite diagonal matrix and its dimension is equal to the number of output channels. The state quadratic penalty term, the control energy penalty term, and the output deviation integral penalty term are integrated in the time domain and summed to construct the integral performance index functional, wherein the integration time domain of the integral performance index functional is a continuous interval from time zero to the terminal time.

3. The LQG control method for the integral configuration stage according to claim 1, characterized in that, When obtaining the augmented state-space model and augmented state estimation vector of the loading control system based on the original state-space equations, process noise covariance matrix, measurement noise covariance matrix, and system state observation vector, the process includes: The deviation vector is introduced as an integral state variable to establish an augmented state space model, which includes the original state dynamic equation and the integral state dynamic equation. A Kalman filter is constructed based on the process noise covariance matrix, the measurement noise covariance matrix, and the augmented state space model. An augmented state estimation vector is obtained based on the Kalman filter and the system state observation vector.

4. The LQG control method for the integral configuration stage according to claim 3, characterized in that, When introducing the deviation vector as an integral state variable to establish an augmented state-space model, the following is included: Extract the system matrix, input matrix, output matrix, and direct transfer matrix from the original state-space equations to determine the dimension of the original state vector; The deviation vector is used as a new integral state vector, and the derivative of the integral state vector is defined as the deviation vector itself, to construct the integral state dynamic equation. The original state vector and the integral state vector are vertically concatenated to obtain the augmented state vector, the dimension of which is the sum of the original state dimension and the output dimension. Based on the system matrix, the input matrix, and the output matrix, the augmented state space model is constructed, wherein the augmented state space model includes an augmented system matrix, an augmented input matrix, and an augmented output matrix.

5. The LQG control method for the integral configuration stage according to claim 4, characterized in that, When constructing a Kalman filter based on the process noise covariance matrix, the measurement noise covariance matrix, and the augmented state-space model, and obtaining the augmented state estimation vector based on the Kalman filter and the system state observation vector, the process includes: The sensor measurement data of the loading control system during the offline calibration phase are collected, and the initial values ​​of the process noise covariance matrix and the measurement noise covariance matrix are estimated based on statistical analysis methods. The process noise covariance matrix is ​​expanded into an augmented process noise covariance matrix with the same dimension as the augmented state vector, while retaining the original dimension of the measurement noise covariance matrix; A Kalman filter is constructed based on the augmented system matrix, the augmented input matrix, and the augmented process noise covariance matrix. Based on the augmented output matrix and the measurement noise covariance matrix, the measurement update equation of the Kalman filter is constructed to obtain the augmented state estimation vector.

6. The LQG control method for the integral configuration stage according to claim 1, characterized in that, When establishing the extended Riccati differential equation based on the augmented state-space model and the integral performance index functional, and solving for the optimal feedback gain matrix, the following steps are included: Extract the state weight matrix corresponding to the state quadratic penalty term, the control weight matrix corresponding to the control energy penalty term, and the integral state weight submatrix corresponding to the output deviation integral penalty term from the integral performance index functional. Construct a combined weight matrix that matches the dimension of the augmented state space model. The combined weight matrix consists of the state weight matrix, the integral state weight submatrix, and a cross-coupling term. The cross-coupling term is used to characterize the performance correlation between the original state and the integral state. For a continuous-time system, an extended Riccati differential equation corresponding to the augmented system matrix, the combined weight matrix, and the control weight matrix is ​​established, and a symmetric positive definite solution matrix is ​​obtained by using the inverse time integration method. For discrete-time systems, the corresponding extended algebraic Riccati equation is established, and the solution matrix is ​​obtained by using an iterative numerical algorithm. Based on the solution matrix, the augmented input matrix, and the control weight matrix, the optimal feedback gain matrix is ​​calculated, which includes the original state feedback submatrix and the integral state feedback submatrix.

7. The LQG control method for the integral configuration stage according to claim 1, characterized in that, When performing linear feedback operation on the augmented state estimation vector based on the optimal feedback gain matrix to generate control commands for the loading control system, the following steps are included: The optimal feedback gain matrix is ​​split into an original state feedback gain submatrix and an integral state feedback gain submatrix according to the block structure of the original state vector and the integral state vector. The original state feedback gain submatrix is ​​multiplied with the original state estimation component in the augmented state estimation vector to obtain the original state feedback component. The integral state feedback gain submatrix is ​​multiplied with the integral state estimation component in the augmented state estimation vector to obtain the integral state feedback component. The original state feedback component and the integral state feedback component are vector-superimposed, and a preset feedforward compensation term is added to generate the optimal control command. Through amplitude limiting and rate constraint processing, the optimal control command is converted into an actual control signal that conforms to the controlled object and serves as the control command of the loading control system. The amplitude limiting process includes a dynamic adjustment mechanism for the upper and lower amplitude values.

8. The LQG control method for the integral configuration stage according to claim 1, characterized in that, After performing linear feedback operation on the augmented state estimation vector based on the optimal feedback gain matrix to generate the control command for the loading control system, the method further includes: The real-time tracking error between the measured output vector and the desired output vector of the loading control system is monitored, and the absolute mean of the real-time tracking error is calculated as a steady-state error index. When the steady-state error index exceeds the preset error threshold and the duration exceeds the preset time window, the adaptive adjustment process of the integral action intensity is triggered.

9. An LQG control system for an integral configuration stage, applied to the LQG control method for the integral configuration stage as described in any one of claims 1-8, characterized in that, include: The first analysis module is used to obtain the measured output vector, the expected output vector, and the system state observation vector of the loading control system in the current control cycle, and to construct an integral performance index functional based on the deviation vector between the expected output vector and the measured output vector. The integral performance index functional includes a state quadratic penalty term, a control energy penalty term, and an output deviation integral penalty term. The second analysis module is used to obtain the augmented state space model and the augmented state estimation vector of the loading control system based on the original state space equation, process noise covariance matrix, measurement noise covariance matrix and system state observation vector of the loading control system. The matrix solving module is used to establish the extended Riccati differential equation based on the augmented state-space model and the integral performance index functional, and solve for the optimal feedback gain matrix. The loading control module is used to perform linear feedback calculation on the augmented state estimation vector based on the optimal feedback gain matrix, and generate control commands for the loading control system.

10. The LQG control system for the integral configuration stage according to claim 9, characterized in that, Also includes: Error adjustment module, used for: The real-time tracking error between the measured output vector and the desired output vector of the loading control system is monitored, and the absolute mean of the real-time tracking error is calculated as a steady-state error index. When the steady-state error index exceeds the preset error threshold and the duration exceeds the preset time window, the adaptive adjustment process of the integral action intensity is triggered.

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