An elastic control method for linear uncertain systems based on multi-rate state measurement information

Abstract

This invention discloses an elastic control method for linear uncertain systems based on multi-rate state measurement information. The method includes establishing a linear dynamic model and a state estimation model based on multi-rate state measurement information of the controlled system; acquiring state measurement information of the controlled system; resetting the state of the state estimation model based on the state measurement information; designing an elastic control law based on the linear dynamic model and the state estimation model; inputting control commands based on the elastic control law into the actuator to stabilize the state of the controlled system; and controlling the system with a period T. s The above process is repeated at intervals until control ends. This invention can maintain stable system operation even when there are parameter uncertainties, actuator errors, and irregular updates of state measurement information.

Description

Technical Field

[0001] This invention relates to the fields of control science and engineering technology, and in particular to an elastic control method for linear uncertain systems based on multi-rate state measurement information. Background Technology

[0002] In many practical engineering systems, such as industrial automation control systems, networked control systems, and intelligent equipment control systems, the controlled system is often affected by factors such as system parameter perturbations, external disturbances, and actuator errors, which may lead to a decline in system performance or even instability. Therefore, improving the stability and robustness of control systems under uncertain environments has become an important topic in control theory research.

[0003] On the other hand, in practical networked control systems, due to factors such as communication bandwidth limitations, network congestion, and data transmission interference, the controller often struggles to acquire the state measurement information of the controlled system at fixed intervals, resulting in a multi-rate characteristic in the state sampling time interval. This multi-rate measurement characteristic can adversely affect the stability of the control system.

[0004] Currently, control methods for uncertain systems mainly include robust control, fault-tolerant control, and disturbance observation control. However, these methods are typically based on the assumption that the controller can acquire the state information of the controlled system at a fixed sampling period. In practical engineering applications, due to the uncertainty of communication networks and the limitation of transmission bandwidth, it is often difficult to acquire state measurement information at a fixed period, resulting in randomness or uncertainty in the state sampling time.

[0005] Furthermore, while some existing control methods consider system parameter perturbations or actuator errors, they rarely simultaneously consider the impact of multi-rate state measurement information and actuator input perturbations on system stability. Therefore, in practical networked control environments, the robustness of existing methods remains insufficient. To address this, a flexible control method is needed that can maintain stable system operation even with parameter uncertainties, actuator errors, and irregular updates to state measurement information, applicable to industrial automation control systems, networked control systems, and intelligent equipment control systems. Summary of the Invention

[0006] Purpose of the invention: The purpose of this invention is to provide an elastic control method for linear uncertain systems based on multi-rate state measurement information, which can maintain stable system operation even when there are parameter uncertainties, actuator errors, and irregular updates of state measurement information.

[0007] Technical solution: To achieve the above objectives, the present invention provides an elastic control method for linear uncertain systems based on multi-rate state measurement information, comprising:

[0008] Step 1: Establish a linear dynamic model of the controlled system;

[0009] Step 2: Establish a state estimation model based on multi-rate state measurement information;

[0010] Step 3: Obtain the state measurement information of the controlled system;

[0011] Step 4: Reset the state of the state estimation model based on the state measurement information;

[0012] Step 5: Design the elastic control law based on the linear dynamics model and the state estimation model;

[0013] Step 6: Input the control command based on the elastic control law into the actuator to stabilize the state of the controlled system;

[0014] Step 7, with period T s Repeat steps 3-6 at intervals until control ends.

[0015] Preferably, the linear dynamic model is expressed as:

[0016] ,

[0017] In the formula, Let be the state vector of the controlled system. State vector rate of change, State vector The specific value at time point t, To control the specific value of the input at time t, m and n are positive integers. and Given a constant matrix, It is a time-varying matrix.

[0018] Preferably, the time-varying matrix is ​​shown as follows:

[0019] ,

[0020] In the formula, and Given a matrix, It is an unknown time-varying matrix. It is an identity matrix.

[0021] Preferably, the state estimation model is expressed as:

[0022]

[0023] In the formula, This represents the estimated rate of change of the state vector. This represents the estimated state vector at time t. This represents the estimated state vector at the reset time. To control the gain; , representing the state vector The set of times for measurement updates T1 and T2 are positive real numbers. .

[0024] Preferably, the state measurement information of the controlled system is acquired through sensors and data communication links, and the set is updated. Count variable .

[0025] Preferably, the state reset is performed by: when the controller receives state measurement information from the controlled system, forcibly instructing... .

[0026] Preferably, the design elastic control law is: the control input in the state estimation model is expressed as: In the formula, To control gain perturbation, and Given a matrix, It is a time-varying matrix that satisfies ; , , express Positive semidefinite matrix This is an auxiliary matrix.

[0027] Beneficial Effects: The present invention has the following advantages: The control method proposed in this invention can maintain stable system operation even when there are parameter uncertainties, actuator errors, and irregular updates of state measurement information. It has strong robustness and adaptability and can be applied to fields such as industrial automation control systems, networked control systems, robot control systems, and intelligent equipment control systems. In addition, by improving the stability and reliability of the control system, the present invention reduces the system failure rate, improves equipment operating efficiency, thereby reducing maintenance costs and improving the overall system performance, and has certain engineering application value and economic benefits. Attached Figure Description

[0028] Figure 1 This is a schematic diagram of the method flow in Example 1;

[0029] Figure 2 This is a state evolution curve diagram of the controlled system in Example 2;

[0030] Figure 3 This is a graph showing the change in control input in Example 2;

[0031] Figure 4 This is a schematic diagram illustrating the change in the sampling period in Example 2. Detailed Implementation

[0032] The technical solution of the present invention will be described in detail below with reference to the embodiments and accompanying drawings.

[0033] Example 1

[0034] like Figure 1 As shown, this embodiment provides an elastic control method for a linear uncertain system based on multi-rate state measurement information, including the following:

[0035] Step 1: Establish a linear dynamic model of the controlled system.

[0036] Consider a controlled system whose dynamic model can be established as a linear system with norm-bounded uncertainties:

[0037] ,

[0038] In the formula, Let be the state vector of the controlled system. State vector rate of change, State vector The specific value at time point t, To control the specific value of the input at time t, m and n are positive integers. and Given a constant matrix, The time-varying matrix, representing system perturbation, can be expressed as:

[0039] ,

[0040] In the formula, and Given a matrix, It is an unknown time-varying matrix. It is an identity matrix.

[0041] State vector of the controlled system Due to data transmission congestion and interference, only in unpredictable situations... Measurements are updated continuously. Represents a counting variable. Indicates the first Each sampling time.

[0042] Further definition , representing the state vector The set of times for measurement updates, and assume the existence of two positive real numbers. Let T1 be the minimum sampling interval and T2 be the maximum sampling interval, such that:

[0043] .

[0044] Step 2: Establish a state estimation model based on multi-rate state measurement information.

[0045] By utilizing the state measurement information of the controlled system received in the previous moment, the following state estimation model can be established (for approximating the true state). ):

[0046]

[0047] In the formula, This represents the estimated rate of change of the state vector. This represents the estimated state vector at time t. This represents the estimated state vector at the reset time. To control the gain. When the controller receives a new measurement, it... Force a reset of the estimation status to ensure that the estimated value is consistent with the actual value.

[0048] Step 3: Acquire the state measurement information of the controlled system through sensors and data communication links, and update the set. Count variable .

[0049] The sensor collects the status of the controlled system in real time and transmits the measurement information through the communication link. Transmitted to the controller, and the sampling time set is updated simultaneously. Count variable ( = +1).

[0050] Step 4: Reset the state of the state estimation model established in Step 2. Specifically, when the controller receives the state measurement information of the controlled system, it forces... The reset operation ensures that the estimated state vector is consistent with the true state vector at the sampling time, thus eliminating estimation errors.

[0051] Step 5: Design the elastic control law based on the model from Step 1 and Step 2.

[0052] Considering control input perturbation, It can be represented as ,in, To control gain perturbation, and Given a matrix, It is a time-varying matrix that satisfies .

[0053] Given two positive constants and ,but The following linear inequality can be constructed by solving:

[0054]

[0055] In the formula, It can be represented as:

[0056]

[0057] In the formula, , Let be the matrix to be solved. express Positive semidefinite matrix as well as A positive scalar must satisfy:

[0058] ,

[0059] , .

[0060] but Can be designed as .

[0061] Step 6: Send control commands Input actuators stabilize the state of the controlled system;

[0062] Step 7, with period T s Repeat steps 3-6 at intervals until control ends, where T s To control the period, satisfy T s ≤T2, ensuring the sampling interval is within the allowable range.

[0063] In this invention, the controller design is primarily based on solving for the control gain using the linear matrix inequality method. In practical applications, other robust control methods or optimization control methods, such as H∞ control or model predictive control, can also be used to achieve similar functionality. Different methods may differ in computational complexity and control performance, but all can achieve stable control of uncertain systems.

[0064] Example 2

[0065] Based on Embodiment 1, an elastic control method for a linear uncertain system based on multi-rate state measurement information is provided. This embodiment designs a state stabilization simulation experiment for the linear system. In the simulation, the relevant parameters of the controlled system are set as follows:

[0066] , ,

[0067] , ,

[0068] , and Set to respectively .

[0069] The initial conditions are set as follows: .

[0070] make , but It can be obtained as .

[0071] Figure 2 The figure shows the state evolution curve of the controlled system during the simulation. As can be seen from the curve, although the initial state of the controlled system deviates significantly from the value of 0, it shows a convergence trend after the control starts and has a very small steady-state error.

[0072] Figure 3 The graph shows the change in control input during the simulation. It can be seen that the greater the deviation of the controlled system state from 0, the greater the required control input. However, overall, the amplitude of the control input can vary within a limited range.

[0073] Figure 4 The simulation reflects the variation of the sampling period during the simulation process. Although the sampling period varies randomly within a relatively large range of 0.1s to 0.6s, the state of the controlled system can still remain stable under the influence of system parameter perturbations and control input errors, which verifies the effectiveness of the proposed method.

Claims

1. A method for resilient control of a linear uncertain system based on multi-rate state measurement information, characterized by, include: Step 1: Establish a linear dynamic model of the controlled system; Step 2: Establish a state estimation model based on multi-rate state measurement information; Step 3: Obtain the state measurement information of the controlled system; Step 4: Reset the state of the state estimation model based on the state measurement information; Step 5: Design the elastic control law based on the linear dynamics model and the state estimation model; Step 6: Input the control command based on the elastic control law into the actuator to stabilize the state of the controlled system; Step 7, repeat steps 3-6 with a set period T s as an interval until the control ends.

2. The linear uncertain system elasticity control method according to claim 1, wherein, The linear dynamic model is expressed as follows: ， wherein is the state vector of the controlled system, denotes the state vector of the rate of change, denotes the state vector of the specific value at the time point t, is the specific value of the control input at time t, m, n are positive integers, and is a known constant matrix, is a time-varying matrix.

3. The elastic control method for linear uncertain systems according to claim 2, characterized in that, The time-varying matrix is ​​shown as follows: ， In the formula, and Given a matrix, It is an unknown time-varying matrix. It is an identity matrix.

4. The elastic control method for a linear uncertain system according to claim 2, characterized in that, The state estimation model is expressed as follows: ， In the formula, This represents the estimated rate of change of the state vector. This represents the estimated state vector at time t. This represents the estimated state vector at the reset time. To control the gain; , representing the state vector The set of times for measurement updates T1 and T2 are positive real numbers. .

5. The elastic control method for a linear uncertain system according to claim 4, characterized in that, The system acquires state measurement information of the controlled system through sensors and data communication links, and updates the dataset. Count variable .

6. The elastic control method for a linear uncertain system according to claim 4, characterized in that, The state reset is performed when the controller receives state measurement information from the controlled system, and then... .

7. The elastic control method for a linear uncertain system according to claim 4, characterized in that, The design elastic control law is: the control input in the state estimation model is expressed as: In the formula, To control gain perturbation, and Given a matrix, It is a time-varying matrix that satisfies ; , , express positive semidefinite matrix This is an auxiliary matrix.

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