Observer mismatch rejection based constraint design method for anti-windup

Abstract

The application provides a design method of an anti-saturation constraint device based on observer mismatch suppression, comprising the following steps: performing mechanism analysis on an anti-saturation failure phenomenon caused by observer input mismatch in a closed-loop control system; determining a setting scheme of an anti-saturation constraint device capable of suppressing observer mismatch based on the mechanism analysis result, wherein the setting scheme comprises a connection relationship of the anti-saturation constraint device in the closed-loop system and a constraint rate executed by the anti-saturation constraint device, and the connection relationship comprises a connection mode of the anti-saturation constraint device with a controller, an observer and a controlled object in the closed-loop control system, and the constraint rate is determined based on a saturation characteristic of an actuator in the controlled object and the connection relationship. By using the design method provided by the application, a setting scheme of an anti-saturation constraint device for fundamentally suppressing observer mismatch can be obtained.

Description

Technical Field

[0001] This application belongs to the field of intelligent equipment and automatic control technology, specifically relating to a design method for an anti-saturation constraint based on observer mismatch suppression. Background Technology

[0002] Feedback control systems with observers are currently widely used in aircraft attitude control, ship heading control, and motion control of intelligent agents such as robots. In the process of executing control commands of closed-loop control systems, actuators in the controlled objects, such as servo motors, motors, and hydraulic valves, generally have nonlinear constraints such as amplitude limits, rate limits, dead zones, and hysteresis. Among these, actuator saturation is the most common type of input constraint problem.

[0003] Currently, anti-saturation strategies for feedback control systems with observers are mostly implemented by adding auxiliary compensators, constructing additional dynamic systems, designing switching logic, or refactoring feedback loops. While these methods can alleviate short-term saturation problems in some scenarios, they often have drawbacks such as complex structures, numerous parameters, difficult debugging, poor reproducibility, and high engineering implementation costs. Some methods can maintain stability when the actuator is saturated for a short time, but when the saturation duration is long, problems such as disturbance estimation drift, increased system oscillation, or even divergence may still occur. Summary of the Invention

[0004] The purpose of this application is to provide a method for designing anti-saturation constraint based on observer mismatch suppression, the method comprising the following steps: Mechanism analysis of anti-saturation failure caused by observer input mismatch in closed-loop control system; Based on the mechanistic analysis results, a configuration scheme for the anti-saturation constraint that can suppress observer mismatch is determined. This configuration scheme includes the connection relationship of the anti-saturation constraint in the closed-loop control system and the executed constraint rate. The connection relationship includes the connection method between the anti-saturation constraint and the controller, observer and controlled object of the closed-loop control system. The constraint rate is determined based on the saturation characteristics of the actuator in the controlled object and the connection relationship.

[0005] The design method provided in this application first analyzes the mechanism of the failure of the anti-saturation capability of a closed-loop control system with an observer, and determines that the introduction of observation mismatch excitation terms into the control system is the root cause of the system's difficulty in exiting a long-term saturation state. Then, it evaluates the effects of different anti-saturation schemes on eliminating or improving the observation mismatch excitation terms, and determines the optimal anti-saturation constraint setting scheme. The closed-loop control system with anti-saturation constraint designed based on this method does not require the addition of high-order anti-saturation compensators, complex switching logic, or additional dynamic systems. It can fundamentally improve the system's anti-saturation capability simply by modifying the observer input source. Attached Figure Description

[0006] Figure 1 This is a schematic diagram of a typical closed-loop control system architecture. Figure 2 This is a flowchart of a method for designing an anti-saturation constraint based on observer mismatch suppression according to an embodiment of this application; Figure 3 This is a schematic diagram of the architecture of a traditional ADRC control system; Figure 4 A schematic diagram of the control process between actuators and entities in a controlled object; Figure 5 A schematic diagram illustrating the mechanism by which anti-saturation failure is caused by input mismatch to the observer; Figure 6 This is a schematic diagram illustrating the mechanism of anti-saturation failure caused by ESO input mismatch in a traditional ADRC control system. Figure 7 This is a schematic diagram of the architecture of an anti-saturation scheme aimed at suppressing observation mismatch excitation terms; Figure 8 A schematic diagram of the architecture after adding an anti-saturation constraint to a traditional ADRC control system to suppress observation mismatch excitation terms; Figure 9 This is a schematic diagram of a closed-loop control system architecture that uses an additional compensator to resist saturation. Figure 10 This is a schematic diagram of a closed-loop control system architecture that resists saturation through a control law reconfigurator. Figure 11 This is a schematic diagram of the architecture of an unmanned surface vessel ADRC control system with an anti-saturation restraint provided according to an embodiment of this application; Figure 12 This is a schematic diagram of the architecture of a traditional ADRC (Advanced Dynamic Control and Rescue) system for unmanned vessels. Figure 13 This is a schematic diagram of the architecture of an ADRC control system for an unmanned surface vessel with an additional compensator. Figure 14 for Figure 11The diagram shows the changes in rudder angle and heading angle of the control system under long-term saturation conditions. Figure 15 for Figure 12 The diagram shows the changes in rudder angle and heading angle of the control system under long-term saturation conditions. Figure 16 for Figure 13 The diagram shows the changes in rudder angle and heading angle of the control system under long-term saturation conditions. Figure 17 This is a schematic diagram comparing the observation errors of three control systems. Detailed Implementation

[0007] The present application will now be further described based on preferred embodiments and with reference to the accompanying drawings.

[0008] In the description of the embodiments of this application, it should be noted that the terms "upper," "lower," "inner," and "outer," etc., indicating orientation or positional relationships based on the orientation or positional relationships shown in the accompanying drawings, or the orientation or positional relationships commonly used when the product of this application is in use, 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, and therefore should not be construed as a limitation on this application. Furthermore, in the description of this application, the terms "first," "second," etc., are used to distinguish different units, but these are not limited by the manufacturing order, nor should they be construed as indicating or implying relative importance. Their names may differ in the detailed description and claims of this application. In addition, for ease of understanding, various components in the drawings have been enlarged or reduced, but this is not intended to limit the scope of protection of this application.

[0009] The vocabulary used in this specification is for illustrative purposes and is not intended to limit the scope of this application. It should also be noted that, unless otherwise expressly specified and limited, the terms "set," "connected," and "linked" 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, a direct connection, or an indirect connection via an intermediate medium; or they can refer to the internal communication between two components. Those skilled in the art will understand the specific meaning of these terms in this application.

[0010] Figure 1 The basic architecture of a feedback control system with an observer is shown, such as Figure 1 As shown, this feedback control system consists of a controller and an observer, and its signal flow is as follows: Reference signal The input is sent to the controller, which then uses the reference signal and the observation signal output by the observer. Generate control quantity , On the one hand, the input enters the controlled object to drive it; on the other hand, it is inputted to the observer; the controlled object responds to the control input. And generate an output signal The output signal It is also fed back to the observer, which uses the control quantity. and the output signal of the controlled object It estimates the internal state or total disturbance of the system in real time and outputs the observed signal. The signal is sent to the controller to correct the generated control input, thus forming a complete closed-loop feedback control loop. Compared to traditional closed-loop control architectures that do not have an observer (relying solely on output feedback), Figure 1 The architecture shown reconstructs the system state or disturbance that cannot be directly measured through the observer, enabling the controller to achieve more accurate compensation and better dynamic performance.

[0011] Understandably, in practical engineering applications, the specific implementation methods of controllers and observers can be selected according to the actuator type and dynamic characteristics of the controlled object, thereby constructing systems such as Active Disturbance Rejection Control (ADRC) systems (using extended state observers ESO), state feedback control systems based on Luenberger observers, control systems based on Kalman filters and extended Kalman filters, control systems based on disturbance observers, and sliding mode control systems (using sliding mode observers). These control systems respectively use corresponding types of observers to achieve state reconstruction or disturbance estimation.

[0012] In the process of controlling the controlled object using the aforementioned feedback control system with an observer, actuator saturation constraint is a common problem affecting the system's control accuracy. When the reference command value is large, external disturbances are strong, or there is a mismatch in the system model, the ideal control quantity output by the controller will be affected. It may exceed the physical capacity of the actuator, causing the actual control quantity acting on the controlled object to enter a saturation state. At this time, the actual control effect on the controlled object is no longer equal to the ideal control command output by the controller, but equal to the actual control quantity after being limited by the actuator saturation stage. This leads to the system entering a saturation state, which manifests as a decrease in system response speed, deterioration of tracking accuracy, increase in overshoot, or even loss of stability.

[0013] To avoid system saturation, several desaturation strategies or schemes have been disclosed, such as: An additional compensator is added to the output side of the controller to correct the control quantity entering the actuator of the controlled object, thereby preventing the actuator of the controlled object from entering saturation; During the process of generating control laws within the controller, a control law switching layer is added. Based on the system state, condition judgments are made and control laws are switched. For saturation states, the switched control laws are executed to suppress the saturation of the controlled object. Adding a separate error feedback layer to the system, or adding an error feedback layer before the observer's output signal is fed back to the controller, aims to correct the observer's observation results and reduce the degree of system saturation.

[0014] However, the existing anti-saturation / desaturation strategies mentioned above compensate for the consequences after the controller output has already decoupled from the actuator. While effective when the system is in a saturated state for a short period, they fail when the system is saturated for an extended period. The reason is as follows: 1) When the actuator saturates, the ideal control quantity output by the controller is inconsistent with the actual control quantity received by the object. If the observer still uses the ideal control quantity for state updates, the internal model of the observer will not match the input channel of the real object, resulting in an increase in observation error. 2) Meanwhile, since the real-time adjustment of the control law depends on the observer's estimation of system error and disturbance, the observer will misjudge the lack of control action caused by actuator saturation as total disturbance, external disturbance or model uncertainty in the case of input mismatch, thus amplifying the disturbance estimation bias. 3) Furthermore, when the observer misjudges a large disturbance, the controller will further increase the control output to try to compensate for the "disturbance", causing the actuator to fall into a deeper saturation region, forming a vicious cycle.

[0015] It is evident that if the actuator cannot exit the saturation state in a timely manner after entering saturation, the input mismatch of the observer will cause the control loop in the closed-loop control system to enter a vicious cycle of "increased estimation error → inaccurate control quantity + saturation of actual action quantity → mismatch of observation quantity → further increase in observation error". This will cause the system to lose its ability to exit the saturation state by its own control under long-term saturation. In this application, this phenomenon of continuous system saturation and inability to exit controllably due to the gradual accumulation of observer input mismatch is referred to as "anti-saturation failure caused by observer input mismatch".

[0016] The above analysis shows that none of the existing anti-saturation strategies fundamentally solve the problem of inconsistency between the control input to the observer and the actual control input executed by the controlled object. Furthermore, when the system is in a saturated state for an extended period, the anti-saturation effect inevitably declines or becomes unstable. For example, while adding a compensator to the controller output can mitigate short-term shocks, it is more suitable for conditions where the saturation duration is short, the error is not too large, the object is nearly linear, and bandwidth separation is established. Once the system is saturated for a long time, if the observer continues to use incorrect inputs, the error will continue to accumulate after prolonged saturation, causing the compensator's effect to rapidly decline. Additionally, the logic judgments or error correction modules added by some anti-saturation strategies introduce new additional links and couplings in the closed-loop control system. The more additional links there are, the more difficult the parameter tuning becomes, and in engineering, it may even introduce new instabilities.

[0017] It is evident that only by analyzing the mechanism of the aforementioned anti-saturation failure phenomenon and identifying the root cause of the problem can we determine the solution that can fundamentally solve the problem from among various alternatives. This will enhance the system's ability to suppress and resist prolonged saturation, thereby eliminating the factors causing the aforementioned problems. Therefore, this application provides a method for designing an anti-saturation constraint based on observer mismatch suppression through embodiments, such as... Figure 2 As shown, the method includes the following steps: Step 1: Analyze the mechanism of anti-saturation failure caused by observer input mismatch in the closed-loop control system; Step two: Based on the mechanistic analysis results, determine the configuration scheme of the anti-saturation constraint that can suppress observer mismatch. The configuration scheme includes the connection relationship of the anti-saturation constraint in the closed-loop control system and the executed constraint rate, wherein... The connection relationship includes the connection method between the anti-saturation constraint and the controller, observer and controlled object of the closed-loop control system. The constraint rate is determined based on the saturation characteristics of the actuator in the controlled object and the connection relationship.

[0018] The following detailed description of the specific implementation of steps one and two in this method, in conjunction with the accompanying drawings and specific embodiments, will be provided in detail.

[0019] <Step 1> Step 1 is used to evaluate the impact of different inputs of the observer on the system's anti-saturation capability when the system is in a long-term saturation state. Specifically, in Step 1, control-related signals output from different functional modules are input into the observer to analyze the relationship between the observation error of the control-related signals entering the observer in the saturation state and the observation result from the observer's output. Based on the analysis results, the ability of the closed-loop control system to exit saturation from a long-term saturation state is evaluated when the source of the observer's control signals is different.

[0020] In the embodiments of this application, control quantity related signals refer to various control quantities aimed at applying control to the controlled object, such as ideal control quantities directly output from the controller. and to The control quantity that has not yet entered the actuator of the controlled object after various processing (including but not limited to correction, optimization, constraint, transformation, switching, etc.).

[0021] The following analysis, using specific implementation examples, examines the changes in the observer's error under system saturation conditions after control input signals from different sources enter the observer.

[0022] A. Analysis of the observation error and desaturation capability of a closed-loop control system with direct input of ideal control variables to the observer. Figure 3 This is a topology diagram of a traditional ADRC (Active Disturbance Rejection) control system, such as... Figure 3 As shown, in the ADRC control system, the controller consists of a tracking differentiator (TD) and state error feedback (e.g., linear state error feedback LSEF or nonlinear state error feedback NLSEF), while the observer uses an extended state observer (ESO). Therefore, this topology is... Figure 1 This is a specific implementation of a closed-loop control system with an observer.

[0023] To clearly explain the root cause of the error, through... Figure 4 Further abstracting the driving actions of the actuators and the dynamic processes of the entity within the controlled object, it can be understood that the actuators and the controlled entity should be interpreted broadly. An actuator refers to a device that converts the received control quantity into physical actions such as force, torque, or flow rate, including but not limited to servo motors, motors, hydraulic cylinders, articulated motors, throttle valves, thrust vectoring nozzles, piezoelectric ceramics, heating rods, and flow valves. An entity refers to the part of the controlled object subjected to the physical actions exerted by the aforementioned devices, including but not limited to the bodies of various aircraft, vehicles, and ships, the joints of various robots, rockets and satellites, nanoscale workbenches, and reaction vessels. Under the drive of these devices, the entity's posture, velocity, temperature, and other states change and can be output through various measuring devices.

[0024] Figure 5 This illustrates a closed-loop control system after the controlled object is abstracted into actuators and entities. Figure 6 This illustrates the ADRC control system after the controlled object is abstracted into actuators and entities.

[0025] refer to Figures 4 to 6In a traditional ADRC control system, the control quantity related signal input to the observer ESO is the ideal control quantity output from the state error feedback. Once the control quantity enters the controlled object, it will be input to the actuator, which will then drive the entity to change its state.

[0026] Obviously, the action of an actuator is constrained by physical laws. Therefore, its effect on the entity must exhibit saturation characteristics. Depending on the type of actuator and entity, these saturation characteristics may include: amplitude saturation characteristics (e.g., the upper limit of the rudder angle), asymmetric saturation characteristics (e.g., the asymmetry between the extension force and retraction force of a hydraulic cylinder), rate saturation characteristics (e.g., the upper limit of the motor speed), and first-order or higher-order constraint characteristics of the actuator (e.g., the first-order inertia of a motor, the second-order oscillation of a servo motor), etc.

[0027] The reflection of these saturation characteristics on the actuator side is that there are saturation constraint elements in the actuator: the control quantity actually executed by the actuator is relative to the ideal control quantity. The output after applying saturation constraints In this application, the actual control quantity that acts on the driving entity after being constrained by the saturation constraint link in the actuator is referred to as the true control quantity. .

[0028] For a second-order ADRC system, the actual dynamics of the controlled object are: , in, These are state variables that are directly measurable by the system (such as position). For the total system disturbance, For actual control gain, As mentioned above, this is the actual control quantity output by the actuator.

[0029] according to Figure 3 and Figure 6 The control-related signals for the extended state observer (ESO) in traditional ADRC are: This refers to the ideal control quantity calculated by the controller. Therefore, the extended state observer (ESO) of the traditional ADRC is designed as follows: , in, for The estimated value, for The estimated value of the first derivative, This is an estimate of the total system disturbance (including internal uncertainties and external disturbances). for The estimated value, , , This is the observer gain.

[0030] Define the total disturbance as The dynamics of the controlled object can then be expressed as: .

[0031] Define state observation error Total disturbance estimation error Subtracting the object dynamics from the ESO equations yields the error dynamics of the ESO in a traditional ADRC control system: .

[0032] Obviously, when the system is not in a saturated state, the saturation constraint in the actuator is not "triggered," therefore However, once the system becomes saturated, such as Figures 4 to 6 As shown, and This will produce a deviation because the control input signal entering the observer is an ideal control input. Therefore, for the observer ESO in a second-order ADRC control system, when the system is in saturation, the observer error term in the system... The expression is: , In the above formula, In the context of system saturation, the additional negative factor that increases the error of the observation result due to the input mismatch of the observer is referred to as the observation mismatch excitation term in this application, which is an additional excitation term introduced into the observation result due to the inconsistency between the control quantity related signal input by the observer and the actual control quantity actually executed by the controller in the controlled object.

[0033] When the actuator becomes saturated Then observe the mismatched excitation term The term will continue to act on the error dynamics of ESO, creating a vicious cycle: actuator saturation. → Item-driven ESO error Increasing → ESO incorrectly attributes this error caused by input mismatch to the total disturbance. This leads to the total disturbance estimate. Deviation from the true value → The controller calculates the control quantity based on the erroneous disturbance estimate. .if Overrated or underrated It will increase further → Enlargement leads to If the size increases further, the system will fall into deeper saturation, making it difficult to escape saturation on its own, thus forming a closed-loop positive feedback. This is essentially a windup phenomenon in the observer channel.

[0034] B. Analyze the observation error and desaturation capability of a closed-loop control system with anti-saturation constraints. Figure 7 A topology for an anti-saturation scheme aimed at achieving consistency between observer and actuator inputs is shown, such as... Figure 7 As shown, the anti-saturation scheme specifically involves adding an anti-saturation constraint (referred to as the constraint in the accompanying drawings and text) to the closed-loop control system to synchronously suppress the observation mismatch excitation term of the observer. Specifically, the input of this constraint is directly connected to the output of the controller, and its output is directly connected to the input of the observer and the input of the actuator in the controlled object. Through this configuration, the ideal control quantity output by the controller will first pass through the constraint, thus becoming a corrected control quantity. This corrective control input will be simultaneously input to both the observer and the actuator in the controlled object.

[0035] If the constraint rate is set according to the saturation characteristics of the actuator in the controlled object (for example, setting the constraint rate to be consistent with the saturation characteristics of the actuator), then First, it is constrained by the constraint and becomes When entering the executor of the controlled object again, the constraints of the saturation constraint loop of the executor will not be "triggered". , Always satisfied That is, the control input signal of the observer. The actual control quantity executed by the actuator Always maintain consistency.

[0036] Figure 8 The topology obtained after applying the anti-saturation scheme to the ADRC control system is shown below. Figure 8 The anti-saturation mechanism of this anti-saturation scheme is illustrated using the ADRC system with anti-saturation constraint shown as an example.

[0037] The control input related signal from ESO is converted from the ideal control input. Transform into a corrected control quantity The revised ESO equation is as follows: , Re-deriving the ESO error kinetic equation, we can obtain that as the number of errors increases... Figure 8 After the constraint shown is applied to suppress the observation mismatch excitation term, the ESO dynamic equation is: because Therefore, after being constrained by the constraint... Upon entering the controller, the constraint of the constraint saturation constraint loop is not "triggered," and the ESO error dynamic equation becomes: At this point, the additional observation mismatch excitation term caused by the observer input mismatch has disappeared. Therefore, the duration of saturation will not further disrupt the ESO error structure, as long as... Bounded, With bounded and reasonable ESO parameters, the observation error remains bounded. The controller will not continue to push the command into deeper saturation due to "false disturbances that are incorrectly estimated". When the reference decreases, the error decreases, and the external disturbance weakens, the system will have the opportunity to naturally exit saturation.

[0038] In some preferred embodiments, the settings can be further optimized. Figure 7 , Figure 8 The boundedness of observation error and desaturation capability of the closed-loop control system of the anti-saturation constraint device shown are quantitatively analyzed.

[0039] Specifically, quantitative analysis can be performed in two steps, with the controlled object as one example below. Taking an uncertain SISO system as an example, this quantitative analysis process can be illustrated. The state of the system can be represented as follows: in, The system gain is known in sign. The disturbance is a system disturbance, which may be bounded or locally bounded. Bounded, or the derivative of the total perturbation is bounded; The saturation characteristic of the actuator, i.e., the expression for the saturation constraint element used to describe the control quantity applied to the input, is a statically bounded nonlinear characteristic of the actuator. Clearly, when using… Figure 7 , Figure 8 The following is a scheme for setting up the anti-saturation constraint: The first step is to determine the boundedness of the error in the closed-loop control system after adding an anti-saturation constraint to synchronously suppress the observation mismatch excitation term.

[0040] The following are reasonable preconditions: Assumption 1: Gain parameters of the Extended State Observer (ESO) , , Choose a polynomial that makes the characteristic polynomial It is a Hurwitz polynomial, meaning that all its eigenvalues ​​have negative real parts. This assumption is a fundamental premise of all ESO designs and has been widely verified and applied in existing technologies.

[0041] Assumption 2: Total system disturbance and its first derivative In practical engineering, globally consistent boundedness exists, meaning there exists a constant. and This makes it possible for all ,have , This assumption aligns with the characteristics of all real physical systems, where the rate of change of any physical quantity cannot be infinite.

[0042] As can be deduced above, when the constraint outputs... With respect to the actual execution of the actuator When they are strictly equal, Figure 8 In the topology shown, the ESO error kinetic equation is: , Write it in matrix form: , Where the observation error vector State matrix Input matrix .

[0043] Assumption 1 states that the matrix As a Hurwitz matrix, according to the Lyapunov stability theory of linear systems, there exists a symmetric positive definite matrix. and It satisfies the Lyapunov equation: , Constructing Lyapunov functions: , right Differentiating along the error dynamics equation, we get: , Expanding and substituting into the Lyapunov equation, we get: , According to the properties of matrix norm, we have: , in For matrix The smallest eigenvalue, This represents the Euclidean 2-norm.

[0044] According to the Cauchy-Schwarz inequality, we have: , Using Young's inequality ,Pick We can obtain: , Substituting the above two equations into The expression is: , Simplifying, we get: , in It is a constant that depends only on the observer (ESO) parameters.

[0045] And because ,so Substituting into the above equation, we get: , in It is a constant that depends only on the ESO parameters.

[0046] Assuming 2, For all Therefore: , Applying the above inequality from 0 to Integrating, we get: , when hour, ,therefore: , because Therefore, the final bound of the observation error is: .

[0047] Through the above derivation process, we can obtain the result for 7. Figure 8 Conclusion 1 from the quantitative analysis of the anti-saturation constraint setting scheme shown: Under the condition that assumptions 1 and 2 are true, Figure 7 , Figure 8 In the topology shown, the observation error of the closed-loop control system (e.g., the ESO observation error in an ADRC control system) , , It is globally eventually uniformly bounded, and this boundedness is independent of the duration of saturation.

[0048] The error dynamics equations of the traditional ADRC scheme include a persistent observation mismatch excitation term. When the system is saturated for a long time, the observation mismatch excitation term will accumulate continuously, causing the observation error to increase continuously and eventually diverge. As can be seen from the previous derivation, using Figure 7 , Figure 8 The topology (i.e., adding an anti-saturation constraint aimed at aligning the observer input with the actuator input) fundamentally eliminates the observation mismatch excitation term. The final bound of the observation error depends only on the upper bound of the total perturbation derivative and the ESO parameter, and is independent of the saturation duration. Even if the system remains in deep saturation for a long time (e.g., several hours), the observation error will not diverge.

[0049] The second step is to determine the desaturation capability of the closed-loop control system after adding an anti-saturation constraint to synchronously suppress the observation mismatch excitation term.

[0050] As can be seen from Conclusion 1 above, when adopting Figure 7 , Figure 8 The anti-saturation scheme shown, which involves adding a constraint to the closed-loop control system to synchronously suppress observation mismatch excitation terms, eventually ensures that the system observation error is uniformly bounded, i.e., a constant exists. This makes it possible for all sufficiently large ,have .

[0051] Without loss of generality, assume that in a closed-loop control system, the controller generates the ideal control quantity based on the following linear state error feedback control law: , Will Substituting into the above equation and simplifying, we get: .

[0052] Define tracking error , Then the above formula can be written as: , As can be seen from Conclusion 1 derived above, the observation error , , It is eventually uniformly bounded, therefore it has a constant. , making For all sufficiently large Established.

[0053] When the system is in a saturated state ,in This represents the maximum output amplitude of the actuator. Assume... ( If the situation is completely symmetrical, then the dynamic equation of the controlled object is: , We can obtain: , If the reference signal meets the following conditions: , in Let be the upper bound of the total disturbance, then: , Therefore, the second derivative of the tracking error Tracking error and It will gradually decrease.

[0054] When the tracking error decreases to a certain extent, we have: , At this point, the ideal control quantity satisfy: .

[0055] Therefore, the actuator exits the saturation state, and the system restores its normal linear control performance.

[0056] Through the above derivation, we can obtain the following for 7. Figure 8 Conclusion 2 from the quantitative analysis of the anti-saturation constraint setting scheme shown: When the reference signal A closed-loop control system will necessarily exit the saturation state within a finite time when the following conditions are met: .

[0057] In traditional ADRC control systems, due to the continuous divergence of observation errors, even if the reference signal satisfies the conditions in the above equation, the controller will output excessively large control values ​​due to incorrect total disturbance estimation, causing the system to never exit saturation. In contrast, Figure 7 , Figure 8 The anti-saturation scheme shown is that after adding an anti-saturation constraint to the closed-loop control system to synchronously suppress the observation mismatch excitation term, the observation error of the closed-loop control system always remains bounded, and when the external conditions are met, it can controllably (within an engineering-acceptable time) exit saturation.

[0058] C. Analyze the observation error and desaturation capability of the closed-loop control system with other anti-saturation functional modules. Figure 9 This paper presents a topology for anti-saturation by adding an additional compensator type in the closed-loop control system. The specific architecture is as follows: it retains the traditional observer input (ideal control variable). In addition, an extra saturation error compensator is added to calculate the saturation error. The error is then injected into the compensator for compensation before being input into the observer.

[0059] This anti-saturation scheme adopts a "post-compensation" approach, attempting to offset the impact of the observed mismatch excitation term using an additional compensator after it occurs. That is, this anti-saturation scheme uses asynchronous compensation for anti-saturation. However, this anti-saturation strategy cannot fundamentally solve the problem of mismatch between the observer input and the actual control quantity. It can only passively track the results after the mismatch occurs. Not only can it not completely eliminate the observed mismatch excitation term, but the error will still accumulate to divergence under long-term saturation. At the same time, the additional compensator introduces new parameters that need to be tuned, increasing the complexity of engineering implementation. Moreover, the compensator itself has dynamic characteristics, which may create new coupling with the original system and cause instability.

[0060] Figure 10 The topology of an anti-saturation scheme is shown, which adds a saturation error feedback gain adjustment module to the control law reconfigurator in a closed-loop control system. This scheme suppresses the saturation effect by modifying the error feedback law of the controller. Its architecture is to retain the traditional observer input and introduce a saturation error feedback term into the control law. When the system enters saturation, the feedback gain is automatically reduced to limit the growth of the control quantity.

[0061] Similarly, this scheme does not solve the root cause of the observer input mismatch. The mismatch excitation term still exists in the observer error dynamics. When the system is saturated for a long time, the observation error will continue to accumulate, eventually leading to the failure of the control law. The reconstructed control law reduces the robustness of the original ADRC system and decreases its ability to suppress model errors and external disturbances. Control law reconstruction requires redesigning all parameters, which is difficult to implement in engineering.

[0062] Table 1 below shows a performance comparison of three different anti-saturation schemes.

[0063] Table 1 Step Two After completing the mechanism analysis of the anti-saturation failure phenomenon caused by the observer input mismatch in step one, the specific setting scheme of the constraint used for anti-saturation in the closed-loop control system can be determined in step two based on the analysis results.

[0064] In fact, the analysis in step one has already determined that... Figure 7 , Figure 8In the anti-saturation scheme shown, by setting an anti-saturation constraint in the closed-loop control system to synchronously suppress the observer mismatch excitation term, that is, designing the anti-saturation scheme with the goal of aligning the observer input with the actuator input, the problem of the system losing its anti-saturation capability due to observer input mismatch can be eliminated at its root. Furthermore, under the conditions that the reference signal is bounded, the total disturbance is bounded, the observer error is bounded, and the control gain is appropriately selected, even if the system enters a saturated state for various reasons, the direct erroneous excitation of the observer (ESO) by the actuator saturation has been eliminated from the error dynamics structure, ensuring that the system always has the ability to controllably exit saturation. Therefore, in some preferred embodiments, the final determined anti-saturation constraint setting scheme is as follows: The input of the anti-saturation constraint is directly connected to the output of the controller, and the output is directly connected to the input of the observer and the input of the actuator in the controlled object. Based on this connection and the saturation characteristics of the actuator in the controlled object, the specific form of the constraint rate can be further determined. Preferably, the constraint rate is configured as follows: This ensures that the corrected control quantity output after applying the aforementioned constraint rate is not constrained by the saturation constraint loop of the actuator. In other words, as mentioned earlier, the constraint rate applied by the anti-saturation constraint device should ensure... The corrected control quantity output after the constraint is applied. After entering the actuator, the actual control quantity executed by the actuator. Always equal to . Specific Implementation To verify the performance of the closed-loop control system with anti-saturation constraint designed using the method of this application, in one specific embodiment, using... Figure 8 The design of the closed-loop control system for an unmanned surface vessel (USV) is illustrated using the ADRC architecture with anti-saturation constraint. Figure 11 This ADRC unmanned surface vessel control system with anti-saturation restraints is shown, such as Figure 11 As shown, the controlled objects include a servo motor model and an unmanned vessel model. The servo motor model is the actuator, and the unmanned vessel model is the controlled entity. Under the control of the servo motor, it turns. The ADRC architecture includes an observer ESO, a state error feedback loop, and a constraint. The input of the constraint is connected to the output of the state error feedback loop. Its constraint rate is consistent with the saturation constraint characteristics (rudder speed limiting characteristic and rudder angle limiting characteristic) of the servo motor model. Its output correction control quantity is input to the servo motor model and the ESO respectively.

[0066] The reference signal is a step signal, which simulates the command that causes the system to enter a saturated state under extreme conditions. By analyzing the actual output control quantity (rudder angle) of the system servo model, the actual output quantity (heading angle) of the unmanned ship model, and the observation error of ESO, the desaturation performance of the control system under saturation conditions can be evaluated.

[0067] In comparison, Figure 12 , Figure 13 The architectures of unmanned surface vessel (USV) control systems based on traditional ADRC designs and USV ADRC control systems with additional compensators are shown respectively.

[0068] Figures 14 to 16 The changes in rudder angle and heading angle after the three control systems enter long-term saturation are shown respectively, such as Figure 14 As shown, after the anti-saturation constraint obtained using the design method of this application is added to the ADRC architecture, even after the system enters long-term saturation, the servo model's rudder angle (i.e., the actual control quantity) can still exit saturation within a controllable time period, thus maintaining stable heading angle tracking capability even in the extreme case where the command is a step signal; through Figure 15 , Figure 16 As can be seen, in traditional ADRC architectures and schemes using additional compensators, after the system enters long-term saturation, the rudder angle will oscillate repeatedly between the positive and negative amplitude limits, causing the unmanned vessel to repeatedly turn back relative to the desired direction, making it impossible to controllably exit from the deep saturation state.

[0069] Furthermore, it can be seen that when using Figure 11 In the architecture shown, since the constraint has constrained the control quantity entering the actuator based on the saturation characteristics of the controlled object, the controller section does not need to set the tracking differentiator TD. In this case, it can still cope well with the impact of step signals.

[0070] Figure 17 The observation errors of the control systems for the three architectures are further illustrated, with Figures a, b, and c corresponding to... Figure 11 , Figure 12 , Figure 13 As can be seen from the system architecture, when using the anti-saturation constraint, the estimated results of the observer output remain stable, and the total perturbation estimate is naturally bounded. Under the other two architectures, the observation results exhibit various problems such as oscillation, jumps, distortion, and exceeding reasonable limits. This further proves the viewpoint proposed in this application that observation mismatch leads to a decrease in the system's desaturation capability.

[0071] The specific embodiments of this application have been described in detail above. For those skilled in the art, several improvements and modifications can be made to this application without departing from the principle of this application, and these improvements and modifications also fall within the protection scope of the claims of this application.

Claims

1. A method for designing an anti-saturation constraint based on observer mismatch suppression, characterized in that, Includes the following steps: Mechanism analysis of anti-saturation failure phenomenon caused by observer input mismatch in closed-loop control system; Based on the mechanistic analysis results, a configuration scheme for the anti-saturation constraint that can suppress observer mismatch is determined. This configuration scheme includes the connection relationship of the anti-saturation constraint in the closed-loop control system and the executed constraint rate. The connection relationship includes the connection method between the anti-saturation constraint and the controller, observer and controlled object of the closed-loop control system. The constraint rate is determined based on the saturation characteristics of the actuator in the controlled object and the connection relationship.

2. The method for designing an anti-saturation constraint based on observer mismatch suppression according to claim 1, characterized in that, The mechanism analysis of the anti-saturation failure phenomenon caused by observer mismatch in the closed-loop control system includes: This paper analyzes the relationship between the source of the control quantity-related signals entering the observer and the observation results output by the observer in the closed-loop control system under saturation conditions. as well as, Based on the analysis results, the ability of the closed-loop control system to exit saturation from a long-term saturation state is evaluated when the sources of the control signals entering the observer are different.

3. The method for designing an anti-saturation constraint based on observer mismatch suppression according to claim 1, characterized in that, The control-related signals used for evaluation should include at least the following: The ideal control quantity directly output by the controller, and the corrected control quantity output after the ideal control quantity is input into the anti-saturation constraint.

4. The method for designing an anti-saturation constraint based on observer mismatch suppression according to claim 3, characterized in that, The saturation characteristics of the actuator include at least one of the following characteristics: Amplitude saturation characteristics, asymmetric saturation characteristics, rate saturation characteristics, and first-order or higher-order constraint characteristics of actuators.

5. The method for designing an anti-saturation constraint based on observer mismatch suppression according to claim 3, characterized in that, The anti-saturation constraint is configured to synchronously suppress observation mismatch excitation terms by ensuring that the observer input and actuator input in the closed-loop control system remain consistent. Specifically, the observation mismatch excitation terms are: The additional excitation term introduced into the observation result because the control quantity related signal input to the observer is inconsistent with the actual control quantity executed by the controller in the controlled object.

6. The method for designing an anti-saturation constraint based on observer mismatch suppression according to claim 5, characterized in that, The synchronization suppression of the observation mismatch excitation term specifically includes: The observation mismatch excitation term is always absent from the error dynamics equation of the observer.

7. The method for designing an anti-saturation constraint based on observer mismatch suppression according to claim 5, characterized in that, The connection relationship of the anti-saturation constraint in the closed-loop control system is as follows: The input of the anti-saturation constraint is directly connected to the output of the controller, and the output is directly connected to the input of the observer and the input of the actuator.

8. The method for designing an anti-saturation constraint based on observer mismatch suppression according to claim 7, characterized in that, The constraint rate is configured as follows: This ensures that the corrected control quantity output after passing through the constraint rate is not constrained by the saturation constraint link of the actuator.

9. The method for designing an anti-saturation constraint based on observer mismatch suppression according to claim 8, characterized in that, Also includes: A quantitative analysis is performed on the boundedness of observation error and desaturation capability of the closed-loop control system with the aforementioned anti-saturation constraint.

10. The method for designing an anti-saturation constraint based on observer mismatch suppression according to claim 9, characterized in that, When the anti-saturation constraint is set in the closed-loop control system: The observation error of the closed-loop control system is globally eventually uniformly bounded, and its boundedness is independent of the saturation duration. When the reference signal The closed-loop control system will be able to controllably exit the saturation state when the following conditions are met: ， in, Actual control gain The estimated value, This represents the maximum output amplitude of the actuator. This is the upper bound of the total disturbance.

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