257 results about "Backstepping" patented technology

The invention relates to the technical field of injection molding pressure control, in particular to a multi-stage pressure closed-loop compensation system and method for high-precision double-color injection molding, and the system comprises an interface gradient positioning module, a flow resistance state recognition module, a fitting function reconstruction module, a time sequence deviation triggering module and a gain reverse correction module. According to the method, the high-density measuring point data is collected, the interface radial pressure gradient change is extracted through the finite difference method, the stably-arranged nodes at the material intersection can be accurately locked, and the flow resistance state of the flow channel is judged according to the slope difference value of the screw speed and the pressure intensity change. A linear boosting or index slow increasing strategy is automatically switched to reconstruct a pressure function form, local high-pressure accumulation characteristics of a product sensitive area are accurately matched, the coincidence degree of a time window drift trend and a slope sudden change window is monitored, historical displacement and pressure errors are converted into backstepping factors through an iterative learning model, and the backstepping factors are calculated. And a driving gain curve is initialized and revised, so that forming deviation caused by thermal drift of equipment is eliminated.

A system, computer readable storage medium and method for controlling a trajectory of coordinated time-varying maneuvers of a geometric formation of unmanned vehicles is disclosed. The system includes unmanned vehicles, each configured with communication circuitry to communicate between the vehicles. A subset of the unmanned vehicles function as leader vehicles, with the remaining vehicles functioning as follower vehicles for leader-follower maneuvering. The system further includes an actuator suite configured to adjust the direction and orientation of each vehicle, a sensor suite for stabilization and navigation, and a flight controller for maintaining stable maneuvering, even in the presence of actuator faults and sensor deception attacks. Processing circuitry is configured with a reinforcement learning neural network that includes identifier, actor, and critic radial basis function neural networks to estimate movement, adjust control actions, and assess vehicle performance based on feedback signals, including corrupted signals from the sensor suite due to deception attacks.

The invention discloses an unmanned agricultural machine path tracking preset performance control method and system, and the method comprises the steps: collecting the pose information of an unmanned agricultural machine, building an unmanned agricultural machine path tracking error kinematic model, and designing a finite time preset performance function based on the unmanned agricultural machine path tracking error kinematic model. The constraint is converted through nonlinear mapping; based on the Lyapunov stability theory, adopting a backstepping method to recursively design an actual control law, and according to the actual control law, performing inverse transformation on the input of the unmanned agricultural machine tracking control system in the error kinematics model of the unmanned agricultural machine tracking control system to obtain the front wheel steering angle of the unmanned agricultural machine. According to the method, convergence is completed within finite time, and transient control performance and steady control performance of a path tracking control system are considered.

The invention relates to a system inertia boundary backstepping method based on frequency dynamic indexes and distributed node equivalent inertia analysis, and belongs to the field of power optimization. The method comprises the following steps: dividing a frequency response process into an inertia response stage, a primary frequency modulation stage and a secondary frequency modulation stage; constructing a multi-source frequency response unified equivalent model; an equivalent inertia boundary inversion method based on RoCoF and Nadr dual constraints is provided, a frequency safety boundary is converted into a constraint expression for the equivalent total inertia of a system, and an inertia boundary required under given power disturbance is reversely deduced; the method further comprises the steps of introducing static load voltage characteristic correction during inertia boundary inversion; the method further comprises the step of constructing a frequency support-oriented regionalization control strategy. According to the method, the safety support boundary of the low-inertia emergency power supply system is researched from the overall level and the regional level, and a theoretical basis is provided for refined frequency control and resource optimization layout.

The invention provides an ocean current interference resistant fault-tolerant control method and system for a robot multi-motor propulsion system, and the method comprises the steps: inputting the actual and expected position error and speed error of an underwater robot into a self-adaptive backstepping sliding mode path tracking controller, and obtaining the thrust needed by tracking motion; introducing a propeller weight matrix representing the fault degree of the propeller into a weighted pseudo-inverse method, optimizing the propeller weight matrix by adopting an intelligent algorithm to obtain an optimal propeller weight matrix, and performing thrust distribution on thrust required by tracking motion through the weighted pseudo-inverse method to obtain a thrust distribution result; according to the operation and thrust distribution results of the multiple motors, the parameters of all the motors are adjusted in a self-adaptive mode through a multi-motor fault-tolerant control strategy; and each motor remotely controls the underwater robot based on the parameters after self-adaptive adjustment, and obtains the actual position and speed of the underwater robot at the current moment for loop closing.

The invention provides a heterogeneous motorcade prediction control method based on a path information protection mechanism, and relates to the technical field of network connection unmanned vehicle cooperative control and intelligent traffic. Firstly, a path information protection mechanism is provided for preventing an alien invading vehicle from tracking a motorcade and ensuring the safety of motorcade path information. In addition, a predictor model is established to improve the estimation performance of the adaptive law, and a variable gain nonlinear expansion state observer is designed to approach and compensate the total disturbance. Then, by introducing a variable-gain hyperbolic tangent tracking differentiator, the problem of'complexity explosion 'caused by repeated derivation of a virtual controller in a backstepping method is avoided; and finally, a distributed prediction cooperative controller is constructed, and stable and safe driving of the whole heterogeneous network connection fleet is ensured.

The invention discloses an event-triggered adaptive fixed time control method for a random nonlinear switching system. The method comprises the following steps: constructing a model of the random nonlinear switching system; introducing an event triggering mechanism; designing a fixed time control strategy; and designing an event-triggered fixed-time adaptive controller based on a backstepping method design framework. According to the event-triggered adaptive fixed time control method for the random nonlinear switching system, an event-triggered control strategy is adopted to reduce the communication burden of the system. A new controller is stably constructed by using fixed time, and the upper bound of convergence time is irrelevant to initial conditions; meanwhile, by introducing nonlinear mapping, a random nonlinear system with symmetric and asymmetric output constraints is converted into a new unconstrained system, and random switching of the control system is realized by using a switching signal.

According to the cooperative control method and system of the non-linear multi-agent system, under the condition that communication link faults are considered, a non-linear dynamic model of each single-connecting-rod mechanical arm is established, and unknown uncertain non-linear dynamic states in the single-connecting-rod mechanical arms are fuzzified through a fuzzy logic system; a mixed event triggering mechanism is introduced, so that state information of a leader is estimated, and the communication frequency is effectively reduced; and constructing a virtual controller and an actual controller by utilizing a backstepping method based on the estimated state information, so as to control the position of the following mechanical arm to be synchronous with the expected trajectory of the leading mechanical arm under the condition of being influenced by the communication link fault. According to the method, the state of the multi-single-connecting-rod mechanical arm system can be kept consistent and stable tracking control can be achieved under the condition that communication link faults and nonlinear uncertainty exist without global information.

The invention discloses a hydraulic system preset time dynamic surface position control method, which is based on a dynamic surface control framework, innovatively introduces a preset time-varying function, and designs a nonlinear robust position controller with preset time. Aiming at the position control problem of the hydraulic cylinder of the hydraulic system, the differential explosion problem frequently occurring in the classic backstepping control design of the hydraulic system is avoided, the influence of measurement noise on the control precision is reduced, the controller design is simplified, and the excellent transient performance of the system within the preset time is guaranteed; and the convergence time can be clearly determined and does not depend on initial conditions of the system, so that the method has high-precision tracking performance.

The invention belongs to the technical field of EL system control, and discloses a preset performance control method considering dynamic and constraint of an execution mechanism. The method comprises the following steps: firstly, establishing a system dynamics model considering dynamic and input saturation constraints of an executing mechanism; then, designing an asymmetric tubular performance boundary to restrain a system tracking error, and defining a conversion error according to the system tracking error; meanwhile, a disturbance observer based on immersion and invariance is designed, and composite disturbance is estimated. Furthermore, a tubular preset performance controller is designed by adopting a backstepping method, a virtual control law and an expected torque are constructed, and a multi-state auxiliary system is introduced to compensate the input saturation influence. And finally, a control instruction is generated by integrating the auxiliary system state, the virtual control law, the expected torque and the interference estimation value, and the control instruction acts on the system after being processed by a saturation function. According to the method, actuator dynamics, input saturation and external disturbance can be processed at the same time, and tracking errors are ensured to strictly follow a preset performance boundary.

The invention discloses an unmanned ship adaptive optimal interference control method based on reinforcement learning, and particularly relates to the technical field of unmanned ship automatic control, and the method comprises the steps: building an unmanned ship trajectory kinematics model based on the position information and heading angle information of an unmanned ship under a geodetic coordinate system, and the corresponding speed information under an unmanned ship appendage coordinate system; the method comprises the following steps: establishing an unmanned ship trajectory dynamics model by considering the control operation of the unmanned ship and the time-varying environment interference problems of wind, waves, flow, unmodeled dynamics and the like in a marine environment in which the unmanned ship is located; introducing a radial basis function neural network based on a set unmanned ship trajectory mathematical model; designing a self-adaptive interference observer to estimate and offset time-varying environment interference in unmanned ship trajectory tracking; based on a radial basis function neural network and an interference observer, an unmanned ship adaptive interference suppression controller is designed by using an adaptive vector backstepping method.

The invention provides a quadrotor unmanned aerial vehicle fault-tolerant control method and system considering random disturbance, and belongs to the field of unmanned aerial vehicle flight control. The method comprises the steps that a random control system model fusing Wiener process random disturbance, actuator faults and input saturation is established, a six-degree-of-freedom control problem is decoupled into a position and attitude tracking sub-problem, and an expected attitude angle is inversely solved; applying constraints to the state variables by adopting a mixed constraint strategy fusing a delay state conversion function and nonlinear state dependence mapping; based on a self-adaptive backstepping method control framework, a controller is designed for six-degree-of-freedom sub-channels of the four-rotor unmanned aerial vehicle, and final input control signals of the degree-of-freedom sub-channels are obtained; and constructing a comprehensive Lyapunov function covering six degrees of freedom of the unmanned aerial vehicle, and proving that all signals of a closed-loop system are finally consistent and bounded. According to the invention, multiple complex factors can be coped with synchronously, the flight stability and reliability of the unmanned aerial vehicle in a complex environment are improved, and the method is suitable for multi-scene quadrotor unmanned aerial vehicle control.

The invention discloses an unmanned ship event triggering adaptive tracking control method based on an improved optimization backstepping technology. The method comprises the following steps: S1, establishing a motion mathematical model of a three-degree-of-freedom unmanned ship considering external interference; s2, designing a fixed time disturbance observer based on the motion mathematical model, and estimating external marine environment disturbance without depending on velocity derivative information; s3, designing an event triggering mechanism based on the position error of the unmanned ship so as to measure a control input signal without depending on an additional sensor; and S4, adopting an improved optimal backstepping control strategy based on actor-commentator reinforcement learning, and directly estimating a cost function gradient by using a neural network so as to generate a final control law, thereby eliminating complex matrix differential operation required in a traditional method. The invention also discloses a system for realizing the method. According to the invention, the control precision, robustness and real-time performance of trajectory tracking of the unmanned ship in a complex marine environment are improved.

The invention provides a speed-measurement-free unmanned ship tracking control method and system based on absolute position sensing. Aiming at the problem that a following boat cannot acquire speed information due to failure of a pilot boat speed sensor or communication failure, a distributed finite time state observer is designed, and the speed of a pilot boat is estimated in real time by combining an absolute position and positioning information. And designing an auxiliary controller by adopting a backstepping method based on the observation speed, and constructing a stability constraint. And a model prediction control framework based on a distributed Lyapunov function is further proposed, so that the multi-unmanned ship system can realize expected formation trajectory tracking and attitude consistency only depending on self-sensing and positioning information, and meanwhile, the formation stability is ensured. According to the method, under the condition that the speed of the pilot ship cannot be obtained, the speed can still be accurately estimated, and the control strategy can be optimized online, so that the intelligent sensing, positioning precision, control performance and robustness of the unmanned ship formation system are remarkably improved.

The invention provides an unmanned surface vehicle course tracking control method with signal quantization based on a double-expansion observer, and the method comprises the steps: building a third-order response type unmanned surface vehicle course control mathematical model according to the characteristics of a ship and the sea condition information of a surrounding environment; designing a double-expansion observer model for simultaneously estimating matched interference and non-matched interference in the ship course tracking control system and observing uncertain items and external interference in the ship control system; based on a backstepping method and a dynamic surface control algorithm, a course controller of the unmanned surface vehicle is designed, and the calculation complexity brought by a virtual control law is reduced; based on the Lyapunov stability theory, the stability of the designed unmanned surface vehicle course tracking control system with state quantization and input quantization is proved, all signals in a closed-loop system are consistent and bounded in a semi-global mode, and the tracking error is arbitrarily small by adjusting parameters of a controller.

The invention provides a preset time adaptive fuzzy attitude control method and system for multiple unmanned aerial vehicles, and relates to the technical field of multi-unmanned aerial vehicle cooperative control, and the method comprises the steps: obtaining a communication topological relation of a to-be-controlled multi-unmanned aerial vehicle system and the structure information of a single unmanned aerial vehicle; establishing an attitude dynamics model of the single unmanned aerial vehicle according to the structure information of the single unmanned aerial vehicle, and converting the model into a state model; based on the state model, designing a preset time series-parallel estimation model for estimating the state of the unmanned aerial vehicle; designing a controller and a composite adaptive law based on the communication topological relation in combination with a preset time series-parallel estimation model and a backstepping method; and carrying out adaptive backstepping control on the attitude of the multi-unmanned aerial vehicle system under a frame of preset time control by using a controller and a composite adaptive law, the approximation precision of the fuzzy logic system is improved by using a serial-parallel estimation model; and by using a preset time technology, the consistent target tracking of the multi-six-rotor unmanned aerial vehicle is realized.

The invention discloses a bipartite consistency control method of an unmanned aerial vehicle cluster under lagging full-state constraint, and relates to the technical field of unmanned aerial vehicle cluster cooperative control, comprising the following steps: establishing an unmanned aerial vehicle attitude dynamic model subjected to lagging full-state constraint and input saturation; constructing a coordinate conversion mechanism, and converting an original constrained system into an equivalent unconstrained system; constructing a cooperation-competition coexistence topology communication network, and defining an error dynamic state in combination with a self-adaptive backstepping control technology; an interval type-2 fuzzy logic system and a self-triggering communication protocol are integrated, and a self-adaptive fuzzy self-triggering fixed-time bipartite consistency controller is designed. According to the method, feasibility conditions do not need to be preset, through innovative coordinate conversion and control strategies, the problem of fixed-time dichotomy consistency control of the unmanned aerial vehicle cluster under lagging full-state constraint and input saturation is effectively solved, meanwhile, the network communication load is remarkably reduced by means of a self-triggering mechanism, and the system reliability is improved. And the control precision and the resource utilization efficiency of the system are improved.

This invention discloses a control method and system for a dual-link manipulator based on a neural network observer, comprising the following steps: Step 1. Establishing a dynamic model of the dual-link manipulator under external attacks and disturbances; Step 2. Establishing a neural network observer based on the dynamic model; Step 3. Establishing a control scheme for the dual-link manipulator based on reinforcement learning, the dynamic model, and the neural network observer; Step 4. Performing adaptive safety control of the dual-link manipulator based on the control scheme within the backstepping framework; This invention observes attacks and disturbances caused by unknown factors, as well as rapidly changing attacks and disturbances; Through a performance index function, the controller enables the control of the dual-link manipulator; The technical solution of this invention utilizes the learning ability of reinforcement learning algorithms and employs gradient descent to design an adaptive update rate for the Actor-Critic neural network, enabling the approximate controller to approximate the actual controller.

The invention provides a motorcade active-disturbance-rejection control method and system with a variable time interval strategy. The method comprises the following steps: acquiring state information of each vehicle in a vehicle queue system; the leader vehicle and the following vehicle carry out information transmission; under the condition of considering external disturbance, a vehicle dynamics model referring to the Newton second law is established, and a variable time interval strategy is constructed; compensating unmodeled dynamic and external disturbances in the vehicle dynamics model by using a time-varying gain expansion state observer in an active disturbance rejection control technology, and constructing a virtual controller and an actual controller based on a backstepping method; and according to the constructed virtual controller and the actual controller, realizing position and speed synchronization of the following vehicle and the leading vehicle in the queue under the condition of considering unmodeled dynamics and external disturbance. According to the method, the non-smooth problem at the saturation threshold is solved, the fluctuation influence can be effectively reduced, the safety is guaranteed, and the passing efficiency is improved; and the problem of gain attenuation is solved while the high gain characteristic is reserved.

The invention discloses a method and a device for designing a multi-anti-interference incremental backstepping observer based on specified time, and belongs to the technical field of signal tracking and processing. The method comprises the following steps: establishing a system dynamics model containing time-varying disturbance and model uncertainty items; scaling the tracking error and the estimation error by using a scaling function so as to realize the accurate convergence of the system state and the disturbance estimation within the specified time T; combining the scaled error, introducing an incremental backstepping control thought, and designing an incremental backstepping observer capable of processing model uncertainty and multiple disturbances at the same time; under the condition that the total disturbance and the derivative thereof are assumed to be bounded, stability analysis is carried out through a Lyapunov function, and constraint conditions of system stability convergence are deduced; and finally, verifying the effectiveness and superiority of the observer under various input and disturbance working conditions through simulation. The method is suitable for a high-dynamic and time-sensitive precision control system.

The invention discloses a multi-mechanical-arm system random predefined time control method based on event triggering, belongs to the technical field of control, is used for time control of a multi-mechanical-arm system, and comprises the steps that a kinetic equation of the multi-mechanical-arm system is introduced, a track error tracking system is introduced, and a consensus error of the multi-mechanical-arm system is obtained; an unknown function in a kinetic equation of the multi-mechanical-arm system is estimated, a virtual control signal, a self-adaption rate and an event triggering mechanism are designed according to a self-adaption backstepping method, and stability analysis is conducted in combination with the Lyapunov stability theory. An event triggering mechanism is adopted at the same time, the updating frequency of the controller is reduced, and consensus errors of the experimental multi-mechanical-arm system can be converged into a small neighborhood within predefined time of 1 s in combination with the consensus errors of the experimental multi-mechanical-arm system.

The invention discloses a safety control method of a high-order chain type multi-agent system under spoofing attack, and belongs to the technical field of safety control of multi-agent systems. The method comprises the following steps: establishing a dynamic model of a high-order chain type multi-agent system; constructing an extreme attack scene in which all communication links are subjected to bounded spoofing attacks; based on a backstepping control method, a distributed fixed time security control protocol is designed for a system, and the protocol counteracts attack influence by designing a virtual control strategy and a Lyapunov function; a Lyapunov stability theory is utilized to prove that under the action of the protocol, a system tracking error can be converged to zero within fixed time, so that safe and consistent tracking is realized. The defect that the prior art mainly aims at a linear system or only can realize asymptotic convergence is overcome, the method is particularly suitable for scenes such as non-complete constraint wheeled mobile robots, and the robustness and the rapid recovery capability of the system under extreme spoofing attacks are effectively improved.

The invention discloses a hydrofoil with an adjustable attack angle for an electric control type boat and a control system, relates to the technical field of attack angle control, is used for solving the hidden danger of grounding caused by insufficient underwater distance and limited lift force compensation during navigation in a shallow water area, and comprises a working condition judgment module, a backstepping fitting module, a risk grade judgment module and an attack angle execution module, the modules are in signal connection; the working condition judgment module obtains a water depth value, a draught value and a water leaving height value through a sensor, calculates a bottom gap and compares the bottom gap with a safe minimum gap, and judges shallow water working condition triggering; the backstepping fitting module calculates the actual lift force by combining the gravity, the buoyancy and the vertical acceleration of the boat body when the shallow water working condition is triggered, and fits the shallow water corrected lift force slope; the risk grade judgment module calculates the residual available lifting force and the lifting force required by lifting, and sets a risk flag bit through a dual-condition criterion; and the attack angle execution module adjusts the attack angle according to the risk flag bit to realize closed-loop control.

The application belongs to the technical field of distributed vehicle platoon control, and provides a vehicle platoon control method and system with a time-varying gain extended state observer, which comprises establishing a vehicle dynamics model; external disturbances are estimated in real time based on the time-varying gain extended state observer, and the initial differential peak value phenomenon is effectively inhibited; the stability analysis of the observer system is discussed in different cases, and it is verified that the time-varying gain extended state observer has a more rigorous and simple stability proof process; an extended state observer for compensating external disturbances and unknown nonlinear terms of the model is designed, a virtual controller and an actual controller are constructed by using the backstepping method based on the extended state observer and the fixed-time stability theory; by designing a fast fixed-time backstepping control method, the system state converges to the expected signal in a fixed time, and the system obtains good tracking performance.

The application relates to the technical field of multi-spacecraft cooperative control, and discloses a multi-spacecraft grouping consistency restraint control method and device under optimized FLS, which comprises the following steps: acquiring the network topology of a heterogeneous multi-spacecraft system and constructing a multi-subgroup directed communication topology network, constructing a spacecraft attitude control system model based on modified Rodrigues parameters; approximating unknown nonlinear terms in the model through a fuzzy logic system, constructing a fuzzy logic system based on a gradient descent algorithm and Armijo line search criterion; constructing a restraint control term and using a backstepping method to construct a virtual control law, combining the output of the fuzzy logic system based on the gradient descent algorithm and the Armijo line search criterion to construct an actual control input law, so that grouping consistency restraint control of the heterogeneous multi-spacecraft system is realized. The application can improve real-time approximation precision and adaptive step length adjustment capability while guaranteeing grouping consistency, and can enhance topology applicability and task cooperation flexibility.

The application discloses a rocket attitude self-adaptive control method and system based on reinforcement learning, and belongs to the technical field of rocket attitude control. The method constructs an adaptive controller for controlling the rocket attitude through a backstepping method, and the adaptive controller is used for realizing the self-adaptation of the rocket to unknown disturbances based on an Actor-Critic (AC) of reinforcement learning, so that the system can rapidly converge to a desired state, unknown nonlinear observation is realized without depending on an internal model, and the tracking control of the rocket attitude is realized.

This invention addresses the common failure problems encountered by actuators during the flight of heavy-lift launch vehicles in disturbed environments. It studies a method for achieving rocket attitude stabilization and tracking under complex conditions, proposing an adaptive fault-tolerant backstepping attitude control design method. First, to avoid attitude singularities, a quaternion-based kinematic and dynamic model of the launch vehicle oriented towards actuator failures is established. Based on this model, an adaptive fault-tolerant backstepping attitude controller is designed to adaptively estimate and compensate for uncertainties and external disturbances, handling potential failures and ensuring the stability of the control system. The algorithm proposed in this invention is more effective and superior than traditional adaptive backstepping methods.

The present application belongs to the technical field of trajectory tracking control of nonholonomic wheeled mobile robots, and specifically discloses a trajectory tracking control method and system for nonholonomic wheeled mobile robots. In the trajectory tracking process of the nonholonomic wheeled mobile robot, the present application method converges the position tracking error and the attitude tracking error to an arbitrarily small compact set near the origin within a limited time through steps such as designing an adaptive neural state observer, a finite-time command filter, an error compensation mechanism, a virtual control input, and an actual control signal. The present application not only avoids the calculation complexity explosion problem caused by repeated derivation of the virtual control signal in the traditional backstepping method, but also guarantees that the trajectory tracking error of the nonholonomic wheeled mobile robot converges to an arbitrarily small neighborhood within a limited time under the conditions of unknown nonlinear dynamics and unmeasurable speed, and all signals in the closed-loop system are ultimately bounded.

A recursive RISE control method and system for maglev train levitation systems is disclosed. The control method includes: constructing the dynamic equations and voltage balance equations of the electromagnets based on a single-point levitation system, and then constructing a dynamic model of the single-point levitation system accordingly; designing a virtual control law, and then designing a recursive RISE controller based on the backstepping method by combining the dynamic model of the single-point levitation system and the virtual control law; performing stability analysis on the RISE controller to obtain its stability conditions; and, based on satisfying the stability conditions, using the RISE controller to perform real-time control of the levitation gap of the maglev train levitation system. This invention has excellent anti-interference capabilities, reducing the impact of external interference or model uncertainty on levitation accuracy. Furthermore, by handling the nonlinear relationship between voltage and current through the backstepping method, this invention avoids the model mismatch problem caused by linearization.

This invention discloses a method for improving the synchronization stability of a grid-connected inverter based on backstepping, comprising: setting a low-pass filter in the active power-frequency droop control loop of the grid-connected inverter; establishing a corresponding state model based on the dynamic characteristics of the low-pass filter; constructing intermediate state variables according to the state model; and recursively deriving the control input expression based on the intermediate state variables using the backstepping control method to obtain a control law that satisfies the Lyapunov stability condition; introducing the control law into the active power-frequency droop control loop to adjust the output frequency of the grid-connected inverter, thereby optimizing the active power-frequency droop control strategy of the grid-connected inverter. This invention only requires superimposing the designed controller on the synchronization loop to effectively enhance the dynamic stability of the system and avoid instability and oscillations caused by factors such as temperature drift and component aging.