518 results about "Backstepping" patented technology

The invention presents a design method of a four-rotor fault-tolerant controller based on a nonlinear observer. The method includes the following steps: establishing a dynamic model of a four-rotor unmanned aerial vehicle (UAV), and dividing the UAV system into an attitude subsystem and a position subsystem; for the attitude subsystem, establishing a fault model, designing a nonlinear fault observer, carrying out real-time detection and online estimation on an unknown actuator fault, and designing a fault-tolerant controller based on a fast non-singular terminal sliding mode method by using the obtained fault estimation information; and for the position subsystem, inversely solving the control rate and the desired attitude angle of the position subsystem by combining a backstepping methodand a sliding mode method and designing an intermediate virtual quantity. A four-rotor UAV is enabled to track the desired position and yaw angle even when the actuator fails, so as to ensure the stability of the pitch angle and roll angle.

The invention discloses a method in a boat control field and especially relates to the sliding mode-reverse step double loop trace tracking control method of an underactuated unmanned surface vehicle.The method comprises the following steps of firstly, establishing a three-degree-of-freedom motion mathematical model of the heading, the surging and the swaying of the unmanned surface vehicle; then, through an integrated pose sensor, measuring the current position information of the unmanned surface vehicle, combining the real-time position and the reference trace of the unmanned surface vehicle, calculating an error under a boat body coordinate system; and then, designing a kinematic loop trace tracking controller based on a backstepping method, and designing a dynamic loop trace trackingcontroller based on a sliding mode control algorithm. Through a sliding mode-reverse step double loop trace tracking controller, the trace tracking control of the unmanned surface vehicle Is realized,the unmanned surface vehicle can track a linear trace, and the stability and accuracy of unmanned surface vehicle navigation can be increased.

The invention provides an underactuated UUV plane trajectory tracking control method based on dynamic speed adjustment, relating to the motion control technology of an underactuated underwater unmanned vehicle. The invention aims to realize the precise tracking control of an underactuated UUV plane trajectory. The method comprises the steps of (1) a UUV obtains position and attitude information according to a current task, (2) position and attitude error variables are obtained by using the mathematical model of an underactuated UUV, (3) a method of defining a virtual speed error variable to calculate a virtual control rule, (4) combined with a biologically inspired model, the dynamic adjustment of a speed error is carried out, and (5) the control signal generated by a speed adjustment controller is deduced, and the underactuated UUV plane trajectory tracking control is realized. According to the method, the dynamic adjustment of the speed of the underactuated UUV can be carried out, a singular value when a first direction angle error is equal to 90 degrees in a traditional backstepping method is avoided, and the tracking of a circular trajectory in an external constant disturbance is realized.

The invention discloses a specific performance based consistency control method for multiple intelligent agents. The control method comprises that the intelligent agents as communication nodes establish a communication topology; neighbor node and self state information is obtained according to the communication topology; the state information includes the position and speed; a tracking error of aleader is calculated according to the state information; the specific performance of the tracking error is transformed via a design performance function, and a transformed error model is obtained; andaccording to the transformed error model, an event triggering adaptive controller of a follower is designed via a backstepping method and a dynamic surface technology, an event triggering mechanism is designed, and specific performance based consistency control for the intelligent agents is realized. A system can obtain expected transient performance and stable error in the control process rapidly and precisely, the communication cost among the intelligent agents can be reduced, the application range is wide, and the application value is high.

The invention provides a trajectory tracking method for a four-wheel-driven wheeled mobile robot. The method comprises the steps of firstly establishing a kinematic model, a dynamic model and a driving motor model of a system; then designing a kinematic controller for adjusting speed of the system according to a given reference trajectory based on the kinematic model; operating the kinematic controller for obtaining the anticipated torque of a motor according to the speed of a to-be-adjusted system based on the kinematic model; designing a driving motor controller for designing an appropriate driving voltage of the system for satisfying the anticipated torque of the motor based on the driving motor model; and finally performing trajectory tracking control on the four-wheel-driven wheeled mobile robot according to a backstepping robustness trajectory tracking control method. The trajectory tracking method according to the invention realizes a purpose of improving stability of a four-wheel-driven wheeled mobile robot control system in a complicated uncertain environment and furthermore improves system controlling effectiveness on the condition with uncertain factors.

The invention provides a fisheye image correcting method for image stitching. The method corrects two fisheye images partially overlapped with each other through a computer, and finds out a splicing angle of stitching caused by pitch angles during shooting between the two fisheye images by adopting an unique correction principle and utilizing matched pixels in the two fisheye images so as to obtain the pitching angle formed during the shooting of the two fisheye images through backstepping; and the method also avoids adverse impacts, such as inclination, ghosting, and the like, of errors of the pitch angles formed during the shooting on the panorama stitching of the fisheye images through pitching conversion mapping treatment, and has the advantages of better robustness and high accuracy in computation.

The invention provides a hybrid finite time control method for quadrotor accurate trajectory tracking. The method comprises the steps: establishing a kinematic model and a dynamical model of a quad-rotor unmanned aerial vehicle; designing a vertical control law of the vertical motion according to a height tracking error of the quadrotor unmanned aerial vehicle and an adaptive integral sliding surface design; on the basis of a horizontal position tracking error of the quadrotor unmanned aerial vehicle, designing a horizontal control law of the horizontal motion based on a backstepping method; and designing a finite time disturbance observer based on the attitude angle of quadrotor unmanned aerial vehicle and designing a precise attitude stability control law by combining a non-singular terminal sliding-mode control law and the finite time disturbance observer. According to the invention, the quad-rotor is classified into three subsystems of the height, horizontal position and attitude and three kinds of control strategies are designed respectively; and on the basis of the hybrid control scheme, the trajectory tracking error is stabilized rapidly. The accurate trajectory tracking ofthe quadrotor can be realized under the condition that the unknown model parameters and the external disturbance are allowed; and the manipulation is more flexible.

The invention belongs to the technical field of electromagnetic wave polarization detection, and particularly discloses an efficient microwave polarization detection device based on a photonic spin Hall effect. For the detection device, electromagnetic wave to be detected is decomposed into left-hand circularly polarized beam and right-hand circularly polarized beam through the efficient photonic spin Hall effect, the module values and phases of the left-hand circularly polarized beam and right-hand circularly polarized beam are respectively measured, and backstepping is carried out to obtain the polarization of the electromagnetic wave to be detected. The photonic spin Hall effect is realized through linear geometry Berry phase gradient of total-reflection type meta-surface with a spin structure. Compared with the traditional polarization detection manner (linear polarization loudspeakers opposite to each other are used for directly measuring x component and y component of electromagnetic wave), the efficient microwave polarization detection device has the advantages that higher convenience and quickness are achieved, the errors are few, and the stability is better. The operating frequency of the device is 10-14GHz, and the structure constants of meta-atoms are scaled in equal proportion or redesigned, so that the operating frequency can be applied to other operating frequency ranges.

The invention discloses a control method of a hypersonic vehicle orienting the uncertainty condition. The control method comprises the following steps that step S1, full state feedback linearization processing is performed on flight speed V and flight height h according to a hypersonic vehicle longitudinal dynamic equation so as to obtain a corresponding state equation; step S2, an anti-step sliding mode controller is designed according to the state equation, and the double exponential approximation law of the selected sliding mode surface is S<.>=-k<1>|S|<eta>sgn(S)-k<2>|S|<lambda>sgn(S), wherein k<1>>0, K<2>>2, eta>1 and 1>lambda>0 are parameters in the formula; and step S3, a test platform is established based on the anti-step sliding mode controller to perform performance simulation. According to the method, the double exponential sliding mode controller based on the backstepping method is adopted, and switching gain and the problem of buffeting existing in sliding mode control can be effectively reduced by the method.

The invention provides a welding microcell performance test based residual stress detection method, which comprises the following steps of: carrying out a micro-compression-shear test on a welding microcell so as to obtain a load-displacement curve of the welding microcell, establishing a 3D (three-dimensional) finite element model of a micro-compression-shear test process, and carrying out a finite element reverse backstepping method based on an improved Gurson model so as to obtain a true stress-strain relation of the welding microcell; computing the welding residual stress, wherein in the process of carrying out computing on a welding temperature field, the influence of the mechanical property of the welding microcell on the change of the temperature field is not considered; and after the welding temperature field is obtained, in the process of carrying out computing on a welding stress field, taking normal-temperature mechanical property parameters (when the temperature of a weldment is reduced according to the true stress-strain relation of the welding microcell) into a welding computing model, and then obtaining the welding residual stress through computing. The accuracy of the method disclosed by the invention is higher than that of a result obtained by using a residual stress computing method which is implemented through not considering the mechanical property of the welding microcell.

The invention discloses a fixed time formation control method based on a finite time disturbance observer and belongs to the field of multi-unmanned-ship cooperative control. The method comprises thefollowing steps: establishing dynamics and kinematics models of a piloted unmanned ship and a following unmanned ship, establishing an expected trajectory model of a piloted unmanned ship subsystem, and designing a fixed time tracking controller of the piloted unmanned ship subsystem in combination with an integral sliding mode surface so as to realize piloted unmanned ship trajectory control; designing a virtual speed of the following unmanned ship subsystem by adopting a backstepping method to determine a position error between the piloted unmanned ship and the following unmanned ship, and adjusting a tracking error between the piloted unmanned ship and the following unmanned ship by designing a tracking controller of the following unmanned ship; adopting a finite time disturbance observer and providing a fixed time formation control strategy based on a finite time observer in a complex environment in combination with a fixed time control law. Therefore, accurate formation control between the piloted unmanned ship and the following unmanned ship is realized, the maximum convergence time is calculated, the thought of a finite time disturbance observer is provided, and rapid and effective identification of external disturbance can be realized, so that the robustness of an unmanned ship formation system is improved.

The invention discloses a trajectory tracking controlling method of a six-rotor-wing air vehicle, and belongs to the field of controlling of spacecraft instrumentation. The method includes the steps: building a kinematics model of the air vehicle and a dynamics model in which the air vehicle has compound jamming situations based on a Newton-Euler equation; utilizing a second order sliding mode compound jamming motion estimation algorithm of a sign functional integration to offer a continuous jamming compensation term; then adopting a method that a linear differentiator and a nonlinear differentiator are combined to design a nonlinear differentiator with rapid convergence; combining the compound jamming motion estimation algorithm, the nonlinear differentiator and backstepping to design a compound controller of a gesture system of the air vehicle; finally adopting a PD method, designing a position controller of the air vehicle, calculating out gesture angle information needed for tracking a preset trajectory and controlling lift force. According to the trajectory tracking controlling method of the six-rotor-wing air vehicle, under the situation of compound jamming, the air vehicle still has good stability and control performance, and the preset trajectory can be accurately tracked.

The invention discloses a rigid spacecraft performer multi-fault diagnosis and fault tolerance control method. According to the method, the kinetic and dynamic model of a rigid spacecraft attitude control system is put forward, a fault model for existing of both the performance failure fault and the deviation fault of a rigid spacecraft is established, and then a fault detection observer adopting the adaptive threshold technology and a fault estimation observer based on the adaptive technology are respectively established so that online real-time detection and estimation of the fault time and the concrete situation of the fault can be realized, and finally a backstepping sliding mode fault tolerance controller is designed according to fault information established by the fault estimation observer. Attitude stabilization control of the rigid spacecraft under the condition of the performer efficiency damage and the deviation fault can be realized, and the influence of external disturbance on the system and the observers can also be considered in the design process. Besides, the fault detection observer and the fault estimation observer can be independently designed so that the engineering application can be more easily implemented.

The invention provides a four-rotor aircraft sliding mode control method based on a nonlinear disturbance observer. The influence of system uncertainty and external disturbance of the four-rotor aircraft is considered, the method comprises the following steps: firstly, establishing a four-rotor dynamical model considering external disturbance and providing a nonlinear disturbance observer to estimate the actual value of the external disturbance; the invention aims to ensure the stability of a four-rotor aircraft, four-rotor dynamics is decomposed into an attitude subsystem and a position subsystem according to the design thought of double rings, controllers are designed for the two subsystems respectively, the nonsingular fast terminal sliding mode controller designed for the inner ring can ensure fast convergence of the attitude, backstepping and the nonsingular fast terminal sliding mode are combined and applied to an outer ring, the tracking performance is guaranteed, and the methodhas good tracking performance and high robustness for the four-rotor aircraft with system uncertainty and external disturbance.

The invention discloses a method for measuring plantar pressure. The method mainly aims at reducing cost for accurate monitoring of plantar pressure information. A plantar pressure measurement device with lots of sensing points is first utilized for measuring the plantar pressure information; a model is established according to the information and a modeling method put forwards in the method and plantar pressure models; the model can present differences between different persons; finally, a plantar pressure measurement device with few sensing points is used for monitoring the plantar pressure information of a measurer; the plantar pressure information of various position points on the planta pedis is obtained through model backstepping reduction, and therefore complete and accurate plantar pressure information can be obtained through the simple devices. A layout of sensor arrays at different intervals is used for the optimized measurement device with lots of sensing points, and the optimized measurement device with few sensing points is obtained through embeddable structures of sensor units. Two kinds of models are used as the plantar pressure models and include a neural network model and an interpolation model relevant to distance.

The invention discloses a method for controlling a dynamic surface of a flexible joint mechanical arm. The method comprises the following steps of: 1, analyzing a flexible joint mechanical arm system model, and constructing; 2, controlling and designing the dynamic surface of the flexible joint mechanical arm; 3, inspecting tracking performance, and adjusting parameters; and 4, finishing the design. By the method, virtual control is gradually designed for a flexible joint mechanical arm control system model, a first-order low-pass filter is arranged in each step, and the dynamic surface of the flexible joint mechanical arm can be controlled, so that the phenomenon of differential explosion controlled by reverse thrust is eliminated, the semi-global stability of a closed-loop control system can be ensured, and a preset track can be quickly and accurately tracked by the angle of a connecting rod of the flexible joint mechanical arm at the same time. The method has a wide application prospect in the technical field of automatic control.

An AUV horizontal planar path tracking control method based on a neural dynamic model and a backstepping method relates to the technical field of horizontal planar path tracking control of under-actuated AUV. The method improves AUV path tracking control precision. A neural dynamic model theory is introduced and has the characteristics of smooth input and output. Virtual controlled variables appeared in the backstepping method designing process flows by the neural dynamic model, so that complex derivation calculation of the virtual controlled variables is avoided. Compared with a conventional backstepping method, the method prevents a possible parameter blast phenomenon, and substantially improves the control precision of a system.

The invention discloses a multisource disturbance actuator saturation integrated spacecraft relative attitude control method. The method includes: starting from spacecraft relative attitude kinematicand kinetic equations to perform characteristic analysis and classification of multisource disturbances in a system; then, estimating disturbances with different characteristics by taking advantages of estimation performances of a disturbance observer, a radial basis function neural network and an extended state observer; next, designing an anti-saturation compensator to avoid damages caused by saturation upper limit exceeding of a spacecraft execution mechanism; finally, designing a composite controller according to a backstepping method on the basis of multisource disturbance observation values and anti-saturation compensation items. Therefore, adverse effects of multisource disturbances on the system are avoided, system robustness is improved, accurate spacecraft relative attitude control in a saturation range is guaranteed by the execution mechanism, and smoothness in space operation task completion is guaranteed.

The invention belongs to the technical field of trace tracking and dynamic sliding mode control of a UUV (unmanned underwater vehicle), and particularly relates to a UUV trace tracking method based on dynamic sliding mode control. The method comprises the following steps: building a UUV horizontal plane model; obtaining an error variable through coordinate transformation, and performing derivation on the error variable to obtain a derivative coefficient of the error variable; constructing a lyapunov function, and defining a virtual speed control variable to transform attitude tracking into virtual speed control; stabilizing the virtual speed control variable, adaptively estimating system parameter inaccuracy and external time-varying disturbance by a sliding mode control method, and constructing a sliding mode dynamic function; selecting a dynamic sliding mode control law to realize trace tracking of the UUV. By the combination of a backstepping method and an adaptive dynamic sliding mode control technology, the possible problems of modeling uncertainty and unknown environmental disturbance of UUV planar trace tracking and the problem of uncertain system parameters are solved.

The invention discloses a multi-joint industrial mechanical arm backstepping finite time sliding mode control method considering system sum disturbance. The multi-joint industrial mechanical arm backstepping finite time sliding mode control method includes the steps: establishing a multi-joint industrial mechanical arm system model; designing a system three-order expansion state observer for accurately estimating the system sum disturbance item; based on system sum disturbance estimation, and for the system model (2), performing system backstepping finite time sliding mode control rule designby combining the backstepping design idea and the finite time sliding mode technology. The multi-joint industrial mechanical arm backstepping finite time sliding mode control method has strong robustness for nondeterminacy factors, such as model parameter perturbation and external bounded disturbance, and can guarantee fast and stable finite time tracking control of the desired trajectory of the system, so that the designed control method is convenient for application in practical engineering.

The invention discloses an underwater robot sliding mode control method based on adaptive backstepping in order to solve the technical problem that an existing underwater robot control method is poorin practicability. According to the technical scheme, the method comprises the steps that based on the decomposition of a complex nonlinear system, the controlling quantity of a total system is obtained by designing the virtual controlling quantity for a sub-system through the step-by-step recursion of a sliding mode; according to the buffeting problem caused when the system is not sure about theupper bound, and an RBF neural network is introduced into a controller so as to adoptively approach the internal indeterminacy and the external disturbance of the system. Finally, the control over thesystem buffeting is achieved, high-precision tracking control is achieved, the robustness of a closed-loop system is improved, the engineering requirements are met, and the practicability is high.

The invention, which belongs to the automatic driving and intelligent traffic field, provides an adaptive coordination control method for intelligent vehicle steering and braking. The method comprises: (1), an identification method of an expected path is designed and an intelligent vehicle steering and braking coupling dynamics model is established; (2), with a backstepping sliding mode control technology, an intelligent vehicle steering and braking coordination control model is designed by using vehicle horizontal path tracking and braking speed control as objectives; (3), an on-line real-time approaching control law, being similar to that in the step (2), of a fuzzy system is designed and thus adaptive adjustment of the approaching control law is realized, so that a buffeting phenomenon caused by a backstepping sliding mode in dynamic steering and brake coordinated control can be avoided; and (4), stability of the dynamic automobile steering and brake coordinated control system is analyzed. Therefore, defects of strong coupling, non linearity, and parameter uncertainty of the automobile steering and brake dynamics can be overcome effectively; the real-time performance and stability of emergency obstacle avoidance can be guaranteed; dependence on the control model can be eliminated; robustness of parameter uncertainty can be enhanced; the overall performance is improved; and the cost is lowered.

The invention provides a flexible satellite neural network backstepping sliding mode attitude control method, relates to a flexible spacecraft attitude control method, and aims at solving a problem of perturbation generated by plate flexible vibration and antenna rotation and a problem of enhancement of steady state precision and stability of existing attitude control methods. According to the method, a flexible satellite attitude kinetic model is established firstly according to a spacecraft, and then a model formula is processed; a sliding mode attitude controller (which is expressed in the specification) based on a backstepping method is designed; then an RBF neural network approach (eta+htau)sgn(sigma) is adopted; the controller (which is expressed in the specification) is designed; and finally a complete attitude controller (which is expressed in the specification) is obtained. A three-axis attitude controller is designed respectively according to the aforementioned process. The flexible satellite neural network backstepping sliding mode attitude control method is suitable for the field of flexible spacecraft attitude control.

The invention discloses a control method of a driving system of a permanent magnet synchronous motor of an electrical automobile considering iron loss, and provides a control method of a driving system of a permanent magnetic synchronous motor considering iron loss based on a self-adaptive fuzzy backstepping method, which solves the non-linear problem of the power driving and control system of the motor of the electrical automobile, enables the motor to quickly reach the stable running state and is more suitable for the control objects requiring quick dynamic response, such as the driving system of the electrical automobile. The control rules u[d] and u[q] only adopt one self-adaptive parameter theta, so as to reduce the calculation amount. The method has the advantages that the problem of position tracking and control of the permanent magnet synchronous motor considering the iron loss under the conditions of orienting to the site and having undetermined parameter and load torque disturbance is solved; the fuzzy logic system is used for approximating to the unknown non-linear item, and the self-adaptive fuzzy backstepping method is used for enabling the tracking error to approximate to 0; the more accurate control precision is reached, and the ideal position tracking and control effect is ensured.

The present invention discloses an electric vehicle asynchronous motor fuzzy adaptive dynamic surface control method with the consideration of an iron loss. According to the control method, by using the nonlinear function in a fuzzy logic system approximation system, an adaptive backstepping method is used to design a controller, and the dynamic surface control technology and a fuzzy adaptive method are combined. Through introducing a first-order low-pass filter, a 'computing explosion' problem caused by continuous derivation in traditional backstepping control is successfully overcome. In addition, control signals uqs and uds only exist in an adaptive parameter Theta<^>, and the amount of computation is reduced. Through fuzzy adaptive dynamic surface control method adjustment, motor operation can rapidly reaches a stable state and is more suitable for a control object with the need of rapid dynamic response like an electric vehicle driving system, a simulation result shows that the influence of parameter uncertainty is overcome and an ideal control effect is ensured according to the control method, and the rapid and stable response of rotation speed is realized.

The invention discloses an electronic throttle valve adaptive backstepping control method based on a Romberg sliding-mode observer, and relates to the technical field of automobile electronic control. Firstly, in order to solve the problem that the change of the opening degree of an electronic throttle valve can not be measured, the change is estimated through the Romberg sliding-mode observer and based on the electronic throttle valve state equation; secondly, approaching is conducted on the nonlinear unknown quantity-gear clearance torque through the approaching characteristic of an RBF neural network; finally, a control law, an RBF network weight renewing law and an interference adaptive law are designed based on the Lyapunov stability theory and through combination with the nonlinear backstepping control method. By means of the method, the problem that nonlinear factors and some parameters easily change over time during electronic throttle valve control can be well solved, and the control effect and dynamic response performance are further improved.

The invention discloses a four-rotor UAV flight control method based on a fractional order power switching law. A whole controller is of a backstepping control structure, a second-order nonlinear system of a quadrotor UAV is split into two subsystems, control laws that satisfy Lyapunov's stability theory are constructed, and the two subsystems are in series connection through a virtual intermediate control variable to form the complete controller, so that the controller can well adapt to the nonlinearity of the system and have good integrity. At the same time, in order to enhance the anti-disturbance capability and robustness of the controller, in the second backstepping design, the controlled variable is subjected to the sliding mode control design, which introduces the high disturbance resistance and high robustness of the sliding mode control. .

The invention discloses an aircraft track inclination angle control method based on a minimum parameter studying method. The aircraft track inclination angle control method comprises the following four steps; 1, analyzing and modeling a longitudinal aircraft control system; 2, controlling and designing a neural network dynamic surface based on the minimum parameter studying method; 3, testing tracking performance and regulating parameters; and 4, ending the design. In the aircraft track inclination angle control method, for a longitudinal aircraft model, an unknown function of a neural network approximating system is established; the number of parameters to be estimated is reduced by the minimum parameter studying method; the virtual control is gradually designed; a first-order low-pass filter is introduced in each step; and the neural network dynamic surface control is ultimately deduced. A differential explosion phenomenon in a reversal deduction control is overcome, and the rapid and accurate tracking of the aircraft track inclination angle on a preset track can be realized.

The present invention discloses a permanent magnet synchronous motor adaptive sliding mode control method based on a dynamic surface. The method comprises the following steps of: establishing a permanent magnet synchronous motor standardization model with time varying and time lag; applying a single-weight RBF neural network with an approaching function for processing unknown disturbance and unknown system dynamics into the design of a controller; and performing design of an adaptive sliding mode controller in a backstepping frame, wherein a first-order low pass filter is introduced to processthe problem of 'differential item explosion' in a traditional backstepping control, a rapid terminal sliding mode is employed to further improve the tracking precision and obtain better performances,and an adaptive sliding mode control method is employed in a condition of merging of the rapid terminal sliding mode surface, the first-order low pass filter and the RBF neural network. The method reduces the requirements of system accurate modeling and parameter accurate measurement, simplifies the controller design, overcomes the influences of external disturbance, chaos vibration and time varying and time delay on the system and improves the system operation stability and motion precision.

Provided is a four-rotor aircraft output-limited backstepping control method based on an integral sliding mode obstacle Lyapunov function. For the dynamic system of a four-rotor aircraft, an integralsliding mode obstacle Lyapunov function is selected, and a four-rotor aircraft output-limited backstepping control method based on the integral sliding mode obstacle Lyapunov function is designed. Theintegral sliding mode obstacle Lyapunov function is designed in order to ensure that the output of the system is limited within a certain range, avoid too large overshoot and reduce the time of arrival. Therefore, the dynamic response performance of the four-rotor aircraft system is improved. The invention provides a four-rotor aircraft output-limited backstepping control method based on an integral sliding mode obstacle Lyapunov function, which enables the system to have a good dynamic response process.