CN-121798639-B - Flexible joint mechanical arm AISMC compensation control method under singular perturbation decomposition

CN121798639BCN 121798639 BCN121798639 BCN 121798639BCN-121798639-B

Abstract

The invention discloses a flexible joint mechanical arm AISMC compensation control method under singular perturbation decomposition, which belongs to the field of flexible joint mechanical arm control and comprises the following steps of S1, establishing a flexible joint mechanical arm dynamics model containing uncertain compound disturbance and decoupling the model into a slow-change subsystem and a fast-change subsystem, S2, estimating lumped matching disturbance in the slow-change subsystem by using a compensation function observer, S3, constructing an integral sliding mode surface and a self-adaptive approach law with dead zone correction aiming at the slow-change subsystem, designing a linear secondary regulator aiming at the fast-change subsystem, defining a performance index and solving a Rickel equation to obtain an optimal control law, S4, superposing the control law of the slow-change subsystem and the control law of the fast-change subsystem to obtain integral control input, and S5, simulating and verifying. The flexible joint mechanical arm AISMC compensation control method under singular perturbation decomposition has the advantages of track tracking precision, robustness and stability, and wide application prospect.

Inventors

PAN CHANGZHONG
KUANG JIAQI
PAN YINGFENG
ZHANG YUKE

Assignees

湖南科技大学三亚研究院

Dates

Publication Date: 20260508
Application Date: 20260309

Claims (4)

1. The compensation control method of the flexible joint mechanical arm AISMC under singular perturbation decomposition is characterized by comprising the following steps of: S1, establishing a dynamic model of a flexible joint mechanical arm containing uncertain compound disturbance, and decoupling a flexible joint mechanical arm coupling dynamic system containing uncertain compound disturbance into a slow-change subsystem and a fast-change subsystem based on a singular perturbation theory; s2, estimating lumped matching disturbance in the slow-change subsystem by using a compensation function observer, determining an observer gain parameter through pole allocation, and verifying the exponential stability of the observer gain parameter; S3, designing a self-adaptive integral sliding mode controller aiming at the slow-change subsystem, constructing an integral sliding mode surface and a self-adaptive approach law with dead zone correction based on lumped matching disturbance, deducing a control law combined with disturbance feedforward compensation and verifying asymptotic stability of the slow-change subsystem; Designing a linear secondary regulator aiming at the quick-change subsystem, defining performance indexes and solving a Richa lifting equation to obtain an optimal control law, realizing optimal damping inhibition of elastic vibration and verifying asymptotic stability of the quick-change subsystem; S4, superposing a slow-change subsystem control law and a fast-change subsystem control law to obtain an overall control input, and verifying the asymptotic stability of the overall closed-loop system based on a Tikhonov theorem; S5, simulation verification; The step S1 specifically comprises the following steps: S11, based on Spong flexible joint mechanical arm simplified model, the non-matching disturbance of the connecting rod side is included Disturbance matching with motor side Establishing Dynamic model of connecting rod flexible joint mechanical arm: ; in the formula, Represents a positive definite inertia matrix, and ; 、、 Respectively represent the displacement, velocity and acceleration vectors of the joint angle, and ; Representing the matrix of coriolis and centrifugal forces, an ; Represents the gravity vector force, and ; Represents a diagonal positive matrix of joint stiffness coefficients, an ; 、 Respectively represents the angular displacement and the angular acceleration of the rotor of the motor after the action of the speed reducer, and ; Representing the moment of inertia matrix of the joint motor, and ; Representing an articulation motor torque control input vector, an ; S12, introducing the water into the reactor to meet Singular perturbation parameters of (2) Defining a scaled joint stiffness matrix And joint moment And setting the angular displacement of the joint Is a slow subvariable and joint moment Substituting the fast sub-variable into the dynamics model established in S11 to obtain a coupling equation of the slow sub-variable and the fast sub-variable: ; s13, order And control input with slow subsystem Replacement of original joint motor torque control input vector Obtaining the fast sub-variable Is a quasi-steady state value of (2) : ; S14, setting the quasi-steady state value Substituting a coupling equation, and decoupling to obtain a slow-change subsystem taking track tracking as a dominant one: ; Wherein, the ; In the formula, Representing lumped matching perturbations, an ; S15, defining quasi-steady state deviation of fast sub-variables Quasi-steady state deviation of fast sub-variables And a quasi-steady state value Substituting the coupling equation to obtain the information Fast-varying subsystem equations of (2): ; in the formula, Representing fast sub-variable quasi-steady state deviations Second derivative over time; representing a quasi-steady state value Second derivative over time; S16, enabling the quick change subsystem to control input Simultaneous introduction of fast time scales Satisfy the following requirements A fast-changing subsystem with elastic vibration suppression as a main component is obtained: 。
2. The method for compensating and controlling the flexible joint manipulator AISMC under singular perturbation decomposition according to claim 1, wherein the step S2 comprises the following steps of S21, enabling the state quantity of the subsystem to be changed slowly The slow-changing subsystem described in step S14 is rewritten as a form of the following state space equation: ; in the formula, Representing slowly changing subsystem state quantity First derivative with respect to time; representing slowly changing subsystem state quantity First derivative with respect to time; representing an equivalent inertial matrix of the slow-varying subsystem, an ; Representing the coriolis force and centrifugal force matrices; S22, recording disturbance item And consider it as the expanded state of the system, build the following expanded state equation: ; in the formula, Representing an extended state quantity First derivative with respect to time, and ; Representing disturbance terms First derivative with respect to time; s23, constructing a compensation function observer based on an extended state equation, wherein the expression is as follows: ; in the formula, Representing the system state quantity of the observer, and ; Representing system state quantity of observer First derivative with respect to time; Representing a state error feedback gain matrix of the observer, an , Representing the diagonal matrix constructor, And Respectively represent gain matrix Is the first of (2) Diagonal elements; Representing an estimation error of the system state, an , Representing state quantity Corresponding state to observer Deviation of (2); representing state quantity Corresponding state to observer Is used for the deviation of (a), Representing a transpose; A disturbance estimation gain matrix representing the observer, and , Disturbance estimation gain matrix representing observer Is the first of (2) Diagonal elements; representing disturbance terms And (2) estimated value of (2) ; S24, defining an estimation error Subtracting the extended state equation of step S22 from the observer equation of step S23 yields the set of equations for observer error: ; in the formula, 、 And Respectively represent observer error components 、 And First derivative with respect to time; S25, recording error vector of observer The set of equations for the observer error described in step S24 is sorted as follows: ; Wherein, the ; ; In the formula, And Representing block diagonal matrices, respectively And Middle (f) Matrix of sub-blocks, and ; Representing observer error vectors First derivative with respect to time, and , ; Obtaining The characteristic equation of (2) is as follows: ; in the formula, Complex frequency variables representing the characteristic equation; And State error feedback gain matrix respectively representing compensation function observer The first of (3) Diagonal elements; s26, will The pole configuration in the characteristic equation of (2) is as follows Gain parameters are obtained through the following pole allocation relations: ; in the formula, A scaling factor representing the pole configuration; represents observer bandwidth, an ; S27, verifying the stability of the observer when the condition is met When the method is used, routh-Hurwitz criteria prove that the index of the compensation function observer is stable, and the disturbance steady-state estimation error is zero.
3. The compensation control method of the flexible joint manipulator AISMC under singular perturbation decomposition according to claim 2, wherein the step S3 specifically comprises the following steps: s31, designing a self-adaptive integral sliding mode controller to realize track tracking control of a slow-change subsystem; s311, defining a slow-change subsystem tracking error vector , : ; In the formula, Representing a slowly varying subsystem tracking error First derivative with respect to time; Desired trajectory representing joint angle Is a derivative of (2); And Respectively represent tracking error vectors And Is the first of (2) A component; s312, substituting the expression in the step S311 into the state space equation in the step S21 to obtain a system tracking error dynamics equation: ; in the formula, Representing a slowly varying subsystem tracking error Second derivative over time; Representing a desired trajectory Second derivative over time; s313, constructing a sliding mode surface function vector , Representing a sliding mode surface function vector Is the first of (2) Each component, and , And All represent the gain of the positive sliding mode surface, which satisfies , A characteristic polynomial representing the surface of the slide, Representing complex frequency variations in the feature polynomial, Representing the bandwidth of the adaptive integral sliding mode controller; representing a time variable; S314, designing an adaptive approach law with dead zone correction: ; ; in the formula, And Respectively represent And First derivative with respect to time; And All represent dead zone thresholds, and ; And Respectively represent And Reference adjustment coefficients of (a); s315, described in step S313 One derivation is performed and the obtained result is substituted into the observer expression of the compensation function in the step S23, the system tracking error dynamics equation in the step S312 and Obtaining the control law of the slow subsystem : ; Wherein, the Is an estimate of the lumped disturbance; ; in the formula, Representing a sliding mode surface function Is a first derivative of time; Represents a saturation function, an ; And All represent a gain matrix for sliding mode control, an , , And Respectively represent And Is the first of (2) A plurality of adaptive gains; representing a sliding mode surface function Is not limited by the saturation limit of (2); S316, verifying stability of the slow-change subsystem, namely constructing a Lyapunov function of the slow-change subsystem : , Wherein, the ; ; In the formula, Representing adaptive gain And actual gain Is a deviation term of (2); representing adaptive gain And actual gain Is a deviation term of (2); And All represent positive weight coefficients of adaptive error terms in the Lyapunov function, an ; By proving First derivative with respect to time Verifying limited time convergence of a sliding die surface and asymptotic stability of a system; s32, designing a linear secondary regulator to realize the elastic vibration suppression of the quick-change subsystem; S321, performing state modeling on the quick-change subsystem obtained in the step S16, and defining a state vector of the quick-change subsystem Constructing a state equation of the fast-changing subsystem: wherein, the method comprises the steps of, ; ; In the formula, Representing a state matrix of the fast-changing subsystem, and ; A control input matrix representing a fast-changing subsystem, an ; Represents an identity matrix, and ; Representing a fast time scale; s322, defining quadratic performance index of linear quadratic regulator : ; In the formula, Represents a state weight matrix, an ; Representing a control input weight matrix, an ; S323, solving the optimal control law, namely, solving Li Kadi matrix equation Obtaining a forward solution Thereby obtaining the optimal control law of the fast-changing subsystem : ; Wherein K f is the optimal feedback gain, an ; S324, verifying stability of the quick change subsystem, namely constructing a Lyapunov function of the quick change subsystem: ; By proving And verifying asymptotically stability of the fast-changing subsystem.
4. The method for compensating and controlling the flexible joint manipulator AISMC under singular perturbation decomposition according to claim 3, wherein the step S4 specifically comprises the following steps: S41, synthesizing an overall control input, namely synthesizing the slow-change subsystem control law obtained in the step S315 And the fast-changing subsystem optimal control law obtained in step S323 Superposition to obtain integral control input of flexible joint mechanical arm ; And S42, verifying the stability of the whole system, namely, based on the Tikhonov theorem, combining the stability conclusion of the slow-change subsystem and the fast-change subsystem verified in the step S4, and proving the asymptotically stable of the whole closed-loop system.

Description

Flexible joint mechanical arm AISMC compensation control method under singular perturbation decomposition Technical Field The invention relates to the technical field of flexible joint mechanical arm control, in particular to a flexible joint mechanical arm AISMC compensation control method under singular perturbation decomposition. Background With the rapid development of the fields of industrial automation, medical robots, intelligent agriculture and the like, the flexible joint mechanical arm has become a core execution unit of complex scenes such as precise assembly, operation assistance, dynamic sorting and the like by virtue of the advantages of light weight, low energy consumption and high flexibility. The method has the core requirements of realizing high-precision track tracking, effectively inhibiting elastic vibration and resisting the influence of complex working conditions such as load change, external disturbance and the like. The dynamic characteristics of the flexible joint mechanical arm determine the control difficulty that the system presents strong nonlinearity and strong coupling characteristics due to joint elastic deformation, the track tracking and vibration suppression are mutually restricted, the connecting rod side non-matching disturbance and the motor side matching disturbance exist in the actual working condition at the same time, the two disturbance action channels are different and are difficult to uniformly process, and the real-time performance, parameter setting convenience and engineering realizability of the control algorithm are definitely required by industrial production, so that the control challenge is further aggravated. The main flow control technology of the current flexible joint mechanical arm mainly comprises the following steps: 1. The traditional linear control technology is characterized in that PID control is used as a representative, and basic position control is realized through proportional-integral-derivative adjustment, so that the method is widely applied to low-precision and low-dynamic demand scenes. The device has the advantages of simple structure and easy realization, but has poor adaptability to strong nonlinearity and parameter time-varying change of the flexible joint, has insufficient robustness in the face of composite disturbance, cannot consider the requirements of track precision and vibration suppression, and has larger control error. 2. The sliding mode control technology, namely traditional Sliding Mode Control (SMC) and Integral Sliding Mode Control (ISMC), is a common scheme for anti-interference control, and the robustness to uncertainty is improved by means of switching characteristics. However, the traditional SMC has the problem of high-frequency buffeting, and the elastic vibration of joints is easy to excite, so that an actuator is damaged. ISMC eliminates the arrival stage, but lacks a parameter drift suppression mechanism, measurement noise easily causes abnormal gain fluctuation, does not have the system decoupling characteristic, and is difficult to solve the problem of strong coupling. 3. The intelligent control technology, such as neural network control, fuzzy control and the like, approximates a complex dynamics model through nonlinear mapping and is used for solving the problem of strong nonlinearity. The neural network control requires a large amount of sample data training, fitting is easy to occur, the rule formulation of fuzzy control depends on expert experience, the universality and the systematicness are lacking, and the problems of large calculation amount and insufficient instantaneity exist in both technologies, so that the engineering landing difficulty is high. Disclosure of Invention The invention aims to provide a compensation control method for a flexible joint mechanical arm AISMC under singular perturbation decomposition, which solves the technical problems. In order to achieve the above purpose, the invention provides a compensation control method for a flexible joint mechanical arm AISMC under singular perturbation decomposition, which comprises the following steps: S1, establishing a dynamic model of a flexible joint mechanical arm containing uncertain compound disturbance, and decoupling a flexible joint mechanical arm coupling dynamic system containing uncertain compound disturbance into a slow-change subsystem and a fast-change subsystem based on a singular perturbation theory; s2, estimating lumped matching disturbance in the slow-change subsystem by using a compensation function observer, determining an observer gain parameter through pole allocation, and verifying the exponential stability of the observer gain parameter; S3, designing a self-adaptive integral sliding mode controller aiming at the slow-change subsystem, constructing an integral sliding mode surface and a self-adaptive approach law with dead zone correction based on lumped matching disturbance, deducing a control law combined wi