| Flexible systems,combining the flexibility and resilience of low-modulus materials,have avoided the shortcomings of rigid systems with restricted operation environments,low humanmachine interaction safety and high destructiveness.By the advantages of lightweight,low energy consumption,strong environmental adaptability and high operational safety,flexible systems have been widely applied in the aerospace,bioengineering,medical equipment,marine engineering and other areas.However,due to the characteristics of low stiffness and light mass,flexible systems possess infinite degrees of freedom and continuous deformation capabilities under the action of load,which are prone to a large range of coupled rigid motion and elastic deformation.This non-linear coupling effect makes the traditional modeling methods based on small deformation and rotation assumptions inapplicable,which may lead to problems such as linearization of rigid displacement,singularity and difficulty in solving.In addition,flexible systems are typical infinite-dimensional distributed parameter systems with the characteristics of high order,under-drive and incomplete linear feedback,which makes the study of the control methods challenging.Furthermore,influenced by uncertain factors such as the internal bonding structural changes caused by material aging,the incomplete modeling errors caused by the truncation of infinite-dimensional model modes and external environmental disturbances,lowmode and low-damping flexible systems are easily excited to generate complex dynamic responses,which may lead to system divergence and instability in severe cases.Therefore,it is of great theoretical significance and engineering application value to conduct research on the dynamic modeling and uncertainty control of flexible systems.In this paper,the dynamic modeling of flexible systems is studied based on the absolute nodal coordinate method,and the dynamic controller design and the optimization method of the task-driven flexible systems are explored.The main contents and contributions are as follows:(1)Based on the absolute nodal coordinates method,the dynamics model of the flexible systems with large deformation and large rotation is established.For the isoparametric units,the nodal corner coordinates are replaced by the gradient vectors,the generalized elastic forces are derived from the nonlinear strain-displacement relationship in the mechanics of continuous media,the dynamics models are analyzed by the principle of virtual work;based on the continuity equation of isoparametric units and the kinematic sub-connection equation between the components,the dynamics model of flexible systems is obtained by using the matrix transformation;the feasibility and correctness of the dynamics model are verified by an example.(2)The control method for the task-driven flexible systems is proposed by converting trajectory tracking tasks into task constraints.The trajectory tracking tasks for flexible systems are regarded as the task(holonomic or nonholonomic)constraints,and the second-order form task of constraint equations that satisfies the consistency is constructed;based on the dynamic model established by the absolute nodal coordinate method,a driving force model that satisfy the task constraints is established,which could be used to design the feedforward term for the control of flexible systems,enabling the active following of the target trajectory.(3)A robust control method based on uncertainty upper bound information is proposed for the uncertain flexible systems.The uncertain factors such as time-varying parameters,modeling errors and external environment disturbances of the flexible system are analyzed;based on the driving force model,the uncertainty is decomposed into the matched uncertainty and the mismatched uncertainty;by assigning the mismatched uncertainty to the null space of the task constraint based on the system’s driving configuration,the interference of the mismatched uncertainty on the flexible system is avoid;on this basis,the function reflecting the upper bound information of the uncertainty is constructed,which is used to design a robust controller,ensuring that the uncertain flexible systems satisfy the task constraints;the flexible robotic arm under high-frequency residual vibration disturbances is chosen as the verification example,and the simulation results verify the effectiveness and correctness of the control method.(4)The boundary information of the uncertainty in the robust control design of flexible systems mostly relies on offline experimental data,which lacks identification in the real-time control process.To address this problem,an adaptive robust control method for flexible systems is proposed.An identification model is designed to identify the upper bound information of the uncertainty online,which reduces the dependence of the controller on uncertain parameter information;the leakage and dead-zone terms are designed to reduce the control cost and simplify the identification algorithm,which improve the real-time of uncertainty boundary identification;from the perspective of control cost and operation time tradeoff,two types of controller gains are constructed by combining the identified upper bound information,and the design methods for the adaptive robust controllers in segmented and continuous forms are proposed;simulations demonstrate that both types of the adaptive robust controllers can accomplish the trajectory tracking tasks of the flexible system when the accurate upper bound information of the uncertainty is not available.(5)By using the fuzzy set theory to describe the uncertainty of flexible systems,a deterministic(non-if-then fuzzy inference)adaptive robust controller design and its optimization method are proposed.Based on the deterministic adaptive robust controller and the fuzzy information of the uncertainty,a system performance index,including the steady-state performance and transient performance,is established;the fuzzy information of the uncertainty is used for the optimal design of the controller parameters,and the optimization problem is equated to a minimization problem of the fuzzy performance index;for the optimization problem,the existence and uniqueness of its global solution are proven,and the global solution of the minimization problem is solved,which further provides the optimal control parameters in the analytical form,effectively and concisely solving the optimal control problem of flexible systems. |
