FEA-based tracking control of flexible body switching dynamic structure

Abstract

In dynamically switched systems with unknown switching signal, the control system is conventionally designed based on the worst switching scenario to ensure system stability. Such conservative design demands excessive control effort in less critical switching configurations. In the case of continuum mechanics systems, such excessive control inputs result in increased structural deformations and resultant modeling uncertainties. These deformations alter differential equations of motion which cripple the task of control. In this paper, a new approach for tracking control of uncertain continuum mechanics multivariable systems undergoing switching dynamics and unknown time delay has been proposed. Control algorithm is constructed based on the mathematical rigid model of the plant and a Common Lyapunov Function (CLF) is proposed upon sliding hyperplane regarding all switching configurations. Considering the model-based nature of sliding mode control (SMC) and inevitable uncertainties induced from modeling simplifications of continuum system or parameter evaluation errors, Finite Element Analysis (FEA) is utilized to approximate total model uncertainties. To obtain robust stability, instead of conventional switching functions in the construction of control law, the control inputs are selected such that system dynamics reside within stability bounds which are calculated based on the Lyapunov asymptotic stability criterion. Therefore, the unwanted chattering issue caused by continuous switching is not observed in control input signals. Eventually, the accuracy of the proposed method has been verified through the student version of ANSYS® mechanical APDL-based simulations and its effectiveness has been demonstrated in multiple operating conditions.

Feedback control of actuation‐constrained moving structure carrying Timoshenko beam

“…The value of 𝔍 (i)(j) [1|k − 1, 𝛉, 𝛙] must be calculated for all j = 1, 2, …  and then the selected value of the second layer under the i-th column which is illustrated as u (i) (2|k − 1), could be obtained using the instruction presented in Equation (33). The value of the required variables will be stored as s (i) (2|k − 1), z 2(i) (1|k − 1), and w (i) (𝜒, 1|k − 1).…”

“…32 In another research, Homaeinezhad and Fotoohinia presented a finite element-based tracking control of a flexible body switching dynamic structure and considered limited frequency bandwidth for the actuator. 33 In the last two works using discrete-time sliding mode controller, the Lyapunov stability bound can be obtained and the closed loop stability could be ensured. Although significant efforts have been made in References 32,33 to cover the bandwidth limitation, if saturation is added to the problem, the stability of the closed-loop system will no longer be guaranteed.…”

“…Using a rigid model approximation of a flexible system, discrete sliding mode technique, and first‐order dynamics for the actuator, Homaeinezhad and Fotoohinia proposed a vibration monitoring unit embedded in a feedback algorithm in order to control the nonlinear structural vibrations of a moving continuum system 32 . In another research, Homaeinezhad and Fotoohinia presented a finite element‐based tracking control of a flexible body switching dynamic structure and considered limited frequency bandwidth for the actuator 33 . In the last two works using discrete‐time sliding mode controller, the Lyapunov stability bound can be obtained and the closed loop stability could be ensured.…”

“…In the last two works using discrete‐time sliding mode controller, the Lyapunov stability bound can be obtained and the closed loop stability could be ensured. Although significant efforts have been made in References 32,33 to cover the bandwidth limitation, if saturation is added to the problem, the stability of the closed‐loop system will no longer be guaranteed.…”