Stability and Control for Machining of Thin-Walled Structures — A Time-Varying Delayed Distributed Parameter System
- Author(s): Esfandi, Niloufar
- Advisor(s): Tsao, Tsu-Chin
- et al.
Motivated by machining of thin-walled parts this dissertation investigates the modeling and control of dynamic systems, which feature finite-dimensional and distributed-parameter structures interacting with one another over time-varying contacts and time-delayed feedback. The research studies and creates methods for modeling and control of such systems and applies them to a proposed innovative use of industrial robot manipulators and end effectors to act as an active steady rest in the machining of thin-walled parts.
On modeling the combined discrete-continuous structural and machine dynamics with time varying contacts, finite element method (FEM) is employed to discretize and extract dynamic modes of the continuous structure. The time delayed feedback in the machining process is approximated by the semi-discretization method, where only the delay part of the otherwise continuous-time system is approximated by discrete-time delays and proper sampling and holding functions. To enable digital control design, sampling and zero-order hold circuit modeling is applied to the actuators in conjunction with the semi-discretization for the delayed feedback. Followed by lifting technique on the periodic-varying system and order reduction, discrete-time control oriented models for the entire machining system with the actively controlled robots and end effectors are constructed.
Linear optimal control and robust control are investigated and applied to the proposed robot assisted machining system models. In the linear quadratic state estimator feedback control, a new approach is proposed for the formulation of the cost function weighting matrices. The approach essentially places weighting on outputs and their derivatives since output has clear physical meaning in connection to the process performance. The optimal linear state estimators, aka Kalman filters, are designed taking an approach that exploits the dual properties between the linear optimal regulators and state estimators. In the robust control, parameters in the machining process, particularly the cutting stiffness that depends on the tool conditions and part material, are isolated as uncertainties in formulating the control oriented models for mu-synthesis based robust control design.
The above control design methods are applied to the turning of a thin-walled circular wheel with the actively controlled robotic steady rest. The simulation results show that the feedback controlled robotic active steady rest not only can stabilize an otherwise unstable machining system, caused by the well-known machining chatter due to the delayed feedback, but also can improve the machined forms and precision. The increased stability margins with higher speeds and larger depths of cut than possible without the proposed approach suggest the potential of improving the productivity and quality in the machining of thin-walled parts with the proposed control methods for the robotic steady rests.