In this paper, the contouring control problem for the constrained multi-axis motion system is studied. The method of equivalent errors, previously proposed for unconstrained motion systems, is generalized to the system with holonomic constraints. It is shown that the method can be applied to the constrained system provided that the constraints satisfy a proper condition. Because of the constraints, the states in the control law are not completely independent. The unavailable states can be estimated using linear approximation from the constraint equations. As an illustrative example, the proposed method is applied to a parallel motion system with complicated dynamics. A contouring controller is designed using the method of equivalent errors incorporated with integral sliding mode control. Simulation results for contouring circular, elliptic, and square paths verify the effectiveness of the proposed method.
The main purpose of this study is to investigate the multilevel optimization of rotor-bearing systems. The design variables include the shaft inner radius, the bearings stiffness, and the axial position of the bearings and disks. The design objectives are minimization of the shaft weight and transmitted force to the bearings. Constraints are placed on the critical speeds, the maximum shaft bending stress, and the maximum amplitude of the steady state response.
In the multilevel optimization, three levels are considered and each level includes a single objective and/or multiobjective with various design variables and constraints. For each level, the method of feasible direction (MFD) is used. In addition, the weighting method (WM) is used for multiobjective optimization. The dynamic analysis is carried out using the generalized polynomial expansion method.
The results show that the shaft weight and transmitted forces can be simultaneously reduced with the multilevel technique and are better than those obtained using the multiobjective optimization technique with only a single level.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.