Search

This paper presents a receding horizon control (RHC) for an unconstrained input-delayed system. To begin with, we derive a finite horizon optimal control for a quadratic cost function including two final weighting terms. The RHC is easily obtained by changing the initial and final times of the finite horizon optimal control. A linear matrix inequality (LMI) condition on two final weighting matrices is proposed to meet the cost monotonicity, under which the optimal cost on the horizon is monotonically nonincreasing with time and hence the asymptotical stability is guaranteed only if an observability condition is met. It is shown through simulation that the proposed RHC stabilizes the input-delayed system effectively and its performance can be tuned by adjusting weighting matrices with respect to the state and the input. Index Terms--Cost monotonicity, final weighting matrix, input delay, quadratic cost function, receding horizon control (RHC).

In traditional linkage design practice, a designer first decides the specific linkage type, such as a four- or six-bar linkage, and then varies the joint locations and link lengths until the designer finds the desired linkage. The objective of this research is to establish an automatic mechanism synthesis method that determines the linkage type and dimensions during the synthesis process. The synthesis process can be formulated as a minimization problem. However, the process can be extremely difficult and time-consuming unless there is a single unified linkage model that represents any linkage mechanism without complicating kinematic analysis and allows the use of an efficient gradient-based optimizer The main contribution of this investigation is to propose a unified planar linkage model consisting of rigid blocks connected by zero-length springs having real-valued variable stiffness. Stiffness controlling variables are the design variable of the minimization problem and a general planar linkage can be simulated by the spring-connected rigid block model if the stiffness value is chosen appropriately. Though mechanisms involving only revolute joints are investigated and the solved problems are relatively simple, the notion of the block model and the synthesis formulation in real variables are expected to give a different perspective on mechanism synthesis. [DOI: 10.1115/1.2747636] Keywords: automatic mechanism synthesis, spring-connected block model, planar linkage