Trajectory Tracking by TP Model Transformation: Case Study of a Benchmark Problem

The main objective of this paper is to study the recently proposed tensor-product-distributed-compensation (TPDC)-based control design framework in the case of tracking control design of a benchmark problem. The TPDC is a combination of the tensor product model transformation and the parallel distributed compensation framework. In this paper, we investigate the effectiveness of the TPDC design. We study how it can be uniformly and readily executed without analytical derivations. We show that the TPDC is straightforward and numerically tractable, and is capable of guarantying various different control performances via linear matrix inequality (LMI) conditions. All these features are studied via the state feedback trajectory control design of the translational oscillations with an eccentric rotational proof mass actuator system. The trajectory tracking capability for various tracking commands is optimized here by decay rate LMI conditions. Constraints on the output and control of the closed-loop system are also considered by LMI conditions. We present numerical simulations of the resulting closed-loop system to validate the control design.