Benchmark problems have been used to evaluate the performance of a variety of robust control design methodologies by many control engineers over the past 2 decades. A benchmark is a simple but meaningful problem to highlight the advantages and disadvantages of different control strategies. This paper verifies the performance of a new control strategy, which is called combined feedforward and feedback control with shaped input (CFFS), through a benchmark problem applied to a two-mass-spring system. CFFS, which consists of feedback and feedforward controllers and shaped input, can achieve high performance with a simple controller design. This control strategy has several unique characteristics. First, the shaped input is designed to extract energy from the flexible modes, which means that a simpler feedback control design based on a rigid-body model can be used. In addition, only a single frequency must be attenuated to reduce residual vibration of both masses. Second, only the dynamics between control force and the first mass need to be considered in designing both feedback and feedforward controllers. The proposed control strategy is applied to a benchmark problem and its performance is compared with that obtained using two alternative control strategies.
Adaptive Fuzzy Output-Feedback Control Design for a Class of p-Norm Stochastic Nonlinear Systems With Output Constraints