A controller design procedure for two -mass systems with single flexible mode
Many manufacturing machines must execute motions as quickly as possible to achieve profitable high-volume production. Most of them exhibit some flexibility, which makes the settling time longer and controller design difficult. This research develops a control strategy that combines feedforward and feedback control with command shaping for such systems with flexibility. The systems are limited to having collocated actuator and sensor. Each control component has its own objective. First, a feedback controller is designed to increase damping and eliminate steady-state error. Next, an appropriate reference profile is generated using command-shaping techniques to ensure fast point-to-point motions with minimum residual vibration. Finally, a feedforward controller is designed to speed up the transient response. The particular focus of this research is to understand the interactions between these individual control components because there are several constraints to be considered when they are combined for better control performance. Mass ratio Mr, which is the ratio of the actuated mass to the unactuated mass, plays an important role in controller and shaped input design. It is because the characteristic of the flexible plant depends on Mr. So, another focus of this research is to uncover how individual control components are designed depending on Mr. The resulting control strategy turns out to be independent of Mr. Rigid-body model is used for feedback control design, while full-order plant model is used for feedforward design. The proposed PID controller design ensures that two important resonant frequencies, which are the closed-loop resonant frequency and the natural frequency between two positions, nearly match making the design of the input commands much simpler. Selection of peak force for shaped input design to avoid force saturation is dealt with. The resulting control strategy is successfully demonstrated for a generic dimensionless system that incorporates some modeling errors to assess robustness. In addition, it is compared with other control strategies to verify the effectiveness by applying to a benchmark problem. ^
Peter H. Meckl, Purdue University.