Tracking Control of Nonminimum-Phase Flexible Manipulation
Book, Wayne John
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Perfect tracking or asymptotic tracking of the tip position of a flexible manipulator, which is a typical nonminimum-phase system, has been very difficult because of the positive zeros of the nonminimum-phase system and the lack of desired trajectories of flexible coordinates. This paper presents a tracking control scheme combined with the inverse dynamic feedforward control. The inverse dynamic method calculates the feedforward torque that cancels poles and zeros of the nonminimum-phase system. It also generates the desired flexible coordinate values, which match equivalent to the tip position trajectory dynamically. The feedback loop achieves tracking capability with the calculated desired flexible coordinate trajectories. The control scheme has been applied to the tip position control of a single-link flexible manipulator for zero and non-zero initial condition cases. The non-zero initial conditions of the system states are divided into three components of rigid body, causal and anticausal parts. The rigid body component is used for the desired tip trajectory planning and the other components of these are used separately for the calculation of the feedforward torque of causal and anticausal parts. Through simulation and experiment, we explore the effectiveness and limitations of this method for moving non-zero initial condition cases.