On the synthesis of a nominal trajectory for control law of a one-link flexible arm

In this article we propose a method for the design of a nominal trajectory for a flexible one-link manipulator This trajectory is near time-optimal. The torque control law consists of two parts: the commanded feedforward torque and the linear angular position and velocity feedback Feedforward signal is proportional to nominal angular acceleration of the hub. On the first time interval, the feedforward torque approaches continuously to a value that is a little smaller than the maximal possible torque, then it remains constant, and then it goes to zero. On the second interval, the feedforward torque approaches continuously to a value that is a little greater than the minimal possible torque, then it remains constant, and then it goes to zero. On the third time interval, feedforward signal is zeta. We compute the corresponding nominal (desired) angular acceleration, velocity, and position of the hub as functions of time. The last two functions are fed to the linear feedback system. The angular acceleration is such that, on the first time interval, the hub moves with ''large'' acceleration in one direction, and the link bends on the opposite side. On the second time interval, the hub moves with deceleration, and the link bends in the direction of the motion. On the third time interval we stabilize the arm near its desired position. In the experiments, the designed control algorithm was successfully implemented. We analyze these experiments from a theoretical point of view.