Abstract
AbstractA control strategy for swinging up a planar pendulum, from its hanging to its upright position, is presented. Its hinge is actuated by a DC‐motor. In contrast to frequently used models of torque control, the DC‐motor is included as RLC circuits of stator and armature in this paper. The armature voltage is used as input signal, while the stator current is fixed. By passing the horizontal position there is a local loss of controllability, as the motor torque vanishes there. Hamilton's principle is applied and discretized by a variational integrator (VI) in order to compute the optimal feed‐forward control. Thus, the resulting optimal control problem is transferred into a finite‐dimensional optimization problem, and solved by sequential quadratic programming (SQP) methods. The cost function to be minimized is the consumed electrical energy needed to swing up the pendulum in fixed time. In addition to the feed‐forward control (offline), feed‐back control (online) is added in order to stabilize the swing‐up and the upright position. This feedback‐controller is designed as linear‐quadratic regulator (LQR) for the linearization around the nominal trajectory. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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