Brief Swinging up a pendulum by energy control

https://www.control.utoronto.ca/~broucke/ece1653s/Intro/ast_fur96.pdf

Swinging up a Pendulum by Energy Control

Swing-up control, that is the transfer of a pendulum from a pendant state to the inverted one, is a good laboratory experiment of optimal control theory for non-linear control systems. The optimal control can be determined by the maximum principle and obtained as a function of time. Since the control is, however, determined in a feedforward fashion, the control is not robust to disturbances and uncertainties of the system, and the transfer of the state of the pendulum is not assured. In the paper, a robust swing-up control using a subspace projected from the whole state space is proposed. Based on the projected state space or pseudo-state, the control input is determined depending on the partitioning of the state as a bang-bang type control. The control algorithm is applied for a new type of pendulum (TI Tech pendulum), and the effectiveness and robustness of the proposed control are examined by experiments.

Swing-up Control of Inverted Pendulum Using Pseudo-State Feedback:

A bang-bang-type state feedback control algorithm which can swing up a pendulum from a pendant position to an upright position is proposed. In the control system a conventional LQ control method is also employed around the upright position to maintain the pendulum in the upright position after the pendulum has been swung up to this position by the bang-bang control. The control system was constructed and the validity of the control method was examined experimentally. Since the pendulum is attached by a hinge to a rotating arm fixed to a direct drive motorshaft, it contains fewer uncertainties introduced by transmission mechanisms, e.g., a belt and gears in a linear-type inverted pendulum. The advantages of the designed pendulum are that it is small and saves experimental space, and that the robustness of control algorithms can be easily tested with it since known parasitics can be added as uncertainties in the control loops, e.g., a flexible arm can be used instead of a rigid arm. >

Swing up control of inverted pendulum

Inverted pendulums are typical examples of unstable system and have been used for the verification of designed control systems and/or control education in laboratories. In particular, the control of a double inverted pendulum has been known as a good example to show the power of the modern control theory. In this paper we consider about robust state transfer control method of a double pendulum, i.e., swing up control of the pendulum from the hanging position to the upright position. First, we propose a control method based on a energy principle. Secondly, a more robust control method in which the state transfer is realized through a limit cycle is presented. The effectiveness of the proposed methods is shown by the experiments.

F. Wiederkehr

Papers

Observer Based Control of a Double Pendulum