Swing-up control of the acrobot using noncollocated partial feedback linearisation: An algorithmic approach

摘要

The swing-up control of the Acrobot using non-collocated partial feedback linearisation (NCPFL) has been demonstrated extensively in existing literature, whereby a linear state feedback control law which tracks the upright equilibrium point is designed for the linearised proximal pendulum. This control law cannot be designed for the distal pendulum since the Acrobot is underactuated. The distal pendulum will, however, follow a desirable trajectory towards the upright state so long as the initial angular condition of the distal pendulum (q₂(0)) and the frequency response of the existing actuator (ω_η) are finely tuned. There is currently no formalised method of tuning these properties for any specifically configured Acrobot. A novel approach of determining these properties using an adapted binary search algorithm designed to converge on an appropriate set of angular initial conditions for a specified range of ω_nis thus presented. The accommodation of a full range of swing-up for the proximal pendulum is demonstrated through the selection of a sufficiently large ω_n. The relationship between q₁(0) and q₂(0) becomes nonlinear towards the acceptable limits of q₁(0) when ω_nis not sufficiently large. Satisfactory NCPFL-related swing-up control is thus demonstrated on an Acrobot described by one specific set of parameters.