Dependent versus Independent Variable Formulation for the Dynamics and Control of Cranes
Cranes are underactuated mechanical systems with fewer control inputs than the degrees of freedom. Their usual performance goal is to execute a desired load trajectory, which is specified by as many outputs as the control inputs. A solution to the inverse simulation problem, in which the control of the underactuated system required to execute the partly specified motion is determined, is a challenging task. The inverse simulation study is usually formulated in independent variables. In this paper a dependent variable formulation is reported, advantageous in many aspects. The resultant governing equations appear as simple index-three differential-algebraic equations, and an effective numerical code for their solution is discussed.
Zdzislaw Gosiewski and Zbigniew Kulesza
W. Blajer and K. Kołodziejczyk, "Dependent versus Independent Variable Formulation for the Dynamics and Control of Cranes", Solid State Phenomena, Vols. 147-149, pp. 221-230, 2009