In previous research, a controller design procedure via generalized canonical transformations has been proposed to keep the passivity feature of Port-controlled Hamiltonian systems. The procedure has a general form and is applicable to spacecraft's attitude motion described with quaternion parameters. This paper investigates the roles of several design parameters in the generalized canonical transformations. Special attention is placed on the relation between the shape of Lyapunov functions and the convergence speed of the state variables. Furthermore, from the analysis utilizing the linearized form of the Port-controlled Hamiltonian system, the guideline to decide the preferable ratio between two parameters in the design procedure is proposed.