Nonlinear controlled plants with Bogdanov-Takens singularity may experience surprising changes in their number of equilibria, their limit cycles, and/or their stability types when the controllers slightly vary in the vicinity of critical parameter varieties. Each such change is called a local bifurcation. We derive novel results with regards to truncated parametric normal form classification of the generalized cusp plants. Then, we suggest effective nonlinear bifurcation control law designs for precisely locating and accurately controlling many different types of bifurcations for two measurable generalized cusp plants. The first is a general quadratic plant with a possible multi-input linear controller, while the second is a Z(2)-equivariant general plant with a possible multi-input linear Z(2)-symmetry preserving controller. The bifurcations include from primary to quinary bifurcations of either of the following types: saddle-node, transcritical, and pitchfork of equilibria, or Z(2)-equivariant bifurcations of multiple limit cycles through Hopf, homoclinic, heteroclinic, saddle-node, and saddle-connection. Criteria along with an example are proposed for frequency and amplitude-size control of the corresponding oscillating dynamics. Due to the nonlinearity of a ship maneuvering characteristic, there is a need for a controller design in a ship steering system so that the ship follows a desired sea route. The results in bifurcation control analysis are applied to two nonlinear ship course models for such controller designs. Symbolic implementations in Maple and numerical simulations in MATLAB confirm our theoretical results and accurate predictions.