In this paper we compare different nonlinear control design methods by applying them to the planar model of a ducted fan engine. The methods used range from Jacobian linearization of the nonlinear plant and designing an LQR controller, to using model predictive control and linear parameter varying methods. The controller design can be divided into two steps. The first step requires the derivation of a control Lyapunov function (CLF), while the second involves using an existing CLF to generate a controller. The main premise of this paper is that by combining the best of these two phases, it is possible to find controllers that achieve superior performance when compared to those that apply each phase independently. All of the results are compared to the optimal solution which is approximated by solving a trajectory optimization problem with a sufficiently large time horizon.