A novel nonlinear function parameterization model was proposed for nonlinear adaptive controller design. This approach re-parameterizes the nonlinear function with unknown parameters linearly, which simplifies the adaptive controller design significantly. A recently developed passivity based backstepping controller using a physical compressibility energy function for a chamber hydraulic cylinder was augmented with the parameter adaptation law to achieve trajectory tracking. We experimentally demonstrate the effectiveness of the parameterization model, and the adaptive passive controller produces an accurate trajectory tracking performance.