Since variable-displacement open-circuits piston pumps are equipped with diverse compensators or controllers, many different modeling approaches and representations have been developed in the previous research. In the industry, the type of pump design (with an offset between the driving shaft and rotating center of the swash plate to neutralize the swash plate which replaces the bias piston) becomes more popular to reduce manufacturing costs that will be addressed in the research. To facilitate designs of electrohydraulic (EH) controllers and comparison studies of performance, the study proposes a generic state-space model of piston pumps acting in an open-circuit configuration by using generic regulator and unique reference inputs. One major contribution of the work is typical control strategies (including the pressure control, load-sensing control, and power control) in open-circuits pumps, which are described in one generic model. Thus, the model can be expediently used for investigations and improving piston pump designs. Even more important, the model can contribute as a unique and efficient plant to apply various model-based EH control that will be more convenient, intelligent, and less cost than current designs in the industry. Also, most previous modeling work of open-circuit piston pumps only concerns the steady-state results of the pump dynamics to simply the calculations that may ignore some important dynamics. The proposed model considers the high-order dynamics of the pump, such as swash plate velocity and accelerations. The variations caused by these terms are embedded in the model coefficients and regarded as the parameter uncertainties so that the model can take advantage of both modeling linearization and transient dynamics. It is highly challenging to analyze the stability and controllability issues during the design of piston pumps because they are impacted by many nonlinear parameters and operating conditions. So, the study presents another important methodology to analyze and define the critical design specification, such as stability, controllability, and observability. In the proposed model, the dynamical characteristics can be examined and compared by pumping subsystems and overall system in a single consistent platform. The controller gain scheduling and design performance are also able to assessed and determined while defining and specifying design criteria of the pump itself.