The rapid advancement in physical human-robot interaction (HRI) has propelled the growth of soft robot design and, in parallel, soft robot controllers. Controlling soft robots is complex due to their wide range of movements, prompting the use of simplified model-based controllers to provide sufficient information for real-time high dynamic response control performance. However, most modeling techniques face computational efficiency and complexity of parameter identification issues and are hard to apply to real-time controls. To alleviate this, we employ a coupled analytical modeling approach based on Pseudo-Rigid Body Modeling and the Logarithmic Decrement Method for parameter estimation (PRBM+LDM). Using a soft robot hand test bed, we demonstrate the accuracy of PRBM+LDM to model position and force output as a function of pressure input and benchmark its performance. We, then, apply the PRBM+LDM model as a basis for a closed-loop position controller and compare its performance against a simple PID controller. Furthermore, we apply the PRBM+LDM model as a closed-loop force controller and compare its performance with simple constant pressure grasping control by performing small contact areas pinching tasks on low-weight, small objects - a screwdriver, a potato chip, and a brass coin. The PRBM+LDM-based position controller (Average Max. Error across all fingers: 4.37°) outperformed the simple PID position controller (Average Max. Error across all fingers: 20.38°). Furthermore, the PRBM+LDM-based force controller (Potato chip: 86%, Screwdriver: 74.42%, Brass coin: 64.75%) achieved a higher success rate than the constant pressure grasping control (Potato chip: 82.5%, Screwdriver: 70%, Brass coin: 35%) in the pinching tasks. We conclude that the PRBM+LDM modeling technique proves to be a convenient and efficient way to model the dynamic behavior of soft actuators closely and can be used to build high-precision position and force controllers. In application, it realizes stable, flexible grasping of small objects by exerting precise contact force on contact areas.