Safe physical human-robot interaction (pHRI) is fundamentally a problem of interaction dynamics: the robot must track a commanded motion, yield under human forces, respect actuator and joint limits, and stay predictable under persistent contact. Classical impedance control shapes this through a virtual spring-damper, but a sustained force produces the bias $e_\infty=-K_d^{-1}F_h$, trading accuracy for safety. We propose a predictive framework that makes interaction dynamics explicit through a linear double-integrator backbone: an operational-space feedforward cancels gravity and Coriolis terms and normalizes the task inertia, leaving a configuration-independent state-transition matrix with robot dependence isolated in the input matrix. This converts nonlinear torque-controlled pHRI into a linear constrained-control problem, so offset-free tracking, actuator feasibility, sampled-data joint-limit safety, and passivity filtering follow with explicit assumptions. The online realization is a 30-variable convex QP at 100 Hz with a precomputed free-response matrix and a Kalman filter that rejects persistent forces without steady-state error; null-space barrier, one-step joint-limit CBF, and energy-tank filters add conditional safety and task-channel passivity. In MuJoCo simulation of a 7-DOF Franka FR3, the controller attains sub-0.05 mm steady-state error under a sustained 15 N force versus 44.8 mm for classical impedance, sub-millimeter tracking on four 3-D circles, and robustness to measurement noise and 30% inertial mismatch.

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