This paper proposes to use the model predictive controllers (MPC) for servo control of hard-disk-drives (HDD). Nonlinear compensation of high-frequency dynamics is achieved using two control algorithms generated from model predictive control (MPC): classical linear MPC, and MPC technique with multiple coincidence points and a reference trajectory to ensure an exponential convergence towards the reference trajectory. At low-frequency, the resonance compensation is realised using nonlinear model predictive control (NMPC). This paper aims at applying the proposed predictive control solutions to resolve the track-following problem of the read/write (R/W) head of a HDD servo-system in different operating conditions. To the best authors' knowledge, these predictive methods and comparative study at low and high frequency regions have never been conducted before on HDDs. Different scenarios are analysed including nominal case, disturbance rejection, and robustness towards parameters change to show the effectiveness of the proposed control solutions in achieving a precise and fast R/W head positioning. Numerical simulation results of the overall scenarios are presented and compared with those of a proportional integral derivative (PID) controller.