Model predictive control (MPC) often requires solving an optimal control structuredquadratic program (QP), possibly based on an online linearization at each sampling instant. Block-tridiagonal preconditioners have been proposed, combined with the minimal residual (MINRES) method, to result in a simple but efficient implementation of a sparse activeset strategy for fast MPC. This paper presents an improved variant of this PRESAS algorithm, by using a projected preconditioned conjugate gradient (PPCG) method. Based on a standalone C code implementation and using an ARM Cortex-A7 processor, we illustrate the performance of the proposed solver against the current state of the art for embedded predictive control.