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Model predictive control (MPC) has become a hot cake technology for various applications due to its ability to handle multi-input multi-output systems with physical constraints. The optimization solvers require considerable time, limiting their embedded implementation for real-time control. To overcome the bottleneck of traditional quadratic programming (QP) solvers, this paper proposes a robust penalty method (RPM) to solve an optimization problem in a linear MPC. The main idea of RPM is to solve an unconstrained QP problem using Broyden-Fletcher-Goldfarb-Shannon (BFGS) algorithm. The beauty of this method is that it can find optimal solutions even if initial conditions are in an infeasible region, which makes it robust. Moreover, the RPM is computationally inexpensive as compared to the traditional QP solvers. The proposed RPM is implemented on resource-limited embedded hardware (STM32 microcontroller), and its performance is validated with a case study of a citation aircraft control problem. We show the hardware-in-the-loop co-simulation results of the proposed RPM and compared them with the active set method (ASM) and interior point method (IPM) QP solvers. The performance of MPC with the aforementioned solvers is compared by considering the optimality, time complexity, and ease of hardware implementation. Presented results show that the proposed RPM gives the same optimality as ASM and IPM, and outperforms them in terms of speed.