Quadratic programming implementations of model predictive control on arduino for BLDC speed control

Abstract

Many physical process systems have performance limitation regardless the input. This limitation usually occurs in the form of input saturation of actuator as the constraint of the system. To overcome this problem, Model Predictive Control (MPC) may be used due to its capability to compute optimal control signal in the presence of input saturation. The optimal control signal is obtained by solving a quadratic programming (QP) problem with variables' constraints at each time instants. QP problem with lower and upper constraint is known to be equivalent to an algebraic loop involving diagonal upper and lower saturation. Hence, QP can be iteratively computed until its solution converges. A slow computation of QP, however, limits its applications for fast systems with simple digital processor. Therefore, in order to be able to be implemented in real-time embedded applications, a fast algorithm of QP solver is in need. In this paper, a comparison study of two QP implementation, i.e. Projected Gauss Seidel (PGS) and so called Algorithm-2, using Arduino Mega 2560 is presented. In this case, MPC with QP solver using both algorithms is implemented to control the speed of lightly loaded BLDC motor. Before implementation, system modeling, controller designing, and simulation are undertaken. The performance of both iterative algorithms are then compared in terms of average computation time in the simulation and implementation. It can be observed from the results that Algorithm-2 gives a bit faster computation than PGS under same conditions.