An Improved Predictive Controller on the FPGA by Hardware Matrix Inversion

Cheap, efficient, and industrial-grade model predictive controllers are required for extending the use of model predictive control (MPC) to resource-constrained embedded computing platforms and practical industrial fields. In this paper, we implement the matrix inversion on the hardware to improve the computational efficiency of our previously designed MPC controller. For the specific matrices in each iteration of the active-set method, a simple positive definite symmetric matrix inversion algorithm is proposed, which can transform the matrix inversion into iterated matrix multiplication and add operations along with fewer division operations. Its similar matrix calculating formulas in each iteration are block design oriented and able to be speed up by the parallelism and pipeline in the hardware. To avoid extra data transmission, the matrix inversion algorithm and active-set method are combined through the time sequence and architectural design to form an improved predictive controller on a field-programmable gate array (FPGA). The improved predictive controller is implemented on an FPGA-based board especially made for the industrial sites and applied to a holding process of the injection molding, which achieves satisfactory control performance.