Fast Model Predictive Control Algorithms Based On DSP Embedded Platforms

Due to the special features of model prediction, receding horizon optimization and feedback correction, model predictive control (MPC) becomes the most efficient control algorithm in handling complex multi-variables system and has been successfully applied to process industry. The advantages of MPC are based on its ability to handle constraints explicitly, which can predict the future behavior of the system and formularize a quadratic programming (QP) problem with the inputs, states and outputs of the system. However, the QP problems have to be solved online, which involves much computation time and and resources thus makes MPC unapplicable in fast dynamic system and other sceneries with limited computation resources. The problem arouse the interests of many researchers in math and control community. To date, the progresses on this topic include some customized online algorithms for MPC, such as interior-point method (IPM) and active-set method (ASM), and some offline methods such as explicit MPC. However, topics such as convergence termination, linear system solving and the combination of online algorithm and offline algorithm are not fully studied. The existed MPC algorithms can neither cover all the applications nor compress the computation time to a full extent.To address the above issues, with the ultimate aim of fast embedded MPC algorithm, this paper studies the topics of termintation criterion, combination of online and offline methods and matrix updating strategy in solving linear equations. The main contributions are summarized as follows:(1) To address a situation in interior-point method that the computation cost exceeds the accuracy improvements, this paper introduces the convergence depth control (CDC) to check the improvements of the iterating point and quit the itereation at an appropriate time to save time. The tests on DSP platform shows that compared with algorithms based on traditional termination criterion, our algorithm can save 50% computation time on average. Besides,30% computation time can be saved even under the worst cases.(2) To tackle the problems of slow online searching and unbalanced distribution of critical regions, this paper introduces k-d tree to implement the explicit MPC with coustmized updating strategy. Cratical reigons information are stored in the k-d tree offline and the online computation only involves parameter locating; a small QP problem with short horizon would be solved to release control movements and the k-d tree is updated. Simulations indicate that this algorithm can accelerate the QP solving for 6 times on average and twice under the worst cases.(3) To utilize the fact in active-set method that similar linear equations are solved in each iteration, this paper proposes a fast MPC algorithm based on matrix iterative updating strategy. In the algorithm the linear equations are solved with weighted Gram-Schmidt iterative updating method, thus the frequent matrix factorization are avoided to save time. Both the tests on PC and DSP indicate the efficiency of the algorithm.