Complexity simulation of DMC based on quadratic programming

Constrained dynamic matrix control(DMC)is essentially a standard quadratic programming problem with high complexity and long on-line solving time. The Karush-Kuhn-Tucker (KKT) conditions for optimization problems are used to analyze the complexity of DMC algorithm. Therefore, the number of manipulated variables and the length of control horizons are found out to be the mainly restricted two factors of computational efficiency in algorithm, and the time complexity of the algorithm is proportional to the cube of the product of the two factors. Then standard quadratic programming (QP) algorithm was applied to three classical industrial cases which simulated and verified the result. Finally, a curve fitting method was used to compute the maximum size of control system in standard model predictive control implementation time. Thus a theoretical basis was provided for properly choosing the number of manipulated variables and the length of control horizons, reducing the computational complexity of the dynamic matrix control algorithm.