An Output Probabilistic Constrained Optimal Control Algorithm Based on Multivariable MAC and its Application in Looper Control System

Most actual industrial processes are multivariable and constrained complex systems. The state and output of the system also have uncertainty due to the existence of random disturbances. The output of the system is easier to be measured than the state and can more intuitively reflect the running state of the system. Considering the limitations of industrial equipment and the benefits of production, it is generally allowed to have a small portion of the output that can exceed the constraints. As a result, the outputs can be represented as corresponding single probabilistic constraints. In this paper, therefore, an output probabilistic constrained optimal control algorithm based on multivariable model algorithm control (MMAC) is proposed. First, the feedback correction link of the MMAC algorithm is improved, and the predicted outputs are corrected by taking the weighted average of the errors. Then, assuming that the disturbances obey Gaussian distribution, the output probabilistic constraints are transformed into deterministic ones. Next, the optimal control problem is solved as a quadratic programming (QP) problem after combining them with the performance index function of the MMAC. Finally, the proposed algorithm is applied to the looper control system in hot strip rolling process and compared with the single MMAC algorithm to verify its effectiveness.