Digital control design based on predictive models to keep the controlled variables in a given range

The problem of digital control design to keep the controlled variables of a dynamic object in a given range is considered, taking into account the constraints imposed on the manipulated variables. The essence of the problem is to ensure that the process variables are enter and then kept within the required range. The change of variables within the range can be arbitrary. Such problem necessitates the development of special methods for the design of control laws, which are different from the classical approaches, where the control objective is given by a reference signal. An approach to the synthesis of digital control law, based on the use of predictive models, is proposed. In the framework of this approach, the control objective is achieved by introducing a special quadratic cost functional, which includes the penalty term for the output of controlled variables from the required range. Minimization of this functional on the prediction horizon, taking into account the existing constraints on the manipulated variables, ensures that the controlled variables fall in the given range. It is shown that the real-time implementation of the control law imply solving the quadratic programming problem at each instant of discrete time. The effectiveness of the developed control algorithm is illustrated by examples of modeling of oil refining processes in a distillation column.