Generalized Malmquist orthogonal functions based model predictive control

The computational burden could be an issue of traditional model predictive control (MPC) in real-time applications. There are different procedures to cope with this problem such as using explicit MPC or approximation of the control inputs using orthogonal-basis functions. This paper presents the design procedure and experimental validation of a generalized discrete-time Malmquist orthogonal functions-based model predictive control (MbMPC) whose usage can decrease calculation concerns. To the authors’ knowledge, this is the first time the Malmquist functions are introduced into the MPC design. The discrete-time orthogonal Malmquist functions properties are used within this approach for approximating the future control input increments with a smaller number of parameters than in traditional MPC approaches. It is shown that the satisfactory controller and closed-loop system performances can be achieved using smaller number of tuning parameters. The performance of the proposed MbMPC is shown and compared with discrete-time Laguerre orthogonal functions based MPC (LbMPC) applied to a DC motor servo system. The simulation and experimental results demonstrate better IAE, ITAE, ISE and ITSE controller performance indices as well as faster average calculation time in comparison with the LbMPC approach. Additionally, the advantage of using the proposed method is emphasized by showing how the length of the prediction horizon affects the computational burden in comparison to the traditional MPC approaches.