Direct tuning method of gain-scheduled controllers with the sparse polynomials function

In industry, gain-scheduled proportional-integral-derivative (PID) control is performed for nonlinear systems using a look-up table (LUT) that is easy to understand. Compared with the fixed PID, there are many more parameters of the scheduler, and it takes a lot of time to tune them. Also, the ROM storage area increases. To address these problems, in this paper, we propose a gain-scheduled control law using the sparse polynomial functions and a direct parameter tuning method without system identification. The polynomial functions are used instead of LUT to reduce the ROM area. For direct tuning, data-driven control is formulated so that it can be applied to the gain-scheduled control, and the optimal parameters are obtained by the LASSO regression, with which the small contributing parameters of the scheduler become zero, and a sparse controller is obtained. The effectiveness of this method was examined by simulation for two types of nonlinear systems. As a result, it was revealed that a sparse controller with a low calculation cost and a reduced ROM area can be directly obtained without knowing the characteristics of the controlled object for a large number of control parameters of the gain scheduler.