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

Abstract

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.

Non-Iterative Data-Driven Tuning of Model-Free Control Based on an Ultra-Local Model

“…Furthermore, there were some differences in the parameters optimized using the open-loop and closed-loop test data. This may be due to differences in the input/output data, which is understandable from the results [32].…”

“…Here, the system formulation, including the plant and reference model, is the same as in the previous literature [32,35]. The sampling period of the simulation is set to 1 s. The Hammerstein model [36] is given as…”

“…Here, the system formulation, including the plant and reference model, is the same as in the previous literature [32]. Fig.…”

Direct Data-Driven Tuning of Look-Up Tables for Feedback Control Systems

“…We focus on the velocity form of the PID controller (Fig. 2) because it is most common in industry and is compatible with gain-scheduled control [14]. Here, 𝜌 (𝑡), 𝜌 (𝑡), and 𝜌 (𝑡) are the proportional, integral, and derivative gains, respectively; ∆ represents 1 − 𝑧 − ; 𝑧 − is the backward operator.…”

“…The above control methods, which do not use models of the controlled object, are also being applied to industrial systems [7][8][9][10]. VRFT and FRIT have not only been applied to linear systems but they have been extended to nonlinear systems [11][12][13][14], including database-driven FRIT [11], VRFT using neural networks [12], VRFT for linear parameter varying systems [13], and VRFT for sparse gain-scheduled PID [14]. However, direct tuning of the LUT parameters using a data-driven control approach has yet to be reported.…”