U-Model and U-Control Methodology for Nonlinear Dynamic Systems

Abstract

This study presents the fundamental concepts and technical details of a U-model-based control (U-control for short) system design framework, including U-model realisation from classic model sets, control system design procedures, and simulated showcase examples. Consequently, the framework provides readers with clear understandings and practical skills for further research expansion and applications. In contrast to the classic model-based design and model-free design methodologies, this model-independent design takes two parallel formations: (1) it designs an invariant virtual controller with a specified closed-loop transfer function in a feedback control loop and (2) it determines the real controller output by resolving the inverse of the plant U-model. It should be noted that (1) this U-control provides a universal control system design platform for many existing linear/nonlinear and polynomial/state-space models and (2) it complements many existing design approaches. Simulation studies are used as examples to demonstrate the analytically developed formulations and guideline for potential applications.

U-Model-Based Two-Degree-of-Freedom Internal Model Control of Nonlinear Dynamic Systems

“…U-model is a derived control-oriented model set to map almost all classical models into their U-model realization, and converts classical models into controller output -based with time-varying parameters [ 23 ] expressions. U-model establishes a platform for solution of dynamic inversion by solving roots of polynomial equations, which is more generally attractive compared to the other ad hoc approaches/algorithms [ 24 ].…”

“…These two designs are parallel and separable; The difference in U-control between linear models and nonlinear models is the solution with the first-order or higher-order polynomial root-solving. The difference in U-control between polynomial models and state-space models is the one-layer or multi-layer polynomial root-solving; U-control is seamlessly supplemented to the other exist control schemes, for example U-Pole Placement Control (UPPC) [ 26 ], U-General Predictive Control (UGPC) [ 27 ], U-Neuro-Control (UNC) [ 28 ], U-Total Nonlinear Control (UNLC) [ 23 ], and U-Internal Model Control (UIMC) [ 29 ]. …”

“…Therefore, deriving the nonlinear model inversion and enabling the two performance indicators (i.e., tracking and robustness) of the IMC structure to be independently designed are the main challenges and focuses in this paper. Accordingly, this study proposes a framework of U-Model-Based Two-Degree-of-Freedom Internal Model Control (U-TDF-IMC) of nonlinear dynamic systems U-model is a derived control-oriented model set to map almost all classical models into their U-model realization, and converts classical models into controller outputbased with time-varying parameters [23] expressions. U-model establishes a platform for solution of dynamic inversion by solving roots of polynomial equations, which is more generally attractive compared to the other ad hoc approaches/algorithms [24].…”

“…The difference in Ucontrol between polynomial models and state-space models is the one-layer or multilayer polynomial root-solving; 3. U-control is seamlessly supplemented to the other exist control schemes, for example U-Pole Placement Control (UPPC) [26], U-General Predictive Control (UGPC) [27], U-Neuro-Control (UNC) [28], U-Total Nonlinear Control (UNLC) [23], and U-Internal Model Control (UIMC) [29].…”

Adaptive Asymptotic Tracking Control Without Singularity for a Class of Uncertain Quadrotors With Thrust Saturation

“…A lot of research work has been devoted to the control of nonlinear systems under various conditions such as nonholonomic systems [4], nonlinear dynamic systems [5], chaotic secure communication systems [6], and Furuta systems [7]. Several classical methodologies, including backstepping control technique [8]- [11], sliding mode control [12], [13], and adaptive control [14], [15] to handle the quadrotor system's control problem, have been introduced in the literature.…”