Robust control of uncertain nonlinear systems

Developing implementable control tools for uncertain nonlinear systems, while also achieving strong robustness and high precision performance, is a vital goal for modern control theory. Due to the characteristics of excellent control performance and simple implementation, the uncertainty and disturbance estimator (UDE)-based robust control, is such a promising tool and has obtained considerable attention in recent years. The key idea of UDE-based robust control is converting the challenging problem of designing a robust controller into designing filters. This approach adopts a proper filter to estimate and compensate the lumped uncertainty, which may include both the model uncertainties and external disturbances. The two-degree-of-freedom nature of this approach makes it easily tuned and simply implemented. However, the conventional UDE-based robust control has several challenges to be addressed so that the control performance can be further improved and the systems to be applied can be generalized.

In the current literature, there has been no discussion with regards to optimizing the control performance of the UDE-based robust control. Furthermore, the scope of systems where the conventional UDE-based robust control can be applied includes both linear and nonlinear systems. However, there exist several limitations for those systems to be controlled. 1) The controlled systems being considered, either linear or nonlinear, are described by ordinary differential equations (ODE); 2) The controlled systems must satisfy the so-called structural constraint, which means the matching condition between the disturbances/uncertainties and the control input; 3) The full state measurements are required. Removing those limitations will extend the applicability of this approach. This dissertation investigates four specific challenges of the UDE-based robust control, and has the following contributions from four different aspects.

The first contribution solves that challenge of achieving the asymptotic performance by using the UDE-based robust control. Specifically, how to guarantee asymptotic reference tracking and disturbance rejection performance within the hardware limit. To pursue this goal, a systematical design guideline for the filter and the reference model is proposed based on the internal model principle. Experimental results on a servo system are presented as an example to demonstrate its excellent performance, which can actually reach the hardware resolution limit.

Secondly, the dissertation applies the UDE-based robust control to linear partial differential equations (PDE) for the first time by designing a proper infinite dimensional filter. A parabolic type of PDE systems which represents a thermal process is studied. The proposed design also sheds some lights on designs for other types of PDE systems. Numerical simulations are conducted for the validation.

Thirdly, the structural constraint of the UDE-based robust control is solved by introducing a backstepping scheme. The marriage between the UDE and the backstepping scheme effectively attenuates the mismatched disturbances/uncertainties, and also avoids the problem of “complexity explosion” in the conventional backstepping control. Successful practical applications are also demonstrated.

Finally, the UDE-based robust output feedback control is proposed, which removes the requirements of both the structural constraint and the full state measurements. This pushes the scope of applicable controlled systems to a general type of bounded-input-bounded-output (BIBO) nonlinear systems. The desirable control performance and the simple design process can be achieved simultaneously. An experimental validation on a piezoelectric nanopositioning stage is presented as well.

Moreover, the proposed UDE-based output feedback control is successfully applied to a continuous phase tuning problem in a practical project. This project explores the possibility of generalizing the applications of a smart material, vanadium diode (VO2). This material undergoes a metal-insulator transition (MIT) at approximately 68^{o}C, with associated sharp changes in its physical properties. Thus, it is of interest in many potential applications including memory devices, switches, sensors, and optical modulators. For ON/OFF like digital applications, an abrupt switching behavior is ideal. However, to continuously change VO2 metal/insulator phase ratio for analog-like operation, the intrinsic hysteresis characteristic of the VO2 MIT renders the phase tuning becoming a formidable challenge. Fortunately, the proposed controller is capable of mitigating the adverse effect of hysteresis, while also compensating for modeling errors due to manufacturing uncertainties. Extensive experimental studies are presented to show the effectiveness of the proposed method.