In this document, we present the main ideas and results concerning high-gain observers and some of their applications in control. The introduction gives a brief history of the topic. Then, a motivating second-order example is used to illustrate the key features of high-gain observers and their use in feedback control. This is followed by a general presentation of high-gain-observer theory in a unified framework that accounts for modeling uncertainty, as well as measurement noise. The paper concludes by discussing the use of high-gain observers in the robust control of minimum-phase nonlinear systems.

https://onlinelibrary.wiley.com/doi/pdf/10.1002/rnc.3156

High-gain observers in nonlinear feedback control

The theory of high-gain observers has been developed for about twenty years. This paper is a brief introduction to high-gain observers in nonlinear feedback control, with emphasis on the peaking phenomenon and the role of control saturation in dealing with it. The paper surveys recent results on the nonlinear separation principle, conditional servo compensators, extended high-gain observers, performance in the presence of measurement noise, sampled-data control, and experimental testbeds.

High-Gain Observers in Nonlinear Feedback Control

Preisach-type operators model hysteresis via weighted superposition of a large (and even infinite) number of basic hysteretic elements (called hysterons), and they have proven capable of capturing various complicated hysteretic behaviors. While inverse compensation is an effective approach to control of hysteretic systems, inversion of Preisach-type operators is a bottleneck in demanding, high-speed applications due to the high computational cost. In this paper a novel and general framework is proposed for fast inversion of a wide class of Preisach-type operators, by exploiting the massive parallelism offered by field-programmable gate arrays (FPGAs) to process the inherently parallel hysteresis operators. The theory, algorithm, and implementation of the inversion are presented. The inversion output is computed iteratively with guaranteed convergence (up to machine precision) provided the hysteresis operator is piecewise monotone and Lipschitz continuous. For an operator consisting of m hysterons, the proposed approach shows a computational complexity of O(log m), in contrast to O(m) for methods using general DSPs. The effectiveness of the fast inversion approach is demonstrated by implementation results on open-loop tracking of kHz reference signals, based on inversion of a Krasnosel'skii-Pokrovskii operator.

/pdf/fast-inverse-compensation-of-preisach-type-hysteresis-1x8qm87ac2.pdf

Fast inverse compensation of Preisach-type hysteresis operators using field-programmable gate arrays

The paper considers the discrete-time implementation of a class of backstepping adaptive controllers for uncertain nonlinear systems in the parametric strict-feedback form. The stability of the resultant sampleddata system cannot be guaranteed when the direct discretization of the continuous-time backstepping controller is applied to the same system via a sampling and hold device. Therefore, the paper has presented a sampled-data control scheme which involves first modifying the existing continuous-time controller and then discretizing it using the forward Euler method. It has been shown that the proposed control guarantees in a semi-global sense the boundedness of all the variables of the overall sampled-data system under some conditions. Particularly, the state of the nonlinear system to be controlled can converge to any arbitrarily small neighbourhood of the origin.

Sampled-data adaptive control of a class of nonlinear systems

We consider multirate sampled-data output feedback control of smart material actuated systems where the measurement sampling rate is made faster than the control update rate. This scheme combines a discrete-time high-gain observer with a hysteresis inversion controller where the hysteresis is modeled using a Preisach operator. We show that the sampled-data output feedback controller achieves stabilization with respect to a closed set in the presence of hysteresis modeling uncertainty. Experimental results for the control of a shape memory alloy actuated rotary joint are provided.

J.H. Ahrens

Papers

Multirate Sampled-Data Output Feedback Control of Smart Material Actuated Systems