Date of final exam: 29/05/2000

E-mail: zack@bode.disp.uniroma2.it

Tutor: Prof.  S. Nicosia, Università di Roma "Tor Vergata"

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Uniting local and global controllers for anti-windup synthesis   ___________________________________________________________________________________________________________

Advisor:

Prof.  S. Nicosia, Università di Roma "Tor Vergata", Prof.  A.R. Teel, University of California, Santa Barbara

Summary of the thesis

"Anti-windup compensation" denotes systematic modifications to linear control systems to recover (as much as is possible) the linear performance also when saturation is present at the plant's input.

In this thesis, anti-windup techniques proposed in the literature over the years have been studied and considered. In particular, great deal of attention has been paid to the L₂ anti-windup technique proposed by Teel in 1997 (at the European Control Conference). This technique has been extended in the thesis and applied to a number of theoretical and experimental case studies, thus providing constructive anti-windup compensation schemes that apply to a wide variety of applications of interest. Among these, a significant result achieved on an industrial system within a cooperative research project with Newport Corporation, led to great improvement of the commercial product performance through a redesign of the anti-windup protection.

Active vibration isolation systems are high precision devices where a number of isolating stages separate the isolated environment from the noisy one. By measuring the relative displacement between two bodies on the isolating system, the vibration induced from the environment can be detected and attenuated, typically through high-gain control loops. Unfortunately, these high gains lead to severe windup phenomena, and, when the plant's input reaches the saturation limits, isolation can be lost for significantly long times, causing undesired delays of the manufacturing process. The anti-windup scheme designed in this thesis has been applied to a theoretical vibration isolation system and, subsequently, to the industrial system Elite 3 by Newport Corporation. This industrial system is among the most accurate active isolating systems commercially available nowadays. The isolation recovery time of the isolating table after saturation is hit has been improved of more than an order of magnitude through the employment of the new anti-windup compensation scheme. A US patent has been filed for this new compensation scheme.

In the thesis, theoretical aspects associated with anti-windup compensation have also been studied. In particular, solutions have been given to the problem of anti-windup design for linear systems with asymptotically unstable modes, based on appropriate assumptions on the control system. Exponentially unstable linear plants are associated with a bounded region of null-controllability (namely, the subset of the state-space from which trajectories can be driven to zero by a measurable open-loop control input). While the null-controllability region is unbounded in the stable and marginally unstable directions, its boundedness in the exponentially unstable directions highly complicates the anti-windup design. As a matter of fact, if trajectories cross the null-controllability boundaries, not only they cannot anymore be driven to zero, but they unrecoverably diverge to infinity. To deal with such phenomena, positive invariance of suitable subsets of the state-space need to be guaranteed to keep the trajectories within certain safety regions. This last feature, is often in contrast with the small-signal performance requirement of the controlled system that is desirable and feasible. Thus, it might lead to conservative control designs that penalize the local performance to preserve stability in (typically seldom) situations where signals become too large. Through a systematic construction based on a local, high-performance, controller and a global, low-performance, stabilizing action designed for the saturated plant, an anti-windup compensation scheme has been proposed that preserves the small signal behavior of the high-performance controller and modifies it preserving stability and partially recovering performance when saturation is hit or when trajectories approach the null-controllability boundaries. This anti-windup compensation scheme has been validated on a theoretical example constituted by the linearized longitudinal dynamics of an aggressive open-loop unstable aircraft (McDonnell Douglas Tailless Advanced Fighter Aircraft), whose dynamics, arising from wind-tunnel data, have been taken from the literature. The resulting scheme shows high maneuverability of the aircraft and feasibility of very aggressive maneuvers, via simulations that reproduce responses to standard pilot stick commands (doublet commands of different amplitudes and speed) and simulations of piloted flight, where a simple pilot model taken from the literature has been employed.

A last topic dealt with in this thesis is the employment of anti-windup schemes for the design of multicontrolled schemes where smooth authority transfer between different controllers (and, possibly, a manual control input) is guaranteed. Based on the L₂ anti-windup scheme, the well-known "bumpless transfer" feature has been achieved for the multicontrolled system, showing highly improved performance with respect to previous schemes on examples taken from the literature. The bumpless scheme has also been employed for the design of highly reliable control schemes via hardware redundancy. A reliable scheme with 3 redundant controllers, which guarantees failure detection and handling, has been applied to an example showing very satisfactory results.
 

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