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U of M College of Engineering Control Seminar Series Sponsored by Ford Motor Company, General Motors, and Whirlpool |
Reference Tracking in Feedback Control with
Saturating Actuators
Professor Pierre Kabamba
Department of Aerospace Engineering
University of Michigan
This presentation addresses analysis and controller synthesis
problems for systems with saturating actuators. Three problems are considered, namely: characterizing the
quality of asymptotic tracking for deterministic references such as step, ramp
and parabolic inputs; characterizing the quality of tracking for band-limited
random references; and developing a controller synthesis method for random
reference tracking.
The solution to the first problem is based on extending the
well-known notion of system type to systems with saturating actuators. It is shown that the roles of
controller poles and plant poles are different, and, based on this, new system
types are defined. Asymptotic
tracking errors are characterized according to these system types. In addition, the notion of trackable
domain is introduced, which characterizes limitations in asymptotic tracking
due to actuator saturation. These
results may be useful for selecting controllers and/or actuators that ensure
desired trackable domains and steady state errors in feedback systems with
saturating actuators.
The solution to the second problem is provided by introducing the
notion of saturating random sensitivity function. This function, obtained using the method of stochastic
linearization, characterizes the stationary tracking error for band-limited
random references. Several of its
functionals, referred to as tracking quality indicators, are introduced to
characterize complex tracking behaviors that arise in feedback systems with saturating
actuators. Various causes of poor
tracking (e.g., static unresponsiveness, lagging, oscillatory responses,
controller wind-up, and limitations due to finite trackable domains) can be
identified by these indicators.
The saturating random sensitivity function and tracking quality
indicators are useful for predicting the quality of tracking in feedback
systems with saturating actuators.
The
solution to the third problem is given by extending the standard H-infinity
technique to systems with saturating actuators. This extension, referred to as SH-infinity where 'S' stands
for saturating, is utilized for shaping the saturating random sensitivity
function in order to obtain desired tracking quality indicators. The effectiveness of this method is demonstrated
by applying it to the problem of hard disk servo design.
Joint work with:
Yongsoon Eun and Semyon Meerkov.
3:30 – 4:30 p.m.