NONQUADRATIC COST AND NONLINEAR FEEDBACK CONTROL

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/57832/1/BernsteinNonquadraticCost1993.pd

The Whirling Blade and the Steaming Cauldron

Ths dissertation applies recent theoretical developments in control to two practical examples. The first example is control of the primary circuit of a pressurized water nuclear reactor. This is an interesting example because the plant is complex and its dynamics vary greatly over the operating range of interest. The second example is a thrust-vectored ducted fan engine, a nonlinear flight control experiment at Caltech. The main part of this dissertation is the application of linear parameter-dependent control techniques to the examples. The synthesis technique is based on the solution of linear matrix inequalities (LMIs) and produces a controller whch acheves specified performance against the worst-case time variation of measurable parameters entering the plant in a linear fractional manner. Thus the plant can have widely varying dynamics over the operating range, a quality possessed by both examples. The controllers designed with these methods perform extremely well and are compared to H∞, gain-scheduled, and nonlinear controllers. Additionally, an in-depth examination of the model of the ducted fan is performed, including system identification. From this work, we proceed to apply various techniques to examine what they can tell us in the context of a practical example. The primary technique is LMI-based model validation. The contribution ths dissertation makes is to show that parameter-dependent control techniques can be applied with great effectiveness to practical applications. Moreover, the trade-off between modelling and controller performance is examined in some detail. Finally, we demonstrate the applicability of recent model validation techruques in practice, and discuss stabilizability issues

Equivalence of robust stabilization and robust performance via feedback

One approach to robust control for linear plants with structured uncertainty as well as for linear parameter-varying (LPV) plants (where the controller has on-line access to the varying plant parameters) is through linear-fractional-transformation (LFT) models. Control issues to be addressed by controller design in this formalism include robust stability and robust performance. Here robust performance is defined as the achievement of a uniform specified $L^{2}$-gain tolerance for a disturbance-to-error map combined with robust stability. By setting the disturbance and error channels equal to zero, it is clear that any criterion for robust performance also produces a criterion for robust stability. Counter-intuitively, as a consequence of the so-called Main Loop Theorem, application of a result on robust stability to a feedback configuration with an artificial full-block uncertainty operator added in feedback connection between the error and disturbance signals produces a result on robust performance. The main result here is that this performance-to-stabilization reduction principle must be handled with care for the case of dynamic feedback compensation: casual application of this principle leads to the solution of a physically uninteresting problem, where the controller is assumed to have access to the states in the artificially-added feedback loop. Application of the principle using a known more refined dynamic-control robust stability criterion, where the user is allowed to specify controller partial-state dimensions, leads to correct robust-performance results. These latter results involve rank conditions in addition to Linear Matrix Inequality (LMI) conditions.Comment: 20 page

Linear Control Theory with an ℋ∞ Optimality Criterion

This expository paper sets out the principal results in ℋ∞ control theory in the context of continuous-time linear systems. The focus is on the mathematical theory rather than computational methods

Stabilization of uncertain linear systems: an LFT approach

This paper develops machinery for control of uncertain linear systems described in terms of linear fractional transformations (LFTs) on transform variables and uncertainty blocks with primary focus on stabilization and controller parameterization. This machinery directly generalizes familiar state-space techniques. The notation of Q-stability is defined as a natural type of robust stability, and output feedback stabilizability is characterized in terms of Q-stabilizability and Q-detectability which in turn are related to full information and full control problems. Computation is in terms of convex linear matrix inequalities (LMIs), the controllers have a separation structure, and the parameterization of all stabilizing controllers is characterized as an LFT on a stable, free parameter