Generalizations of H-infinity optimization. Control of rotating stall

Citation

D'Andrea, Raffaello (1997) Generalizations of H-infinity optimization. Control of rotating stall. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/4R8P-RR02. https://resolver.caltech.edu/CaltechETD:etd-01092008-110959

Abstract

Arguably one of the most significant contributions to the field of optimal control has been the formulation and eventual solution of the H∞ design problem. Armed with this mathematical tool, designs which are robust to plant uncertainty and insensitive to plant parameters can be performed in a systematic and rigorous fashion.

The H∞ methodology, however, typically leads to conservative designs. The reasons are twofold. The first is that the plant uncertainty can only be accounted for in an approximate manner, with the result that designs are performed for a set of allowable systems which is larger than what is being modeled; thus the resulting control strategy is forced to guard against non-realizable situations, potentially sacrificing system performance. The second has to do with the physical interpretation of H∞ optimization: the minimization of a system's power to power gain. Thus it is implicitly assumed in the design process that the worst case disturbance is allowed to be an arbitrary power signal, such as a sinusoid. This is clearly a poor modeling choice for many types of physical disturbances, such as sensor or thermal noise, wind gusts, and impulsive forces.

The main contribution of this dissertation is the extension of H∞ optimization to allow for general closed loop design objectives which address the two limitations outlined above. In particular, non-conservative, computationally tractable, linear matrix inequality based methods for control design are developed for a certain class of physically motivated uncertain systems. In addition, these new techniques can accommodate constraints on the allowable disturbances, excluding unrealistic disturbances from the design process.

Another contribution of this dissertation is an attempt to view control in the broader context of system design. Typically, a control algorithm is only sought after the system to be controlled has already been designed, and the type and location of the actuators and sensors has been determined. For most applications, however, the level of performance which can be attained by any control strategy is dictated by the dynamics of the plant. Thus from a system level, the above methodology is not optimal, since the control design process is decoupled from the design of the rest of the system. By adopting the behavioral framework for systems, an optimization problem where the given system is not treated as an input-output operator, a natural assumption when considering first principles models, is formulated and solved. The interpretation of the above extension of H∞ optimization is that of designing optimal systems.

In contrast to the general purpose tools developed in the first part of the dissertation and summarized above, the second part deals with an actual experimental problem, that of controlling rotating stall using pulsed air injection in a low-speed, axial flow compressor. By modeling the injection of air as an unsteady shift in the compressor characteristic, the viability of various air injection orientations are established. A control strategy is developed which controls the pulsing of air in front of the rotor face based on unsteady pressure measurements near the rotor face. Experimental results show that this technique eliminates the hysteresis loop normally associated with rotating stall. A parametric study is used to determine the optimal control parameters for suppression of stall. The resulting control strategy is also shown to suppress surge when a plenum is present. Using a high fidelity model, the main features of the experimental results are duplicated via simulations. The main contributions of this part of the dissertation are a simple control scheme which has the potential of greatly increasing the operability of compressors, and a low-order modeling mechanism which captures the essential features of air injection, facilitating subsequent analyses and control designs which make use of air injectors.

Thesis Files