Control and Estimation Oriented Model Order Reduction for Linear and Nonlinear Systems

Optimization based controls are advantageous in meeting stringent performance requirements and accommodating constraints. Although computers are becoming more powerful, solving optimization problems in real-time remains an obstacle because of associated computational complexity. Research efforts to address real-time optimization with limited computational power have intensified over the last decade, and one direction that has shown some success is model order reduction. This dissertation contains a collection of results relating to open- and closed-loop reduction techniques for large scale unconstrained linear descriptor systems, constrained linear systems, and nonlinear systems. For unconstrained linear descriptor systems, this dissertation develops novel gramian and Riccati solution approximation techniques. The gramian approximation is used for an open-loop reduction technique following that of balanced truncation proposed by (Moore, 1981) for ordinary linear systems and (Stykel, 2004) for linear descriptor systems. The Riccati solution is used to generalize the Linear Quadratic Gaussian balanced truncation (LQGBT) of (Verriest, 1981) and (Jonckheere and Silverman, 1983). These are applied to an electric machine model to reduce the number of states from $>$100000 to 8 while improving accuracy over the state-of-the-art modal truncation of (Zhou, 2015) for the purpose of condition monitoring. Furthermore, a link between unconstrained model predictive control (MPC) with a terminal penalty and LQG of a linear system is noted, suggesting an LQGBT reduced model as a natural model for reduced MPC design. The efficacy of such a reduced controller is demonstrated by the real-time control of a diesel airpath. Model reduction generally introduces modeling errors, and controlling a constrained plant subject to modeling errors falls squarely into robust control. A standard assumption of robust control is that inputs/states/outputs are constrained by convex sets, and these sets are ``tightened'' for robust constraint satisfaction. However, robust control is often overly conservative, and resulting control strategies cannot take advantage of the true admissible sets. A new reduction problem is proposed that considers the reduced order model accuracy and constraint conservativeness. A constant tube methodology for reduced order constrained MPC is presented, and the proposed reduced order model is found to decrease the constraint conservativeness of the reduced order MPC law compared to reduced order models obtained by gramian and LQG reductions. For nonlinear systems, a reformulation of the empirical gramians of (Lall et al., 1999) and (Hahn et al., 2003) into simpler, yet more general forms is provided. The modified definitions are used in the balanced truncation of a nonlinear diesel airpath model, and the reduced order model is used to design a reduced MPC law for tracking control. Further exploiting the link between the gramian and Riccati solution for linear systems, the new empirical gramian formulation is extended to obtain empirical Riccati covariance matrices used for closed-loop model order reduction of a nonlinear system. Balanced truncation using the empirical Riccati covariance matrices is demonstrated to result in a closer-to-optimal nonlinear compensator than the previous balanced truncation techniques discussed in the dissertation.PHDNaval Architecture & Marine EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/140839/1/riboch_1.pd

Low-dose megavoltage cone-beam CT imaging using thick, segmented scintillators

Megavoltage, cone-beam computed tomography (MV CBCT) employing an electronic portal imaging device (EPID) is a highly promising technique for providing soft-tissue visualization in image-guided radiotherapy. However, current EPIDs based on active matrix flat-panel imagers (AMFPIs), which are regarded as the gold standard for portal imaging and referred to as conventional MV AMFPIs, require high radiation doses to achieve this goal due to poor x-ray detection efficiency (~2% at 6 MV). To overcome this limitation, the incorporation of thick, segmented, crystalline scintillators, as a replacement for the phosphor screens used in these AMFPIs, has been shown to significantly improve the detective quantum efficiency (DQE) performance, leading to improved image quality for projection imaging at low dose. Toward the realization of practical AMFPIs capable of low dose, soft-tissue visualization using MV CBCT imaging, two prototype AMFPIs incorporating segmented scintillators with ~11 mm thick CsI:Tl and Bi 4 Ge 3 O 12 (BGO) crystals were evaluated. Each scintillator consists of 120 _ 60 crystalline elements separated by reflective septal walls, with an element-to-element pitch of 1.016 mm. The prototypes were evaluated using a bench-top CBCT system, allowing the acquisition of 180 projection, 360° tomographic scans with a 6 MV radiotherapy photon beam. Reconstructed images of a spatial resolution phantom, as well as of a water-equivalent phantom, embedded with tissue equivalent objects having electron densities (relative to water) varying from ~0.28 to ~1.70, were obtained down to one beam pulse per projection image, corresponding to a scan dose of ~4 cGy–-a dose similar to that required for a single portal image obtained from a conventional MV AMFPI. By virtue of their significantly improved DQE, the prototypes provided low contrast visualization, allowing clear delineation of an object with an electron density difference of ~2.76%. Results of contrast, noise and contrast-to-noise ratio are presented as a function of dose and compared to those from a conventional MV AMFPI.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/90773/1/0031-9155_56_6_001.pd