Regulation in Switched Bimodal Linear Systems

In the past few decades, significant progress has been made in addressing control problems for a variety of engineering systems having smooth dynamics. In practice, one often encounters also non-smooth systems in various branches of science and engineering, such as for example mechanical systems subject to impact. Motivated by the read/write head flying height regulation problem in hard disk drives, where the close proximity of the read/write head to the disk surface results in intermittent contact between the two and a bimodal system behavior, this thesis studies the output regulation problem in switched bimodal linear systems against known and unknown exogenous input signals. The regulation problems in bimodal systems presented in this thesis are solved within sets of Q-parameterized controllers, in which the Q parameters are designed to yield internal stability and exact output regulation in the closed loop switched system. The proposed parameterized controllers are constructed mainly in two steps. The first step is based on constructing a switched observer-based state feedback central controller for the switched linear system. The second step involves augmenting the switched central controller with additional dynamics (i.e. Q parameter) to construct a parameterized set of switched controllers. Based on the proposed sets of Q-parameterized controllers, four main regulation problems are addressed and corresponding regulator synthesis algorithms are proposed. The first problem concerns regulation against known deterministic exogenous inputs, where no stability or structural constraints are imposed on the Q parameter. The second problem is similar to the first, except that the Q parameter is constrained to be a linear combination of basis functions. This structure of the Q parameter is considered in the rest of the thesis. The third problem involves regulation against exogenous inputs involving known deterministic components and unknown random components, and where the regulator is designed subject to an H2 performance constraint. The last problem involves the development of adaptive regulators against unknown sinusoidal exogenous inputs. The different regulator synthesis algorithms are developed based on solving sets of linear matrix inequalities or bilinear matrix inequalities. The last two proposed regulation methods are successfully evaluated on an experimental setup motivated by the flying height regulation problem in hard disk drives, and involving a mechanical system with switched dynamics.Ph