Composite control of non-linear singularly perturbed systems: a geometric approach

Using a geometric approach, a composite control—the sum of a slow control and a fast control—is derived for a general class of non-linear singularly perturbed systems. A new and simpler method of composite control design is proposed whereby the fast control is completely designed at the outset. The slow control is then free to be chosen such that the slow integral manifold of the original system approximates a desired design manifold to within any specified order of ε accuracy.

Exact design manifold control of a class of nonlinear singularly perturbed systems

The integral manifold approach captures from a geometric point of view the intrinsic two-time-scale behavior of singularly perturbed systems. An important class of nonlinear singularly perturbed systems considered in this note are fast actuator-type systems. For a class of fast actuator-type systems, which includes many physical systems, an explicit corrected composite control, the sum of a slow control and a fast control, is derived. This corrected control will steer the system exactly to a required design manifold.

Composite control of non-linear singularly perturbed systems: a geometric approach

Using a geometric approach, a composite control—the sum of a slow control and a fast control—is derived for a general class of non-linear singularly perturbed systems. A new and simpler method of composite control design is proposed whereby the fast control is completely designed at the outset. The slow control is then free to be chosen such that the slow integral manifold of the original system approximates a desired design manifold to within any specified order of ε accuracy.

Exact design manifold control of a class of nonlinear singularly perturbed systems

The integral manifold approach captures from a geometric point of view the intrinsic two-time-scale behavior of singularly perturbed systems. An important class of nonlinear singularly perturbed systems considered in this note are fast actuator-type systems. For a class of fast actuator-type systems, which includes many physical systems, an explicit corrected composite control, the sum of a slow control and a fast control, is derived. This corrected control will steer the system exactly to a required design manifold.

Crystal design approaches for the synthesis of paracetamol co-crystals

Crystal engineering principles were used to design three new co-crystals of paracetamol. A variety of potential cocrystal formers were initially identified from a search of the Cambridge Structural Database for molecules with complementary hydrogen-bond forming functionalities. Subsequent screening by powder X-ray diffraction of the products of the reaction of this library of molecules with paracetamol led to the discovery of new binary crystalline phases of paracetamol with trans-1,4- diaminocyclohexane (1); trans-1,4-di(4-pyridyl)ethylene (2); and 1,2-bis(4-pyridyl)ethane (3). The co-crystals were characterized by IR spectroscopy, differential scanning calorimetry, and 1H NMR spectroscopy. Single crystal X-ray structure analysis reveals that in all three co-crystals the co-crystal formers (CCF) are hydrogen bonded to the paracetamol molecules through O−H···N interactions. In co-crystals (1) and (2) the CCFs are interleaved between the chains of paracetamol molecules, while in co-crystal (3) there is an additional N−H···N hydrogen bond between the two components. A hierarchy of hydrogen bond formation is observed in which the best donor in the system, the phenolic O−H group of paracetamol, is preferentially hydrogen bonded to the best acceptor, the basic nitrogen atom of the co-crystal former. The geometric aspects of the hydrogen bonds in co-crystals 1−3 are discussed in terms of their electrostatic and charge-transfer components.