Computation of regions of constrained stability for nonlinear control systems

Computation of regions of constrained stability for nonlinear control system

Flame tube parametric studies for control of fuel bound nitrogen using rich-lean two-stage combustion

An experimental parametric study of rich-lean two-stage combustion in a flame tube is described and approaches for minimizing the conversion of fuel-bound nitrogen to nitrogen oxides in a premixed, homogeneous combustion system are evaluated. Air at 672 K and 0.48 MPa was premixed with fuel blends of propane, toluene, and pyridine at primary equivalence ratios ranging from 0.5 to 2.0 and secondary equivalence ratios of 0.5 to 0.7. Distillates of SRC-II, a coal syncrude, were also tested. The blended fuels were proportioned to vary fuel hydrogen composition from 9.0 to 18.3 weight percent and fuel nitrogen composition from zero to 1.5 weight percent. Rich-lean combustion proved effective in reducing fuel nitrogen to NO sub x conversion; conversion rates up to 10 times lower than those normally produced by single-stage combustion were achieved. The optimum primary equivalence ratio, where the least NO sub x was produced and combustion efficiency was acceptable, shifted between 1.4 and 1.7 with changes in fuel nitrogen content and fuel hydrogen content. Increasing levels of fuel nitrogen content lowered the conversion rate, but not enough to avoid higher NO sub x emissions as fuel nitrogen increased

On-line digital computer control of the NERVA nuclear rocket engine

The problem of on-line digital computer control of the NERVA nuclear rocket engine is considered. Proposed is a method of State Dependent State Variable Feedback (SDSVF) as a practical approach to the control of NERVA and other complex nonlinear and/or time-varying systems. The difficulties inherent in other design methods are avoided by defining the optimal closed loop system in terms of a desired transfer function, rather than a performance index to maximize or minimize

The Chirality operators for Heisenberg Spin Systems

The ground state of closed Heisenberg spin chains with an odd number of sites has a chiral degeneracy, in addition to a two-fold Kramers degeneracy. A non-zero chirality implies that the spins are not coplanar, and is a measure of handedness. The chirality operator, which can be treated as a spin-1/2 operator, is explicitly constructed in terms of the spin operators, and is given as commutator of Permutation operators.Comment: 7 pages, report IC/94/23. E-mail: [email protected]

The design of linear multivariable control systems using modern control theory /with applications to coupled core reactor control/

Linear multivariable control system design using modern control theory, and application to coupled core reactor contro

Quantum transport through single-molecule junctions with orbital degeneracies

We consider electronic transport through a single-molecule junction where the molecule has a degenerate spectrum. Unlike previous transport models, and theories a rate-equations description is no longer possible, and the quantum coherences between degenerate states have to be taken into account. We present the derivation and application of a master equation that describes the system in the weak-coupling limit and give an in-depth discussion of the parameter regimes and the new phenomena due to coherent on-site dynamics

The Variable Gradient Method of Generating Liapunov Functions with Application to Automatic Control Systems

The contribution of this thesis is the introduction and development of the variable gradient method of generating Liapunov functions. A Liapunov function, V, is considered to be generated if the form of V is not known before the generating procedure is applied. Two previous attempts at the generation of Liapunov functions to prove global asymptotic stability for nonlinear autonomous systems have been made. These attempts are summarized and evaluated in some detail, as they form the basis for the variable gradient approach proposed in this thesis. It is assumed that the system whose stability is being investigated is represented by n first order, ordinary, nonlinear differential equations in state variable form The particular state variables used throughout the thesis are the phase variables. This was done for convenience. The problem of finding a scalar V(x) to satisfy a particular Liapunov theorem is recast into the problem of finding a vector function, \nabla V, having suitable properties. As the name implies, \nabla V is assumed to be a vector of n elements, \nabla Vi, each of which has n arbitrary coefficients. These coefficients, designated as α ij may be constants or functions of the state variables, In its most general form, the variable gradient is assumed to be V may be determined as a line integral of \nabla V if the following (n-l)n/2 partial differential equations are satisfied. Here \nabla V^ are the elements of the vector \nabla V. The equations (3) are referred to as generalized curl equations. dv/dt may also be determined from \nabla V. An outline of the procedure by which a suitable V and dY/dt may be determined for a particular problem, starting from the variable gradient of (2) is as follows, 1. Assume a gradient of the form (2), 2. From the variable gradient, determine dV/dt by equation (4). 3. In conjunction with and subject to the requirements of the generalized curl equations (3), constrain dV/dt to be at least negative semi- definite, 4. From the now known \nabla V, determine V, 5. Invoke the necessary theorem to establish stability, Numerous examples are worked to illustrate the procedure outlined above, V functions are generated that involve higher order terms in x, integrals, and terms involving three state variables as factors. The problem of determining Hurwitz like criteria for nonlinear systems is considered in some detail. The last chapter attempts to extend .the variable gradient approach to nonautonosnous systems. The results of this chapter, though somewhat marginal, are of interest from the point of view of further researc

Rotational quenching rate coefficients for H_2 in collisions with H_2 from 2 to 10,000 K

Rate coefficients for rotational transitions in H_2 induced by H_2 impact are presented. Extensive quantum mechanical coupled-channel calculations based on a recently published (H_2)_2 potential energy surface were performed. The potential energy surface used here is presumed to be more reliable than surfaces used in previous work. Rotational transition cross sections with initial levels J <= 8 were computed for collision energies ranging between 0.0001 and 2.5 eV, and the corresponding rate coefficients were calculated for the temperature range 2 < T <10,000 K. In general, agreement with earlier calculations, which were limited to 100-6000 K, is good though discrepancies are found at the lowest and highest temperatures. Low-density-limit cooling functions due to para- and ortho-H_2 collisions are obtained from the collisional rate coefficients. Implications of the new results for non-thermal H_2 rotational distributions in molecular regions are also investigated