two degrees of freedom dead beat control system with robustness this paper deals with the design of a two degrees of freedom tdf dead beat controller with both optimal robustness and minimum settling time based on the parametrization of all stabilizing tdf controllers optimal robustness and minimum time control are achieved simultaneously the minimum time dead beat control is constructed for arbitrary real rational reference input at the same time optimal robustness is achieved under the constraint that the error between reference input and output asymptotically vanishes for any plant perturbation that does not violate the internal stability it is proved that under the same robustness criterion irrespective of its length of settling time the optimal robustness of the tdf system is always superior to that of the one degree of freedom odf system as long as its settling time is finite and they become identical only when the settling time of the odf system goes to infinity a numerical example is given to illustrate the theoretical results

random sequential addition a distribution function approach random sequential addition rsa of hard objects is an irreversible process defined by three rules objects are introduced on a surface or ad dimensional volume randomly and sequentially two objects cannot overlap and once inserted an object is clamped in its position the configurations generated by an rsa can be characterized in the macroscopic limit by a unique set of distribution functions and a density we show that these nonequilibrium rsa configurations can be described in a manner which in many respects parallels the usual statistical mechanical treatment of equilibrium configurations kirkwood salsburg like hierarchies for the distribution functions zero separation theorems diagrammatic expansions and approximate equations for the pair distribution function approximate descriptions valid for low to intermediate densities can be combined with exact results already derived for higher densities close to the jamming limit of the process similarities and differences between the equilibrium and the rsaconfigurations are emphasized finally the potential application of rsa processes to the study of glassy phases is discussed

ripple free tracking with robustness despite the previous efforts in deadbeat control a need still exists to offer a generic design methodology for both performance and robustness we propose a hybrid two degree of freedom 2dof controller for the fixed order constrained optimization problem addressing performance and robustness specifications the controller is given in terms of the solution of two diophantine equations simple parameterization of these diophantine equations allows for straight forward optimization and constraint satisfaction for both performance and robustness measures

a direct approach to finding exact invariants for one dimensional time dependent classical hamiltonians for a classical hamiltonian h 1 2 p2 v q t with an arbitrary time dependent potential v q t exact invariants that can be expressed as series in positive powers of p i q p t n 0pnfn q t are examined the method is based on direct use of the equation di dt i t i h 0 a recursion relation for the coefficients fn q t is obtained all potentials that admit an invariant quadratic in p are found and for those potentials all invariants quadratic in p are determined the feasibility of extending the analysis to find invariants that are polynomials in p of higher degree than quadratic is discussed the systems for which invariants quadratic in p have been found are transformed to autonomous systems by a canonical transformation

ripple free deadbeat control of siso discrete systems the ripple free deadbeat control problem for arbitrary not necessarily stable siso linear discrete plants and reference signals is treated it is established that a causal stabilizing ripple free deadbeat controller exists if and only if the zeros of the plant and the poles of the reference signal are disjoint and a complete characterization of all such controllers is obtained solutions to two illustrative problems are presented

a first integral for a class of time dependent anharmonic oscillators with multiple anharmonicities the integrability of the equation q f t q2 g t q3 h t q4 j t q5 is considered particular cases of this equation arise in the study of charged plasma in an axially symmetric magnetic field and in shear free spherically symmetric gravitational fields in general relativity the above equation with only a quadratic term arises in the study of shear free fluids in general a krasinski j math phys 30 433 1989 the equation with a cubic term is applicable when there is an electromagnetic field in special cases we reduce the solution to a quadrature that has solutions in terms of elliptic integrals a lie point symmetry analysis is performed and the different cases that arise are considered for the existence of a symmetry

berry s phase as the asymptotic limit of an exact evolution an example the authors exhibit for arbitrary time variations of the parameters of the generalised harmonic oscillator hamiltonian a canonical transformation which facilitates an exact analysis of quantal phase and classical angle formulae for berry s phase and hannay s angle are readily obtained by taking the adiabatic limit of the exact theory

geometry of random sequential adsorption by sequentially adding line segments to a line or disks to a surface at random positions without overlaps we obtain configurations of the one and two dimensional random sequential adsorption rsa problem we have simulated the one and two dimensional problem with periodic boundary condition the one dimensional simulations are compared with the exact analytical solutions to give an estimate of the accuracy of the simulation in two dimensions the geometrical properties of the rsa configuration are discussed and in addition known results of the rsa process are reproduced various statistical distributions of the voronoi dirichlet vd network corresponding to the rsa disk configuration are analyzed in order to characterize pores in the rsa configuration we introduce circular holes there is a direct correspondence between vertices of the vd network and these holes and also between direct indirect geometrical neighbors and these holes the hole size distribution is found to be a parabola we also find general relations that connect the asymptotic behavior of the surface coverage the correlation function and the hole size distribution

statistical geometry of four calottes on a sphere we calculate the configurational integral and reduced distribution functions for a system of four rigid spherical calottes a model which allows an exact analysis of excluded volume effects resulting from the interplay between statistics and geometry

solutions in closed form and as power series to the real lorenz equations using the method of the lie theory of extended groups and for the parameter values b 1 and r 0 we construct explicitly the general exact solution to the real lorenz equations in terms of jacobian elliptic functions in the context of our approach further possible completely integrable cases of the lorenz system are discussed by considering the result of the painleve analysis for 1 b 2 and r 1 9 and negative values of r the latter case r 0 and 0 not following from the painleve test for other positive parameter values and in the form of appropriate power series we find some particular exact solutions which do not possess the painleve property

statistical mechanics of elastic moduli we consider continuous systems of particles in the framework of classical statistical mechanics and derive a general expression for the static elastic moduli tensor in terms of correlation functions we find sufficient conditions for the vanishing of the shear modulus relationships between these conditions and others insuring translational or rotational invariance are discussed

statistical geometry of hard particles on a sphere analysis of defects at high density abstract we analyse the geometry of the solid phase shaped by densely packed hard calottes on a sphere we show that in this phase topological defects are not distributed at random over the surface but segregate into clusters that give rise to an upper level of organization in the form of a superstructure with icosahedral symmetry

double objective optimal multivariable ripple free deadbeat control this paper presents novel results on optimal multivariable deadbeat control given a discrete time stable linear time invariant plant model we give a simple parameterization of all stabilizing ripple free deadbeat controllers of a given order the free parameter is then optimized in the sense that a quadratic index is kept minimal the optimality criterion has the advantage of accounting for both tracking performance and magnitude of the control effort the proposed design procedure is simple to use and allows the tuning of the controller with a scalar weighting factor simulation results are included to illustrate the effectiveness of the proposed design algorithm

optimal ripple free deadbeat control using an integral of time squared error itse index this paper describes an optimal ripple free deadbeat control strategy for single input single output siso linear sampled data plants the cost function to be minimized is a linear combination of a time weighted cumulative term that penalizes the tracking error that is an integral of time squared error itse cost term and a cumulative term which penalizes the control signal deviations from its steady state value the optimization problem turns out to be convex and closed form solutions are obtained an example is included to illustrate our results

the determination of nonlocal symmetries by the technique of reduction of order autonomous systems of ordinary differential equations can be rewritten as systems of first order ordinary differential equations and one of the dependent variables chosen as a new independent variable some of the variables are eliminated to give a mixed system of first and second order equations for which the determination of point symmetries can be automated without having to make an ansatz on the detailed structure of the symmetry because the coefficient function for the original independent variable appears only as its derivative in the reduced system symmetries which are nonlocal in this variable become local symmetries of the reduced system and can be computed algorithmically

lie symmetries for the charge monopole problem the authors obtain the lie symmetries for the equation of motion of an electric charge interacting with a magnetic monopole fixed at the origin they also discuss the construction of first integrals for this problem

an exact invariant for a class of time dependent anharmonic oscillators with cubic anharmonicity an exact invariant is constructed for a class of time dependent anharmonic oscillators using the method of the lie theory of extended groups the presence of the anharmonic term imposes a constraint on the nature of the time dependence for a subclass it is possible to obtain an energy like integral and a condition under which the motion is bounded

nonlinear canonical transformations i the linear canonical transformation q aq bp p cq dp ad bc 1 q p constant is extended to include terms of the second third and fourth degree products of second degree transformations are used to construct third and fourth degree transformations the question of factorisability of fourth degree transformations is discussed

euclidean invariance in statistical mechanics of classical continuous system it is shown that equilibrium states of classical particles with short range interactions are euclidean invariant whenever their correlation functions have a clustering which is integrable the relation between invariance and clustering is analysed for spatial rotations and internal rotational degrees of freedom the analysis is then extended to the case of long range interactions including the coulomb force and jellium systems

optimal ripple free deadbeat controllers a ripple free deadbeat controller for a system exists if and only if there are no transmission zeros coinciding with the poles of the reference signal approaches to this problem often use the diophantine equation solution however solutions provided by the diophantine equation often exhibit extremely bad transient responses this approach gives a new affine parametrization of solutions of the diophantine equation based on this parametrization lmi conditions are used to provide optimal or constrained controllers for design quantities such as overshoot undershoot control amplitude slew rate as well as for norm bounds such as l1 l2 and l infinity

ermakov and non ermakov systems in quantum dissipative models via the hydrodynamical formulation of quantum mechanics a unified protocol to treat the quantum time dependent harmonic oscillator with friction is presented described by two different models an explicitly time dependent linear schrodinger equation caldirola kanai model and a logarithmic nonlinear schrodinger equation kostin model for the former model an ermakov system that makes it possible to obtain an invariant of ermakov lewis type is derived for the latter model a non ermakov system is derived instead and it is shown that neither an exact nor an approximate invariant of ermakov lewis type exists

zero frequency elastic moduli of uniform fluids a statistical mechanical treatment of equilibrium elasticity of a uniform fluid phase based on density functional theory is presented bulk expressions for the stress tensor and the zero frequency elastic moduli tensor involving the direct correlation function are found

intersecting disks and spheres and statistical mechanics i mathematical basis the calculations of a previous paper on intersecting disks are completed further quantities of interest in connection with intersecting disks and spheres are defined the above considerations are extended to spherical boundary conditions then two applications are stated the penetrable sphere model of widom and rowlinson and the hard sphere system finally the generalization tod dimensional spheres is outlined

lie transformation group solutions of the nonlinear one dimensional vlasov equation the solution of the exact nonlinear one dimensional vlasov equation with a space and time dependent electric field is reduced to the solution of a nonlinear first order ordinary differential equation with two subsidiary equations the reduction holds for any electric field nonlinear in the spatial coordinate or for a subclass of electric fields linear in the spatial coordinate and is equivalent to the solution of a generalized bernstein greene kruskal bgk vlasov equation with a velocity dependent lorentz force the lie method for the solution of differential equations invariant under a transformation group has been used to calculate the group generator the canonical variables and the generalized bgk vlasov equation analytical forms for the functional dependence of the vlasov equation one particle distribution function are given

an exact invariant for the time dependent double well anharmonic oscillators lie theory and quasi invariance groups the author derives an exact energy type invariant for the double well anharmonic oscillators this invariant holds for certain time dependent potential parameters a nonlinear superposition principle is used to solve the nonlinear constraint equations which appear in the resolution

diophantine equations in control a survey abstract this survey is also a tutorial whose aim is to explain the role of diophantine equations in the synthesis of feedback control systems these are linear equations in a ring and result from a fractional representation of the systems involved the cornerstone of the exposition is a simple parametrization of all stabilizing controllers for a given plant one can then choose in principle the best controllers for various applications these ideas evolved from early attempts to use polynomial equations in the design of discrete time linear systems by now they have been extended to continuous time infinite dimensional time varying and non linear systems

equilibrium versus random sequential addition of dimers on a lattice the statistical mechanical properties of particles forming dimers are compared with the results obtained on a two dimensional lattice through a random sequential addition rsa experiment the relation between the most likely fraction of dimers filling the lattice at equilibrium in the disordered phase and the corresponding non equilibrium jamming limit attained through rsa is explored some implications relevant for the physics of the liquid state are also discussed

ripple free robust output regulation and tracking for multirate sampled data control the problem of the robust continuous time asymptotic tracking and disturbance rejection for a multivariable multirate sampled data system is studied the necessity of a continuous time internal model of the exogenous signals except for the constant ones if any for obtaining a ripple free zero error response is proven the conditions are given for the existence of a hybrid control system including possibly a continuous time subcompensator for which the exponential stability and a continuous time convergence to zero of the tracking error are guaranteed at least in a neighbourhood of the nominal parameters this in particular both for when the dead beat convergence of the state free response and the continuous time error response is required at the nominal parameters and for when an exponential convergence with a prescribed rate of decay is required including design procedures of the continuous time and the discrete time subcompensators both for when the available description of the plant has a

parameterization of all multivariable ripple free deadbeat tracking controllers this paper presents an explicit parameterization of all ripple free deadbeat tracking controllers for multi input multi output mimo sampled data control systems the advantages over the previous results are the following first a useful necessary and sufficient condition to obtain a ripple free deadbeat tracking response for mimo sampled data control systems is presented second not only all ripple free mimo deadbeat tracking controllers but also all achievable deadbeat sequences and all control input ones are characterized by completely free parameters in an explicit form third the design method is simple and straightforward the computation consists of simple polynomial matrix equations without involving troublesome calculation such as the reduction to smith mcmillan form fourth the class of the reference inputs for which ripple free deadbeat tracking responses are achieved is generalized finally a numerical example demonstrates that the proposed parameterization makes it easy to clarify the r

statistical geometry of hard particles on a sphere abstract we present a monte carlo study of a two dimensional system of hard particles embedded on the surface of a sphere thermodynamic and structural evidence of an ordering phase transition is found at high densities in spite of the frustration induced on the hexagonal covering by the peculiar topology of the host surface the nature of this transition is analyzed and contrasted with the fluid solid transition occuring in a flat geometry

generalizations of noether s theorem in classical mechanics in this paper a review is presented of various approaches to the generalization of the version of noether s theorem which is presented in most textbooks on classical mechanics its motivation is the controversy still persisting around the possible scope of a noether type theorem allowing for velocity dependent transformations our analysis is centered around the one factor common to all known treatments namely the structure of the related first integral we first discuss the most general framework in which a function of the above mentioned structure constitutes a first integral of a given lagrangian system and show that one cannot really talk about an interrelationship between symmetries and first integrals there we then compare different proposed generalizations of noether s theorem by describing the nature of the restrictions which characterize them when they are situated within the broadest framework we prove a seemingly new equivalence result between the two main approaches that of invaria

equation of state of the hard disk fluid on a sphere from percus yevick equation the percus yevick equation is solved numerically for hard disks on a sphere the effect of curvature of the hosting surface is calculated and an empirical correction to the equation of state is proposed

design of ripple free multivariable robust servomechanisms the application of standard robust servomechanism theory to sampled data systems guarantees asymptotic tracking at sampling instances and between sampling instants the output will normally contain ripple in this note the robust servomechanism theory is extended to sampled data systems and a technique is proposed for ripple free tracking of sinusoids and polynomials it is shown that a continuous internal model is necessary and sufficient to provide ripple free response

first integrals for the modified emden equation q α t q qn 0 it is shown that the modified emden equation q t q qn 0 possesses first integrals for functions t other than kt 1 the function t is obtained explicitly in the case n 3 and parametrically for other n 2 the case n 2 is seen to be particularly difficult to solve