Surface charge density of the track-etched nanopores in polyethylene terephthalate foils

Surface charge is one of the most important properties of nanopores, which determines the nanopore performance in many practical applications. We report the surface charge densities of track-etched nanopores, which were obtained by measuring the streaming current and pore conductance, respectively. Experimental results reveal that surface charge densities depend significantly on the salt concentrations. In addition the values obtained with the pore conductance were always several times higher than those calculated with the streaming current, and the gel-like surface layer on the nanopore was considered to be responsible for this discrepancy.     

A recursive formula for the correlations of Walsh functions

The correlation function of two Walsh functions appears in image processing, signal multiplexing, detection and spectral analysis using Walsh functions. Though Walsh functions are two-valued, their correlation functions are real-valued and rather difficult to evaluate. A recursive formula is developed in this paper to evaluate the correlation functions. Some other properties of the correlation function are also discussed.     

Time-optimal control problem for a linear parameter varying system with nonlinear item

In this paper, we considered a time-optimal control problem for a new type of linear parameter varying (LPV) system which is obtained through data identification in the process of dealing with actual problems. The addition of non-linear terms is compensation for the method that does not require linear expansion at the equilibrium point. Since the objective function is the terminal time which is an implicit function concerning decision variables, it is a non-standard optimal control problem with uncertain terminal time. To find the global optimal solution to this problem, firstly, the control parameterization method is used to transform it into a nonlinear optimization problem of parameter selection, and then the modifed particle swarm optimization (PSO) algorithm is combined to solve the equivalent nonlinear programming problem. Numerical examples are used to illustrate the effectiveness of the proposed algorithm.     

An exact formula for the half-plane pull-in range of a PLL

A second-order phase-lock loop (PLL) that is based on a triangular-characteristic phase detector and imperfect-integrator loop filter is found in many applications where simplicity and economics are major considerations. For many of these applications, digital-logic-compatible reference and VCO signals are used, an exclusive-OR gate implements the phase detector, and the loop filter is constructed from passive components. When designing these loops, the half-plane pull-in range Ω₂ is of interest. Until now, this important loop parameter could only be calculated by using a computer-based technique that numerically integrated the nonlinear differential equation that describes the PLL model. This requirement/limitation is removed here by the development of an exact closed-form formula for Ω₂, the main contribution of this paper. More generally, the value of Ω₂ is dependent on the PLL phase detector characteristic that is used, be it triangular, sinusoidal, or something else. With regard to the value of Ω₂ produced, a comparison is given of two PLLs, both described by the same linear model so that the comparison is meaningful. The first PLL is based on a triangular-characteristic phase detector; the second loop is based on a sinusoidal phase detector.     

An exact formula for the maximum VCO sweep rate of a PLL

In many phase-locked loop (PLL) applications, the natural pull-in mechanism is too slow and unreliable, and it must be accelerated. By adding an externally-generated ramp to its control voltage input, the PLL voltage controlled oscillator (VCO) frequency can be swept towards the input reference frequency in an attempt to speed up the pull-in process. This popular acquisition aid has a significant limitation when it is used in a second-order, Type II PLL. If the applied ramp voltage has a slope magnitude greater than (alternatively, less than) some value R_m, the PLL state can (alternatively, cannot) sweep past the desired lock point, resulting in a phase lock failure (alternatively, success). In general, the maximum sweep rate magnitude R_m can be computed by using a numerical integration-and-search procedure that is described in the PLL literature. A special case exists for a second-order, Type II PLL that incorporates a triangular-characteristic phase detector (with logic-level binary input signals). For this case, it is possible to develop an exact, closed-form expression for R_m, the main result of this paper. For a range of loop parameters most often used in applications, R_m values are computed by using the exact formula, and these are used in two ways. First, they are used to validate the previously-mentioned numerical integration-and-search procedure. Second, they are compared to maximum sweep rate values computed for a PLL that utilizes a sinusoidal phase detector to show that the triangular-phase-detector PLL can be swept significantly faster than the sinusoidal-phase-detector loop.     

Stability analysis of a rotor-AMB system with time varying stiffness

A rotor-active magnetic bearing (AMB) system subjected to a periodically time-varying stiffness with quadratic and cubic nonlinear under tuned, and external excitation is studied. The method of multiple scales is applied to analyze the response of two modes of a rotor-AMB system near the simultaneous combined and sub-harmonic resonance. The stability of the steady-state solution for that resonance is determined and studied applying Rung–Kutta fourth order method. It is shown that the system exhibits many typical nonlinear behaviors, including multiple-valued solutions, jump phenomenon, hardening and softening nonlinear and chaos in the second mode of the system. The effects of the different parameters on the steady-state solutions are investigated and discussed.     

A prevalence formula for automatic relevance feedback in Boolean systems

The implementation of relevance feedback explored here demonstrates the feasibility of query reformulation for boolean retrievals. Improvements to a term prevalence formula used in earlier research are presented along with experimental results that confirm the crucial role of term weights in relevance feedback. In particular, the weighting formula presented here differs significantly from those used by researchers in associative retrieval environments by giving equal weight to a patron's judgements of nonrelevance. The use of negative feedback—by NOTing terms in the negative prevalence range—failed to improve precision, a result that is also considered significant.     

Networked feedback control for nonlinear systems with random varying delays

This paper discusses the controller synthesis problem of a nonlinear networked controlled system subject to delays in the measurement and actuation channels. The communication through the network also suffers non-stationary packet dropouts. The bounded nonlinearities in the plant state satisfy Lipschitz conditions. A Lyapunov function is developed for the closed-loop system considering dynamic output feedback and the resulting stabilization conditions are drawn in the form of linear matrix inequalities to ensure that the system is exponentially stable in the mean-square sense. The developed conditions are represented in the form of a convex optimization problem and the results are tested by simulation on a quadruple-tank process.     

Adaptive learning tracking for robot manipulators with varying trial lengths

This paper proposes adaptive iterative learning control schemes for robot manipulator systems with iteration-varying lengths. To prove the asymptotical convergence of the joint position tracking error along the iteration axis, this paper develops a new composite energy function based on the newly introduced auxiliary variables for the analysis. Moreover, the traditional assumption of identical initialization condition is relaxed to be arbitrarily varying and then an initial rectifying mechanism is introduced to tackle initial shift problem of robotic systems. Illustrative simulations on a two degree-of-freedom robot manipulator are provided to verify the theoretical results.     

PID controller tuning rules for integrating processes with varying time-delays

This paper discusses PID controller tuning for integrating processes with varying time-delays. Most of the existing tuning rules for the first-order lag plus integrator plus delay (FOLIPD) processes that we mainly focus on have the same general structure, and the properties of these rules are discussed in conjunction with varying time-delays. The analysis leads to novel tuning rules, where the maximum amplitude of an arbitrarily varying time-delay can be given as a parameter, which makes the use of the rules attractive in several applications. We will also extend the analysis to integrating processes with second-order lag and apply the design guidelines for a networked control application. In addition, we propose a novel tuning method that optimizes the closed-loop performance with respect to certain robustness constraints while also providing robustness to delay variance via jitter margin maximization. Further, we develop new PID controller tuning rules for a wide range of processes based on the proposed method. The new tuning rules are discussed in detail and compared with some of the recently published results. The work was originally motivated by the need for robust but simultaneously well-performing PID parameters in an agricultural machine case process. We also demonstrate the superiority of the proposed tuning rules in the case process.     

Model free adaptive iterative learning control for a class of nonlinear systems with randomly varying iteration lengths

This paper proposes a novel model free adaptive iterative learning control scheme for a class of unknown nonlinear systems with randomly varying iteration lengths. By applying the dynamic linearization technique along the iteration axis, such systems can be transformed into iteration-depended time varying linear systems. Then, an improved model free adaptive iterative learning control scheme can be constructed only using input and output data of the system. From the rigorous theoretical analysis, it is shown that the mathematical expectation of tracking errors converge to zero as iteration increases. This design does not require any dynamic information of the ILC systems and prior information of randomly varying iteration lengths. An illustrative example verifies the effectiveness of the proposed design.     

Initial conditioned solutions of a second-order nonlinear conservative differential equation with a periodically varying coefficient

The exact solution of the equation

$\text{d}{}^2\text{x}\text{dt}{}^2\text{+dx+d′f(wt)x}{}^3\text{=0,}$

where d, d' and w are positive constants, and ?(wt) is a rectangular periodic function of time is discussed. The equation describes approximately the transversal movement of a particle in an alternating gradient accelerator. The exact solution is obtained in the form of a composite recurrent relation containing five particular solutions. Each of these solutions corresponds to a specific well-defined area of the phase plane of the initial conditions. The dynamical behaviour and the stability of the movement are examined analytically.