A Digitized Representation of the Modified Prandtl–Ishlinskii Hysteresis Model for Modeling and Compensating Piezoelectric Actuator Hysteresis

Piezoelectric actuators are widely used in micromanipulation and miniature robots due to their rapid response and high repeatability. The piezoelectric actuators often have undesired hysteresis. The Prandtl–Ishlinskii (PI) hysteresis model is one of the most popular models for modeling and compensating the hysteresis behaviour. This paper presents an alternative digitized representation of the modified Prandtl–Ishlinskii with the dead-zone operators (MPI) hysteresis model to describe the asymmetric hysteresis behavior of piezoelectric actuators. Using a binary number with n digits to represent the classical Prandtl–Ishlinskii hysteresis model with n elementary operators, the inverse model can be easily constructed. A similar representation of the dead-zone operators is also described. With the proposed digitized representation, the model is more intuitive and the inversion calculation is avoided. An experiment with a piezoelectric stacked linear actuator is conducted to validate the proposed digitized MPI hysteresis model and it is shown that it has almost the same performance as compared to the classical representation.

Modified Key Derivation Function for Enhanced Security of Speck in Resource-Constrained Internet of Things

Randomness is an imperative component in every cryptographic algorithm to guarantee secret keys are unpredictable and secured against all forms of attacks. Speck generated sequence is non-random, a clear sign that it falls beyond the acceptable success rate when tested in statistical analysis. Thus, this study resolves the non-randomness by integrating a novel key derivation function that uses elementary operators designed for lightweight application. This design aims not to compromise performance when implemented on software and hardware. As a result, the modified Speck successfully passed the NIST SP 800 - 22 and Dieharder v3.31.0 Statistical Test Analysis as no p-value is flagged as failed during testing. Hence, making modified Speck cryptographically secured. Nevertheless, a 1.06% decrease in the figure of merit of the modified Speck still makes it worthier in a resource-constrained Internet of Things application as contrasted to Speck because it is proven to be beyond cryptographically secured.

Range-Kernel orthogonality and elementary operators on certain Banach spaces

The characterization of the points in C p : 1 ≤ p < ∞ ( ℋ ) {C}_{p{:}_{1\le p\lt \infty }}\left({\mathcal{ {\mathcal H} }}) , the Von Neuman-Schatten p-classes, that are orthogonal to the range of elementary operators has been done for certain kinds of elementary operators. In this paper, we shall study this problem of characterization on an abstract reflexive, smooth and strictly convex Banach space for arbitrary operator. As an application, we consider other kinds of elementary operators defined on the spaces C p : 1 ≤ p < ∞ ( ℋ ) {C}_{p{:}_{1\le p\lt \infty }}\left({\mathcal{ {\mathcal H} }}) , and finally, we give a counterexample to Mecheri’s result given in this context.

Range-kernel weak orthogonality of some elementary operators

We study the range-kernel weak orthogonality of certain elementary operators induced by non-normal operators, with respect to usual operator norm and the Von Newmann-Schatten p p -norm ( 1 ≤ p < ∞ ) \left(1\le p\lt \infty ) .

A note on some elementary properties and applications of certain operators to certain functions analytic in the unit disk

This scientific note relates to introducing certain elementary operators defined in the unit disk in the complex plane, then determining various applications (specified by those operators) to certain analytic functions, and also revealing a number of possible implications of them.