An improved generalized predictive control algorithm based on the difference equation CARIMA model for the SISO system with known strong interference

ABSTRACT

The single input single output (SISO) system with known strong interference is widely used in various occasions. Due to its strong interference, the control accuracy is hard to guarantee. To solve this problem, an improved generalized predictive control (IGPC) algorithm is developed. The IGPC firstly builds the difference equation CARIMA (Controlled Auto-Regressive Integrated Moving-Average) model of the SISO system and then treats the system as a two input single output (TISO) system and calculates its predictive vector, then transforms it into a SISO system and uses the TISO system predictive vector to calculate the SISO system control increment. A new parameter called phase coefficient is added to inhibit the control lag. Simulations are performed to make the comparison among the traditional GPC, PID control, velocity synchronization control (VSC), fuzzy adaptive PID control (FAPID), model-based robust PID control (BPID) and the IGPC. Results show that IGPC has best performance compared to the others. Finally, experiments are developed which proved that the IGPC algorithm has a higher accuracy in the SISO system with known strong interference than that of VSC.     

The regularity of the multiple higher-order poles solitons of the NLS equation

Based on the inverse scattering method, the formulae of one higher-order pole solitons and multiple higher-order poles solitons of the nonlinear Schrödinger equation (NLS) equation are obtained. Their denominators are expressed as , where is a matrix frequently constructed for solving the Riemann-Hilbert problem, and the asterisk denotes complex conjugate. We take two methods for proving is invertible. The first one shows matrix is equivalent to a self-adjoint Hankel matrix , proving . The second one considers the block-matrix form of , proving . In addition, we prove that the dimension of is equivalent to the sum of the orders of pole points of the transmission coefficient and its diagonal entries compose a set of basis.     

Investigating the Dynamic Viscoelasticity of Single Polymer Chains using Atomic Force Microscopy

In single‐molecule force spectroscopy (SMFS), many studies have focused on the elasticity and conformation of polymer chains, but little attention has been devoted to the dynamic properties of single polymer chains. In this study, we measured the energy dissipation and elastic properties of single polystyrene (PS) chains in toluene, methanol, and N,N‐dimethylformamide using a homemade piezo‐control and data acquisition system externally coupled to a commercial atomic force microscope (AFM), which provided more accurate information regarding the dynamic properties of the PS chains. We quantitatively measured the chain length‐dependent changes in the stiffness and viscosity of a single chain using a phenomenological model consistent with the theory of viscoelasticity for polymer chains in dilute solution. The effective viscosity of a polymer chain can be determined using the Kirkwood model, which is independent of the intrinsic viscosity of the solvent and dependent on the interaction between the polymer and solvent. The results indicated that the viscosity of a single PS chain is dominated by the interaction between the polymer and solvent. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 1736–1743     

On uniform propagation of chaos

In this paper we obtain a time-uniform propagation estimate for a system of interacting diffusion processes. Using a well defined metric function h , our result guarantees a time-uniform estimate for the convergence of a class of interacting stochastic differential equations towards their mean field limit, under conditions that ensure that the decay associated to the internal dynamics term dominates the interaction and noise terms. Our result should have diverse applications, particularly in neuroscience, and allows for models more elaborate than the one of Wilson and Cowan. In particular, the internal dynamics need not be that of linear decay.     

ALMOST PERIODIC SOLUTIONS TO STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS

By applying the properties of almost periodic function and exponential dichotomy of linear system as well as Banach fixed point theorem,we establish the conditions for the existence and uniqueness of square-mean almost periodic solution to some stochastic functional differential equations.     

Comments on “Fuzzy fractional order sliding mode controller for nonlinear systems” [Commun Nonlinear Sci Numer Simulat 15 (2010) 963-978]

The aim of this note is to point out some comments to the article [Delavari H, Ghaderi R, Ranjbar A, Momani S. Fuzzy fractional order sliding mode controller for nonlinear systems, Commun Nonlinear Sci Numer Simulat 15 (2010) 963-978].     

Spectral,Optical and Mechanical studies on pure and thiourea doped ammonium di-hydrogen phosphate NLO single crystals

Pure and thiourea substituted single crystals of ammonium di-hydrogen phosphate have been grown from aqueous solution by isothermal solvent evaporation technique. Doped crystal exhibits prominent changes in physical and chemical properties. Single crystal XRD analyses of the samples are carried out and the results are compared. FTIR and UV–vis–NIR spectral analyses have been employed to identify the presence of various functional groups and the UV cut-off range in the grown crystals. Density measurements have been made and Photoconductivity studies revealed the negative photo conducting nature. Hardness measurement shows that the mechanical strength of the doped crystal is high when compared to pure ammonium di-hydrogen phosphate. The dielectric response of the samples has been studied in the frequency range 100 Hz–5 MHz at room temperature and the results are discussed.     

Weak attractors for the dissipative fractional Heisenberg equation

In this short paper, we consider the long time behaviors of the fractional Heisenberg equation and the existence of a global weak attractor is proved for the shift dynamics in the path space. The key ingredient is some new type of commutator structure introduced in this paper, which seems indispensable in proving the compactness of the dynamics. The technique introduced in this paper may also be useful to other fractional order partial differential equations.