On conjugate difference schemes: the midpoint scheme and the trapezoidal scheme

The preservation of quadratic integrals on approximate solutions of autonomous systems of ordinary differential equations x=f(x), found by the trapezoidal scheme, is investigated. For this purpose, a relation has been established between the trapezoidal scheme and the midpoint scheme, which preserves all quadratic integrals of motion by virtue of Coopers theorem. This relation allows considering the trapezoidal scheme as dual to the midpoint scheme and to find a dual analogue for Coopers theorem by analogy with the duality principle in projective geometry. It is proved that on the approximate solution found by the trapezoidal scheme, not the quadratic integral itself is preserved, but a more complicated expression, which turns into an integral in the limit as t0.Thus the concept of conjugate difference schemes is investigated in pure algebraic way. The results are illustrated by examples of linear and elliptic oscillators. In both cases, expressions preserved by the trapezoidal scheme are presented explicitly.

Data-Driven Model-Free Adaptive Control of Z-Source Inverters

The universal paradigm shift towards green energy has accelerated the development of modern algorithms and technologies, among them converters such as Z-Source Inverters (ZSI) are playing an important role. ZSIs are single-stage inverters which are capable of performing both buck and boost operations through an impedance network that enables the shoot-through state. Despite all advantages, these inverters are associated with the non-minimum phase feature imposing heavy restrictions on their closed-loop response. Moreover, uncertainties such as parameter perturbation, unmodeled dynamics, and load disturbances may degrade their performance or even lead to instability, especially when model-based controllers are applied. To tackle these issues, a data-driven model-free adaptive controller is proposed in this paper which guarantees stability and the desired performance of the inverter in the presence of uncertainties. It performs the control action in two steps: First, a model of the system is updated using the current input and output signals of the system. Based on this updated model, the control action is re-tuned to achieve the desired performance. The convergence and stability of the proposed control system are proved in the Lyapunov sense. Experiments corroborate the effectiveness and superiority of the presented method over model-based controllers including PI, state feedback, and optimal robust linear quadratic integral controllers in terms of various metrics.

Implementation and intelligent gain tuning feedback–based optimal torque control of a rotary parallel robot

Aiming at operating optimally minimizing error of tracking and designing control effort, this study presents a novel generalizable methodology of an optimal torque control for a 6-degree-of-freedom Stewart platform with rotary actuators. In the proposed approach, a linear quadratic integral regulator with the least sensitivity to controller parameter choices is designed, associated with an online artificial neural network gain tuning. The nonlinear system is implemented in ADAMS, and the controller is formulated in MATLAB to minimize the real-time tracking error robustly. To validate the controller performance, MATLAB and ADAMS are linked together and the performance of the controller on the simulated system is validated as real time. Practically, the Stewart robot is fabricated and the proposed controller is implemented. The method is assessed by simulation experiments, exhibiting the viability of the developed methodology and highlighting an improvement of 45% averagely, from the optimum and zero-error convergence points of view. Consequently, the experiment results allow demonstrating the robustness of the controller method, in the presence of the motor torque saturation, the uncertainties, and unknown disturbances such as intrinsic properties of the real test bed.

Determination of the Optimal Values of the Parameters of the PI Controller by Minimum Integral Quadratic Criterion Taking Into Account the Values Transient Damping Coefficient

The problem of determining the optimal the values of the parameters of the PI controller by the quadratic integral criterion taking into account the coefficient of attenuation of the transition process. The problem is presented as a nonlinear mathematical problem programming. Finding the global minimum of the objective function carried out by random search, and to determine the parameters of the PI controller used the expanded amplitude-phase frequency response of the system. An attempt is made to provide designers with an effective tool for solving the above problem. The given graphs and tables facilitate the selection of parameters. To compile a computer program, the visual programming system VBA (Visual Basic for Application) is used. Concrete examples are given.

On Chandrasekhar functional integral inclusion and Chandrasekhar quadratic integral equation via a nonlinear Urysohn–Stieltjes functional integral inclusion

We investigate the existence of solutions for a nonlinear integral inclusion of Urysohn–Stieltjes type. As applications, we give a Chandrasekhar quadratic integral equation and a nonlinear Chandrasekhar integral inclusion.

Existence and global asymptotic stability criteria for nonlinear neutral-type neural networks involving multiple time delays using a quadratic-integral Lyapunov functional

In this paper we consider a standard class of the neural networks and propose an investigation of the global asymptotic stability of these neural systems. The main aim of this investigation is to define a novel Lyapunov functional having quadratic-integral form and use it to reach a stability criterion for the under study neural networks. Since some fundamental characteristics, such as nonlinearity, including time-delays and neutrality, help us design a more realistic and applicable model of neural systems, we will use all of these factors in our neural dynamical systems. At the end, some numerical simulations are presented to illustrate the obtained stability criterion and show the essential role of the time-delays in appearance of the oscillations and stability in the neural networks.