Class Of Second-order Systems Research Articles

Extended Use of the Parameter Observer on a Class of Second-Order Systems

Extended Use of the Parameter Observer on a Class of Second-Order Systems

Non-singular terminal sliding mode control for a class of second-order systems with mismatched uncertainty

Non-singular terminal sliding mode control for a class of second-order systems with mismatched uncertainty

Non-singular terminal sliding mode control for a class of second-order systems with mismatched uncertainty

Non-singular terminal sliding mode control for a class of second-order systems with mismatched uncertainty

Sub-fixed-time control for a class of second order system

In this paper, a new concept “sub-fixed-time stability” (SFTS) is proposed and studied, which means the states can converge to a region of equilibrium points in a fixed time for any initial states’ values. Then, a sufficient condition for it is given and proven. Though SFTS is similar to “practical fixed-time stability” (PFTS), they are not the same, and the sufficient condition for SFTS is much clearer and simpler than PFTS. Next, a sub-fixed-time controller is proposed for a class of second order system. The stability analyses are given in the case without disturbance and with disturbance, respectively. Finally, to illustrate the robustness of the proposed sub-fixed-time controller to different initial conditions, 100 numerical simulations are conducted for 100 initial states’ values.

Stabilisation of second-order bilinear and semilinear systems

In this paper, we deal with stabilisation for a class of second-order systems. We establish several results concerning stabilisation of bilinear systems and we give sufficient conditions for exponential and strong stabilisation of semilinear second-order systems. The obtained results are illustrated by many examples and simulations.

A Filtered Transformation via Dynamic Matrix to State and Parameter Estimation for a Class of Second Order Systems

The problem of state and parameter estimation for a class of second-order time-varying systems is addressed in this paper. Two classes of estimators are designed for the system under different observability assumptions. The design procedure is based on a filtered transformation via dynamic matrix. The dynamic of the matrix is derived using the Immersion and Invariance technique. Adaptive parameter convergence is guaranteed under a weaker condition than traditional persistency of excitation, called non-square-integrability condition. The proposed estimator is shown to be applicable to the input voltage and current estimation from the output voltage of the AC-DC boost converter.

A tuning procedure for the Cascade Proportional Integral Retarded Controller

This work proposes a tuning methodology for the Cascade Proportional Integral Retarded (CPIR) controller applied to a class of second order systems. Unlike the Proportional Integral Retarded (PIR) control law, the CPIR is composed of two nested loops, each of them having its own controller. The inner loop is regulated through an Integral Retarded (IR) Controller and the outer loop uses a proportional (P) controller. It is worth remarking that the stability of both loops must be simultaneously guaranteed, a problem not appearing in the PIR controller. The proposed tuning methodology is based on the spectral abscissa analysis of the Outer loop. The IR controller tuning rules and a double root placement analysis in the CPIR quasy-polynomial allows writing an analytical form of the P proportional gain. Subsequently, this gain is computed by solving a transcendental nonlinear equation. The proposed tuning method is assessed by means of experiments in a laboratory prototype.

Numerical Solution of A Class of Systems of Volterra Polynomial Equations of the First Kind

In this paper, a class of second-order systems of Volterra nonlinear integral equations is considered. This class is related to a problem of automatic control of a dynamic object with vector inputs and outputs. A numerical solution technique based on the Newton–Kantorovich method is considered. To verify the efficiency of the algorithms developed, a series of test calculations are carried out.

Further remarks on the effect of multiple spectral values on the dynamics of time-delay systems. Application to the control of a mechanical system

A question of ongoing interest for linear Time-delay systems is to determine conditions on the equation parameters that guarantee the exponential stability of solutions. In recent works a new interesting property of time-delay systems was emphasized. As a matter of fact, the multiple spectral values for time-delay systems was characterized by using a Birkhoff/Vandermonde-based approach. Then, a multiplicity induced stability criteria were exhibited for reduced order systems; scalar delay-equations and a special class of second order systems. This work, further explores such a criteria and shows their applicability to the control of a mechanical system.

Existence of nonconstant periodic solutions for a class of second-order systems with p(t)-Laplacian

In this paper, we investigate a class of second-order p(t)-Laplacian systems with local ‘superquadratic’ potential. By using the generalized mountain pass theorem, we obtain an existence result for nonconstant periodic solutions.

Adaptive suboptimal second-order sliding mode control for microgrids

ABSTRACTThis paper deals with the design of adaptive suboptimal second-order sliding mode (ASSOSM) control laws for grid-connected microgrids. Due to the presence of the inverter, of unpredicted load changes, of switching among different renewable energy sources, and of electrical parameters variations, the microgrid model is usually affected by uncertain terms which are bounded, but with unknown upper bounds. To theoretically frame the control problem, the class of second-order systems in Brunovsky canonical form, characterised by the presence of matched uncertain terms with unknown bounds, is first considered. Four adaptive strategies are designed, analysed and compared to select the most effective ones to be applied to the microgrid case study. In the first two strategies, the control amplitude is continuously adjusted, so as to arrive at dominating the effect of the uncertainty on the controlled system. When a suitable control amplitude is attained, the origin of the state space of the auxiliary system becomes attractive. In the other two strategies, a suitable blend between two components, one mainly working during the reaching phase, the other being the predominant one in a vicinity of the sliding manifold, is generated, so as to reduce the control amplitude in steady state. The microgrid system in a grid-connected operation mode, controlled via the selected ASSOSM control strategies, exhibits appreciable stability properties, as proved theoretically and shown in simulation.

Sufficient conditions for the stability of a class of second order systems

This paper provides sufficient conditions to assess the stability and Input-to-State stability of a class of second-order systems by only looking at the structure of the dynamic equations. These results are proven by using the Variable Gradient Method to build suitable Lyapunov functions. The paper includes a number of relevant examples that highlight the value of the contribution.

System Identification of a Class of Second-Order Continuous System

An identification method of a class of second-order continuous system is proposed. This method constructs a discrete-time identification model, forms a set of linear equations. The parameters can be obtained by least square method. Simulation results show that the method is effective for a class of second-order system, and is not only for step response but also for square wave signal.

Existence of homoclinic solutions for a class of second order systems

In this paper we study the existence of nontrivial homoclinic solutions for a second order differential equation of the form q ̈ + A q ̇ − L ( t ) q + W q ( t , q ) = 0 . Here, we assume that A is a antisymmetric constant matrix, L ( t ) is a continuous positive definite symmetric matrix valued function depending periodically on t and assume that potential W is asymptotically quadratic as | q | → 0 and | q | → ∞ .

Cooperative control of multi-agent dynamical systems in target-enclosing operations using cyclic pursuit strategy

This article is concerned with formation stability analysis of distributed cooperative control for target-enclosing operations by multiple homogeneous dynamic agents. To this end, we first present an on-line path generator design method based on a cyclic pursuit scheme. Then, we provide Lyapunov and asymptotic stability conditions which should hold for the above path generation laws. These conditions are derived based on a simple stability analysis method for linear systems with a generalised frequency variable. The formation control scheme combined with a cyclic pursuit based distributed on-line path generator satisfying the derived stability conditions guarantees the required global convergence property with theoretical rigour. Furthermore, in order to show its distinctive features clearly, we present how to analyse a global formation stability for multi-agent systems, where each agent is modelled as a class of second-order systems and is locally stabilised by a proportional-derivative (PD) controller. Some simulation examples illustrate the distinctive features of the proposed method and the achievement of a desired pursuit pattern.

The local linking theorem with an application to a class of second-order systems

In the present paper, some existence theorems are obtained concerning periodic and homoclinic solutions for a class of second-order systems by means of a local linking theorem.

Variable structure control for a class of nonlinear systems with mismatched uncertainties

A scheme to stabilize nonlinear time-varying systems with both matched and mismatched uncertainties is proposed in this paper by switching between two control laws: a first-order sliding-mode control and a second-order sliding-mode control. Based on this idea, a variable structure control algorithm is designed for a class of second-order systems. The closed-loop system is globally or locally asymptotically stable. It has been proven that the stability region has relation with the order of the boundary function and the region can be obtained by solving an inequality. The uncertainty considered in this work is also more general than those in the existing works.

Asymptotic behavior of the energy for a class of weakly dissipative second-order systems with memory

A class of second-order abstract systems with memory and Dirichlet boundary conditions is investigated. By suitable Liapunov functionals, existence of solutions as well as asymptotic behavior, are determined. In particular, when the memory kernel decays exponentially, the polynomially decay of the solutions is proved.

A globally stabilizing hybrid variable structure control strategy

A hybrid variable structure control strategy for a class of second order systems is presented in this paper. It relies on a system state decomposition into regions, and on a suitable event-driven switching among the corresponding control laws. By enforcing conventional and unconventional sliding-mode behaviors, as well as avoiding the generation of limit cycles, the proposed strategy proves to globally asymptotically stabilize the origin of the system state space.

GAIN REDUCTION IN HYBRID SLIDING MODE CONTROL OF SECOND ORDER SYSTEMS

A hybrid sliding mode control strategy for a class of second order systems is presented in this paper. It is characterized by an event-driven gain reduction mechanism relying on a decomposition of the system state into regions. By enforcing sliding mode behaviors on a suitable set of sliding manifolds, while avoiding the generation of limit cycles, the proposed strategy proves to globally asymptotically stabilize the origin of the system state space.