On the practical h-stabilization of nonlinear time-varying systems: application to separately excited DC motor

Purpose The purpose of this paper is to report on the global practical uniform h-stabilization for certain classes of nonlinear time-varying systems and its application in a separately excited DC motor circuit. Design/methodology/approach Based on Lyapunov theory, the practical h-stabilization result is derived to guarantee practical h-stability and applicated in a separately excited DC motor. Findings A controller is designed and added to the nonlinear time-varying system. The practical h-stability of the nonlinear control systems is guaranteed by applying the appropriate controller based on Lyapunov second method. Another effective controller is also designed for the global practical uniform h-stability on the separately excited DC motor with load. Numerical simulations are demonstrated to verify the effectiveness of the proposed controller scheme. Originality/value The introduced approach is interesting for practical h-stabilization of nonlinear time-varying systems and its application in a separately excited DC motor. The original results generalize well-known fundamental result: practical exponential stabilization for nonlinear time-varying systems.

A Robust Control Scheme for a PVTOL System Subject to Wind Disturbances

In this study, a control scheme that allows performing height position regulation and stabilization for an unmanned planar vertical take-off and landing aerial vehicle, in the presence of disturbance due to wind, is presented. To this end, the backstepping procedure together with nested saturation function method is used. Firstly, a convenient change of coordinates in the aerial vehicle model is carried out to dissociate the rotational dynamics from the translational one. Secondly, the backstepping procedure is applied to obtain the height position controller, allowing the reduction of the system and expressing it as an integrator chain with nonlinear disturbance. Therefore, the nested saturation function method is used to obtain a stabilizing controller for the horizontal position and roll angle. The corresponding stability analysis is conducted via the Lyapunov second method. In addition, to estimate the disturbance due to wind, an extended state observer is used. The effectiveness of the proposed control scheme is assessed through numerical simulations, from which convincing results have been obtained.

An optimal nonlinear control for anti-synchronization of Rabinovich hyperchaotic system

This work derives new results for the anti-synchronization of 4D identical Rabinovich hyperchaotic systems by using two strategies: active and nonlinear control. The stabilization results of error dynamics systems are established based on Lyapunov second method. Control is designed via the relevant variables of drive and response systems. In comparison with previous strategies, the current controller (Nonlinear control) focused on the minimum possible limits for relevant variables. The better performance is realizing the anti- synchronization by designing a control with low terms. After obtaining analytical results of the proposed controller, numircal simulation is carried out using Matlab. The graphical results prove validity and applicability of proposed control without know any parameter.The proposed control has certain significance for reducing the time and complexity for strategy implementation.

On the asymptotic analysis of bounded solutions to nonlinear differential equations of second order

In this paper, we consider two different models of nonlinear ordinary differential equations (ODEs) of second order. We construct two new Lyapunov functions to investigate boundedness of solutions of those nonlinear ODEs of second order. By using the Lyapunov direct or second method and inequality techniques, we prove two new theorems on the boundedness solutions of those ODEs of second order as $t \to \infty $t→∞. When we compare the conditions of the theorems of this paper with those of Meng in (J. Syst. Sci. Math. Sci. 15(1):50–57, 1995) and Sun and Meng in (Ann. Differ. Equ. 18(1):58–64 2002), we can see that our theorems have less restrictive conditions than those in (Meng in J. Syst. Sci. Math. Sci. 15(1):50–57, 1995) and Sun and Meng in (Ann. Differ. Equ. 18(1):58–64 2002) because of the two new suitable Lyapunov functions. Next, in spite of the use of the Lyapunov second method here and in (Meng in J. Syst. Sci. Math. Sci. 15(1):50–57, 1995; Sun and Meng in Ann. Differ. Equ. 18(1):58–64 2002), the proofs of the results of this paper are proceeded in a very different way from that used in the literature for the qualitative analysis of ODEs of second order. Two examples are given to show the applicability of our results. At the end, we can conclude that the results of this paper generalize and improve the results of Meng in (J. Syst. Sci. Math. Sci. 15(1):50–57, 1995), Sun and Meng in (Ann. Differ. Equ. 18(1):58–64 2002), and some other that can be found in the literature, and they have less restrictive conditions than those in these references.

Identification of System with Bouc-Wen Hysteresis

A method of adaptive identification of parameters for a system with Bouc-Wen hysteresis has been developed. The method is based on the use of adaptive observers and resolves the problem of stability of the identification system. Adaptive algorithms of identification were obtained using the Lyapunov second method. The stability proof of the adaptive system is based on the application of Lyapunov vector functions. Adaptive algorithms for adjusting model parameters were developed obtained and finiteness of trajectories in the adaptive system was pointed out.

Bond graph observer for mode identification and discernibility study

This paper presents a new concept for calculating of the bond graph observer gains based on a graphical approach that investigates the Lyapunov Second Method in order to conclude about the observer stability and to search for the adequate gains that stabilize the observer. This new observer is used in the mode identification procedure. In fact, the observer’s residues allow the differentiation between the current mode and the other system modes. In order to guarantee the efficiency of the mode identification procedure, a new bond graph approach is proposed. It concerns the discernibility between the modes in bond graph language. First, it deals with the R-discernibility that introduces the definition of the discernibility through the structural parity residual then returns to a simple calculation of some matrices’ ranks in bond graph language. Second, another bond graph technique is applied to define the discernibility throughout the equivalency between the realizations.

Exponential Stability of Linear Discrete Systems with Variable Delays via Lyapunov Second Method

The paper investigates the exponential stability of a linear system of difference equations with variable delays xk+1=Axk+∑i=1sBikxk-mik, k=0,1,… , where s∈N, A is a constant square matrix, Bik are square matrices, mik∈N∪0, and mik≤m for an m∈N. New criteria for exponential stability are derived using the method of Lyapunov functions and formulated in terms of the norms of matrices of linear terms and matrices solving an auxiliary Lyapunov equation. An exponential-type estimate of the norm of solutions is given as well. The efficiency of the derived criteria is numerically demonstrated by examples and their relations to the well-known results are discussed.

Stability Analysis of a Helicopter with an External Slung Load System

This paper describes the stability analysis of a helicopter with an underslung external load system. The Lyapunov second method is considered for the stability analysis. The system is considered as a cascade connection of uncertain nonlinear system. The stability analysis is conducted to ensure the stabilisation of the helicopter system and the positioning of the underslung load at hover condition. Stability analysis and numerical results proved that if desired condition for the stability is met, then it is possible to locate the load at the specified position or its neighbourhood.

Adaptive Compensator of Single State Elastoplastic Friction Model

A nonlinear friction is an unavoidable phenomenon frequently experienced in mechanical system between two contact surfaces. An adaptive compensator is designed to achieve tracking of a desired velocity trajectory in the presence of friction force described by a single state elastoplastic friction model. The adaptive compensator includes an adaptive observer and a computed force controller. The closed loop system is shown to be stable using Lyapunov second method. Simulation results show the effectiveness of the proposed compensator.

ASYMPTOTIC STABILITY OF DELAY-DIFFERENCE CONTROL SYSTEM VIA MATRIX INEQUALITIES AND APPLICATION

In this paper, we obtain some criteria for determining the asymptotic stability of the zero solution of delay-difference control system in terms of certain matrix inequalities by using a discrete version of the Lyapunov second method. The result has been applied to obtain new stability conditions for some classes of delay-difference control system such as delay-difference control system with multiple delays in terms of certain matrix inequalities. Our results can be well suited for computational purposes.