In this paper we deal with the performance analysis of harmonically forced nonlinear systems of Lur’e type. We use harmonic linearization to obtain a linear approximation of the nonlinear system, and provide a frequency domain condition that guarantees a unique positive real solution to the harmonic balance equation for a certain class of nonlinearities. Furthermore, we provide an estimate on t...

Professor Utkin in his discussion paper proposed an example showing that the amplitude of chattering caused by the presence of parasitic dynamics in systems governed by FirstOrder Sliding-Mode Control (FOSMC) is lower than the obtained using Super-Twisting Algorithm (STA). This example served to motivate this research reconsidering the problem of comparison of chattering magnitude in systems go...

In this letter, an application of energy balance method is applied to solve the nonlinear oscillators with un force. Comparison is made between the modification of harmonic balance method and energy balance method. The results reveal that the energy balance method is very effective and simple. Energy balance method is very effective and convenient and quite accurate to both linear and nonlinear...

The atomic force microscope ~AFM! is a powerful tool for investigating surfaces at atomic scales. Harmonic balance and power balance techniques are introduced to analyze the tapping-mode dynamics of the atomic force microscope. The harmonic balance perspective explains observations hitherto unexplained in the AFM literature. A nonconservative model for the cantilever–sample interaction is devel...

The method of Unrestricted Harmonic Balance (UHB) as exposed and applied to purely t imedependent systems, stiff systems, and chemical waves in the preceding 3 papers is extended to the case of transcendental functions. So, e.g., exponential functions even in mass action kinetics systems occur, if a wider range of temperature is considered as is the case in continuous stirred tank reactors (CST...

In this paper we consider several families of potential non-isochronous systems and study their associated period functions. Firstly, we prove some properties of these functions, like their local behavior near the critical point or infinity, or their global monotonicity. Secondly, we show that these properties are also present when we approach to the same questions using the Harmonic Balance Me...

We propose two methods to find analytic periodic approximations intended for differential equations of Hill type. Here, we apply these methods on the simplest case of the Mathieu equation. The former has been inspired in the harmonic balance method and designed to find, making use on a given algebraic function, analytic approximations for the critical values and their corresponding periodic sol...

A new self-consistent dynamic electro-thermal model for power HBTs is presented coupling a circuit-oriented electrical model, fitted on experimental data, with a full frequency domain thermal model. The thermal model provides the exact frequency behaviour of the device thermal impedance through a quasi-3D approach. The electro-thermal self-consistent solution is achieved, in large-signal period...

Properties of small amplitude oscillations of the single reed woodwind instruments near the oscillation threshold are investigated. Analytical formulae with explicit dependence on the physical parameters of the instrument and instrumentist allow to determine the bifurcation point, the nature of the bifurcation, the amplitude of the first harmonics and the oscillation frequency. The model, which...

Abstract Dynamics and stability of average current control of DC-DC converters are analyzed by sampleddata modeling. Orbital stability is studied and it is found unrelated to the ripple size of the orbit. Compared with the averaged modeling, the sampled-data modeling is more accurate and systematic. An unstable range of compensator pole is found by simulations, and is predicted by sampled-data ...