Suppressing oscillations in nonlinear systems

Oscillations in Nonlinear Pulse-modulated Control Systems

Periodical modes in nonlinear control systems with pulse-width and pulse-frequency modulation are considered. The existence of a fixed point for the shift operator along system’s trajectories is frequently used to establish the existence of a periodical mode. However, this method often fails for pulse modulated systems due to discontinuity of the shift operator. The new geometrical approach is ...

Avoiding and Suppressing Oscillations

Nonlinear Friction Compensation Design for Suppressing Stick Slip Oscillations in Oil Well Drillstrings

Friction appears in all mechanical systems and has a significant impact on control. This paper presents simple but effective nonlinear friction compensation method for a drillstring system, by considering the stickslip motion of the bit on the bottom hole assembly (BHA) in oil wells. Due to nonlinear problem at nearzero velocity where the torque exerted on bit is a function of the bit speed, th...

Nonlinear oscillations and stability domains in fractional reaction-diffusion systems

We study a fractional reaction-diffusion system with two types of variables: activator and inhibitor. The interactions between components are modeled by cubical nonlinearity. Linearization of the system around the homogeneous state provides information about the stability of the solutions which is quite different from linear stability analysis of the regular system with integer derivatives. It ...

Strict Lyapunov Functions for Generating Robust Oscillations in Nonlinear Systems

This paper deals with the problem of generating stable and robust oscillations in triangular nonlinear systems. The proposed method consists of two steps. First, a globally attractive oscillation is generated in a nominal second–order subsystem. Based on a partition of the state space and solving the Lyapunov equation on each part, a strict Lyapunov function is obtained that ensures exponential...