Limit cycle analysis of nonlinear sampled-data systems by gain–phase margin approach

Second order sliding mode tracking controller for inertia wheel pendulum

“…In Orlov et al [24] and Santiesteban et al [26] an asymptotic harmonic generator was introduced through a modified Van der Pol equation tested on a friction pendulum to solve the swing-up problem for an inverted pendulum. Wu et al [30] made an analysis of the limit cycle for nonlinear sampled-data systems via gain-phase testing, M-locus, and the parameters plane. Mart´ınez et al [20] made a study of motion planning and oscillatory control for underactuated systems under geometric control theory.…”

Limit cycle prediction of a neurocontrol vehicle system based on gain-phase margin analysis

“…Gain margin (GM) and phase margin (PM) are two important specifications in the analysis and design of practical control systems. Methods of analyzing the gain-phase margin of linear control systems [18][19][20] and nonlinear systems [21][22][23][24] with adjustable parameters have been developed.…”

Novel analysis of limit cycle for PWM signal of PD control system

“…Thus, it is desirable to reduce the limit cycle frequency. The limit cycle can be analyzed theoretically by using a describing function method [4] and a phase plane method [5,6,7,8]. The describing function method is an approximate procedure for analyzing nonlinear control based on quasilinearization which is an approximation of a nonlinear system by a specific family of input waveforms.…”