Generating Self-Excited Oscillations via Two-Relay Controller

Abstract

A tool for the design of a self-excited oscillation of a desired amplitude and frequency in linear plants by means of the variable structure control is proposed. An approximate approach based on the describing function method is given, which requires that the mechanical plant should be a low-pass filter-the hypothesis that usually holds when the oscillations are relatively fast. The proposed approach is demonstrated via the controller design and experiments on the Furuta pendulum.Index Terms-Frequency domain methods, periodic solution, underactuated systems, variable structure systems.

Adaptive control of rotary inverted pendulum system with time-varying uncertainties

“…, we may haveV i < 0 whenever 2 , then after the convergence of V i+1 (i.e., when t ≥ T i+1 ) to ϕ i+1 + μ i+1 , V i is bounded. We have thus proved that (s i ,w i ) is uniformly ultimately bounded.…”

“…Some swung the pendulum from its hanging position to its upright vertical position [3,9,14,15,31]. Some others tried to create oscillations around its unstable vertical position [2,12,30]. In this paper, we would like to consider the control problem of stabilizing the pendulum around the unstable vertical position when subjected to time-varying uncertainties.…”

Second order sliding mode tracking controller for inertia wheel pendulum

“…In the results published in [2][3][4], the self-oscillations were generated in an inertia wheel pendulum using the two relay controller without tracking control. Consequently, the closed-loop system becomes sensitive to disturbances and uncertainties of the model.…”

“…Now, the proposed framework for trajectory generation under the same methodology and the robust state-feedback tracking controller and its experimental verification constitute the contribution of the paper. Here, we mean that the deviation of the frequency and amplitude of the periodic trajectory at the output of the closed-loop structure proposed in [2][3][4] with respect to the desired ones, depended on the uncertainties of the parameters of the model because formulas to compute the two values of the two-relay controller (c 1 and c 2 ) depend of the values of the inertia, length of the link, and masses, only; while viscous friction level was not considered as part of the formulas however exists in the system. Now, the proposed scheme is robust with respect to effect of the viscous friction and external disturbances which will be rejected using a second-order sliding mode tracking controller.…”

Transverse Linearization for Controlled Mechanical Systems With Several Passive Degrees of Freedom

“…Underactuated mechanical systems are common for robotics applications such as locomotion [8], [9], [35], juggling [5], [19], [21], [25], educational robotics [2], [6], robots with flexible joints [4], [33], etc. Motion planning and motion stabilization tasks for these applications are often solved ad hoc whenever feedback linearization is not applicable.…”