POSITIONAL IMPULSE AND DISCONTINUOUS CONTROLS FOR DIFFERENTIAL INCLUSION

Nonlinear control systems presented in the form of differential inclusions with impulse or discontinuous positional controls are investigated. The formalization of the impulse-sliding regime is carried out. In terms of the jump function of the impulse control, the differential inclusion is written for the ideal impulse-sliding regime. The method of equivalent control for differential inclusion with discontinuous positional controls is used to solve the question of the existence of a discontinuous system for which the ideal impulse-sliding regime is the usual sliding regime. The possibility of the combined use of the impulse-sliding and sliding regimes as control actions in those situations when there are not enough control resources for the latter is discussed.

Fault Sliding Modes—Governing, Evolution and Transformation

A brief summary of fundamental results obtained in the IDG RAS on the mechanics of sliding along faults and fractures is presented. Conditions of emergence of different sliding regimes, and regularities of their evolution were investigated in the laboratory, as well as in numerical and field experiments. All possible sliding regimes were realized in the laboratory, from creep to dynamic failure. Experiments on triggering the contact zone have demonstrated that even a weak external disturbance can cause failure of a “prepared” contact. It was experimentally proven that even small variations of the percentage of materials exhibiting velocity strengthening and velocity weakening in the fault principal slip zone may result in a significant variation of the share of seismic energy radiated during a fault slip event. The obtained results lead to the conclusion that the radiation efficiency of an earthquake and the fault slip mode are governed by the ratio of two parameters—the rate of decrease of resistance to shear along the fault and the shear stiffness of the enclosing massif. The ideas developed were used to determine the principal possibility to artificially transform the slidding regime of a section of a fault into a slow deformation mode with a low share of seismic wave radiation.

Analysis of friction error in CNC machine tools based on electromechanical characteristics

Friction is a kind of inherent and nonlinear disturbance in feed systems, which inevitably deteriorates motion accuracy at velocity reversal. Position error caused by friction is integrally effected by three aspects of feed drives, including command, control, and mechanical subsystems. Unfortunately, the traditional analyses hardly consider all mentioned aspects. Especially, no research has been reported on control characteristic at reverse motion. The purpose of this paper is to reveal the generation mechanism of friction error of a feed drive based on the commercial computer numerical control with three-loop control structure and velocity feedforward and proportional–proportional–integral controllers. Firstly, the generation process of the friction error at velocity reversal is profoundly investigated. Based on it, a simplified control model is conducted to explain transition from presliding to sliding regimes. It is the bond of analyzing friction error from command, control, and mechanical subsystems. Subsequently, the processes of presliding, acceleration, and adjustment stages are analyzed. Moreover, analytical formulas are derived to predict the durations of three stages and describe the shape of friction error. Then, the contour errors of linear and circular motion caused by friction can be predicted online. Experiments are introduced to verify the effectiveness of the proposed methods and formulations.

A study of friction vibration absorber: impact of friction modeling on the efficacy of the absorber and friction coefficient optimization

In this paper, a one degree of freedom system connected to a friction vibration absorber is considered. Friction vibration absorber reduces mechanical vibrations using the dissipation of the energy through friction between both bodies. However, the contact between both bodies and the optimal parameters design deserve to be examined closely. In this paper, the effect of friction modeling is first investigated. Two friction modelings are considered: macroscopic (Coulomb) and microscopic (Dahl and LuGre), according to physical and tribological behaviors. For each model, the responses are determined in sticking and sliding regimes of motion and a comparison is made to conclude on the efficacy of the friction absorber. Second, the optimization of friction coefficient is established using two approaches: Den Hartog optimal parameters and the minimization of the frequency displacement of the main mass.