Control of a class of multibody underactuated mechanical systems with discontinuous friction using sliding-mode

This is the author accepted manuscript. The final version is available from the publisher via the DOI in this record.This paper studies sliding-mode control of a class of multibody underactuated systems with discontinuous friction presenting on the unactuated configuration variable with consideration of parametric uncertainties. Global motion for this class system including sticking, stick-slip, and slip regimes are analyzed, and their corresponding equilibria are identified. Our control objective is to avoid the sticking and stick-slip regimes while track a desired velocity in the slip regime. The proposed sliding-mode controllers are robust to parametric uncertainties, and their stabilities are proved by using the Lyapunov direct method. Two examples, a mass-spring-damping system and a drill-string system, are used to demonstrate the validity of the proposed controllers.The author(s) received no financial support for the research, authorship, and/or publication of this articl

Sliding Mode Control

The main objective of this monograph is to present a broad range of well worked out, recent application studies as well as theoretical contributions in the field of sliding mode control system analysis and design. The contributions presented here include new theoretical developments as well as successful applications of variable structure controllers primarily in the field of power electronics, electric drives and motion steering systems. They enrich the current state of the art, and motivate and encourage new ideas and solutions in the sliding mode control area

Impulse-Based Hybrid Motion Control

The impulse-based discrete feedback control has been proposed in previous work for the second-order motion systems with damping uncertainties. The sate-dependent discrete impulse action takes place at zero crossing of one of both states, either relative position or velocity. In this paper, the proposed control method is extended to a general hybrid motion control form. We are using the paradigm of hybrid system modeling while explicitly specifying the state trajectories each time the continuous system state hits the guards that triggers impulsive control actions. The conditions for a stable convergence to zero equilibrium are derived in relation to the control parameters, while requiring only the upper bound of damping uncertainties to be known. Numerical examples are shown for an underdamped closed-loop dynamics with oscillating transients, an upper bounded time-varying positive system damping, and system with an additional Coulomb friction damping.Comment: 6 pages, 4 figures, IEEE conferenc

Motion stabilization in the presence of friction and backlash: a hybrid system approach

In this paper a hybrid system approach is considered to deal with backlash and friction induced nonlinearities in mechanical control systems. To describe the low velocity frictional behaviour a linearized friction model is proposed. The novelty of this study is that based on the introduced friction model, the stability theorems developed for hybrid systems can directly be applied for controller design of mechanical systems in the presence of Stribeck friction and backlash. During the controller design it is assumed that the size of the backlash gap is unknown and the load side position and velocity cannot be measured. For motion control an LQ controller is applied. A condition is formulated for the control law parameters to guarantee the asymptotic stability of the control system. Simulation measurements were performed to confirm the theoretical results

Second order sliding mode control of underactuated Mechanical systems I: Local stabilization with application to an inverted pendulum

International audienceSecond order sliding mode control synthesis is developed for underactuated mechanical systems, operating under uncertainty conditions. In order to locally stabilize an underactuated system around an unstable equilibrium, an output is specified in such a way that the corresponding zero dynamics is locally asymptotically stable. Then, the desired stability property of the closed-loop system is provided by applying a quasihomogeneous second order sliding mode controller, driving the system to the zero dynamics manifold in finite time. Although the present synthesis exhibits an infinite number of switches on a finite time interval, it does not rely on the generation of first order sliding modes, while providing robustness features similar to those possessed by their standard sliding mode counterparts. A second order sliding mode appears on the zero dynamics manifold which is of co-dimension greater than the control space dimension. Performance issues of the proposed synthesis are illustrated in numerical and experimental studies of a cart-Pendulum system