scispace - formally typeset
Search or ask a question
Journal ArticleDOI

Control of a Class of Underactuated Mechanical Systems Using Sliding Modes

TL;DR: A sliding mode control algorithm is presented to robustly stabilize a class of underactuated mechanical systems that are not linearly controllable and violate Brockett's necessary condition for smooth asymptotic stabilization of the equilibrium, with parametric uncertainties.
Abstract: In this paper, we present a sliding mode control algorithm to robustly stabilize a class of underactuated mechanical systems that are not linearly controllable and violate Brockett's necessary condition for smooth asymptotic stabilization of the equilibrium, with parametric uncertainties. In defining the class of systems, a few simplifying assumptions are made on the structure of the dynamics; in particular, the damping forces are assumed to be linear in velocities. We first propose a switching surface design for this class of systems, and subsequently, a switched algorithm to reach this surface in finite time using conventional and higher order sliding mode controllers. The stability of the closed-loop system is investigated with an undefined relative degree of the sliding functions. The controller gains are designed such that the controller stabilizes the actual system with parametric uncertainty. The proposed control algorithm is applied to two benchmark problems: a mobile robot and an underactuated underwater vehicle. Simulation results are presented to validate the proposed scheme.
Citations
More filters
Journal ArticleDOI
TL;DR: The aim is to give implementable sliding mode design solutions for complex motion systems, actuators and supply converters by providing a frame for further study of sliding mode applications in motion control systems.
Abstract: This paper presents a comprehensive overview of the application of Variable Structure Systems (VSSs) with Sliding Mode (SM) methods in motion control systems. Our aim is to give implementable sliding mode design solutions for complex motion systems, actuators and supply converters. This paper provides a frame for further study of sliding mode applications in motion control systems.

347 citations

Journal ArticleDOI
TL;DR: In this paper, a survey of underactuated mechanical systems (UMS) is presented, from its history to the state-of-the-art research on modelling, classification, control, and to some extent, provides some unique insights for bottleneck issues and future research directions.
Abstract: An underactuated mechanical system (UMS) is a system which has fewer independent control actuators than degrees of freedom to be controlled. Control of UMS is considered as one of the most active fields of research because of its diverse engineering applications. This survey reviews UMS from its history to the state-of-the-art research on modelling, classification, control, and to some extent, provides some unique insights for bottleneck issues and future research directions.

238 citations

Journal ArticleDOI
TL;DR: The stabilities of both the disturbance observer and the controlled closed-loop system are proved by the Lyapunov theorem and a choice method of optimal gain matrices of the high-order disturbance observer is obtained as the solution of an optimization problem.
Abstract: In this note, a high-order disturbance observer for a class of underactuated robotic systems with mismatched uncertainties is proposed To improve its estimation performance, a choice method of optimal gain matrices of the high-order disturbance observer is obtained as the solution of an optimization problem A high-order disturbance observer based sliding mode control method is also designed for this class of underactuated robotic system with mismatched disturbance The stabilities of both the disturbance observer and the controlled closed-loop system are proved by the Lyapunov theorem Simulations on a benchmark Acrobot system demonstrate the efficiency of proposed approaches

150 citations


Cites background from "Control of a Class of Underactuated..."

  • ...Several types of research deal with general underactuated systems (see [9]–[12]), while their methods lack the ability to suppressing both the matched and mismatched uncertainties....

    [...]

Journal ArticleDOI
TL;DR: A new approach of tracking control is investigated for the 7000-m Jiaolong manned submarine vehicle (MSV) and can achieve more satisfactory tracking result with a less control effort compared to a typical backstepping method.
Abstract: In this paper, a new approach of tracking control is investigated for the 7000-m Jiaolong manned submarine vehicle (MSV). First, the formulation of control allocation problem and some background information about tracking control of the 7000-m Jiaolong MSV are presented. Then, a kinematic controller is derived. The filter design using bioinspired model is employed to handle the speed jump problem and to make sure that each thruster is within the saturation limit. The kinematic controller is then extended to incorporate a sliding-mode control technique to complete the dynamic control. The system stability is guaranteed, and tracking errors asymptotically converge to zero by Lyapunov stability theory. Another interesting phenomenon is that the bioinspired method can achieve more satisfactory tracking result with a less control effort compared to a typical backstepping method. Finally, simulations illustrate the performance of the derived cascaded tracking control technique.

126 citations

Journal ArticleDOI
TL;DR: In this paper, the design of robust nonlinear controllers based on both conventional and hierarchical sliding mode techniques for double-pendulum overhead crane systems is studied, where a first-order sliding surface is provided and a proper control scheme is generated to stabilize the surface.
Abstract: This study focuses on the design of robust nonlinear controllers based on both conventional and hierarchical sliding mode techniques for double-pendulum overhead crane systems. In the first approach, a first-order sliding surface is provided and a proper control scheme is generated to stabilize the surface. In the second approach, two levels of sliding surfaces are proposed and the control scheme is designed based on the stability of the second-level surface. We also prove the stability of the first-level sliding surface. To verify the quality of the proposed controllers, simulation for a particular type of overhead crane systems is implemented. Simulation results show that all state trajectories asymptotically converged to desired values.

126 citations

References
More filters
Book
01 Jan 1985
TL;DR: In this paper, a systematic feedback design theory for solving the problems of asymptotic tracking and disturbance rejection for linear distributed parameter systems is presented, which is intended to support the development of flight controllers for increasing the high angle of attack or high agility capabilities of existing and future generations of aircraft.
Abstract: : The principal goal of this three years research effort was to enhance the research base which would support efforts to systematically control, or take advantage of, dominant nonlinear or distributed parameter effects in the evolution of complex dynamical systems. Such an enhancement is intended to support the development of flight controllers for increasing the high angle of attack or high agility capabilities of existing and future generations of aircraft and missiles. The principal investigating team has succeeded in the development of a systematic methodology for designing feedback control laws solving the problems of asymptotic tracking and disturbance rejection for nonlinear systems with unknown, or uncertain, real parameters. Another successful research project was the development of a systematic feedback design theory for solving the problems of asymptotic tracking and disturbance rejection for linear distributed parameter systems. The technical details which needed to be overcome are discussed more fully in this final report.

8,525 citations

01 Jan 1983
TL;DR: In this paper, the authors considered the problem of determining when there exists a smooth function u(x) such that x = xo is an equilibrium point which is asymptotically stable.
Abstract: We consider the loca1 behavior of control problems described by (* = dx/dr) i=f(x,u) ; f(x,0)=0 o and more specifically, the question of determining when there exists a smooth function u(x) such that x = xo is an equilibrium point which is asymPtotically stable. Our main results are formulated in Theorems 1 and 2 be1ow. Whereas it night have been suspected that controllability would insure the exlstence of a stabilizing control law, Theorem I uses a degree-theoretic argument to show this is far from being the case. The positive result of Theorem 2 can be thought of as providing an application of high gain feedback in a nonlinear setting. 1. Introduction In this paper we establish general theorems which are strong enough to irnply, among other things, that a) there is a continuous control law (u,v) = (u(xry, z) rv(x,y,z)) which makes the origin asympEoticatly stable for x=u y=v z=xy and that b) there exists no continuous control law (urv) = (u(xryrz), v(x,y,z)) which makes the origin asymptotically stable for 181

2,833 citations

Journal ArticleDOI
01 Mar 1988
TL;DR: In this paper, the design of variable-structure control (VSC) systems for a class of multivariable, nonlinear, time-varying systems is presented.
Abstract: The design of variable-structure control (VSC) systems for a class of multivariable, nonlinear, time-varying systems is presented. Using the Utkin-Drazenovic method of equivalent control and generalized Lyapunov stability concepts, the VSC design is described in a unified manner. Complications that arise due to multiple inputs are examined, and several approaches useful in overcoming them are developed. Recent developments are investigated, as is the kinship of VSC and the deterministic approach to the control of uncertain systems. All points are illustrated by numerical examples. The recent literature on VSC applications is surveyed. >

1,860 citations

Book
01 Jan 1978
TL;DR: An electric dynamically operated storage element comprises two energy stores and circuitry is provided for applying periodically repeating phase clock pulses simultaneously to the energy stores through the charging circuits.
Abstract: An electric dynamically operated storage element comprises two energy stores. Each store has a charging circuit including a rectifying element and a discharging circuit including a controlled respectively variable resistance connected in series with the rectifying element. Also, circuitry is provided for applying periodically repeating phase clock pulses simultaneously to the energy stores through the charging circuits.

1,802 citations