Lyapunov-Based Controller for the Inverted Pendulum Cart System

Ibáñez, Carlos Aguilar; Frías, Octavio Gutiérrez; Castañón, M. Suárez

doi:10.1007/s11071-005-7290-y

Cited by 76 publications

(26 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Equations (1) and (2) are normalised, following the approach used in Ibañez et al (2005), to simplify algebraic manipulation of them in developing the affine form of the equations. The affine form of equations brings about the controller design easy.…”

Section: Model Simplificationmentioning

confidence: 99%

“…The robustness, however, is achieved starting from a control Lyapunov function (CLF) and redesign domination (Sepulchre et al, 1997;Jankovic et al, 1999). Lyapunov function-based (LFB) controllers have been used in many application such as ball on beam (Aguilar-Ibanez, 2009), turbo charged diesel engine (Jankovic and Kolmanovsky, 2000) and transportation systems (Ibañez et al, 2005). This paper contributes to the construction of a Lyapunov function and controller design for the statically unstable TWRs, which does not exist in literature.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Lyapunov function-based non-linear control for two-wheeled mobile robots

Kausar¹,

Stol²,

Patel³

2013

IJBBR

View full text Add to dashboard Cite

This article presents a non-linear feedback control framework for two-wheeled mobile robots. The approach uses a constructive Lyapunov function which allows the formulation of a control law with asymptotic stability of the equilibrium point of the system and a computable stability region. The dynamic equations are simplified through normalisation and partial feedback linearisation. The latter allows linearisation of only the actuated coordinate. Description of the control law is complemented by the stability analysis of the closed loop dynamics of the system. The effectiveness of the method has been illustrated by its good performance and less control demand through simulations conducted for two control tasks: upright position stabilisation and velocity tracking for a statically unstable two wheeled mobile robot.

show abstract

Section: Model Simplificationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Lyapunov function-based non-linear control for two-wheeled mobile robots

Kausar¹,

Stol²,

Patel³

2013

IJBBR

View full text Add to dashboard Cite

show abstract

“…There are many papers presented which have taken the inverted pendulum-cart dynamical system for implementing the various control schemes [18−23] . A Lyapunov function based control of inverted pendulum cart system is presented in [23]. Quad-rotor, another example of underactuated strongly coupled nonlinear system is presented in [24] in which the adaptive backstepping sliding mode approach is used for the trajectory tracking control.…”

Section: Introductionmentioning

confidence: 99%

Optimal Control of Nonlinear Inverted Pendulum System Using PID Controller and LQR: Performance Analysis Without and With Disturbance Input

Prasad

Tyagi

Gupta

2014

Int. J. Autom. Comput.

186

101

View full text Add to dashboard Cite

Abstract:Linear quadratic regulator (LQR) and proportional-integral-derivative (PID) control methods, which are generally used for control of linear dynamical systems, are used in this paper to control the nonlinear dynamical system. LQR is one of the optimal control techniques, which takes into account the states of the dynamical system and control input to make the optimal control decisions. The nonlinear system states are fed to LQR which is designed using a linear state-space model. This is simple as well as robust. The inverted pendulum, a highly nonlinear unstable system, is used as a benchmark for implementing the control methods. Here the control objective is to control the system such that the cart reaches a desired position and the inverted pendulum stabilizes in the upright position. In this paper, the modeling and simulation for optimal control design of nonlinear inverted pendulum-cart dynamic system using PID controller and LQR have been presented for both cases of without and with disturbance input. The Matlab-Simulink models have been developed for simulation and performance analysis of the control schemes. The simulation results justify the comparative advantage of LQR control method.

show abstract

“…On the other hand, many practical physical devices can be modeled by equations with the feedforward form, such as the cart-pendulum system in [4], the ball-beam with a friction term in [19] and the PVTOL aircraft in [21]. Therefore, the stabilization problem of feedforward systems rapidly became an interesting research field and received many important results, see, e.g., [1,[3][4][5][6][7]9,18,24,25] and the references therein.…”

mentioning

confidence: 99%

Global asymptotic stabilization of stochastic feedforward nonlinear systems with input time-delay

Liu

Wang

et al. 2015

Nonlinear Dyn

View full text Add to dashboard Cite

The state-feedback stabilization problem of stochastic feedforward nonlinear systems with input time-delay is considered in this paper. By using the homogeneous domination idea and choosing an appropriate Lyapunov-Krasovskii functional, the delayindependent state-feedback controller is explicitly constructed such that the closed-loop system is globally asymptotically stable in probability. A simulation example is provided to demonstrate the effectiveness of the proposed design method.

show abstract

Lyapunov-Based Controller for the Inverted Pendulum Cart System

Cited by 76 publications

References 15 publications

Lyapunov function-based non-linear control for two-wheeled mobile robots

Lyapunov function-based non-linear control for two-wheeled mobile robots

Optimal Control of Nonlinear Inverted Pendulum System Using PID Controller and LQR: Performance Analysis Without and With Disturbance Input

Global asymptotic stabilization of stochastic feedforward nonlinear systems with input time-delay

Contact Info

Product

Resources

About