LMI-based LSVF control of a class of nonlinear systems with parametric uncertainty: an application to an inverted pendulum system

This paper proposes a novel passivity cascade technique (PCT)-based control for nonlinear inverted pendulum systems. Its main objective is to stabilize the pendulum’s upward states despite uncertainties and exogenous disturbances. The proposed framework combines the estimation properties of radial basis function neural networks (RBFNs) with the passivity attributes of the cascade control framework. The unknown terms of the nonlinear system are estimated using an RBFN approximator. The performance of the closed-loop system is further enhanced by using the integral of angular position as a virtual state variable. The lumped uncertainties (NN—Neural Network approximation, external disturbances and parametric uncertainty) are compensated for by adding a robustifying adaptive rule-based signal to the PCT-based control. The boundedness of the states is confirmed using the passivity theorem. The performance of the proposed approach was assessed using a nonlinear inverted pendulum system under both nominal and disturbed conditions.

Download Full-text

A Method of Robust Control for Nonlinear Inverted Pendulum System

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.562-564.1650 ◽

2012 ◽

Vol 562-564 ◽

pp. 1650-1654

Author(s):

Ke Yong Shao ◽

Miao Miao Tian ◽

Qing Yu Wu

Keyword(s):

Bp Neural Network ◽

Inverted Pendulum ◽

Linear Part ◽

Parametric Uncertainty ◽

Control Law ◽

Pendulum System ◽

Nonlinear Part ◽

Inverted Pendulum System ◽

Coordinate Transfer ◽

Backstepping Algorithm

In this paper, the controller of inverted pendulum with parametric uncertainty and nonlinearity was proposed. The controller was composed of two terms. Control law of linear part of the system was obtained by Coordinate Transfer and Backstepping algorithm. To the nonlinear part and uncertainty of the system which are usually not accords with the form of Backstepping algorithm, a BP neural network was applied to the design of the controller. Method submitted in this paper was less restrictive to the form of the nonlinear system, and has a wider universality. At the end of the paper, simulations proved the effectiveness of the proposed method.

Download Full-text

Oscillatory Tracking Control of a Class of Nonlinear Systems

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.4005495 ◽

2012 ◽

Vol 134 (3) ◽

Cited By ~ 4

Author(s):

Zheng Wang ◽

Yi Guo

Keyword(s):

Nonlinear Systems ◽

Tracking Control ◽

State Feedback ◽

Inverted Pendulum ◽

Feedforward Control ◽

Initial Conditions ◽

Pendulum System ◽

Physical Systems ◽

Inverted Pendulum System ◽

State Measurement

Vibration control is an effective alternative to conventional feedback and feedforward control. Motivated by its important application in physical systems and few results on general oscillatory tracking control, we consider tracking control of a class of nonlinear systems using oscillation in the paper. We propose a new oscillatory control design using general averaging analysis for the tracking problem. Based on the oscillation functions associated with accessible vibrating components of the system, oscillatory control is designed to track a desired trajectory. Comparing to existing oscillatory tracking control, our approach is robust to initial conditions. We show the effectiveness of the proposed method by two simulation examples, which include a second-order nonholonomic integrator and the inverted pendulum system. For the inverted pendulum system, we show that our designed oscillatory control does not need state feedback to track a desired trajectory, which is desirable for systems where state measurement is not feasible.

Download Full-text