Velocity and position control of a wheeled inverted pendulum by partial feedback linearization

2005 ◽  
Vol 21 (3) ◽  
pp. 505-513 ◽  
Author(s):  
K. Pathak ◽  
J. Franch ◽  
S.K. Agrawal
Keyword(s):  
Feedback Linearization ◽  
Inverted Pendulum ◽  
Position Control ◽  
Wheeled Inverted Pendulum ◽  
Partial Feedback Linearization ◽  
Partial Feedback

Discrete-time backstepping control with nonlinear adaptive disturbance attenuation for the inverted-pendulum system

2019 ◽  
pp. 014233121986777
Author(s):  
Fatih Adıgüzel ◽  
Yaprak Yalçın
Keyword(s):  
Discrete Time ◽  
Feedback Linearization ◽  
Inverted Pendulum ◽  
Backstepping Control ◽  
Disturbance Attenuation ◽  
Pendulum System ◽  
Inverted Pendulum System ◽  
Partial Feedback Linearization ◽  
Partial Feedback ◽  
Backstepping Controller

A discrete-time backstepping controller with an active disturbance attenuation property for the Inverted-Pendulum system is constructed in this paper. The main purpose of this study is to show that Immersion and Invariance (I & I) approach can be used to design a nonlinear observer for disturbance estimation and demonstrate its effectiveness considering a nonlinear system with an unstable equilibrium point, namely Inverted-Pendulum system, by utilizing the estimated values in backstepping control design. All designs are directly performed in discrete-time domain to obtain directly implementable observer and controller in discrete processors with superior performance compared to emulators. The Inverted-Pendulum system is not in strict feedback form therefore backstepping procedure cannot be directly applied. In order to enable backstepping construction, firstly a partial feedback linearization is performed and afterwards a novel discrete-time coordinate transformation is proposed. Prior to the construction of partial feedback linearizing and backstepping controller, a nonlinear disturbance estimator design is proposed with Immersion and Invariance approach. The estimated disturbance values used in the partial feedback linearization and construction of the backstepping controller. The global asymptotic stability of the estimator and local asymptotic stability of overall closed loop system are proved in the sense of Lyapunov. Performance of proposed direct discrete-time backstepping control with discrete I & I observer is compared with a backstepping sliding mode controller with another nonlinear disturbance observer (NDO) by simulations.

The Research on Human Simulating Intelligent Control of the Inverted Pendulum Based on Feedback Linearization

2013 ◽  
Vol 710 ◽  
pp. 511-514 ◽  
Author(s):  
Ling Zhang ◽  
Shi Zhong Hu
Keyword(s):  
Intelligent Control ◽  
Feedback Linearization ◽  
Inverted Pendulum ◽  
Interference Control ◽  
Lqr Control ◽  
Partial Feedback Linearization ◽  
Partial Feedback ◽  
The Stability ◽  
Triple Inverted Pendulum ◽  
Better Than

In this paper, the partial feedback linearization was made for the non-linear model of the triple inverted pendulum, by means of the differential geometry. Then the simulation and analysis of tracking control and interference control were made, which combined with the human simulating intelligent control and LQR control in the system. The results show that the human simulating intelligent control can achieve better control results than the LQR control, it not only can effectively improve the stability of the system, but also the anti-interference ability is better than LQR control, it meets the control requirements of the triple inverted pendulum.

Optimal Band-Limited Trajectory Planning and Control for an Inverted Wheeled Pendulum

2004 ◽  
Author(s):  
Kaustubh Pathak ◽  
Sunil K. Agrawal
Keyword(s):  
Trajectory Planning ◽  
Feedback Linearization ◽  
Position Control ◽  
Sinc Function ◽  
High Frequency Signal ◽  
Linear Controller ◽  
Plane Orientation ◽  
Partial Feedback Linearization ◽  
Partial Feedback ◽  
Band Limited

Mobile inverted pendulum robots consist of an elongated pendulum body with two motors mounted on it for driving the wheels. The velocity and position control of such a vehicle is challenging because of the coupling of the pendulum’s pitch angle from the vertical and the Cartesian motion of the vehicle. On using a nonlinear transform to effect partial feedback linearization, the system dynamics transforms to two subsystems: a linear system with the vehicle’s pitch and in-plane orientation, and a nonlinear system of internal dynamics. In this paper, the problem of utilizing such a partial feedback linearization for optimal trajectory planning of such vehicles is considered. Due to the resulting linear subsystem with vehicle pitch and in-plane orientation, these configuration variables can be controlled by a linear controller (C) using a nonlinear feedback. The planning approach presented in this paper considers the time-constant (τ) of the linear controller C explicitly. A band-limited Sinc-function interpolation is used to plan the variables in the method of collocation. This ensures that high frequency signal content which cannot be handled by the controller C, is absent in the planned trajectory, making the plan better implementable by the controller. The planned trajectory takes the vehicle from point to point, while keeping the vehicle pitch bounded and avoiding obstacles. The optimality condition considered in the algorithm is the length of the path. The optimization problem posed after collocation, is then solved using a standard Sequential Quadratic Programming (SQP) solver. Simulation results show that the tracking controller C is able to follow the planned trajectory when no initial planar Cartesian error is present.

Identification and Model Predictive Position Control of Two Wheeled Inverted Pendulum Mobile Robot

2015 ◽  
Vol 73 (6) ◽  
Author(s):  
Amir A. Bature ◽  
Salinda Buyamin ◽  
Mohamad N. Ahmad ◽  
Mustapha Muhammad ◽  
Auwalu A. Muhammad
Keyword(s):  
Mathematical Model ◽  
System Identification ◽  
Mobile Robot ◽  
Inverted Pendulum ◽  
Position Control ◽  
Superior Performance ◽  
System A ◽  
Wheeled Inverted Pendulum ◽  
Simulation Results ◽  
Real Plant

In order to predict and analyse the behaviour of a real system, a simulated model is needed. The more accurate the model the better the response is when dealing with the real plant. This paper presents a model predictive position control of a Two Wheeled Inverted Pendulum robot. The model was developed by system identification using a grey box technique. Simulation results show superior performance of the gains computed using the grey box model as compared to common linearized mathematical model. 

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