Motion Controller Design of Wheeled Inverted Pendulum with an Input Delay Via Optimal Control Theory

Zhou, Yusheng; Wang, Zaihua

doi:10.1007/s10957-015-0759-z

Cited by 20 publications

(9 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The dynamics equations of the TWIP model can be obtained by using the Euler-Lagrange equations for nonholonomic systems as done in our previous paper [28]:…”

Section: Problem Statementmentioning

confidence: 99%

“…Now, it is in the position to design the controller by following the method proposed in [27]. Firstly, by introducing an integral transformation given by (28) the delayed system (23) is transformed into an equivalent delay-free system as follows:…”

Section: Optimal Integral Sliding Mode Control Designmentioning

confidence: 99%

“…In addition, time delays in controllers and uncertainties from modeling or measurement or perturbation are usually inevitable in real applications, but they are usually ignored in the literature [1]. The most popular methods to deal with input delay are related to the prediction-based compensation control strategy [26][27][28]. However, input delay is very important especially when some robust controls with high-frequency switching mechanism such as sliding mode controls are used, where the existence of input delay would lead to reversed control if the input delay is ignored.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Turning Motion Control Design of a Two-Wheeled Inverted Pendulum Using Curvature Tracking and Optimal Control Theory

Zhou

Wang

Chung

2019

J Optim Theory Appl

Self Cite

View full text Add to dashboard Cite

This paper presents a control design method for implementing planar turning motion of a two-wheeled inverted pendulum with an input delay. The control task requires that the inverted pendulum is kept stabilized during the whole turning motion process along a pre-settled curve. Firstly, by using the theory of planar curve, key observations about the motion law of the two-wheeled mobile chassis are made and they are used to set up a dynamical trajectory tracking target. Then, by adjusting the parameters in the tracking target and the weights in the quadratic performance criterion, the optimal integral sliding mode controller based on a linear quadratic regulator is designed for keeping the vehicle body stabilized and tracking a circular path for the two-wheeled inverted pendulum. An illustrative example is given to demonstrate the validity of the theory with numerical simulation. Keywords Two-wheeled inverted pendulum • Input delay • Curvature tracking • Optimal control • Dynamical tracking target

show abstract

“…The dynamics equations of the TWIP model can be obtained by using the Euler-Lagrange equations for nonholonomic systems as done in our previous paper [28]:…”

Section: Problem Statementmentioning

confidence: 99%

Section: Optimal Integral Sliding Mode Control Designmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Turning Motion Control Design of a Two-Wheeled Inverted Pendulum Using Curvature Tracking and Optimal Control Theory

Zhou

Wang

Chung

2019

J Optim Theory Appl

Self Cite

View full text Add to dashboard Cite

show abstract

“…The Lagrangian is the difference between system's kinetic and potential energies. The Lagrangian function of the system is described by [11]:…”

Section: System Modelingmentioning

confidence: 99%

“…where represents the forced function of the system, ( , , ) represent generalized states for the system. Figure 1: The two wheeled inverted pendulum structure [18] Total kinetic energy for the two wheeled inverted pendulum system is [11]:…”

Section: System Modelingmentioning

confidence: 99%

Full State Feedback 𝐇𝟐 and H-infinity Controllers Design for a Two Wheeled Inverted Pendulum System

Ali¹,

Shareef²

2018

ETJ

View full text Add to dashboard Cite

In this work, two robust controllers, which are full state feedback, 2 and full state feedback ∞ controllers are proposed for the two wheeled inverted pendulum system. The nonlinear equations for the two wheeled inverted pendulum system are developed using Euler-Lagrange equation. The system parameters changes are considered to show the effectiveness of the proposed robust controllers. These controllers are proposed not only to stabilize the pendulum in upright position but also to drive the position to track a given reference input. The results show that more desirable robustness and time response specifications can be achieved using the proposed controllers. The effectiveness of the proposed controllers is verified experimentally using real two wheeled inverted pendulum system.

show abstract

Adaptive Neural Delay Feedback Control of a Typical Robot on a Slope

Ji,

Sun,

Pan

et al. 2024

Optim Control Appl Methods

View full text Add to dashboard Cite

In this article, an adaptive neural delay feedback control strategy is proposed for the motion control of a two‐wheel self‐balancing robot (TWSBR) on a slope with an input delay. Based on the Lagrange equation, the dynamic model of the robot is derived. Given a target trajectory vector, the corresponding error system is obtained. An input delay and uncertainties are considered. First, the system with an input delay is transformed into a delay‐free one. Second, a quadratic performance optimization criterion is defined, and a linear quadratic regulator (LQR) controller is designed to minimize the error between the system's state vector and the target vector. Thirdly, an integral sliding mode controller is added to the LQR controller to enhance the system's robustness. To reduce the “chattering” phenomenon, an adaptive neural delay feedback control scheme is developed based on the adaptive learning of the uncertainties' upper bound by a radial basis function neural network (RBFNN). It is demonstrated that a relaxation process exists at the beginning of the upslope motion. As the input delay increases, the swing range of the center of gravity of the pendulum expands. The angle can converge to the steady state more quickly, but the relaxation time is still 0.031 s which has nothing to do with the input delay. An example of the back‐and‐forth motion of a TWSBR on a slope can verify an excellent agreement between theoretical analysis and numerical results.

show abstract

Motion Controller Design of Wheeled Inverted Pendulum with an Input Delay Via Optimal Control Theory

Cited by 20 publications

References 16 publications

Turning Motion Control Design of a Two-Wheeled Inverted Pendulum Using Curvature Tracking and Optimal Control Theory

Turning Motion Control Design of a Two-Wheeled Inverted Pendulum Using Curvature Tracking and Optimal Control Theory

Full State Feedback 𝐇𝟐 and H-infinity Controllers Design for a Two Wheeled Inverted Pendulum System

Adaptive Neural Delay Feedback Control of a Typical Robot on a Slope

Contact Info

Product

Resources

About