Inverted Pendulum Optimal Control Based on First Principle Model

Dušek, František; Honc, Daniel; Sharma, Karan; Havlicek, Libor

doi:10.1007/978-3-319-33389-2_7

Cited by 2 publications

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“…For readers' convenience and also for comparison, the differences between the ZG method and the optimal control method are presented as below [21,[26][27][28].…”

Section: Comparison With Other Methodsmentioning

confidence: 99%

Introduction, Concepts and Preliminaries

Zhang

Qiu

2020

Zhang-Gradient Control

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In this chapter, we firstly discuss the importance for the research of the division-by-zero (DBZ) problem, and briefly introduce the Zhang-gradient (ZG) method investigated in this book. Then, we explain the essential concepts of several terms frequently used in this book, together with an illustrative example provided. Moreover, we introduce the basic principle of the ZG method for control as well as the general design procedure of a DBZ-conquering ZG controller systematically and methodologically. Finally, for comparative purposes, we present the differences between the ZG method and other types of control methods in detail.

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“…For readers' convenience and also for comparison, the differences between the ZG method and the optimal control method are presented as below [21,[26][27][28].…”

Section: Comparison With Other Methodsmentioning

confidence: 99%

Introduction, Concepts and Preliminaries

Zhang

Qiu

2020

Zhang-Gradient Control

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“…According to the control purposes of inverted pendulum, the control of the IPC system can be generally divided into three aspects, i.e., swing-up control [8,9], stabilization control [10,11], and tracking control [12,13]. Specifically, the swingup control is basically used to swing up the pendulum from the stable pendant position toward the unstable upward position; the stabilization (or say, balance) control is to maintain the pendulum at its upright position; and the tracking control is to achieve the purpose that the cart or the pendulum can track a desired trajectory, which is often more difficult to realize than the balance control.…”

Section: Introductionmentioning

confidence: 99%

Pendulum Tracking Control of IPC System

Zhang

Qiu

2020

Zhang-Gradient Control

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The pendulum control of the IPC system is one of the most important issues in nonlinear control theory and has been widely investigated. Nevertheless, the control of pendulum tracking and swinging up has often been addressed separately. In this chapter, by applying the ZG method, two different types of tracking controllers (termed z2g0 controller and z2g1 controller, respectively) are designed for the IPC system. Importantly, the z2g1 controller not only realizes the simultaneous control of pendulum swinging up and pendulum angle tracking, but also conquers the DBZ problem elegantly without using any switching strategy. Besides, corresponding theoretical analyses on the convergence performance of z2g0 and z2g1 controllers are provided. Moreover, the boundedness of both control input u and its derivative u of the z2g1 controller is investigated and proven. Computer simulations with three illustrative examples are conducted to show the efficacy of z2g0 and z2g1 controllers for the pendulum tracking control of the IPC system. In particular, comparative simulation results substantiate the superiority of the z2g1 controller for the control of pendulum tracking (including swinging up) of the IPC system in conquering the DBZ problem.

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Inverted Pendulum Optimal Control Based on First Principle Model

Cited by 2 publications

References 2 publications

Introduction, Concepts and Preliminaries

Introduction, Concepts and Preliminaries

Pendulum Tracking Control of IPC System

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