Stabilization of Cart Inverted Pendulum System using LQR, Two-Loop PID, and Regional Pole Placement techniques

This paper describes how to simulate and control the two DoF inverted pendulum system, a dynamics of multibody system. The control strategy used is based on the conventional feedback method for the stabilisation of the two DoF inverted pendulum system. Simulation study has been done shows that conventional method i.e. pole placement control strategy is capable to control multi input and multi output of the two DoF inverted pendulum system successfully. The result shows that pole placement control strategy gives satisfactory response that is presented in time domain.

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State Space Based Linear Controller Design for the Inverted Pendulum

Acta Technica Jaurinensis ◽

10.14513/actatechjaur.v12.n2.499 ◽

2019 ◽

Vol 12 (2) ◽

pp. 130-147 ◽

Cited By ~ 2

Author(s):

Miklós Kuczmann

Keyword(s):

State Space ◽

Inverted Pendulum ◽

Controller Design ◽

Pole Placement ◽

Space Representation ◽

Linear Quadratic ◽

Linear Quadratic Optimal Control ◽

Pendulum System ◽

Linear Controller ◽

Inverted Pendulum System

In a previous survey paper the detailed PID controller design to stabilize the inclination angle as well as the horizontal movement of an inverted pendulum system has been presented. In this paper the linear controller design based on the state space representation is shown step by step. Pendulum model is based on EulerLagrange modeling, and the nonlinear state space model is linearized in the unstable upward position, finally pole placement by Ackermann formula and Bass–Gura equation, moreover linear quadratic optimal control are presented. The pendulum has been inserted into a virtual reality laboratory, which is suitable to use in model based control teaching.

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Linear quadratic regulator and pole placement for stabilizing a cart inverted pendulum system

Bulletin of Electrical Engineering and Informatics ◽

10.11591/eei.v9i3.2017 ◽

2020 ◽

Vol 9 (3) ◽

pp. 914-923

Author(s):

Mila Fauziyah ◽

Zakiyah Amalia ◽

Indrazno Siradjuddin ◽

Denda Dewatama ◽

Rendi Pambudi Wicaksono ◽

...

Keyword(s):

Mathematical Model ◽

System Performance ◽

Inverted Pendulum ◽

Linear Quadratic Regulator ◽

Pole Placement ◽

Underactuated System ◽

Mechanical Transmission ◽

Linear Quadratic ◽

Pendulum System ◽

Inverted Pendulum System

The system of a cart inverted pendulum has many problems such as nonlinearity, complexity, unstable, and underactuated system. It makes this system be a benchmark for testing many control algorithm. This paper presents a comparison between 2 conventional control methods consist of a linear quadratic regulator (LQR) and pole placement. The comparison indicated by the most optimal steps and results in the system performance that obtained from each method for stabilizing a cart inverted pendulum system. A mathematical model of DC motor and mechanical transmission are included in a mathematical model to minimize the realtime implementation problem. From the simulation, the obtained system performance shows that each method has its advantages, and the desired pendulum angle and cart position reached.

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