On LQR controller design for an inverted pendulum stabilization

Chacko, Sanjay Joseph; Abraham, Rajesh Joseph

doi:10.1007/s40435-022-01079-0

Cited by 10 publications

(3 citation statements)

References 20 publications

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“…Some researchers propose creating an even higherlevel cost function that penalizes various signals, where the optimization parameters are the weightings in the original quadratic cost function: examples include aiming to minimize the settling time using heuristic optimization techniques [5], creating an analytical gradient-based optimization approach to ensure both the error and control signal end up close to zero [6]; also using algebraic, deterministic, and heuristic approaches that relate multiple time-domain specifications to the weightings in [7], [8], and [9], respectively. Some propose penalizing control effort in the higher-level cost function as well: for examples, running genetic algorithms to find weightings that minimize a summation of the integral of time multiplied absolute error and the integral of squared controller output [10], trying evolutionary algorithms [11], [12] or adaptive particle swarm optimization [13] to find solutions where the system will meet multiple performance indexes simultaneously; also comparing different types of optimization algorithms applied to a similar multi-objective performance function [14].…”

Section: Introductionmentioning

confidence: 99%

Applied Design of Optimal PID-with-Feedforward Control Using Two-Parameter Behavior Models

Smith

2024

Preprint

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This paper proposes a two-parameter method for adjusting and tuning control systems in order to explore trade-offs in light of real-world objectives and constraints; the user-friendly mechanism draws parallels between robot and human behavior easily understood at an intuitive level. Firstly, the general behavior model enables a designer to adjust weightings in a cost function using two behavior traits, potentially to create 3D plots that illustrate trade-offs. Secondly, the specific behavior model allows someone to explore trade-offs or tune the control gains in real time, for a specific situation or for personal preference, again using only two intuitive behavior traits. Both methods also facilitate a simple strategy of just choosing between a few distinctive behavior types. Moreover, the framework provides a possible model for understanding how some behavior qualities might arise due to the natural constraint of feedback in systems, with implications for programming relatable behaviors into robots. A nonlinear optimal quadratic tracking design for the PID-with-feedforward control of a robot link demonstrates the practical design methodology.

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Section: Introductionmentioning

confidence: 99%

Applied Design of Optimal PID-with-Feedforward Control Using Two-Parameter Behavior Models

Smith

2024

Preprint

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“…Controller structures can be basically examined as linear and non-linear controllers. Linear controllers used in IPS can be summarized as proportional integral derivative (PID) [9], PI, PD [10], Linear-quadratic regulator (LQR) [11,103,104], linear-quadratic-gaussian (LQG) [104], 𝑯 𝟐 and 𝑯 ∞ optimal control [12], etc. The PID controller commonly used in IPS control shows excellent performance due to its robustness in different operation conditions.…”

Section: Introductionmentioning

confidence: 99%

Comprehensive Review of Different Pendulum Structures in Engineering Applications

Hazem

Bingül

2023

IEEE Access

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For years, the pendulum system has been the most popular experimental setup for education and research in robotics and control theory. This paper examines the different kinematic and dynamic structures of pendulum systems, which are frequently used in literature, considering their usage in various engineering fields. Each pendulum system resembles a real physical system, allowing for a deeper understanding of the system's behavior. While each pendulum has its own advantages and disadvantages, they are subjective and depend on the field of application and method of use. This paper aims to review and simplify the understanding of the various pendulum systems used in research and applications, presenting a summary of the general properties of pendulum systems to the researcher.INDEX TERMS Pendulum systems, robotics, control theory and engineering modelling,

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“…An optimal controller with a linear-quadratic quality ratio (LQR) is often used to solve nonlinear problems. Examples of the use of this method can be found in the literature [18][19][20][21]. One of the methods used to control inverted pendulums in the field of AI is the use of neural networks [22,23].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Controller for an Inverted Pendulum Using the Trigonometric Function

Lower

2023

Applied Sciences

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In this paper, a nonlinear controller (TR) for an inverted pendulum using the trigonometric function is presented. The TR controller is a new proposal, which is represented by a simple mathematical formula. TR operation does not require complex calculations, so it can be applied even to the simplest microcontrollers. Tuning the TR controller is very simple, and the range of stable operation is very wide. Simulation tests of the TR controller showed that the controller is effective even for deviations exceeding 50∘. The TR controller tests were compared to the results of a PID controller. The TR controller is designed to stabilise an inverted pendulum in the equilibrium point, a state in which the pendulum is in a upright position. Stabilisation for other deflection-angle set points was not taken into account. During the research, steps were taken to simulate phenomena characteristic of real solutions. An inertial block and a disturbance were introduced into the test system. Despite the introduced difficulties, the TR controller effectively stabilised the pendulum without the need to retune the controller settings. Consequently, the TR controller is an attractive alternative to previously applied solutions for the stabilisation of an inverted pendulum.

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On LQR controller design for an inverted pendulum stabilization

Cited by 10 publications

References 20 publications

Applied Design of Optimal PID-with-Feedforward Control Using Two-Parameter Behavior Models

Applied Design of Optimal PID-with-Feedforward Control Using Two-Parameter Behavior Models

Comprehensive Review of Different Pendulum Structures in Engineering Applications

Nonlinear Controller for an Inverted Pendulum Using the Trigonometric Function

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