Discrete-Time State-Feedback Controller with Canonical Form on Inverted Pendulum (on a cart)

TL;DR

This paper presents a discrete-time state-feedback controller in canonical form for stabilizing an inverted pendulum on a cart, demonstrating stability under various initial conditions and sampling times.

Contribution

It introduces a novel canonical form-based state feedback control method specifically designed for the inverted pendulum system.

Findings

The controller maintains stability with sampling time T under 0.2 seconds.

The design effectively stabilizes the system from large initial deviations.

The approach achieves reliable upright position control despite system nonlinearities.

Abstract

The scope of inverted pendulum has been widely studied as one of the notable research with respect to standing in balance. The concept of this pendulum is similar to missile guidance, meaning that the center of drag is ahead that of gravity. Mathematical model of inverted pendulum on a cart is moreover presented in this paper. Various rewarding parameters are proposed from the displacement of the pivot, angular rotation, to external force exerted on the carriage so as to gain its equilibrium points and the linearized systems. Due to the severe risk of instability, a reliable closed-loop state feedback controller is designed to stabilize in upright position, even with large deviations. The specific concept proposed is to apply the canonical form of computing the determinant of gain $K$ leading to $K_d$. The results show that the constructed design can maintain the stability of the system by applying three sorts of initial condition and choosing sampling time $T$ under $0.2$ with small possible degrading performance.