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The concepts of stability and balance represent many critical problems faced by engineering today. The inverted pendulum on a cart is one such non-linear, unstable, multivariate system whose goal is to determine a suitable control action…

This study investigates the performance of cascade PID control architecture applied to an inverted pendulum on a cart system through both simulation and experimental implementation. A nonlinear model of the system was developed using…

We consider linear time-invariant dynamic systems in the single-input, single-output (SISO) framework. In particular, we consider stabilization of an inverted pendulum on a cart using a force on the cart. This system is easy to stabilize…

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…

A double inverted pendulum plant has been in the domain of control researchers as an established model for studies on stability. The stability of such as a system taking the linearized plant dynamics has yielded satisfactory results by many…

Control of compliant mechanical systems is increasingly being researched for several applications including flexible link robots and ultra-precision positioning systems. The control problem in these systems is challenging, especially with…

Linear quadratic Gaussian (LQG) control is a well-established method for optimal control through state estimation, particularly in stabilizing an inverted pendulum on a cart. In standard laboratory setups, sensor redundancy enables direct…

Inverted pendulums constitute one of the popular systems for benchmarking control algorithms. Several methods have been proposed for the control of this system, the majority of which rely on the availability of a mathematical model.…

Creating a simulation of a system enables the tuning of control systems without the need for a physical system. In this paper, we employ Lagrangian Mechanics to derive a set of equations to simulate an inverted pendulum on a cart. The…

This paper presents the control and stabilization of the rotary inverted pendulum based on a general controller scheme. The proposed scheme has its foundation in classical control theory, and the importance of an integrator in disturbance…

This article presents a unified approach to quadratic optimal control for both linear and nonlinear discrete-time systems, with a focus on trajectory tracking. The control strategy is based on minimizing a quadratic cost function that…

In the present paper we focus our attention on the design of the feedback-based feed-forward controller asymptotically stabilizing the double-pendulum-type crane system with the time-varying rope length in the desired end position of…

Traditional linear control strategies have been extensively researched and utilized in many robotic and industrial applications and yet they do not respond to the total dynamics of the systems. To avoid tedious calculations for nonlinear…

We propose controller synthesis for state regulation problems in which a human operator shares control with an autonomy system, running in parallel. The autonomy system continuously improves over human action, with minimal intervention, and…

Growing advancements in reinforcement learning has led to advancements in control theory. Reinforcement learning has effectively solved the inverted pendulum problem and more recently the double inverted pendulum problem. In reinforcement…

The inverted pendulum is a non-linear unbalanced system that needs to be controlled using motors to achieve stability and equilibrium. The inverted pendulum is constructed with Lego and using the Lego Mindstorm NXT, which is a programmable…

This paper proposes the design of gain-scheduled static output feedback controllers for the stabilization of continuous-time linear parameter-varying systems with $\mathcal{L}_2$-gain performance. The system is transformed into the form of…

This study evaluates the application of a discrete action space reinforcement learning method (Q-learning) to the continuous control problem of robot inverted pendulum balancing. To speed up the learning process and to overcome technical…

An integral extension of state-feedback controllers for linear time-varying plants is proposed, which preserves performance of the nominal controller in the unperturbed case. Similar to time-invariant state feedback with integral action,…

The discipline of automatic control is making increased use of concepts that originate from the domain of machine learning. Herein, reinforcement learning (RL) takes an elevated role, as it is inherently designed for sequential decision…