Related papers: PID Optimization Using Lagrangian Mechanics
The rodwheel is a wheel equipped with a rod motorized on the axle. This paper proposes a Lagrangian approach to find the state equations of the rodwheel rolling on a plane without friction. The approach takes advantage of a symbolic…
The Helmholtz conditions are necessary and sufficient conditions for a system of second order differential equations to be variational, that is, equivalent to a system of Euler-Lagrange equations for a regular Lagrangian. On the other hand,…
The connections between optimal control and Bayesian inference have long been recognised, with the field of stochastic (optimal) control combining these frameworks for the solution of partially observable control problems. In particular,…
Solving optimal control problems for transport-dominated partial differential equations (PDEs) can become computationally expensive, especially when dealing with high-dimensional systems. To overcome this challenge, we focus on developing…
Solving optimal control problems for transport-dominated partial differential equations (PDEs) can become computationally expensive, especially when dealing with high-dimensional systems. To overcome this challenge, we focus on developing…
Using the policy gradient algorithm, we train a single-hidden-layer neural network to balance a physically accurate simulation of a single inverted pendulum. The trained weights and biases can then be transferred to a physical agent, where…
We review some recent results on the theory of Lagrangian systems on Lie algebroids. In particular we consider the symplectic and variational formalism and we study reduction. Finally we also consider optimal control systems on Lie…
A gauge independent method of obtaining the reduced space of constrained dynamical systems is discussed in a purely lagrangian formalism. Implications of gauge fixing are also considered.
We deal with regular Lagrangian constrained systems which are invariant under the action of a symmetry group. Fixing a connection on the higher-order principal bundle where the Lagrangian and the (independent) constraints are defined, the…
This article proposes a data-driven PID controller design based on the principle of adaptive gain optimization, leveraging Physics-Informed Neural Networks (PINNs) generated for predictive modeling purposes. The proposed control design…
This paper presents a simulation-based comparison between the two controllers, Proportional Integral Derivative (PID), a classical controller and Linear Quadratic Regulator (LQR), an optimal controller, for a linearized quadrotor model. To…
In chemical process applications, model predictive control effectively deals with input and state constraints during transient operations. However, industrial PID controllers directly manipulates the actuators, so they play the key role in…
The paper presents necessary and sufficient conditions for the order reduction of optimal control systems. Exploring the corresponding Hamiltonian system allows to solve the order reduction problem in terms of dynamical systems,…
Pendulum-driven systems have emerged as a notable modification of vibro-impact mechanisms, replacing the conventional mass-on-spring oscillator with a pendulum. Such systems exhibit intricate behavior resulting from the interplay of…
In this paper, modification of the classical PID controller and development of open-loop control mechanisms to improve stability and robustness of a differential wheeled robot are discussed. To deploy the algorithm, a test platform has been…
We are introducing a model-free control and a control with a restricted model for finite-dimensional complex systems. This control design may be viewed as a contribution to "intelligent" PID controllers, the tuning of which becomes quite…
This article investigates the modeling and control of Lagrangian systems involving non-conservative forces using a hybrid method that does not require acceleration calculations. It focuses in particular on the derivation and identification…
In this paper, is used the Lagrangian classical mechanics for modeling the dynamics of an underactuated system, specifically a rotary inverted pendulum that will have two equations of motion. A basic design of the system is proposed in…
Proportional-Integral-Differential (PID) control is widely used in industrial control systems. However, up to now there are at least two open problems related with PID control. One is to have a comprehensive understanding of its robustness…
"Model-free control" and the corresponding "intelligent" PID controllers (iPIDs), which already had many successful concrete applications, are presented here for the first time in an unified manner, where the new advances are taken into…