Related papers: PID Optimization Using Lagrangian Mechanics
The canonical proportional-integral-derivative (PID) control approach has been widely used in industrial application due to their simplicity and ease of use. However, its corresponding controller parameters are hard to be adjusted,…
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 apply methods of the so-called `inverse problem of the calculus of variations' to the stabilization of an equilibrium of a class of two-dimensional controlled mechanical systems. The class is general enough to include, among others, the…
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…
We propose a Proportional Integral Derivative (PID) controller-based coaching scheme to expedite reinforcement learning (RL).
A geometric form of Euler-Lagrange equations is developed for a chain pendulum, a serial connection of $n$ rigid links connected by spherical joints, that is attached to a rigid cart. The cart can translate in a horizontal plane acted on by…
Safety is essential for reinforcement learning (RL) applied in real-world tasks like autonomous driving. Chance constraints which guarantee the satisfaction of state constraints at a high probability are suitable to represent the…
Proportional-Integral-Derivative (PID) control has been the workhorse of control technology for about a century. Yet to this day, designing and tuning PID controllers relies mostly on either tabulated rules (Ziegler-Nichols) or on classical…
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…
Proportional-integral-derivative (PID) controller is widely used across various industrial process control applications because of its straightforward implementation. However, it can be challenging to fine-tune the PID parameters in…
Safety is essential for reinforcement learning (RL) applied in the real world. Adding chance constraints (or probabilistic constraints) is a suitable way to enhance RL safety under uncertainty. Existing chance-constrained RL methods like…
This paper develops numerical methods for optimal control of mechanical systems in the Lagrangian setting. It extends the theory of discrete mechanics to enable the solutions of optimal control problems through the discretization of…
This paper presents an alternate form for the dynamic modelling of a mechanical system that simulates in real life a gantry crane type, using Euler's classical mechanics and Lagrange formalism, which allows find the equations of motion that…
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.…
Overall, in any system, the proportional term, integral term, and derivative term combined to produce a fast response time, less overshoot, no oscillations, increased stability, and no steady-state errors. Eliminating the steady state…
Proportional-Integrator-Derivative (PID) controller is used in a wide range of industrial and experimental processes. There are a couple of offline methods for tuning PID gains. However, due to the uncertainty of model parameters and…
Proportional-Integral-Derivative (PID) scheme is the most commonly used algorithm for designing the controllers for unmanned aerial vehicles (UAVs). However, tuning PID gains is a non trivial task. A number of methods have been developed…
Proportional-Integral-Derivative (PID) control is used for automatically regulating a measurable quantity to a desired setpoint. It is widely used in different types of classical control electronics. Here, we show how extending the feedback…
Controlled Lagrangian and matching techniques are developed for the stabilization of relative equilibria and equilibria of discrete mechanical systems with symmetry as well as broken symmetry. Interesting new phenomena arise in the…
The design of Proportional Integral-Derivative (PID) controller is involved to gain infinite stiffness using active vibration control system and it is a modification of previous work. The PID controller is a control loop feedback mechanism…