Extension of PID Regulators to Dynamical Systems on Smooth Manifolds (M-PID)

Fiori, Simone

doi:10.1137/19m1307743

Cited by 7 publications

(4 citation statements)

References 30 publications

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“…The remaining task is to identify the upper bounds for b φ and b v . From their expressions in (18), we know that b φ = ρ X ≤ ρ v and obtain the result in (19) for the upper bound of b φ with k 0 = ρ . The vector b v can be considered as a combination of two terms b v1 = [k p βJH∇φ; −βJ∇F l b ∇φ] and b v2 = [βJHX; −ρJ∇F l b X].…”

Section: First-stage Variable Changementioning

confidence: 99%

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Left-Invariant PID Control Almost Globally Stabilizes Rigid-Body Attitudes with Right-Invariant Biases

Zhang,

Liu,

Hou

et al. 2023

Electronics

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This paper studies the robust stabilization of rigid-body attitudes represented by a special orthogonal matrix. A geometric proportional–integral–derivative (PID) controller is proposed with all the input commands defined in the dual space so*(3) of a Lie algebra for left-invariant systems evolving on a Lie group SO(3). Almost global asymptotic stability (AGAS) of the close system is proved by constructing a gradient-descent Lyapunov function after explicitly performing two stages of variable change. The attitudes are stabilized to the stable equilibrium despite the influence of inertially fixed biases. The convergent behaviors and the robustness to biases are verified by numerical simulations.

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Section: First-stage Variable Changementioning

confidence: 99%

“…Results in [19] also extended the classical PID to that for both first-order and second-order systems on smooth manifolds.…”

Section: Introductionmentioning

confidence: 98%

Left-Invariant PID Control Almost Globally Stabilizes Rigid-Body Attitudes with Right-Invariant Biases

Zhang,

Liu,

Hou

et al. 2023

Electronics

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“…As the most widely used control algorithm in industrial processes, PID controller has attracted a great deal of attention, and considerable mathematical research efforts have been made in recent years. [29][30][31] In particular, since the celebrated Newton's second law describing the motion equation is second order, the system with second order is most extensively studied. 32 In Reference 33, a method to select gains of a discrete PID controller for a class of second order systems was presented.…”

Section: Introductionmentioning

confidence: 99%

“…In addition, PID control responds quickly and can realize dynamic adjustment of the system in a real‐time environment. As the most widely used control algorithm in industrial processes, PID controller has attracted a great deal of attention, and considerable mathematical research efforts have been made in recent years 29–31 . In particular, since the celebrated Newton's second law describing the motion equation is second order, the system with second order is most extensively studied 32 …”

Section: Introductionmentioning

confidence: 99%

Control of coupled nonaffine multiagent stochastic systems by classical PID

Yuan

2024

Intl J Robust & Nonlinear

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The classical PID (proportional‐integral‐derivative) control is the most basic and widely used control algorithm in engineering systems by far. Whether PID control can effectively deal with coupled multiagent uncertain nonlinear dynamics is well worth investigating. In this article, a class of PID controlled multiagent stochastic systems with coupled uncertain dynamics is considered, where the control input is nonaffine. Each agent has its own regulation objective, and only has access to its own regulation error information for PID feedback. First, a PID parameter set will be constructed explicitly based on some prior knowledge about the nonlinear functions, such that the overall multiagent system can be stabilized globally in the mean square sense, as long as the PID parameters are chosen from the constructed set. Moreover, the regulation error will be proven to have an upper bound proportional to the noise intensity along the reference signal. Furthermore, it will be shown that the regulation error of each agent can be arbitrarily small by choosing the PID parameters suitably large. Finally, the theoretical results will be verified by simulations.

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A Leader-following Rendezvous Control Design for the Cucker-Smale Model on the Infinite Cylinder

2022

2022 IEEE 61st Conference on Decision and Control (CDC)

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Extension of PID Regulators to Dynamical Systems on Smooth Manifolds (M-PID)

Cited by 7 publications

References 30 publications

Left-Invariant PID Control Almost Globally Stabilizes Rigid-Body Attitudes with Right-Invariant Biases

Left-Invariant PID Control Almost Globally Stabilizes Rigid-Body Attitudes with Right-Invariant Biases

Control of coupled nonaffine multiagent stochastic systems by classical PID

A Leader-following Rendezvous Control Design for the Cucker-Smale Model on the Infinite Cylinder

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