Robust PID controller design for nonlinear systems

Veselý, Vojtech; Korosi, Ladislav

doi:10.1515/jee-2018-0009

Cited by 3 publications

(2 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The control 47 and observation of Lipschitz nonlinear systems 48,49 has been analysed in several works. Tube-based MPC has been applied to nonlinear Lipschitz systems 50 , but the NLPV design paradigm is not used, which essentially means that more complex nonlinear optimization procedure had to be implemented.…”

Section: Lipschitz Nonlinearitiesmentioning

confidence: 99%

“…This function, indeed, agrees with a Lipschitz condition. 46 The control 48 and observation of Lipschitz nonlinear systems 49,50 have been analysed in several works. We note that tube-based MPC algorithms have been applied to nonlinear Lipschitz systems 51 and also to arbitrary nonlinear systems, [52][53][54][55] but the NLPV design paradigm has not yet been used, which essentially means that more complex nonlinear optimization procedure had to be implemented.…”

Section: Lipschitz Nonlinear Parameter Varying Systemsmentioning

confidence: 99%

See 1 more Smart Citation

An input‐to‐state stable model predictive control framework for Lipschitz nonlinear parameter varying systems

Morato

Normey-Rico

Sename

2020

Intl J Robust & Nonlinear

View full text Add to dashboard Cite

This paper develops a state-feedback Model Predictive Control (MPC) framework for Nonlinear Parameter Varying (NLPV) systems with explicit Lipschitz nonlinearities along the input trajectory. Considering a guess for the evolution of the scheduling parameters along the prediction horizon, the proposed optimization procedure for the MPC design includes a terminal stage cost, a contracting terminal region constraint and nominal predictions scheduled with respect to this guess. The terminal region is taken so that it is monotonically decreasing to a predetermined set, which guarantees recursive feasibility of the algorithm with respect to a bound on the admissible uncertainties (introduced from the scheduling parameter guess). The terminal set is a scheduled robust control invariant set for Lipschitz nonlinear systems, computed through some proposed LMIs. The inclusion of the terminal ingredient also serves to demonstrate Input-to-State Quadratic Stability. This paper ends with a successful numerical simulation example of the technique applied to the control of a Semi-Active automotive suspension system equipped with Electro-Rheological dampers.

show abstract

Section: Lipschitz Nonlinearitiesmentioning

confidence: 99%

Section: Lipschitz Nonlinear Parameter Varying Systemsmentioning

confidence: 99%

An input‐to‐state stable model predictive control framework for Lipschitz nonlinear parameter varying systems

Morato

Normey-Rico

Sename

2020

Intl J Robust & Nonlinear

View full text Add to dashboard Cite

show abstract

D-stable Controller Design for Lipschitz NLPV System

2019

View full text Add to dashboard Cite

Dynamics of Cardiovascular Muscle Using a Non-Linear Symmetric Oscillator

Bhattacharjee

Banerjee²,

Rakshit³

et al. 2021

Symmetry

View full text Add to dashboard Cite

In this paper, a complete non-linear symmetric oscillator model using the Hamiltonian approach has been developed and used to describe the cardiovascular conduction process’s dynamics, as the signal generated from the cardiovascular muscle is non-deterministic and random. Electrocardiogram (ECG) signal is a significant factor in the cardiovascular system as most of the medical diagnoses can be well understood by observing the ECG signal’s amplitude. A non-linear cardiovascular muscle model has been proposed in this study, where a modified vanderPol symmetric oscillator-based equation is used. Gone are the days whena non-linear system had been designed using the describing function technique. It is better to design a non-linear model using the Hamiltonian dynamical equation for its high accuracy and flexibility. Varying a non-linear spring constant using this type of approach is more comfortable than the traditional describing function technique. Not only that but different initial conditions can also be taken for experimental purposes. It never affects the overall modeling. The Hamiltonian approach provides the energy of an asymmetric oscillatory system of that cardiovascular conduction system. A non-linear symmetric oscillator was initially depicted by the non-linear mass-spring (two degrees of freedom) model. The motion of an uncertain non-linear cardiovascular system has been solved considering second-order approximation, which also demonstrates the possibility of introducing spatial dimensions. Finally, the model’s natural frequency expression has also been simulated and is composed of the previously published result.

show abstract

Robust PID controller design for nonlinear systems

Cited by 3 publications

References 14 publications

An input‐to‐state stable model predictive control framework for Lipschitz nonlinear parameter varying systems

An input‐to‐state stable model predictive control framework for Lipschitz nonlinear parameter varying systems

D-stable Controller Design for Lipschitz NLPV System

Dynamics of Cardiovascular Muscle Using a Non-Linear Symmetric Oscillator

Contact Info

Product

Resources

About