State‐limiting PID controller for a class of nonlinear systems with constant uncertainties

Abstract

Summary Proportional Integral Derivative (PID) controllers still represent the core control method for achieving output regulation of either linear or nonlinear systems in the majority of industrial applications. However, conventional PID control cannot guarantee specific state constraint requirements for the plant, when the system introduces uncertainties. In this paper, a novel nonlinear PID control that achieves output regulation and guarantees a desired state limitation below a given value for a wide class of nonlinear systems with constant uncertainties is proposed. Using nonlinear ultimate boundedness theory, it is shown that the proposed state‐limiting PID (sl‐PID) control maintains a given bound for the desired system states at all times, ie, even during transients, whereas an analytic method for selecting the controller gains is also presented to ensure closed‐loop system stability and convergence at the desired equilibrium. Two nonlinear engineering examples that include an electric motor and a dc/dc converter are investigated using the conventional PID and the proposed sl‐PID to validate the superiority of the proposed controller in achieving the desired output regulation with a given bounded state requirement.

Grid-Supporting Three-Phase Inverters With Inherent Root Mean Square Current Limitation Under Balanced Grid Voltage Sags

“…In addition, I max rms is the maximum rated inverter RMS current which is defined by the user or the technical limitations of the inverter. Motivated by the recently proposed nonlinear statelimiting PI controller structure presented in [25], the dynamics for the controller state σ are given as…”

“…As it is explained in [25], the nonlinear dynamics have been carefully designed to avoid a continuously oscillating behavior of the controller state σ and additionally ensure that the controller dynamics slow down, i.e. σ → 0, as σ → ± π 2 (near the limits of the state σ), which illustrates an inherent integrator anti-windup property.…”

“…In this paper, a novel nonlinear control approach for threephase grid-supporting inverters that inherently limits the RMS inverter current without the need of saturation units is proposed and analyzed. Inspired by the recently developed state-limiting PI controller in [25], the proposed controller is formulated to incorporate the widely used droop control concept and provide the necessary ancillary services to the grid. Then, using invariant set theory, it is rigorously proven for the first time that the proposed scheme ensures a desired limitation of the RMS inverter current below a given maximum value during the entire operation, i.e.…”

Novel droop control design for overvoltage protection of DC microgrids with a constant power load

“…Inspired by the sl-PI controller in [21], the novel droop control strategy defines the control input, i ini , in the following form…”

Two-layer nonlinear control of DC-DC buck converters with meshed network topology

“…Our proposed controller architecture contains a decentralised primary controller ensuring operation safety for inputs currents and a receding horizon distributed controller for voltage regulation. The analysis of the primary controller hinges on extending the approach of Konstantopoulos and Baldivieso-Monasterios (2020) where the authors propose a state-limiting converter based on the concept of Bounded Integral Controller (BIC); we prove asymptotic stability inside a compact set representing a desired safety set using a Lyapunov approach defined on this set. We study the interconnection properties between voltages and currents under the scope of the cascaded systems approach; our results show that the kernel of the network Laplacian matrix defines an attractive set which yields an ISS type result.…”