Anti-windup TS Fuzzy PI-like Control for Discrete-Time Nonlinear Systems with Saturated Actuators

Lopes, Adriano; Leite, Valter J. S.; Silva, Luís Felipe Prada e; Guelton, Kevin

doi:10.1007/s40815-019-00781-0

Cited by 40 publications

(11 citation statements)

References 39 publications

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“…Hence, the designed controller is capable of following piecewise constant references and rejecting exogenous disturbances. Consider the nonlinear plant borrowed from Lopes et al [30], where a discrete‐time version of this model is addressed. The system consists of two tanks coupled, where one of them has a nonlinear solid inside.…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…For 0.28 m ≤ h 1 ≤ 0.48 m, the system can be written as a polytope, whose vertices are

A_{1} = [\begin{array}{cc} - 0.0111 & 0.0111 \\ 0.0155 & - 0.0193 \end{array}], A_{2} = [\begin{array}{cc} - 0.0111 & 0.0111 \\ 0.0238 & - 0.0282 \end{array}],

B_{u 1} = B_{u 2} = {([], \begin{matrix} center center \\ array 0.5432 \times 1 0^{- 4} & array 0 \end{matrix})}^{⊤}, C_{1} = C_{2} = ([], \begin{matrix} center center \\ array 0 & array 1 \end{matrix}), D_{1} = D_{2} = 0

, and matrices of disturbance are

B_{w 1} = {([], \begin{matrix} center center \\ array 0.5432 \times 1 0^{- 3} & array 0 \end{matrix})}^{⊤}

B_{w 2} = {([], \begin{matrix} center center \\ array 0.7432 \times 1 0^{- 3} & array 0 \end{matrix})}^{⊤}

. Similarly to Lopes et al [30], we use an augmented version of the controlled systems to include both the state feedback control action and an integrator over the tracking error, to ensure perfect tracking under piecewise constant references. The augmented system, due to the added integrator, is described by

\begin{matrix} right \dot{x} & left = A (α) x + B (α) sat () \end{matrix}

…”

Section: Numerical Experimentsmentioning

confidence: 99%

See 1 more Smart Citation

ISS control for continuous‐time systems with filtered time‐varying parameter and saturating actuators

Ferreira

Figueiredo

Lacerda

et al. 2022

Asian Journal of Control

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This paper presents new convex conditions to design robust and linear parameter varying (LPV) gains for continuous time-varying systems subject to saturating actuator and energy bounded disturbances. The input-to-state stability conditions are used to design controllers ensuring the minimization of the  2 -gain between the disturbance input and the controlled output. Furthermore, optimization procedures to maximize the estimate of the region of attraction, and the bound to the control signal as well, are formulated. The efficacy of the proposed methods is illustrated with numerical examples, including a reference tracking problem, where realistic simulations are performed.

show abstract

Section: Numerical Experimentsmentioning

confidence: 99%

“…For 0.28 m ≤ h 1 ≤ 0.48 m, the system can be written as a polytope, whose vertices are

A_{1} = [\begin{array}{cc} - 0.0111 & 0.0111 \\ 0.0155 & - 0.0193 \end{array}], A_{2} = [\begin{array}{cc} - 0.0111 & 0.0111 \\ 0.0238 & - 0.0282 \end{array}],

B_{u 1} = B_{u 2} = {([], \begin{matrix} center center \\ array 0.5432 \times 1 0^{- 4} & array 0 \end{matrix})}^{⊤}, C_{1} = C_{2} = ([], \begin{matrix} center center \\ array 0 & array 1 \end{matrix}), D_{1} = D_{2} = 0

, and matrices of disturbance are

B_{w 1} = {([], \begin{matrix} center center \\ array 0.5432 \times 1 0^{- 3} & array 0 \end{matrix})}^{⊤}

B_{w 2} = {([], \begin{matrix} center center \\ array 0.7432 \times 1 0^{- 3} & array 0 \end{matrix})}^{⊤}

\begin{matrix} right \dot{x} & left = A (α) x + B (α) sat () \end{matrix}

…”

Section: Numerical Experimentsmentioning

confidence: 99%

ISS control for continuous‐time systems with filtered time‐varying parameter and saturating actuators

Ferreira

Figueiredo

Lacerda

et al. 2022

Asian Journal of Control

Self Cite

View full text Add to dashboard Cite

show abstract

“…We exploit the state-feedback structure to propose a mode-dependent proportional-integral (PI) action for the system (1). The controller is designed to ensure null steady-state error for piecewise constant references at each mode i, and thus the integral action is applied over the tracking error (Lopes et al, 2020) e(k) = r(k) − y(k),…”

Section: Problem Formulation and Preliminariesmentioning

confidence: 99%

Command Governor strategy based on region of attraction control switching

Sousa

Silva²,

Lúcia

et al. 2020

Anais Do Congresso Brasileiro De Automática 2020

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The command governor (CG) is a useful strategy to avoid constraints violation in case of control reconfiguration or operational conditions changes, like switched systems mode changes. In general, the structure of the CG specializes in producing an alternative reference signal to drive a closed-loop system to the desired reference while avoiding constraints violations in the control signal, state-space, or combinations of them. In this paper, we propose a simple strategy that modifies the conventional structures of the CG and supervisor, yielding a switched rule based on the estimated controllers' region of attraction. We present some simulations to illustrate the proposal's potential and compare it with a competitor scheme exploiting a dwell-time approach. The results suggest that our approach adds new possibilities of CG and supervisor design, reducing the transition time between system modes and improving the closed-loop performance indexes.

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“…To ensure stability and output tracking under actuator saturation, a fuzzy PIlike discrete-time time controller has been proposed in [22] for Takagi-Sugeno systems where the gains of the controller and the anti-windup compensator are designed simultaneously. Nevertheless, these approaches cannot be directly applied to systems with asymmetric saturation.…”

Section: Introductionmentioning

confidence: 99%

Switching Anti-Windup Design for Discrete-Time Switched Systems Under Input Saturation

Houti

Berdjag

Defoort

et al. 2022

Preprint

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In this paper, the tracking problem for discrete-time switched systems subject to actuator saturation and exogenous input is considered. The considered class of systems encompasses discrete-time systems subject to asymmetric saturation or time-varying saturation. Using switched Lyapunov functions and L2-gain analysis, a one-step method is proposed to design the controller and the anti-windup compensator. Some sufficient conditions are derived to guarantee local asymptotic stability and L2-performance of the closed-loop system in terms of linear matrix inequalities (LMI). To illustrate the advantages of the proposed scheme, comparisons with existing schemes are provided. At last, the effectiveness of the proposed scheme is illustrated on the velocity tracking problem of a heavy train with asymmetric saturation constraints.

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Anti-windup TS Fuzzy PI-like Control for Discrete-Time Nonlinear Systems with Saturated Actuators

Cited by 40 publications

References 39 publications

ISS control for continuous‐time systems with filtered time‐varying parameter and saturating actuators

ISS control for continuous‐time systems with filtered time‐varying parameter and saturating actuators

Command Governor strategy based on region of attraction control switching

Switching Anti-Windup Design for Discrete-Time Switched Systems Under Input Saturation

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