Two‐Controller Anti‐Windup Design for Enlarging Domain of Stability of Actuator Constrained State‐Delay Systems

This paper presents a robust gain‐scheduled H∞ controller to improve lateral stability and handling of four‐wheel‐independent‐drive electric vehicles possessing active front steering system with considerations of state delay. The time delay for the state is assumed as uncertain time‐invariant but has a known constant bound. By considering the tyre cornering stiffness represented by the norm‐bounded uncertainty and the time‐varying longitudinal velocity described by a polytope with finite vertices, and the vehicle lateral dynamics model is converted into the uncertain vehicle linear parameter‐varying (LPV) state‐delayed system. The resulting delay‐dependent robust gain‐scheduling state feedback H∞ controller is finally designed utilizing the constructed Lyapunov‐Krakovskii functional, and solved via a set of delay‐dependent linear matrix inequalities (LMIs). Simulations for various driving scenarios are implemented using MATLAB/SIMULINK‐CARSIM. The simulation results show the effectiveness of the proposed controller.

{(∥∥, z)}_{2} \leq γ {(∥∥, w)}_{2}

To design the controller, we introduce the following lemmas. Lemma Assuming

a (\cdot) \in ℜ^{n_{a}}, b (\cdot) \in ℜ^{n_{b}}

and

Φ \in ℜ^{n_{a} \times n_{b}}, X \in ℜ^{n_{a} \times n_{a}}, Y \in ℜ^{n_{a} \times n_{b}}

and

Z \in ℜ^{n_{b} \times n_{b}}

,then the following inequalities hold:

2 \int_{Φ} a^{T} (σ) ϕb (σ) \leq \int_{Φ} Ψ^{T} ([], \begin{matrix} X & Y - ϕ \\ {(Y - ϕ)}^{T} & Z \end{matrix}) Ψdσ

where

[\begin{matrix} X & Y \\ Y^{T} & Z \end{matrix}] \leq 0, Ψ = [\begin{matrix} a (σ) \\ b (σ) \end{matrix}]

Lemma Let Γ = Γ T ,

\overset{Υ}{true}

and

\overset{ϑ}{true}

are real matrices with compatibl...…”

Section: Robust Gain‐scheduling H∞ Controller Designmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Stabilizing Vehicle Lateral Dynamics with Considerations of State Delay of AFS for Electric Vehicles via Robust Gain‐Scheduling Control

Jin¹,

Yin²,

Li³

et al. 2015

“…The design of a compensation method, which is based on variable structure systems to avoid both amplitude and rate input saturation by means of an auxiliary loop, is presented in . In the enlargement of the domain of stability of an actuator constrained state time‐delay system with a novel dynamic two controller anti‐windup design is proposed. The recent research on model predictive control in which constraint handling is given to cope with the actuator physical limitations is also relevant .…”

Section: Introductionmentioning

confidence: 99%

Hysteresis‐Based Design of Dynamic Reference Trajectories to Avoid Saturation in Controlled Wind Turbines

Tutivén

Vidal

Acho

et al. 2016

The main objective of this paper is to design a dynamic reference trajectory based on hysteresis to avoid saturation in controlled wind turbines. Basically, the torque controller and pitch controller set-points are hysteretically manipulated to avoid saturation and drive the system with smooth dynamic changes. Simulation results obtained from a 5MW wind turbine benchmark model show that our proposed strategy has a clear added value with respect to the baseline controller (a well-known and accepted industrial wind turbine controller). Moreover, the proposed strategy has been tested in healthy condition but also in presence of a realistic fault where the baseline controller caused saturation to finally conduct to instability.

“…The point is that relatively few works have dealt with the problem of controlling delayed systems through saturating actuators. In the AWC is designed to ensure L 2 stability of the operator relating the control saturation error

\overset{u}{true} = u - s a t ((), u)

(the difference between the control input u generated in the closed‐loop without input saturation and the same signal passed through the saturation nonlinearity) to

\overset{z}{true} = z - \overset{z}{true}

(the error between the control system performance outputs with and without input saturation). However, the class of inputs (references, disturbances) for which the condition

\overset{u}{true} \in L_{2}

holds is not explicitly defined.…”

Section: Introductionmentioning

confidence: 99%

Tracking Performance Achievement for Continuous‐Time Delayed Linear Systems Subject to Actuator Saturation and output Disturbances

Mahjoub¹,

Assche²,

Giri³

et al. 2014

Controlling continuous‐time input‐delayed nonminimum‐phase linear systems is addressed in the presence of actuator saturation and output‐disturbances. Focusing on output‐reference tracking, the control design is dealt with in the pseudo‐polynomials ring. A quite appealing L2 ‐tracking performance is shown to be achievable in the presence of arbitrary inputs i.e. the output reference and the output disturbance. The performance is formulated in terms of a well defined output‐reference mismatch error (ORME), depending on the inputs’ rate and their compatibility with the actuator saturation constraint.