An LPV control approach for comfort and suspension travel improvements of semi-active suspension systems

Lam, Anh; Spelta, Cristiano; Savaresi, Sergio M.; Sename, Olivier; Dugard, Luc; Delvecchio, Diego

doi:10.1109/cdc.2010.5717271

Cited by 15 publications

(25 citation statements)

References 17 publications

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“…In this paper, we consider the realistic behavior of a magneto‐rheological damper by using the following nonlinear equation as in the work of Lozoya‐Santos et al:

F_{m r} = c_{0} ((), {\overset{z}{true}}_{s} - {\overset{z}{true}}_{u s}) + k_{0} false(z_{s} - z_{u s} false) + f_{I} \tanh ((), c_{1} false({\overset{z}{true}}_{s} - {\overset{z}{true}}_{u s} false) + k_{1} false(z_{s} - z_{u s} false)),

where c 0 , k 0 , and k 1 are constant parameters, and the controllable force coefficient is described by f I = y m r I , which varies according to the electrical current I in the coil (0 ≤ f I min ≤ f I ≤ f I max ). The parameter values used in this paper belong to the quarter‐car Renault Mégane Coupé equipped with a magneto‐rheological damper presented in the work of Do et al…”

Section: Application To Quarter‐car Suspension Modelmentioning

confidence: 99%

“…The variable f I is positive and fulfills with the dissipativity constraint. According to the works of Do et al, the positivity problem is solved by defining u 1 = f I − F 0 , where F 0 is the mean value of f I such that F 0 = ( f I min + f I max)/2, where f I min = 0 [ N ] and f I max = 800 [ N ]. Therefore, on the basis of the previous results, system (58) is rewritten as

\overset{x}{true} false(t false) = A ((), ρ_{2} ((), x false(t false))) x false(t false) + B ((), ρ_{1} ((), x false(t false))) u false(t false)

y false(t false) = C x false(t false),

where

u false(t false) = ([], \begin{matrix} center center \\ array u_{1} (t) & array z_{r} (t) \end{matrix})

A (ρ_{2} (x (t))) = A_{0} + ρ_{2} (x (t)) F_{0} [\begin{array}{cccc} 0 & 0 & 0 & 0 \\ - \frac{k_{0}}{m_{s}} & - \frac{c_{0}}{m_{s}} & \frac{k_{0}}{m_{s}} & \frac{c_{0}}{m_{s}} \\ 0 & 0 & 0 & 0 \\ \frac{k_{0}}{m_{u s}} & \frac{c_{0}}{m_{u s}} & - \frac{k_{0}}{m_{u s} ...} \end{array}]

…”

Section: Application To Quarter‐car Suspension Modelmentioning

confidence: 99%

“…where c 0 , k 0 , and k 1 are constant parameters, and the controllable force coefficient is described by f I = y mr I, which varies according to the electrical current I in the coil (0 ≤ f Imin ≤ f I ≤ f Imax ). The parameter values used in this paper belong to the quarter-car Renault Mégane Coupé equipped with a magneto-rheological damper presented in the work of Do et al 52 Therefore, the dynamical equations (55) are rewritten as…”

Section: Lpv Quarter-car Suspension Modelmentioning

confidence: 99%

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Generalized dynamic observers for quasi‐LPV systems with unmeasurable scheduling functions

Pérez-Estrada

Osorio-Gordillo

Darouach

et al. 2018

Intl J Robust & Nonlinear

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Summary This paper presents a generalized dynamic observer design for polytopic quasi–linear parameter‐varying systems where the parameters are depending on unmeasured state variables. It generalizes the existing results on the proportional observers and proportional‐integral observers. Conditions of existence and stability are given through the Lyapunov approach. Its design is obtained in terms of a set of linear matrix inequalities. A semiactive suspension example illustrates the performance and effectiveness of the proposed approach.

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“…In this paper, we consider the realistic behavior of a magneto‐rheological damper by using the following nonlinear equation as in the work of Lozoya‐Santos et al:

F_{m r} = c_{0} ((), {\overset{z}{true}}_{s} - {\overset{z}{true}}_{u s}) + k_{0} false(z_{s} - z_{u s} false) + f_{I} \tanh ((), c_{1} false({\overset{z}{true}}_{s} - {\overset{z}{true}}_{u s} false) + k_{1} false(z_{s} - z_{u s} false)),

Section: Application To Quarter‐car Suspension Modelmentioning

confidence: 99%

\overset{x}{true} false(t false) = A ((), ρ_{2} ((), x false(t false))) x false(t false) + B ((), ρ_{1} ((), x false(t false))) u false(t false)

y false(t false) = C x false(t false),

where

u false(t false) = ([], \begin{matrix} center center \\ array u_{1} (t) & array z_{r} (t) \end{matrix})

A (ρ_{2} (x (t))) = A_{0} + ρ_{2} (x (t)) F_{0} [\begin{array}{cccc} 0 & 0 & 0 & 0 \\ - \frac{k_{0}}{m_{s}} & - \frac{c_{0}}{m_{s}} & \frac{k_{0}}{m_{s}} & \frac{c_{0}}{m_{s}} \\ 0 & 0 & 0 & 0 \\ \frac{k_{0}}{m_{u s}} & \frac{c_{0}}{m_{u s}} & - \frac{k_{0}}{m_{u s} ...} \end{array}]

…”

Section: Application To Quarter‐car Suspension Modelmentioning

confidence: 99%

Section: Lpv Quarter-car Suspension Modelmentioning

confidence: 99%

See 1 more Smart Citation

Generalized dynamic observers for quasi‐LPV systems with unmeasurable scheduling functions

Pérez-Estrada

Osorio-Gordillo

Darouach

et al. 2018

Intl J Robust & Nonlinear

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show abstract

“…In our previous works [16] and [17], the LPV framework is used to model the nonlinear damper characteristics, and, also to consider the actuator saturation as a scheduling parameter (this approach can be referred to [6]). The performance on suspension deflection, along with comfort and road holding, is managed by using some frequency-based weighting functions.…”

Section: Introductionmentioning

confidence: 99%

Control design for LPV systems with input saturation and state constraints: An application to a semi-active suspension

Silva

Sename

et al. 2011

IEEE Conference on Decision and Control and European Control Conference

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This paper proposes a control design strategy for LPV systems subject to additive disturbances in the presence of actuator saturation and state constraints. LMI conditions are derived in order to simultaneously compute an LPV controller and an anti-windup gain that ensures the boundedness of the trajectories, considering that the disturbances belong to a given admissible set. The disturbance attenuation is addressed via an H ∞ constraint. Besides, state constraints (corresponding to the local validity of the LPV model and system structural limits) are always assured. The theoretical results are applied to a quarter-car model rewritten in the LPV framework where the passivity constraint is recast to the saturation one. The interest of the provided methodology is emphasized by simulations. I. INTRODUCTIONIn the last years, many studies have focused on the control of saturated (in states, control inputs...) systems which are present in almost real applications. For a system with input saturation, there is usually an inconsistency between the states of the plant and those of the controller because of the saturated actuator between the system control input and the controller output. This effect, usually called windup, dramatically degrades the closed-loop performances or even worse causes the system instability. To preserve the consistency, the input to controller needs to be changed by an appropriate signal, which is provided by a called antiwindup compensator. Usually, when a system is subject to actuator saturation, two main issues arise: the guarantee of stability (global or local) and the minimization of the performance degradation. There are two methods to solve these problems: two-step and one-step design. The traditional two-step method first designs a linear controller without considering the input saturation effect and then add an anti-windup compensator to minimize the adverse effects of control input saturation on closed-loop performance [1], [2]. For the one step approach, the controller and an antiwindup compensator (static in general) are simultaneously computed [3], [4]. It can be noticed that the control design with input saturation is a nonlinear problem. However, many solutions have been proposed to model the saturation effect in such a way that the problem can be treated within a linear framework, for example: the polytopic differential inclusion

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“…An active roll control system based on a modified suspension system was developed with distributed control architecture in [4]. A new H ∞ /LPV control method to improve the trade-off between comfort and suspension travel was proposed by [5].…”

Section: Introductionmentioning

confidence: 99%

Hierarchical design of electro-hydraulic actuator control for vehicle dynamic purposes

Varga

Németh

Gáspár

2014

2014 European Control Conference (ECC)

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Abstract-The paper proposes a hierarchical control design of an electro-hydraulic actuator, which is incorporated in the active anti-roll bars. The aim of the control system is to generate a reference torque, which is required by the vehicle dynamic control. The control-oriented model of the actuator is formulated in two subsystems. The upper-level hydromotor is described in a linear form, while the lower-level spool valve is a polynomial system. These subsystems require different control strategies. At the upper-level a Linear Parameter Varying control is used to guarantee performance specifications. At the lower-level a Control Lyapunov Function-based algorithm, which creates discrete control input values of the valve, is proposed. The interaction between the two subsystems is guaranteed by the spool displacement, which is control input for the upper-level and must be tracked by the lower-level control. The spool displacement has physical constraints, which must also be incorporated into the control design. The operation of the actuator control system is illustrated through a simulation example.

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An LPV control approach for comfort and suspension travel improvements of semi-active suspension systems

Cited by 15 publications

References 17 publications

Generalized dynamic observers for quasi‐LPV systems with unmeasurable scheduling functions

Generalized dynamic observers for quasi‐LPV systems with unmeasurable scheduling functions

Control design for LPV systems with input saturation and state constraints: An application to a semi-active suspension

Hierarchical design of electro-hydraulic actuator control for vehicle dynamic purposes

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