Unified $\mathcal{H}_{\infty}$ Observer for a Class of Nonlinear Lipschitz Systems: Application to a Real ER Automotive Suspension

Abstract

This paper presents an extension of the synthesis of a unified H∞ observer for a specific class of nonlinear systems. The objectives are to decouple the effects of bounded unknown input disturbances and to minimize the effects of measurement noises on the estimation errors of the state variables by using H∞ criterion, while the nonlinearity is bounded through a Lipschitz condition. This new method is developed to estimate the damping force of an Electro-Rheological (ER) damper in an automotive suspension system, and is implemented on the INOVE testbench from GIPSA-lab (1/5-scaled real vehicle) for real-time performance assessment. Both simulation and experimental results demonstrate the effectiveness of the proposed observer to estimate the damper force in real-time, face to measurement noises and road disturbances.

A Nonlinear Observer for Robust Fault Reconstruction in One-Sided Lipschitz and Quadratically Inner-Bounded Nonlinear Descriptor Systems

“…Furthermore, there are a wide range of functions that have finite RMS values, including piecewise continuous polynomial functions, as well as periodic signals such as sinusoids, all of which are often encountered in practical systems [2]. Assumption 2 is also not restrictive and has been widely utilised in existing observer schemes [10], [14], [19], [26], [44], and will be used to construct the observer.…”

“…for all Tx 1 , Tx 2 ∈ R, where x = Tx 1 − Tx 2 , g = g (Tx 1 ) − g (Tx 2 ) , R ⊆ R b , and α, β, γ ∈ R, where α, β, and γ are known constants. Remark 2: Most schemes in the literature assume the nonlinear function to be TL (i.e., there exists a positive constant l f that satisfies l f x ≥ g ) [1], [14], [19], [21], [37]. If a nonlinear function is TL, then it is also OSL with α > 0 and QIB with β = 0 and γ = l 2 f > 0.…”

“…• The works by [5], [7], [14], [15], [17]- [19], [23], [26], [28]- [31], [35]- [39], [41], [46], [49] do not consider faults entering the nonlinear function, and are therefore cannot be applied.…”

A nonlinear parameter varying observer for real‐time damper force estimation of an automotive electro‐rheological suspension system

“…By using the Lipschitz condition to bound the nonlinearity, the authors developed several works, 13,1415 in that context. In particular, References [13] and [14] proposed an H ∞ and a unified H ∞ observers using two accelerometers to estimate the damper force in the semi-active suspension system, respectively. However, the variations of the damper force amplification function of the voltage input were not considered in the design step and they were only bounded which may induce some conservatism.…”

Further studies on state estimation of discrete‐time nonlinear parameter varying systems based on a new multiinstant switching observer

“…[11][12][13][14] Furthermore, on most occasions, the more advanced nonlinear parameter varying (NLPV) systems (using a nonlinear structure instead of reducing to a linear one) can be more appropriate, and may lead to less conservatism and much overapproximation. [15][16][17][18] On the other hand, observer-based state estimation has been actively investigated due to its paramount importance concerning observing complex system states which must be helpful toward understanding the complicated behavior of the considered plants. [19][20][21][22][23][24] Recently, the design problem of vehicle state observer has been solved by designing a NLPV observer that depends on online accessible time-varying parameters.…”