This paper addresses the problem of identifying Wiener systems constituted of nonparametric linear dynamics and backlash nonlinearities. The linear subsystem is arbitrary but stable. The backlash ...nonlinearity borders are almost arbitrary-shape. In particular, these are allowed to be nonsmooth, noninvertible and crossing. A frequency identification method is developed to estimate the system frequency response function (at a given set of frequencies) and the backlash nonlinearity borders (within a given working domain). The identification method involves sine excitations and consistent estimators designed using analytic geometry tools, e.g. fictive limit cycles; informative backlash limit cycles; spread- and orientation-compatibility.
Hammerstein system identification is considered in presence of preload and dead zone nonlinearities. The discontinuous feature of these nonlinearities makes it difficult to get a single system ...parameterization involving linearly all unknown parameters (those of the linear subsystem and those of the nonlinearity). Therefore, system identification has generally been dealt with using multiple stage schemes including different parametrizations and several data acquisition experiences. However, the consistency issue has only been solved under restrictive assumptions regarding the identified system. In this paper, a new identification scheme is designed and shown to be consistent under mild assumptions.
This paper addresses the problem of Wiener system identification. The underlying linear subsystem is stable but not necessarily parametric. The nonlinear element in turn is allowed to be ...nonparametric, noninvertible, and nonsmooth. As Wiener models are uniquely defined up to an uncertain multiplicative factor, it makes sense to start the frequency identification process estimating the system phase (which is common to all models). To this end, a consistent estimator is designed using analytic geometry tools. Accordingly, the system frequency behavior is characterized by a family of Lissajous curves. Interestingly, all these curves are candidates to modelling the system nonlinearity, but the most convenient one is the less spread of them. Finally, the frequency gain is in turn consistently estimated optimizing an appropriate cost function involving the obtained phase and nonlinearity estimates.
The problem of modeling vehicle longitudinal motion is addressed for front wheel propelled vehicles. The chassis dynamics are modeled using relevant fundamental laws taking into account aerodynamic ...effects and road slop variation. The longitudinal slip, resulting from tire deformation, is captured through Kiencke's model. A highly nonlinear model is thus obtained and based upon in vehicle longitudinal motion simulation. A simpler, but nevertheless accurate, version of that model proves to be useful in vehicle longitudinal control. For security and comfort purpose, the vehicle speed must be tightly regulated, both in acceleration and deceleration modes, despite unpredictable changes in aerodynamics efforts and road slop. To this end, a nonlinear controller is developed using the Lyapunov design technique and formally shown to meet its objectives i.e. perfect chassis and wheel speed regulation.
The problem of identifying Hammerstein-like systems containing dynamic nonlinearities, of the switch or backlash types, is considered. Interestingly, the nonlinearity borders are nonparametric ...borders (i.e. of unknown structure) and so are allowed to be noninvertible and cross each other. A semi-parametric identification approach is developed to estimate the linear subsystem parameters and
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points on both nonlinearity borders. It relies on two main experiments designed so that during each one, the focus is on one lateral border exciting
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specific points. Doing so, the initial nonparametric identification problem is decomposed into two simpler problems involving static parametric nonlinearities. The new problems are dealt with independently using least squares type estimators. It is formally shown that the experiments generate persistently exciting signals ensuring the consistency of all involved parameter estimators.
A two-stage parameter identification method is developed for Hammerstein systems containing backlash nonlinearities bordered by parametric arbitrary-shape lines. In the first stage, a persistently ...exciting input is designed so that the linear subsystem can be made decoupled from the nonlinear element. Therefore, linear subsystem identification is coped with using a least squares estimator enjoying consistency, due to input persistent excitation. Then, the backlash parameters are estimated using appropriate periodic exciting signals and consistent parameter estimators.
The problem of controlling synchronous motors, driven through AC/DC rectifiers and DC/AC inverters is addressed. The control objectives are threefold: (i) forcing the motor speed to track a varying ...reference signal in presence of motor parameter uncertainties; (ii) regulating the DC Link voltage; (iii) assuring a satisfactory power factor correction (PFC) with respect to the power supply net. First, a nonlinear model of the whole controlled system is developed in the Park-coordinates. Then, a robust nonlinear controller is synthesized using the damping function version of the backstepping design technique. A formal analysis based on Lyapunov stability and average theory is developed to describe the control system performances. Despite parameter uncertainties, all control objectives are proved to be asymptotically achieved up to unavoidable but small harmonic errors (ripples).
We are considering the problem of controlling a DC-DC switched power converter of the Buck type. The converter involves an inherent control limitation; accordingly the control signal (duty ratio) can ...only take values in the interval (0, 1) . In the relevant literature, such a physical control limitation is generally not taken into account when designing the converter regulators. This is only dealt with in the control implementation stage, placing an isolated limiter between the (linear) controller and the controlled system. Furthermore, the presence of such a limiter is generally ignored when analyzing the closed-loop control system. In the present paper, the control signal limitation is dealt with using a nonlinear regulator that involves an internal limiter. The resulting closed-loop control system is shown to be equivalent to a nonlinear feedback involving a linear dynamics block in closed-loop with a nonlinear static element. Using absolute stability tools, sufficient conditions are established for the involved feedback to be L 2 -stable. If these conditions are respected when choosing the control design parameters then the regulator meets its objectives (closed-loop stability and output reference tracking). It is worth noting that, though the focus is made on a specific power converter, the paper includes an important theoretical dimension that may be of general interest.
► A theoretical framework of a global control strategy of induction machine is studied. ► The control consider the magnetic saturation and relative power equipments. ► The proposed strategy involves ...a multi-loop nonlinear adaptive controller. ► Objectives are: speed regulation, flux optimization and power factor correction.
A great deal of interest has been paid to induction machine control over the last years. However, most previous works have focused on the speed/flux/torque regulation supposing the machine magnetic circuit to be linear and ignoring the machine power conversion equipments. The point is that speed regulation cannot be ensured in optimal efficiency conditions, for a wide range of speed-set-point and load torque, unless the magnetic circuit nonlinearity is explicitly accounted for in the motor model. On the other hand, the negligence of the power conversion equipments makes it impossible to deal properly with the harmonic pollution issue due to ‘motor – power supply grid’ interaction. This paper presents a theoretical framework for a global control strategy of the induction machine and related power equipments. The proposed strategy involves a multi-loop nonlinear adaptive controller designed to meet the three main control objectives, i.e. tight speed regulation for a wide range speed-reference variation, flux optimization for energy consumption and power factor correction (PFC). Tools from the averaging theory are resorted to formally describe the control performances.
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