Investigation of the Hammerstein hypothesis in the modeling of electrically stimulated muscle

To restore functional use of paralyzed muscles by automatically controlled stimulation, an accurate quantitative model of the stimulated muscles is desirable. The most commonly used model for isometric muscle has had a Hammerstein structure, in which a linear dynamic block is preceded by a static nonlinear function, To investigate the accuracy of the Hammerstein model, the responses to a pseudo-random binary sequence (PRBS) excitation of normal human plantarflexors, stimulated with surface electrodes, were used to identify a Hammerstein model but also four local models which describe the responses to small signals at different mean levels of activation. Comparison of the local models with the Linearized Hammerstein model showed that the Hammerstein model concealed a fivefold variation in the speed of response. Also, the small-signal gain of the Hammerstein model was in error by factors up to three. We conclude that, despite the past widespread use of the Hammerstein model, it is not an accurate representation of isometric muscle. On the other hand, local models, which are more accurate predictors, can be identified from the responses to short PRBS sequences. The utility of local models for controller design is discussed

Weiner Model Drop Test Identification of a Light Amphibious Airplane

The new approach of the Weiner model for identifying drop test dynamics of a light amphibious airplane is presented in this paper. Unlike the traditional identification method of the Hammerstein model using LS-SVM with Gaussian radial basis serving as the kernel function, the small-signal excitation input is used to estimate the linear block of the Weiner model. Then, the static nonlinearity function of the model is identified through LS-SVM. The RMSE of the proposed Weiner model is 0.48805 and 0.38246 for the strut and wheel of the landing gear. The proposed Weiner model has better identification performance than the Hammerstein model and the traditional governing equation of the landing gear. The drop experiment of the light amphibious airplane is carried out not only to prove standard airworthiness compliance but also to verify the identifiability, accuracy, and performance of system identification

Identification of Nonlinear Systems Structured by Wiener-Hammerstein Model

Wiener-Hammerstein systems consist of a series connection including a nonlinear static element sandwiched with two linear subsystems. The problem of identifying Wiener-Hammerstein models is addressed in the presence of hard nonlinearity and two linear subsystems of structure entirely unknown (asymptotically stable). Furthermore, the static nonlinearity is not required to be invertible. Given the system nonparametric nature, the identification problem is presently dealt with by developing a two-stage frequency identification method, involving simple inputs

Two-stage shape memory alloy identification based on the Hammerstein - Wiener model

from the two stages was obtained for a specific shape memory alloy wire and for specific environmental conditions. This data was used in the modeling process. The final model consists of a combination of the models from the two stages, which represent the behavior of the shape memory alloy actuator where the input signal is the pulse-width modulation signal and the output signal are the position of the actuator. Our results indicate that our model has a very similar response to the behavior of the real actuator. This model can be used to tune different control algorithms, simulate the entry system before manufacture and test on real devices.The research leading to these results has received funding from the Exoesqueleto para Diagnostico y Asistencia en Tareas de Manipulación (DPI2016-75346-R) Spanish research project and from RoboCity2030-DIH-CM, Madrid Robotics Digital Innovation Hub, S2018/NMT-4331, funded by Programas de Actividades I + D en la Comunidad de Madrid and cofunded by Structural Funds of the EU

A new kernel-based approach for overparameterized Hammerstein system identification

In this paper we propose a new identification scheme for Hammerstein systems, which are dynamic systems consisting of a static nonlinearity and a linear time-invariant dynamic system in cascade. We assume that the nonlinear function can be described as a linear combination of $p$ basis functions. We reconstruct the $p$ coefficients of the nonlinearity together with the first $n$ samples of the impulse response of the linear system by estimating an $np$-dimensional overparameterized vector, which contains all the combinations of the unknown variables. To avoid high variance in these estimates, we adopt a regularized kernel-based approach and, in particular, we introduce a new kernel tailored for Hammerstein system identification. We show that the resulting scheme provides an estimate of the overparameterized vector that can be uniquely decomposed as the combination of an impulse response and $p$ coefficients of the static nonlinearity. We also show, through several numerical experiments, that the proposed method compares very favorably with two standard methods for Hammerstein system identification.Comment: 17 pages, submitted to IEEE Conference on Decision and Control 201