INVESTIGATION OF THE HAMMERSTEIN HYPOTHESIS IN THE MODELING OF ELECTRICALLY STIMULATED MUSCLE

To restore functional use of paralyzed muscles by automatically contro lled stimulation, an accurate quantitative model of the stimulated mus cles is desirable. The most commonly used model for isometric muscle h as had a Hammerstein structure, in which a linear dynamic block is pre ceded by a static nonlinear function, To investigate the accuracy of t he Hammerstein model, the responses to a pseudo-random binary sequence (PRBS) excitation of normal human plantarflexors, stimulated with sur face electrodes, were used to identify a Hammerstein model but also fo ur local models which describe the responses to small signals at diffe rent mean levels of activation. Comparison of the local models with th e Linearized Hammerstein model showed that the Hammerstein model conce aled a fivefold variation in the speed of response. Also, the small-si gnal 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 t he other hand, local models, which are more accurate predictors, can b e identified from the responses to short PRBS sequences. The utility o f local models for controller design is discussed.