Nonlinear modelling and control of electrically stimulated muscle: A local model network approach

Human muscle can be made to contract by electrical stimulation. There are many well established uses for this technique and new applications are being investigated. We are interested in two uses: restoration of function to paralysed limbs and reconfiguration of one of the back muscles to assist a failing heart. Muscle modelling has been widely studied in the past. Model types range from biophysical models, which are based on the structure and processes of actual muscles, through analogue models, to purely mathematical descriptions. The latter are derived only from the input (neural activation) and the output (mechanical response) signals. We are searching for mathematical models, which firstly can represent the complex nonlinear behaviour of muscle and secondly are controller oriented, that is that controller design based on such models is possible. We have developed a number of dynamic muscle models based on force measurements taken from isometric contracting muscles stimulated by an irregular pulse train. The results of experimental investigations have shown that a simple linear transfer-function model of muscle response can be rather inaccurate over the full operational range. The muscle response is significantly nonlinear with respect to the level of stimulation. However, the experiments with linear system identification provide results which can be used to choose structure parameters of a dynamic model. Nonlinear models based on local model networks (LMNs) are able to capture the nonlinear effects and to provide accuracy over a wide operational range. We investigate the use of an LMN with local linear models, describe the type of network model used, the training algorithm, and show some typical experimental results based on real measured data. We address the synthesis of feedback controllers for physical muscle. The simple linear transfer function model forms the basis for the design of a robust linear controller. The structure of the LMN derived previously is exploited as the basis of a non-linear control design: the local controller network. We compare the performance of both controller designs in simulation experiments.