A non-linear approach to modelling and control of electrically stimulated skeletal muscle
This thesis is concerned with the development and analysis of a non-linear approach to modelling and control of the contraction of electrically stimulated skeletal muscle. For muscle which has lost nervous control, artificial electrical stimulation can be used as a technique aimed at providing muscular contraction and producing a functionally useful movement. This is generally referred to as Functional Electrical Stimulation (FES) and is used in different application areas such as the rehabilitation of paralysed patient and in cardiac assistance where skeletal muscle can be used to support a failing heart. For both these FES applications a model of the muscle is essential to develop algorithms for the controlled stimulation. For the identification of muscle models, real data are available from experiments with rabbit muscle. Data for contraction with constant muscle length were collected from two muscle with very different characteristics. An empirical modelling approach is developed which is suitable for both muscles. The approach is based on a decomposition of the operating space into smaller sub-regions which are then described by local models of simple, possibly linear structure. The local models are blended together by a scheduler, and the resulting non-linear model is called a Local Model Network (LMN). It is shown how a priori knowledge about the system can be used directly when identifying Local Model Networks. Aspects of the structure selection are discussed and algorithms for the identification of the model parameters are presented. Tools of the analysis of Local Model Networks have been developed and are used to validate the models. The problem of designing a controller based on the LMN structure is discussed. The structure of Local Controller Networks is introduced. These can be derived directly from Local Model Networks. Design techniques for input-output and for state feedback controllers, based on pole placement, are presented. Aspects of the generation of optimal stimulation patterns (which are defined as stimulation patterns which deliver the smallest number of pulses to obtain a desired contraction) are discussed, and various techniques to generate them are presented. In particular, it is shown how a control structure can be used to generate optimal stimulation patterns. A Local Controller Network is used as the controller with a design based on a non-linear LMN model of muscle. Experimental data from a non-linear heat transfer process have been collected and are used to demonstrate the basic modelling and control principles throughout the first part of the thesis.