Copyright @ IFAC Adaptive Systems in Control and Signal Processing, Glasgow, Scotland, UK, 1998 SLIDING MODE BASED PARAMETER ESTIMATION FOR NONLINEAR CONTROLLER DESIGN A.I.Bhatti· S.K.Spurgeon· X.Y.Lu· • Department of Engineering, University of Leicester, Leicester LEi 7RH. England Abstract: This paper seeks to find models appropriate for non linear control methods which are based on the generalised controller canonical form. Various sliding mode controller design techniques (Sira-Ramirez. 1993a: Lu and Spurgeon, 1997) exploit the fact that a nonlinear system model is available in generalised controller canonical form. In this paper a sliding mode based method is established to estimate the parameters of a model in the generalised controller canonical form. This model can then be used to design nonlinear controllers. It is shown that the method is robust against a certain class of uncertainties. Copyright @ 1998 IFAC Keywords: Sliding mode, Variable structure, Parameter estimation, Estimators, Adaptive systems 1. I;-.;rTRODUCTION In the current control literature most of the robust controller design techniques are based on iinear models. This represents a serious limitation; as the controller is based on a linear model, so some part of the performance has to be compromised against robustness. It may be expected that a controller will perform better if it is based on the actual nonlinear model. However it is very difficult to find generic nonlinear controller design techniques. The literature in this field is not as rich as in the case of linear model based con- trollers. In order to devise a generic sliding mode controller synthesis method for a non linear model based on traditional sliding mode control theory, the system needs to have a specific structure or canonical form which is difficult to achieve as sys- tem transformation in nonlinear systems is neither straight forward nor generic. Fliess (1990) pro- posed a particular Generalised Controller Canon- ical Form (GCCF) for nonlinear controller de- This canonical form has been subsequently used by Sira-Ramirez (1993a:1993b) and Lu and Spurgeon (1997) to introduce new dynamic slid- 243 ing mode based controller design schemes. These methods render sliding mode control theory appli- cable to a broader class of non linear systems . Cer- tain nonlinear systems may be readily expressible in GCCF form. For example, the standard nonlin- ear state space equations may be eliminated into a relationship between input and output derivatives from which the GCCF readily follows. However, this elimination process is not always straight forward. Further, state space equations may not be available. To facilitate wider application of these control methods it is necessary to consider estimation methods to generate the GCCF. .\'onlinear system identification. unlike linear iden- tification. is a developing field. The problem has been investigated from different viewpoints, each having some advantages and disadvantages. How- ever, no consensus has yet been made as to the best approach. The problem becomes more severe if the identified nonlinear model is to be restricted to a specific form , such as the GCCF repre- sentation associated with many dynamic sliding mode control methods . Dynamic neural networks (DNN) or recurrent neural networks present one