A study on neuro sliding mode control for nonminimum phase systems having an unstable internal dynamics

Abstract

In this dissertation, new sliding mode control methods using neural networks are developed. Although the conventional sliding mode control is simple and insensitive to uncertainties, it has three main problems. The first one is chattering due to the discontinuous switching function in the control input. The second one is the assumption of known bounds of uncertainties. The last one is how to control the magnitude of undershoot in nonminimum phase (NMP) systems. In order to overcome these problems, we propose a new neuro sliding control using neural networks as a feedback controller. Multilayer neural networks with an error back-propagation learning algorithm are used to compensate for arbitrary uncertainties existing in the system. By virtue of the action of neural networks, the proposed control scheme reduces the steady state error which is intrinsically occurred by the boundary layer method for alleviating the chattering. Moreover, the proposed controller does not require a priori knowledge of the bounds of uncertainties. We show that the performance of tracking control depends on the learning capability of neural networks of which the learning rates can be obtained from the local convergence condition of the weight update rule. In order to control the magnitude of undershoot in NMP systems, a new control scheme using two sliding manifolds is proposed. The control design is based on two sliding manifolds which are in charge of control in turn. One is used for convergence of the state trajectory to the origin and the other for maintaining the magnitude of undershoot to the desired value. The stability of the proposed control scheme is proved with Lyapunov function method. Computer simulations show the effectiveness of the proposed control scheme.