Sliding Mode Control Using Neural Networks

Abstract

Variable structure control with sliding mode, which is commonly known as sliding mode control (SMC), is a nonlinear control strategy that is well known for its robust characteristics (Utkin, 1977). The main feature of SMC is that it can switch the control law very fast to drive the system states from any initial state onto a user-specified sliding surface, and to maintain the states on the surface for all subsequent time (Utkin, 1977), (Phuah et al., 2005 a). The conventional SMC has two disadvantages (Ertugrul & Kaynak, 2000), (Slotine & Sastry, 1983), which are the chattering phenomenon (Slotine & Sastry, 1983), (Young et al., 1999) and the difficulty in calculating the equivalent control law of SMC that requires a thorough knowledge of the parameters and dynamics of the nominal controlled plant (Ertugrul & Kaynak, 2000), (Slotine & Sastry, 1983), (Hussain & Ho, 2004). Many methods of SMC using neural networks (NN) have been proposed (Phuah et al., 2005 a), (Ertugrul & Kaynak, 2000), (Hussain & Ho, 2004), (Phuah et al., 2005 b), (Yasser et al., 2007), (Topalov et al., 2007). In this paper, sliding mode controls using NN are proposed to deal with the problem of eliminating the chattering effect and the difficulty in calculating the equivalent control law of SMC that requires a thorough knowledge of the parameters and dynamics of the nominal controlled plant. The first method of this method applies a method using a simplified form of the distance function proposed in (Phuah et al., 2005 a), (Phuah et al., 2005 b). Furthermore, the simplified distance function of our method uses a sliding surface in the space of the output error and its derivations, as proposed in (Yasser et al., 2006 a), (Yasser et al., 2006 c), instead of the space of the states error to construct a corrective control input. Thus, no observer is required in the proposed method. Moreover, we also propose the application of an NN to construct the equivalent control input of SMC. The weights of the NN are adjusted using a backpropagation algorithm as in (Yasser et al., 2006 b). Hence, a thorough knowledge of the parameters and dynamics of the nominal controlled plant is not required for calculating the equivalent control law. Finally, a stability analysis is carried out, and the effectiveness of this first control method is confirmed through computer simulations. This first method has been previously discussed in (Yasser et al., 2007). The second method of this paper applies an NN to produce the gain of the corrective control of SMC. Furthermore, the output of the switching function the corrective control of SMC is applied for the learning and training of the NN. There is no equivalent control of SMC is used in this second method. As in the first method, this second method applies a method using a sliding surface in the space of the output error and its derivations, as proposed in