Dynamic Fuzzy Sliding Mode Control of Underwater Vehicles

Abstract

A novel dynamic fuzzy sliding mode control (DFSMC) algorithm is developed for heading angle control of autonomous underwater vehicles (AUV’s) in horizontal plane. At first, we design single input fuzzy sliding mode control (SIFSMC) based on mamdani type fuzzy inference system. The SIFSMC offers significant reduction in rule inferences and simplify the tuning of control parameters. Practically, it can be easily implemented by a look up table using a low cost advanced processor. The control structure provides robustness under the influence of parameter uncertainties and environmental disturbances. Next, we proposed fuzzy adaptation techniques in SIFSMC algorithm to vary the base of input–output membership functions of fuzzy inference engine. This adaptation law provides minimum reaching time to track desired trajectory path and also eliminate chattering effects. So far, the dynamics of AUV’s are highly nonlinear, time varying and hydrodynamic coefficients of vehicle are difficult to be accurately estimated a prior, because of the variations of these coefficients with different operating conditions. These types of difficulties cause modeling inaccuracies of AUV’s dynamics. Therefore, Traditional control techniques may not be able to handle these difficulties promptly and can’t guarantee the desired tracking performance. On the other hand, sliding mode control (SMC) is the suitable choice for control of AUV’s, because of its appreciable features such as design simplicity with robustness to parameter uncertainty and external disturbances. But, it has the inherent problem of chattering phenomenon which is the high frequency oscillations of the controller output and another difficulty in the calculation of equivalent control. Therefore, overall knowledge of the plant dynamics is required for this purpose. These problems are suitably circumvented by combining basic principles of sliding mode and fuzzy logic controllers (FLC’s). With this scheme, the stability and robustness of the FLC algorithm is ensured by the SMC law. By incorporating SMC in to fuzzy logic provides a possible solution to alleviate the chattering phenomena and to achieve zero steady state error. However, the parameters of membership function can’t be adjusted to afford optimal control efforts under the occurrence of uncertainties. Therefore, DFSMC is designed for regulating heading angle in horizontal plane, under the influence of parametric uncertainties (as added mass, hydrodynamic coefficients, lift and drag forces), highly coupled nonlinearities and environmental disturbances (like ocean currents and wave effects). This chapter focuses on design of two supervisory fuzzy systems for tuning of boundary layer and hitting gain which are the basic parameters of fuzzy sliding mode control (FSMC) algorithm. The proposed control algorithm is developed from fuzzy inference module, which has single input as a sliding surface and single output as control signal. The input–output membership functions are depends on base values such as boundary layer, equivalent control and hitting gain. The idea behind this control scheme is to update width of boundary layer and hitting gain, due to which the supports of input–output fuzzy membership functions are varied with the help of two fuzzy approximators. Simulation results shows that, the output tracking response has minimum reaching time and tracking error in the approaching phase along with chattering problem can also reduced. The performance of proposed control strategy has been evaluated by comparison with conventional SMC and FSMC. A summary of fuzzy adaptation schemes in FSMC algorithm are given for enhancing tracking performance of AUV’s. Finally, research directions for adopting optimal fuzzy supervisory techniques in sliding mode based fuzzy algorithm are suggested.