Discrete Sliding Mode Control Law for Attitude & Altitude Control of Quadrotors with a Sliding Surface of PID Structure

This paper presents the design of control law for an unmanned quadrotor aerial vehicle based on discrete sliding mode control (DSMC). The nonlinear dynamics of the quadrotor gets perturbed with modelling uncertainties and exogenous disturbance. Actuator saturation further incorporates nonlinearity in the system dynamics which makes the control problem a challenging one and motivates the authors to design a DSMC law. The proposed design of DSMC with sliding surface of tracking error with Proportional-Integral-Derivative (PID) structure followed by Gao’s reaching law demonstrates improved performance in contexts of command tracking, stability and control effort compared to the traditional Sliding Mode Control (SMC) with sliding surface of PD structure. The stability of the proposed control law is theoretically justified using Lyapunov-based stability analysis. Unlike continuous SMC proposed DSMC law filters out the high frequency noise and disturbance in the output response and automatically restricts the chattering frequency to the sampling frequency in the control signal. An exhaustive comparative analysis of the proposed design in simulation with the competing controllers demonstrates the superiority of the design and suggests its suitability for practical applications.