Control of discrete time systems based on recurrent Super-Twisting-like algorithm

Robust discrete-time super twisting formation protocol for a 6-DOF Quadcopter swarm

This paper contains a discrete-time higher-order sliding mode control for achieving the formation of a 6-Degrees of Freedom (DOF) Quadcopter swarm using the concept of a discrete Multi-agent system (DMAS). A graph theory is used to represent the communication between the Quadcopters and a leader-follower approach of DMAS is used to design the discrete super-twisting (DST) protocol for the formation of a 6-DOF Quadcopter swarm. The DST protocol not only ensures robustness but also reduces the convergence time and the chattering during the formation process of Quadcopters in a swarm. The stability condition of the formation is also derived using the Lyapunov function. The protocol is validated for the formation of 5 Quadcopters in the given pattern. The simulation results show that the formation is achieved in a finite time. Further to show the efficacy of the DST formation protocol, the results are compared with the first-order discrete-time sliding mode controllers designed by switching type reaching law and non-switching type of reaching law. As the first-order discrete-time sliding mode controllers have a significant amount of quasi-sliding mode band (QSMB) in the sliding surface during the operations, the DST protocol of higher-order discrete-time sliding mode control is preferred. From the comparative analysis, it is inferred that the DST protocol performs better for the formation of a 6-DOF Quadcopter swarm.

Adaptive super-twisting sliding mode altitude trajectory tracking control for reentry vehicle

This paper addresses the altitude trajectory tracking control problem of reentry vehicle subject to bounded uncertainty. A new continuous adaptive super-twisting sliding mode control (ASTSMC) method is developed based on conventional super-twisting sliding mode control (STSMC) and adaptive gain technique, which can improve tracking accuracy and achieve high control performance. Based on adaptive gain technique, the designed ASTSMC method requires no prior information on uncertainty and avoids the overestimation of control gain, then the unexpected chattering phenomenon is alleviated. By employing fast power rate reaching law and modified fast nonsingular terminal sliding mode (FNTSM) surface, the designed controller achieves faster convergence and stronger robustness than conventional STSMC methods. Furthermore, the finite-time stability of closed-loop system is proved through Lyapunov theory. Simulation results are executed to validate the superiority of the proposed controller.

Zero-Width Quasi-Sliding Mode Band in the Presence of Non-Matched Uncertainties

Sliding mode control strategies are well known for ensuring robustness of the system with respect to disturbance and model uncertainties. For continuous-time plants, they achieve this property by confining the system state to a particular hyperplane in the state space. Contrary to this, discrete-time sliding mode control (DSMC) strategies only drive the system representative point to a certain vicinity of that hyperplane. In established literature on DSMC, the width of this vicinity has always been strictly greater than zero in the presence of uncertainties. Thus, ideal sliding motion was considered impossible for discrete-time systems. In this paper, a new approach to DSMC design is presented with the aim of driving the system representative point exactly onto the sliding hyperplane even in the presence of uncertainties. As a result, the quasi-sliding mode band width is effectively reduced to zero and ideal discrete-time sliding motion is ensured. This is achieved with the proper selection of the sliding hyperplane, using the unique properties of relative degree two sliding variables. It is further demonstrated that, even in cases where selection of a relative degree two sliding variable is impossible, one can use the proposed technique to significantly reduce the quasi-sliding mode band width.

Optimal interval type-2 fuzzy fractional order super twisting algorithm: A second order sliding mode controller for fully-actuated and under-actuated nonlinear systems

In this paper, a novel interval type-2 fuzzy fractional order super twisting algorithm (IT2FFOSTA) which is essentially a second order sliding mode controller is presented. The proposed IT2FFOSTA enhances fractional order super twisting algorithm (FOSTA) by taking advantage of an interval type-2 fuzzy fractional order sliding surface (IT2FFOSS) for some classes of fully-actuated and under-actuated nonlinear systems in presence of uncertainty. The FOSTA significantly reduces the amount of chattering and the IT2FFOSS results in decreasing the tracking error, control effort, and chattering level. In order to control under-actuated systems, a hierarchical sliding surface is employed. The multi-tracker optimization algorithm is utilized to adjust the controller's parameters; this leads to an optimal performance for the IT2FFOSTA. To examine the performance of the IT2FFOSTA, some simulation and experimental tests on three examples of different classes of fully-actuated and under-actuated systems, including ball and plate, inverted pendulum, and ball and beam systems are carried out. The simulation and experimental results demonstrate the superiority of the IT2FFOSTA in reducing the amount of chattering, tracking error, and control effort compared to those of the other control methods.

Design of an adaptive super-twisting decoupled terminal sliding mode control scheme for a class of fourth-order systems

This paper proposes an adaptive super-twisting decoupled terminal sliding mode control technique for a class of fourth-order systems. The adaptive-tuning law eliminates the requirement of the knowledge about the upper bounds of external perturbations. Using the proposed control procedure, the state variables of cart-pole system are converged to decoupled terminal sliding surfaces and their equilibrium points in the finite time. Moreover, via the super-twisting algorithm, the chattering phenomenon is avoided without affecting the control performance. The numerical results demonstrate the high stabilization accuracy and lower performance indices values of the suggested method over the other ones. The simulation results on the cart-pole system as well as experimental validations demonstrate that the proposed control technique exhibits a reasonable performance in comparison with the other methods.