Fast terminal sliding‐mode finite‐time tracking control with differential evolution optimization algorithm using integral chain differentiator in uncertain nonlinear systems

Abstract

SummaryThis paper presents a fast terminal sliding-mode tracking control for a class of uncertain nonlinear systems with unknown parameters and system states combined with time-varying disturbances. Fast terminal sliding-mode finite-time tracking systems based on differential evolution algorithms incorporate an integral chain differentiator (ICD) to feedback systems for the estimation of the unknown system states. The differential evolution optimization algorithm using ICD is also applied to a tracking controller, which provides unknown parametric estimation in the limitation of unknown system states for trajectory tracking. The ICD in the tracking systems strengthens the tracking controller robustness for the disturbances by filtering noises. As a powerful finite-time control effort, the fast terminal sliding-mode tracking control guarantees that all tracking errors rapidly converge to the origin. The effectiveness of the proposed approach is verified via simulations, and the results exhibit high-precision output tracking performance in uncertain nonlinear systems. KEYWORDS differential evolution, differentiator, nonlinear systems, terminal sliding mode, tracking | INTRODUCTIONSliding-mode control (SMC) is an efficient control scheme and has been widely applied in nonlinear systems. Sliding-mode control has many attractive features such as insensitivity to the model errors and parametric uncertainties.1,2 Given its advantages, SMC provides powerful techniques to complicated nonlinear dynamic systems for tracking control, including robotic manipulator systems, 3 active suspension vehicle systems, 4 induction motor drive systems, 5,6 power systems, 7 and spacecraft systems. The tracking problems using evolutionary optimization in complicated nonlinear systems attract much more attention. Evolutionary optimization algorithms are considered as a powerful optimization tool in solving nonlinear and complicated search spaces.9 Sliding-mode control combined with evolutionary optimization algorithms is presented to improve the tracking performances for complicated nonlinear systems, such as genetic algorithms 10 and particle swarm algorithms. 11,12 These methods have difficulty solving a class of nonlinear tracking problems of unknown system states with time-varying disturbances, which causes an impact on the convergence and stability of the tracking systems.In limited situations, the system states are unknown and needs to be estimated. Along with time-varying disturbances, the differential evolution (DE) optimization algorithm using an integral chain differentiator (ICD) proposed in

A new practical robust control of cable‐driven manipulators using time‐delay estimation

“…To effectively settle this issue, a novel STA with TDE was proposed for robot manipulators recently . Exciting results were reported with this method, but improvement can still be made for better performance in the following two aspects: (1) the robust term used in the work of Kali et al, was traditional SM control with linear error dynamics, which may result in slow convergence and low control accuracy around the equilibrium point, and it has been demonstrated that terminal SM (TSM) control can ensure better control performance than the traditional SM one; and (2) the standard STA was used and may lead to relative poor performance under the situation that system states are far from the equilibrium point.…”

A Robotic Drilling End-Effector and Its Sliding Mode Control for the Normal Adjustment

“…Extracting the derivatives of real-time signals is a common problem. For the signals that are encountered in practical applications, developing the differentiator to take derivative is a realistic option [25]. The general structure of the differentiator is expressed as:…”

Practical adaptive fractional‐order nonsingular terminal sliding mode control for a cable‐driven manipulator

“…[15][16][17][18][19][20] Originally, linear error dynamics were combined with TDE leading to asymptotic stability, which, however, is not robust enough for some complex systems under strong lumped disturbance. Thus, the terminal sliding mode (TSM) control and its improved version, [21][22][23][24][25][26][27] which can ensure finite-time stability and high tracking precision, were integrated with TDE. [28][29][30] These TDE-based TSM controllers can effectively take advantage of TDE and TSM techniques, resulting in model-free robust controllers while still conquering the practical limitations of their own.…”