Fixed‐time sliding mode observer‐based controller for a class of uncertain nonlinear double integrator systems

Abstract

This paper investigates a fixed‐time convergence issue using the sliding mode observer‐based controller for a class of uncertain nonlinear double integrator systems. This observer‐based controller is designed assuming that only the first state measurement is available and there is no information about external disturbances and modeling uncertainties. A new form of sliding mode observer in combination with a sliding mode controller is designed to estimate unmeasured state and unknown disturbances and uncertainties as well as provide the estimated data in the control law. A novel form of sliding surfaces for the robust observer‐based controller is proposed for which fixed‐time convergence is guaranteed to achieve trajectory tracking. In the proposed fixed‐time scheme, the bound on the settling time is user‐defined using design parameters regardless of the system's initial conditions. The control law and observer law are designed such that the chattering issue is alleviated in the control signal. The stability analysis of the closed‐loop system using the observer‐based controller is established via the Lyapunov theory. The validity of the controller design is tested by applying and simulating an example of a robot manipulator in Simulink/MATLAB. The superiority of the proposed method is demonstrated by comparing it with two other methods from the relevant literature.

Review on challenges for robotic eye surgery; surgical systems, technologies, cost‐effectiveness, and controllers

“…Briefly, the controllers 64,68,146,150 have been implemented experimentally in the real robots and have been tested only in simulation. [147][148][149]151 The sclera force plays a fundamental role in robotic eye surgery, and this force is controlled by Adaptive Norm Control (ANC) and Adaptive Component Control (ACC) methods. 59 These methods have been used to control the scleral force of eye surgery with the SHER robot and the results show that the ANC method can maintain scleral force at a safe level.…”

“…In Table 5, some controller algorithms of eye surgical robots are compared. Briefly, the controllers 64,68,146,150 have been implemented experimentally in the real robots and have been tested only in simulation 147–149,151 …”

Adaptive prescribed performance sliding mode control based on time‐varying barrier function

“…It is well-known that sliding mode control (SMC) is an attractive control scheme which has many outstanding features such as insensitivity to external disturbances and robustness to matched plant uncertainties, with a very large frame of applications fields in earlier studies [1][2][3]. The robustness properties of the SMC with respect to parameter variations and disturbances have been proved [4].…”

A novel output redefinition method for nonlinear H∞attitude stabilization of a flexible spacecraft

“…A flexible spacecraft body consists of a rigid hub and flexible appendages. In the literature, the spacecraft hub attitude angles are often selected as the attitude dynamic model's output [4,[6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. In this approach, the flexible appendages' vibration effect is considered as an unknown vibrational disturbance torque and the attitude controller should overcome, in addition to the model uncertainties and the environmental disturbances.…”

“…However, the chattering phenomenon in the above methods creates unacceptable complications in the practical applications [18]. A few modifications at the cost of accuracy degradation [17,20], the higher order SMC scheme [16,21], and finite-time integral TSMC [9,13] and fixed-time SMC [6][7][8] are presented with chattering-free control signal. But complicated theoretical analysis and heavy computation are involved [8].…”