A 2-Link Robot with Adaptive Sliding Mode Controlled by Barrier Function

Abstract

This paper focuses on designing several controllers to attenuate the chattering problem: a conventional sliding mode controller (CSMC) with a barrier function (BF) and a saturation function (SF), and an adaptive sliding mode controller (ASMC) with SF as well as ASMC with BF. The key distinction between CSMC and ASMC lies in the fact that ASMC doesn't require knowledge of the upper bounds of uncertainties and the determination of gain. ASMC can minimize the magnitude of control signals to an acceptably low level. Despite perturbations such as parameter uncertainty (PU), external disruption (ED), and the friction coefficient of Coulomb (CF), both CSMC and ASMC can effectively handle the 2-link robot. They stabilize the robot manipulator and achieve the required joint position. Due to the ASMC's lower controller gain compared to CSMC, the amplitude of the chatter (zigzag motion) has been minimized. Simulation results using MATLAB 2018a/Simulink demonstrate that the ASMC outperforms the CSMC in achieving more favorable outcomes.

Design of an Adaptive Integral Sliding Mode Controller for Position Control of Electronic Throttle Valve

“…A well-liked methodology for developing a dependable controller technique in contemporary control systems is the SMC. This type of controller is composed of two phases, the reaching phase and the sliding phase [27]. Figure 2 below shows these two phases: In the reaching phase, the state trajectory will begin from any initial position and then oriented toward the switching surface S=0; hence, the sliding phase will be started at this instant as shown in Figure 2 [33].…”

“…where, 𝑢𝑢 𝑑𝑑𝑑𝑑𝑑𝑑 represents the discontinuous control portion and 𝑢𝑢 𝑛𝑛 represents the nominal control part. The definition of the discontinuous control portion, 𝑢𝑢 𝑑𝑑𝑑𝑑𝑑𝑑 , is as follows [27]:…”

“…This controller's construction uses 𝑢𝑢 𝑛𝑛 in the same way as an integral sliding mode controller (ISMC) [33]. On other hand, the discontinuous controller part, u dis is obtained in the same manner as an adaptive sliding mode controller (ASMC) is designed [27].…”

“…Finally, the complete equation of AISMC can be described by replacing Eqs. ( 9) and (27) in Eq. ( 6).…”

“…Higher Order Sliding-Mode design and control of an electronic throttle control system were present in the studies [24,25]. An idea for an adaptive sliding mode control mechanism has been outlined [26][27][28][29][30] to control the position of the ETV. Furthermore, integral sliding mode control was implemented in certain works to control ETV's angular position [31,32].…”